Methods, compositions and systems for solid-state barocaloric applications

Abstract

The invention provides methods, compositions, and systems for barocaloric applications such as cooling, heating, and energy storage.

Description

BACKGROUND OF THE INVENTION Currently, more than 20% of the world’s electricity is used for cooling, including for the storage of foods and medicine, air conditioning of populated spaces and buildings, and more recently, removing heat from electronics and data centers. With the world's increasing population demanding more comfortable living conditions and smaller, faster, and more powerful electronics, the demand for cooling is expected to continue to increase. Conventional cooling technologies, which have been around since the early 19th century, rely primarily on vapor compression cycles of hydrofluorocarbons that have a high global warming potential. In addition, next-generation electronics require aggressive cooling for sufficient thermal management, but current cooling methods cannot be scaled down to the dimensions of microchips. Thus, there is a pressing need to find new cooling technologies that are environmentally friendly and amenable to miniaturization. Solid-state cooling based on caloric materials offers the potential to overcome many challenges associated with traditional cooling technologies. Caloric materials are a class of solids that undergo solidsolid phase transitions driven by magnetic, electrical, or mechanical stimuli. In a typical cooling cycle, the stimulus is applied adiabatically to induce a phase change—typically to a more ordered state—which leads to a large increase in temperature. Once the temperature has re-equilibrated by dissipating excess heat to a heat sink, the stimulus is removed, reverting the caloric material to its original phase—now at a lower temperature—that can be used to remove heat from a heat source. Because these phase transitions occur entirely in the solid state, refrigeration cycles can be achieved without using greenhouse gases. Until recently, materials exhibiting magnetocaloric, elastocaloric, and electrocaloric effects have been viewed as most promising. However, in magnetocaloric cooling, the requirement of a large magnetic field (H >2 T) and the cost of expensive rare-earth magnetic materials have prevented widespread industrial and commercial applications. In elastocaloric materials, a short fatigue life has limited their utilization. Electrocaloric materials have also lagged behind as they require the energetically expensive production of electric fields, whose value is limited by the breakdown field. To date, many materials such as natural rubbers, shape-memory alloys and intermetallic compounds, antiferromagnetic compound (MnsGaN), ionic conductors (Agl), ferroelectric ceramic (BaTiOs), ferrielectric organic salts, organic molecule-based switchable dielectrics, 3D hybrid perovskites (with a general chemical formula of ABXs), and organic plastic crystals have been explored as barocaloric materials. However, these materials are often not ideal for practical refrigeration due to low thermodynamic efficiencies, small entropy changes associated with pressure-induced transitions (dozens of joules per kilogram per kelvin), small latent heats, the need to operate at non-ambient temperatures, large thermal hysteresis, high operating pressures, and a lack of mechanical durability and synthetic tunability. Most importantly, rational synthetic manipulation of these materials to establish fundamental structure-property relationships and to improve their performance is difficult. Thus, there is a need for new methods, compositions, and systems for barocaloric applications. SUMMARY OF THE INVENTION The invention provides methods, compositions, and systems for barocaloric applications, e.g., cooling, heating, and energy storage. In one aspect, the invention provides a method of heating or cooling employing a barocaloric cycle including providing heat energy to a composition including an organic layer including optionally substituted C>3 alkyl chains (e.g., C>4 alkyl chains), wherein the organic layer is in a disordered state and wherein the organic layer is between first and second inorganic layers or includes a head group capable of hydrogen bonding, halogen bonding, and / or electrostatic interaction with a counterion (e.g., an anion such as a halide); applying compression to the composition to induce the organic layer to undergo an exothermic phase transition to an ordered state, releasing latent heat; removing the latent heat while the composition is compressed; and removing the compression to allow the composition to revert to the disordered state. In some embodiments, the composition includes first and second inorganic layers separated by the organic layer. In some embodiments, the compression is hydrostatic or mechanical and / or the latent heat is removed by a heat sink. In some embodiments, the organic layer includes a C>3 alkyl ammonium species (e.g., C>4 alkyl, e.g., C4-36,e.g., C4-18), such as a species selected from: V - .-x ..-X. ,.X ... 0$ s-fX ' Cs$ d f f f F F F F F F F n f n f n f x '^X' f f' f f' f C4Rs hX .-"x .."x .-Sx. '-V* -V 0 C*CH In some embodiments, the organic layer is an organic bilayer. In some embodiments, the organic layer includes a compound of formula (CnH2n+i)(Cn7H2m+i)NH2X, where n is 1 -3 or 4-36 and m is 4-36; and X is a monoanionic species (e.g., a halide (e.g., F, Cl, Br, or I) or a non-halide anion, such as NO3-, CIO3-, 2 CIO4-, H2PO4-, HSO4-, CN-, HCOO-, N3-, N(CN)2-, BF4-, BH4-, PFe; SCN; orOCN). In certain embodiments, n = m and n = 4-36. In certain embodiments, n = 1-3 and m = 4-36 (e.g., where n = 1 and m = 6, 8, 10, 12, or 18). In some embodiments, the composition is a 2D perovskite. In some embodiments, the 2D perovskite 5 includes a transition metal halide. In some embodiments, the 2D perovskite includes Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Pd, Cd, Re, Pt, or Hg. In some embodiments, the 2D perovskite includes a tetrahedral or octahedral transition metal complex. In some embodiments, the halide of the transition metal halide is F, Cl, Br, or I. In some embodiments, the transition metal halide includes a monovalent metal cation and a trivalent metal cation. In some embodiments, the 2D perovskite is of formula 10 [(R1)x(R2)i-x]2MXyX'4-y, where R1 and R2 are independently optionally substituted alkylammonium species, X and X’ are different halides, x is a real number between 0-1, y is 0-4, M is a transition metal (e.g., Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Pd, Cd, Re, Pt, or Hg); and where if y = 0 or 4, R1 £ R2 and x / 0 or 1. In some embodiments, the organic layer includes two different molecular structures. In some 15 embodiments, the first and second inorganic layers include a silicate. In some embodiments, the composition includes a metal alkyl phosphonate salt. In some embodiments, the composition includes a compound ofthe following table: 08 01 26 Type Chemical Formula (OA)2MnCI4 (DA)2MnCl4 2-D perovskite (NA)2MnCI4 (NA)2CuCl4 (DA)2CuCl4 (NA)2CuCI3Br (NA)2CuCI2Br2 (NA)2CuCIBr3 (DA)2CuCI3Br (DA)2CuCI2Br2 Mixed 2D perovskites (DA)2CuCIBr3 [(NA)o.75(DA)o.25]2CuCl4 [(NA)o.5(DA) o.5]2CuCl4 [(NA)o.25(DA)o.75]2CuCl4 [(NA)o.25(UA)o.75]2CuCl4 [(NA)o.5(UA) o.5]2CuCl4 [(NA)o.5(DA) o.5]2CuCI2Br2 (n-C6Hi3)2NH2Br Di-n-alkyI ammonium salt (n-C8Hi7)2NH2CI (n-C6Hi3)2NH2CI (n-C6Hi3)2NH2l (n-C8Hi7)2NH2Br (n-Ci2H25)2NH2CI (n-Ci2H25)2NH2Br (n-CioH2i)2NH2CI (n-CwH2i)2NH2Br (n-CwH2i)2NH2l (n-Ci2H2s)2NH2Br (n-Ci8H37)2NH2CI (n-CisH37)2NH2Br (n-Ci2H25)(CH3)NH2Br (n-Ci2H25)(CH3)NH2CI Intercalation compound (first-row transition metal) FeOCI«Ci4H29NH2 Ni(CN)2-Ci2H25NH2 Ni(CN)2« C12H25NH2 intercalated between montmorillonite (smectite) (Cl8H37)sNH+ Self-Assembled Monolayer (CisH37)4N+ Self-Assembled Monolayer Layered metallo-alkylphosphonate Mg(O3PC22H45) DA = decylammonium, NA = nonylammonium, and UA = undecylammonium. In some embodiments, the compression results from a pressure change of less than 500 bar, e.g., less than 300 bar. In some embodiments, the compression results in a reversible entropy change of more than 200 J kg-1 K~1. In some embodiments, the compression is provided using a pressure transmitting medium (PTM). In some embodiments, the method includes providing a gas to the PTM that induces a change in a thermal property of the composition. In some embodiments, the change in thermal property is a lowering of a phase transition temperature and / or a barocaloric effect inversion. In some embodiments, the method further includes removing the gas from the PTM. In some embodiments, the gas is an inert gas that permeates into a free volume of the organic layer. In some embodiments, permeated gas interacts with the composition. In some embodiments, permeation and interaction of the gas with the composition together induce a lowering of a phase transition and / or a barocaloric effect inversion. In some embodiments, the gas is nitrogen, argon, krypton, xenon, methane, ethane, propane, butane, sulfur hexafluoride, or carbon dioxide. In an aspect, the invention provides a method of storing thermal energy employing by providing a composition including an organic layer including optionally substituted C>3 alkyl chains (e.g., C>4 alkyl chains, e.g., C4-36 alkyl chains) at a first temperature and a first pressure, wherein the composition is in an ordered state and wherein the organic layer is between first and second inorganic layers or includes a head group capable of hydrogen bonding, halogen bonding, and / or electrostatic interaction with a counterion; and reducing compression on the composition to a second pressure to induce a phase transition in the composition to a disordered state, thereby storing energy. In some embodiments, the method further includes increasing compression on the composition to apply a third pressure to revert the composition to an ordered state and release heat energy. In some embodiments, the composition includes first and second inorganic layers separated by the organic layer. In some embodiments, the compression is hydrostatic or mechanical. In some embodiments, the organic layer includes a C>3 alkyl (e.g., C>4 alkyl, e.g., C4-36 alkyl) ammonium species, such as: Os 0^(000)(¾ es ^cook's CW <W ow CjOC^ In some embodiments, the organic layer is an organic bilayer. In some embodiments, the organic layer includes a compound of formula (CnH2n+i)(Cn7H2m+i)NH2X, where n is 1 -3 or 4-36 and m is 4-36; and X is a monoanionic species (e.g., a halide (e.g., F, Cl, Br, or I) or a non-halide anion, such as NO3-, CIOs-, CIO4-, H2PO4-, HSO4-, CN-, HCOO-, Ns-, N(CN)2-, BF<, BH4-, PFS-, SCN-, or OCNj. In certain embodiments, n = m andn - 4-36. In certain embodiments, / 7=1-3 and m - 4-36 (e.g., where n = 1 and m = 6, 8, 10, or 12). In some embodiments, the composition is a 2D perovskite. In some embodiments, the 2D perovskite includes a transition metal halide. In some embodiments, the 2D perovskite includes Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Pd, Cd, Re, Pt, or Hg. In some embodiments, the 2D perovskite includes a tetrahedral or octahedral transition metal complex. In some embodiments, the halide of the transition metal halide is F, Cl, Br, or I. In some embodiments, the transition metal halide includes a monovalent metal cation and a trivalent metal cation. In some embodiments, the 2D perovskite is of formula 5 08 01 26 [(R1)x(R2)i-x]2MXyX'4-y, where R1 and R2 are independently optionally substituted alkylammonium species, X and X’ are different halides, x is a real number between 0-1, y is 0-4, M is a transition metal (e.g., Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Pd, Cd, Re, Pt, or Hg); and where if y = 0 or 4, R1 £ R2 and x / 0 or 1. 5 In some embodiments, the organic layer includes two different molecular structures. In some embodiments, the inorganic layer includes a silicate. In some embodiments, the composition includes a metal alkyl phosphonate salt. In some embodiments, the composition includes a compound of the following table: Type Chemical Formula (OA)2MnCl4 (DA)2MnCl4 2-D perovskite (NA)2MnCI4 (NA)2CuCI4 (DA)2CuCI4 Mixed 2D perovskites (NA)2CuCI3Br (NA)2CuCI2Br2 (NA)2CuCIBr3 (DA)2CuCI3Br (DA)2CuCI2Br2 (DA)2CuCIBr3 [(NA)o.75(DA)o.25]2CuCl4 [(NA)o.5(DA)o.5]2CuCl4 [(NA)O.25(DA)O.75]2CUCI4 [(NA)o.25(UA)o.75]2CuCl4 [(NA)o.5(UA)o.5]2CuCl4 [(NA)o.5(DA)o.5]2CuCl2Br2 (n-C6Hi3)2NH2Br (n-C8Hi7)2NH2CI (n-C6Hi3)2NH2CI (n-C6Hi3)2NH2l (n-C8Hi7)2NH2Br (n-Ci2H25)2NH2CI (n-C8Hi7)2NH2l Di-n-alkyI ammonium salt (n-CioH2i)2NH2CI (n-CioH2i)2NH2Br (n-CioH2i)2NH2l (n-Ci2H25)2NH2Br (n-Ci8H37)2NH2CI (n-Ci8H37)2NH2Br (n-Ci2H25)(CH3)NH2Br (n-Ci2H25)(CH3)NH2CI Intercalation compound FeOCKi4H29NH2g (first-row transition metal) Ni(CN)2«Ci2H2sNH2h Ni(CN)2-Ci2H25NH2h intercalated between montmorillonite (smectite) (Cl8H37)sNH+ Self-Assembled Monolayer (ClsH37)4N+ Self-Assembled Monolayer Layered metallo-alkylphosphonate Mg(O3PC22H4s) In some embodiments, the compression is provided using a pressure transmitting medium (PTM) and the method includes providing a gas to the PTM that induces a change in a thermal property of the composition. In some embodiments, the gas is an inert gas that is able to permeate a free volume of the 5 organic layer. In some embodiments, the permeated gas interacts with the composition. In some embodiments, permeation and interaction of the gas with the composition together induce a lowering of a phase transition and / or a barocaloric effect inversion. In some embodiments, the gas is nitrogen, argon, krypton, xenon, methane, ethane, propane, butane, sulfur hexafluoride, or carbon dioxide. In some embodiments, the change in thermal property is a lowering of a phase transition temperature 10 and / or a barocaloric effect inversion. In an aspect, the invention provides a 2D perovskite composition including first and second layers of a transition metal halide and an organic layer including a C>3 alkyl (e.g., C>4 alkyl, e.g., C4-36 alkyl chains) ammonium species selected from: In an aspect, the invention provides a 2D perovskite composition having formula [(R1)x(R2)i-x]2MXyX'4-y, where R1 and R2 are independently optionally substituted alkylammonium species, X and X’ are different halides, x is between 0-1, y is 0-4, M is a transition metal (e.g., Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Pd, Cd, Re, Pt, or Hg); and where if y = 0 or 4, R1 # R2 and x # 0 or 1. 5 In some embodiments, R1 and R2 are independently alkylammonium species of formula CnHzn+iNFV, where n >3 (e.g., n >4, e.g., C436 alkyl). In some embodiments, the 2D perovskite composition has a formula selected from: (NA^CuCIsBr; (NA)2CuCl2Br2; (NA)2CuCIBr3; (DA)2CuCl3Br; (DA)2CuCl2Br2; (DA)2CuCIBr3; [(NA)o.75(DA)o.25]2CuCl4; [(NA)o.5(DA)o.5]2CuCl4; [(NA)o.25(DA)o.75]2CuCl4; 10 [(NA)o.25(UA)o.75]2CuCl4; [(NA)o.5(UA)o.5]2CuCl4; or [(NA)o.5(DA)o.5]2CuCI2Br2. In some embodiments, R1 and R2 are independently alkylammonium species selected from: CjCKXs - x O"’ x 0$ S F £ S' F F F F F F F- F F F F s f s C.XH CsOGsGH 'X.--'' . In some embodiments, X is Cl, and X’ is Br. In an aspect, the invention provides a barocaloric system including a composition including an organic layer including optionally substituted C>s alkyl chains (e.g., C>4 alkyl chains, e.g., C4-36 alkyl chains), 15 wherein the organic layer is between first and second inorganic layers or includes a head group capable of hydrogen bonding, halogen bonding, and / or electrostatic interaction with a counterion; and a source of compression. In some embodiments, the system includes first and second inorganic layers separated by the organic bilayer. In some embodiments, the organic layer includes a compound of formula 20 (CnH2n+i)(CmH2m+i)NH2X, where n is 1 -3 or 4-36 and m is 4-36; and where X is a monoanionic species 8 (e.g., a halide (e.g., F, Cl, Br, or I) or a non-halide anion, such as NO3-, CIO3-, CIO4-, H2PO4-, HSO4-, CN_, HCOO, N3', N(CN)2_, BF4-, BH4-, PFe-, SCN-, or OCN ). In some embodiments, n = m and n = 4-36. In some embodiments, n = 1-3 and m = 4-36 (e.g., where n = 1 and m = 6, 8, 10, or 12). In some embodiments, the source of compression is hydrostatic or mechanical. In some embodiments, the system further includes a heat sink. In an aspect, the invention provides a barocaloric system. The system includes a composition including an organic layer including optionally substituted C>3 alkyl chains. The system further includes a pressure transmitting medium including one or more gases, at least one of which induces a change in a thermal property of the organic layer, and a source of compression. In some embodiments, the at least one gas is an inert gas that is able to permeate a free volume of the organic layer. In some embodiments, the permeated gas interacts with the composition. In some embodiments, an extent of permeation and interaction of the at least one gas with the composition together induce a lowering of a phase transition and / or a barocaloric effect inversion. In some embodiments, the change in thermal property is a lowering of a phase transition temperature and / or a barocaloric effect inversion. In some embodiments, the system includes a pump for controlling the amount of the at least one gas. In some embodiments, the system includes a heat sink. In some embodiments, the system further includes a second organic layer that does not undergo the barocaloric effect inversion. In some embodiments, the at least one gas is nitrogen, argon, krypton, xenon, methane, ethane, propane, butane, sulfur hexafluoride, or carbon dioxide. Definitions The term “about,” as used herein, refers to ±10% of a recited value. The term “alkyl,” as used herein, is meant straight chain or branched saturated groups of carbons. Alkyl groups are exemplified by n-, sec-, iso- and tert-butyl, neopentyl, nonyl, decyl, and the like, and may be optionally substituted with one or more, substituents. Alkyl groups of the invention may include 1 or more carbon atoms, e.g., greater than 2, e.g., 6-15, such as 8-12, in the main chain. Carbon atoms in the main chain may be interrupted with one or more heteroatoms, e.g., O, S, or N. By “aryl” is meant an aromatic cyclic group in which the ring atoms are all carbon. Exemplary aryl groups include phenyl, naphthyl, and anthracenyl. Aryl groups may be optionally substituted with one or more substituents. By “carbocyclyl” is meant a non-aromatic cyclic group in which the ring atoms are all carbon. Exemplary carbocyclyl groups include cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, and cyclooctyl. Carbocyclyl groups may be optionally substituted with one or more substituents. By “halo” is meant, fluoro, chloro, bromo, or iodo. By “heteroaryl” is meant an aromatic cyclic group in which the ring atoms include at least one carbon and at least one O, N, or S atom, provided that at least three ring atoms are present. Exemplary heteroaryl 9 groups include oxazolyl, isoxazolyl, tetrazolyl, pyridyl, thienyl, furyl, pyrrolyl, imidazolyl, pyrimidinyl, thiazolyl, indolyl, quinolinyl, isoquinolinyl, benzofuryl, benzothienyl, pyrazolyl, pyrazinyl, pyridazinyl, isothiazolyl, benzimidazolyl, benzothiazolyl, benzoxazolyl, oxadiazolyl, thiadiazolyl, and triazolyl. Heteroaryl groups may be optionally substituted with one or more substituents. By “heterocyclyl” is meant a non-aromatic cyclic group in which the ring atoms include at least one carbon and at least one O, N, or S atom, provided that at least three ring atoms are present. Exemplary heterocyclyl groups include epoxide, thiiranyl, aziridinyl, azetidinyl, thietanyl, dioxetanyl, morpholinyl, thiomorpholinyl, piperazinyl, piperidinyl, pyrrolidinyl, tetrahydropyranyl, tetrahydrofuranyl, dihydrofuranyl, tetrahydrothienyl, dihydrothienyl, dihydroindolyl, tetrahydroquinolyl, tetrahydroisoquinolyl, pyranyl, pyrazolinyl, pyrazolidinyl, dihydropyranyl, tetrahydroquinolyl, imidazolinyl, imidazolidinyl, pyrrolinyl, oxazolidinyl, isoxazolidinyl, thiazolidinyl, isothiazolidinyl, dithiazolyl, and 1,3-dioxanyl. Heterocyclyl groups may be optionally substituted with one or more substituents. Optional substituents include halo, optionally substituted C3-10 carbocyclyl; optionally substituted C1-9 heterocyclyl having one to four heteroatoms independently selected from O, N, and S; optionally substituted C6-20 aryl; optionally substituted C1-9 heteroaryl having one to four heteroatoms independently selected from O, N, and S; -CN; -NO2; -ORa; -N(Ra)2; -C(=O)Ra; -C(=O)ORa; -S(=O)2Ra; -S(=O)2ORa; -P(=O)Ra?; -O-P(=O)(ORa)?, or -P(=O)(ORa)2, or an ion thereof; wherein each Ra is independently H, optionally substituted C1-6 alkyl; optionally substituted C3-10 carbocyclyl; optionally substituted C1-9 heterocyclyl having one to four heteroatoms independently selected from O, N, and S; optionally substituted Cg-2o aryl; or optionally substituted C1-9 heteroaryl having one to four heteroatoms independently selected from 0, N, and S. BRIEF DESCRIPTION OF THE DRAWINGS Figs. 1A-1B show powder X-ray diffraction data for (CioH2iNHs)2MnCl4 under variable pressures of He obtained at 17-BM-B. Powder patterns at 31 °C (Fig. 1A) show exclusively an ordered phase. Powder patterns obtained at 42 °C (Fig. 1B) show an expanded, disordered phase. Between 37-41 °C, the sample undergoes 0rder-to-disorder transition, exhibiting an increase in the inter-layer spacing. The simulated powder pattern at the bottom is from room temperature crystal structure of the same compound in ordered phase and used as a reference. The peaks from (001) reflections shifted to lower angles, indicating the increase in inter-layer distance. The inter-layer calculated based on the peak positions is 28.74 A (-7.3% increase). Fig. 2 shows variable-temperature powder X-ray diffraction data (CwH2iNH3)2MnCl4 at 1 bar. The thermally-induced order-disorder phase transition shifts to a much higher temperature at higher pressure, demonstrating the pressure-dependence of this phase transition. Fig. 3 shows structural and thermal properties of two-dimensional layered perovskites of the invention. Four different types of functionalized long-chain organic molecules were incorporated to yield (CioH2iNH3)2[MnCl4] (denoted as (Cio)2[MnCl4]), (HO-C8Hi7NH3)2[CuCl4] (denoted as (C8OH)2[CuCl4]), (C4H9OC3H6NH3)2[CuCl4] (denoted as (C3OC4)2[CuCl4]), and (C6H5C4H8NH3)2[CuCl4] (denoted as (C4Ar)2[CuCk]). Left: Powder X-ray diffraction patterns of (CwMMnCk], (C8OH)2[CuCl4], (C3OC4)2[CuCl4], and (C4Ar)2[CuCl4]. These patterns were compared to the simulated pattern of (Cio)2[MnCl4]. In the 10 powder patterns, (001) reflections were primarily observed due to the strong preferred orientation of the samples. The inter-layer spacing for each compound can be calculated based on the peak positions. The powder patterns reveal the high crystallinity and phase purity of all samples. Right: Differential scanning calorimetry (DSC) traces of (CioMMnCk], (C8OH)2[CuCl4], (C3OC4)2[CuCk], and (C4Ar)2[CuCk]. Inset: transition temperatures Ttr, transition enthalpy AH, and transition enthalpy AS. The transition entropy was calculated by: AH = TLAS. DSC measurements reveal that the samples undergo thermally-induced, reversible solid-solid phase transitions involving large changes in entropy. The gravimetry entropy changes of the samples are higher than 100 J kg-1 K1. Notably, the transition enthalpy of (Cio)2[MnCk] is -221 J kg-1 KL In terms of the entropy change, this material is expected to be competitive to some of the best current caloric materials. Figs. 4A-4B show barocaloric cooling with two-dimensional (2-D) metal-halide perovskite. Fig. 4A shows an illustration of a barocaloric cooling cycle driven by pressure-induced order-disorder transitions in a 2-D perovskite. The large barocaloric effects in the 2-D perovskite arise from a chain-melting phase transition of the hydrocarbon chains associated with large changes in volume and conformational entropy. For a conventional barocaloric effect, a cooling cycle begins with an adiabatic (Brayton-like cycle) or isothermal (Stirling-like cycle) increase in pressure that induces a transition from an expanded, high-entropy phase of a material to a contracted, low-entropy phase. Heat released during this exothermic transition is dissipated to a heat sink, returning the material to its original temperature but now at a lower entropy. The pressure is then adiabatically or isothermally decreased to reverse the phase transition, which leads to cooling of a heat source. Fig. 4B is a comparison of entropies of transition, AStr, and transition temperature, Ttr, for select 2-D perovskites with long hydrocarbon chains, (CnH2n+iNH3)2MX4 (n = 7-16; M = Mn, Cd, Cu, Pb; X = Cl, Br, I). The thermally induced phase transitions in 2-D perovskites are accompanied with large changes in entropies and sensitive to the length of hydrocarbon chain and identity of metal-halide layer. Comprehensive summary of phase-change properties is provided in Tables 2 to 4 (ASr and Ttr). In addition, the dependence of phase transition to hydrostatic pressure, dTtr / dP, is estimated for select 2-D perovskites in Table 5. Figs. 5A-5H show thermally induced chain-melting transitions in (DA)2MnCl4 and (NA)2CuBr4 at ambient pressure. Figs. 5A and 5B show differential scanning calorimetry (DSC) traces for (DA)2MnCl4 (Fig. 5A) and (NA)2CuBr4 (Fig. 5B) with heating and cooling rates of 2 K min-1. AStr and enthalpies of transition (AHtr) are shown with thermal hysteresis (AThys) highlighted in grey area. Note that AThys is calculated as the difference between heating and cooling transition onset temperatures, with AThys = Ttr, heating -Ttr, cooling. Figs. 5C and 5D show the temperature dependence of specific volumes for (DA^MnCk (Fig. 5C) and (NA)2CuBr4 (Fig. 5D) obtained from variable-temperature powder X-ray diffraction and He pycnometry measurements, revealing large volume changes for the transitions, AI / pxrd and A Vpyc, respectively. Figs. 5E and 5G show conformations of alkylammonium (CnH2n+tNH3+) chains in the low-temperature (LT) phase crystal structures of (DA^MnCk (n= 10) (Fig. 5E) and (NA)2CuBr4 (n = 9) (Fig. 5G) at 270 K. Atomic displacement parameters are shown at 50% probability for CnH2n+iNH3+ chains. Note that CgHigNH3+ chains are disordered over two positions. Figs. 5F and 5H show variable-temperature crystal structures of LT and high-temperature (HT) phases of (DA^MnCk (Fig. 5F) and (NA^CuBu (Fig. 5H) that feature order-disorder chain-melting transitions in the organic bilayers. Note that the HT phase crystal structures were obtained at 330 K and 335 K for (DA)2MnCk and (NA)2CuBr4, respectively. Purple, orange, green, brown, grey, and blue spheres represent Mn, Cu, Cl, Br, C, and N atoms, respectively. H atoms are omitted for clarity. Figs. 6A-6J show barocaloric effects in 2-D metal-halide perovskites. Figs. 6A and 6D show DSC measurements at applied pressures for (Fig. 6A) (DA)2MnCk and (Fig. 6D) (NA^CuBu with heating and cooling rates of 2 K min-1. Applications of hydrostatic He pressure increases Ttr. Figs. 6B and 6E show isothermal entropy change, ASt, calculated by the quasi-direct method for (DA>2MnCk (Fig. 6B) and (NA)2CuBr4 (Fig. 6E) on heating and cooling for operating pressures from 40 bar to 150 bar, with shaded area indicating the reversible ASt. The reversible values of ASt can be estimated from the overlap between compression-induced and decompression-induced ASt curves reflected across the temperature axis. Figs. 6C and 6F show direct evaluation of pressure hysteresis, APhys, through quasi-isothermal pressure cycling DSC measurements for (DA)2MnCl4 (Fig. 6C) and (NA)2CuBr4, (Fig. 6F) at 311 K and 307 K, respectively, between 1 and 150 bar pressures. APhys is calculated as the difference between the onset pressures for compression-induced exotherms and decompression-induced endotherms, indicated by the horizontal dashed green lines. From the pressure dependence of heating and cooling onset temperatures, APhys are predicted to be 73 bar and 16 bar for (DA)2MnCl4 and (NA)2CuBr4, at 311 K and 307 K, respectively. Figs. 6G and 6I show variable-temperature powder X-ray diffraction (PXRD) patterns for (DA)2MnCl4 (Fig. 6G) and (NA^CuBu (Fig. 6I) at 360 bar and 300 bar He pressures, respectively, during cooling, with X-ray wavelength of 0.45237 A. Figs. 6H and 6J show the pressure dependence of transition temperature, barocaloric coefficient dTtr / dP, for (DA)2MnCl4 (Fig. 6H) and (NA)2CuBr4 (Fig. 6J), measured through HP-DSC and in situ PXRD experiments. Red and blue symbols indicate Ttr, heating and Ttr, cooling, respectively. Figs. 7A-7B show properties of representative barocaloric materials. Comparison of (Fig. 7A) ASr and Ttr, and (Fig. 7B) AThys, barocaloric coefficient d Ttr / dP, and Prev for leading barocaloric materials. AStr and Ttr determined for endothermic transitions are shown. Prev, calculated through Prev = AThys / |dTtr / dP|, corresponds to the slope of the plot, and dTtr / dP values for exothermic and endothermic transitions are used for conventional and inverse barocaloric materials, respectively. For comparison purpose, AStr is highlighted as an estimate for barocaloric effect ASt, since ASr at ambient pressure represent the maximum entropy change for a pressure-induced phase transition. Note that reported ASt values are heavily influenced by measurement conditions, such as operating pressure. Comprehensive evaluation of barocaloric properties, including reversible and irreversible ASt values, is provided in Tables 18 and 19. Additionally, barocaloric effects associated with chain-melting transitions in other types of compounds are also estimated in Table 20. Figs. 8A-8C show a pressure-tunable thermal energy storage using chain-melting phase transition. Phase transition temperature Ttr during thermal energy storage can be tuned by application and removal of hydrostatic pressure. Fig. 8A shows a typical PT-TES cycle and for materials with conventional barocaloric effects (dTtr / dP >0), the material is first charged with thermal energy at the storage temperature Tstor and initial pressure P, through disordering transition (AStr >0), hydrostatic pressure of AP is then applied to the material outside of the transition. Under the compressed environment, the temperature at which the thermal energy is released (release temperature, Trei) shift to a higher temperature, by (dTtr / dP) x AP. After the stored heat is released, the pressure returns to the original starting pressure P. Note that this cycle can be readily reversed, such that the thermal energy is stored at a higher temperature through the application of pressure AP and released at a lower temperature when the pressure is removed. In Figs. 8B and 8C the temperature span is calculated through the equation ATspan = (d TMP) x AP -AThys, and materials with high barocaloric coefficients and low hysteresis can lead to large temperature span under small operating pressure. With the operating pressure AP, as long as the temperature lies within the temperature span, application or release of the pressure can be exploited to realize on-demand thermal energy storage. In this approach, the thermal energy can be released and stored by applying and removing pressure, respectively. In addition to (DA)2MnCl4 and (NA)2CuBr4 highlighted in this manuscript, other types of compounds containing long-chain hydrocarbons (Table 20), including other 2-D perovskites with different chain length and metal-halide layers (Tables 1 to 5), are predicted to be competitive materials for PT-TES. Fig. 9 illustrates on-demand tuning of phase-change temperatures through pressure. Application of pressure can be used to adjust the phase-change temperature of the TES material on demand, such that the working temperature can be optimized for changing demands of a thermal energy storage. This approach can dramatically increase the versatility of a TES material, as it can store and release the thermal energy across a broad temperature range. Note that the concept of PT-TES can be applied to thermal managements, where an abrupt increase in thermal load at a high temperature (Thigh) can be reduced by shifting the storage temperature of a TES material such that it matches with Thigh. In this condition, the heat can be removed more efficiently and rapidly. Figs. 10A-10D show variable-temperature infrared spectra for (DA)2MnCl4 and (NA)2CuBr4. In Fig. 10A the LT and HT phase spectra were collected 5 K below and 5 K above the phase transition temperature, respectively. Figs. 10B-10D show zoomed in views of three different regions with bands that correspond to NH3 bending (Fig. 10B) and CH2 bending, CH3 bending and CH2 wagging (Fig. 10C), and CH2 rocking bands(Fig. 10D). Key shifts in peak positions are indicated by vertical grey bars, and CH2 wagging bands associated with conformational defects are highlighted with red and purple dashed lines for (DA)2MnCl4 and (NA)2CuBr4, respectively. Note that previous reports on (CnH2n+iNH3)2MCl4 (M = Cd, Mn) perovskites revealed that the peak near 1337 cm-1 does not depend on chain conformation. The IR bands used for conformational analysis are summarized in Table 6. Fig. 11 shows images of mixed halide 2-D perovskites. With increasing bromide concentration, the color of the crystalline compounds changes noticeably, from a bright yellow to an orange, deep red, and finally dark purple. Figs. 12A and 12B show thermodynamic properties of newly discovered barocaloric materials. Fig. 12A shows a comparison of entropy change, AStr, and transition temperature, Ttr, for the mixed halide and mixed cation 2-D perovskites contrasted with non-mixed perovskites (NA)2CuBr4 and (DA)2MnCl4. Fig. 12B shows comparisons of thermal hysteresis, AThys, and barocaloric coefficient, dT / dP, for the five mixed 2-D perovskites as well as (DA)2MnCl4 and (NA)2CuBr4. Note that the minimum operating pressure values (Prev) were calculated based on peak transition temperatures due the broadness of the DSC peaks, and thus Prev shown here are approximately three times higher than the values calculated based on onset AThys values. All five materials fall within an easily accessible pressure range (71 -108 bar), in comparison to previously reported barocaloric compounds (400-4000 bar). As indicated by grey dashed 13 lines, Prev values for [(NA)o.s(DA)o.5]2CuCl4 and [(NA)o.s(DA)o.5]2CuCl2Br2 are 71 bar and 108 bar, respectively, both of which are lower than Prev of (DA)2MnCl4 (dashed green line). Figs. 13A-13C Variable-temperature powder X-ray diffraction (PXRD) patterns for (DA)2CuCl2Br2 at 1 bar of He obtained while cooling from 331 K to 289 K, with an X-ray wavelength of 0.45213 A. In Figs 13A and 13B the PXRD patterns are shown at variable temperatures (as indicated), with grey shades highlighting (001), (002), and (003) reflections. The red and blue patterns correspond to the high-temperature (HT) and low-temperature (LT) phases, respectively, with purple indicating patterns in which both phases are present during the transition from HT to LT phase. Fig. 13C shows a waterfall plot for the variable-temperature PXRD data, with a dashed line indicating the transition temperature (Ttr). Note that the sample was cooled with a cooling rate of 3 K min-1. Figs. 14A-14C show waterfall plots for variable-temperature powder X-ray diffraction (PXRD) data for (DA)2CuCl2Br2 at (Fig. 14A) 80 bar and (Fig. 14B) 300 bar of He obtained while cooling from 335 K to 274 K, with an X-ray wavelength of 0.45213 A. Dashed lines indicate the transition temperatures (Ttr). Note that the sample was cooled with a cooling rate of 3 K min-1. Fig. 14C shows the pressure dependence of the chain-melting transition temperature as determined by HP-DSC (squares) and PXRD (diamonds) is used to calculate the barocaloric coefficient (dT / dP) for (DA)2CuCl2Br2. Fig. 15 shows the temperature dependence of interlayer distances for (DA)2CuCl2Br2 obtained from isobaric PXRD experiments during cooling. Figs. 16A-16D show powder X-ray diffraction (PXRD) patterns for mixed-halide (NA)2CuCl4-xBrx perovskites at 1 bar of He, with an X-ray wavelength of 0.45213 A, for (Figs. 16A-16B) high-temperature (HT) and (Figs. 16C-16D) low-temperature (LT) phase at 311 K and 269 K, respectively. The PXRD patterns are shown at variable halide compositions (as indicated), with grey shades highlighting (002) and (003) reflections that are used to calculate the interlayer distance. Peak positions of (002) and (003) reflections for (NA^CuCL and (NA^CuBu are indicated using dashed lines. The compounds contain nonylammonium (NA, Cg) chains confined within the Cu-X pocket (X = Cl, Br). Figs. 17A-17B show relationships between interlayer distance and other properties of the materials. Fig. 17A shows interlayer distances for mixed-halide (NA)2CuCl4-xBrx perovskites for high-temperature (HT) and low-temperature (LT) phase at 311 K and 269 K, respectively. The change in interlayer distance (Ad), indicated by a dashed arrow, is calculated as the difference between the interlayer distances for HT phase (dHT) and LT phase (dLT), with Ad = dHT - dLT. Fig. 17B shows relationships between the relative change in interlayer distance (Ad / dLT) and the transition entropy (AStr) associated with chainmelting transitions. Fig. 18 shows relationships between the relative change in interlayer distance (Ad / di-) and the transition entropy (AStr) associated with chain-melting transitions for mixed-halide (NA)2CuCl4-xBrx perovskites. Mixed halide perovskite with DA chain (n = 10): volume change (AV) and gravimetric entropy change (AS). Figs. 19A-19D show powder X-ray diffraction (PXRD) patterns for mixed-chain [(NA)i-x(DA)x]2CuCl4 perovskites at 1 bar of He, with an X-ray wavelength of 0.45213 A, for (Figs. 19A-19B) high-temperature (HT) and (Figs. 19C-19D) low-temperature (LT) phase at 321 K and 279 K, respectively. The PXRD 14 patterns are shown at variable chain compositions (as indicated), with grey shades highlighting (002) and (003) reflections that are used to calculate the interlayer distance. Peak positions of (002) and (003) reflections for (NA)2CuCk and (DA^CuCk are indicated using dashed lines. The compounds contain nonylammonium (NA, Cg) and decylammonium (DA, C10) chains confined within the Cu-CI pocket. Figs. 20A and 20B Mixed chain perovskites: volume change (AV) and molar entropy change (AS). Fig. 20A shows interlayer distances for mixed-chain [(NA)i-x(DA)x]2CuCl4 perovskites for high-temperature (HT) and low-temperature (LT) phase at 321 K and 279 K, respectively. Red and blue symbols indicate the interlayer distances in HT and LT phase, respectively. The change in interlayer distance (Ad), indicated by a dashed arrow, is calculated as the difference between the interlayer distances for HT phase (dm-) and LT phase (dir), with Ad = dHT - du. Fig. 20B shows relationships between the relative change in interlayer distance (Ad / di?) and the transition entropy (AStr) associated with chain-melting transitions. Fig. 21 Mixed halide perovskite with DA chain (n = 10): volume change (AV) and and gravimetric entropy change (AS). Relationships between the relative change in interlayer distance (Ad / d.T) and the transition entropy (ASr) associated with chain-melting transitions for mixed-chain [(NA)i_x(DA)x]2CuCk perovskites. Figs. 22A-22D Mixed-chain / mixed-halide (’’double-mixed”) perovskites: ambient-pressure PXRD for both HT and LT phases. Figs 22A-22D show powder X-ray diffraction (PXRD) patterns for compositionally engineered two-dimensional copper halide perovskites at 1 bar of He, with an X-ray wavelength of 0.45213 A, for (Figs. 22A and 12B) high-temperature (HT) and (Figs. 22C and 12D) low-temperature (LT) phase. The PXRD patterns at HT phase and LT phase were obtained at 21 K above and below the transition temperature (Ttr), respectively. The PXRD patterns are shown at variable compositions (as indicated), with grey shades highlighting (002) and (003) reflections that are used to calculate the interlayer distance. The compounds contain nonylammonium (NA, Cg), decylammonium (DA, Cto), and / or undecylammonium (UA, Cn) chains confined within the Cu-X pocket (X = Cl, Br). Figs. 23A and 23B Mixed-chain / mixed-halide (’’double-mixed”) perovskites: volume change and entropy changes. Fig. 23A shows interlayer distances for compositionally engineered two-dimensional copper halide perovskites for high-temperature (HT) and low-temperature (LT) phase. The data for HT (red) and LT (blue) phase were obtained at 21 K above and below the transition temperature (Ttr), respectively. The change in interlayer distance (Ad), indicated by a dashed arrow, is calculated as the difference between the interlayer distances for HT phase (c / ht) and LT phase (cLt), with Ad = dur - oLt. Fig. 23B shows relationships between the relative change in interlayer distance (Ad / di?) and the transition entropy (AStr) associated with chain-melting transitions. Figs. 24A-24C show HP-DSC data for (NA^CuCk: Fig. 24A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for (NA)2CuCk with heating and cooling rates of 2 K min-1. Fig. 24B shows pressure dependence of the major phase transition as determined by HP-DSC. Fig. 24C shows pressure dependence of the minor phase transition as determined by HP-DSC. The data points in the P-T diagram correspond to peak temperature. The minor transition has a noticeably lower entropy, and higher dT / dPand sensitivity to pressure. An “average” dT / dPof 22.1 K kbar1 was determined via the Clausius-Clapeyron relation. Figs. 25A and 25B show HP-DSC data for (DA)2CuCl2Br2. Fig. 25A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for (DA)2CuCl2Br2 with heating and cooling rates of 2 K min-1. Fig. 25B shows pressure dependence of the phase transition as determined by HP-DSC, with peak transition temperatures plotted. A barocaloric coefficient (dT / dP) of 25.8 K kbar1 was determined from the heating curve. Figs. 26A and 26B show HP-DSC data for (DA^CuCbBr. Fig. 26A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for (DA)2CuCl3Br with heating and cooling rates of 2 K min-1. Fig. 26B shows pressure dependence of the phase transition as determined by HP-DSC, with peak transition temperatures plotted. A barocaloric coefficient (d T / dP) of 24.3 K kbar1 was determined from the heating curve. Figs. 27A and 27B show HP-DSC data for [(NA)o.5(DA)o.5]2CuCl4. Fig. 27A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for [(NA)o.5(DA)o.5]2CuCl4 with heating and cooling rates of 2 K min-1. Fig. 27B shows pressure dependence of the phase transition as determined by HP-DSC, with peak transition temperatures plotted. A barocaloric coefficient (d T / dP) of 22.4 K kbar1 was determined from the heating curve. Figs. 28A and 28B show HP-DSC data for [(NA)o.s(UA)o.5]2CuCl4. Fig. 28A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for [(NA)o.5(UA)o.5]2CuCl4 with heating and cooling rates of 2 K min~1. Fig. 28B shows pressure dependence of the phase transition as determined by HP-DSC, with peak transition temperatures plotted. A barocaloric coefficient (d T / dP) of 25.1 K kbar1 was determined from the heating curve. Figs. 29A and 29B show HP-DSC data for [(NA)o.5(DA)o.5]2CuCl2Br2. Fig. 29A shows high-pressure differential scanning calorimetry measurements under applied hydrostatic pressure of helium for [(NA)o.s(DA)o.5]2CuCl2Br2 with heating and cooling rates of 2 K min~1. Fig. 29A shows pressure dependence of the phase transition as determined by HP-DSC, with peak transition temperatures plotted. A barocaloric coefficient (d T / dP) of 24.1 K kbar1 was determined from the heating curve. Figs. 30A and 30B: Evaluation of barocaloric effects for (DA)2CuCl2Br2. Fig. 30A shows DSC measurements for (DA)2CuCl2Br2 under applied hydrostatic pressure with heating and cooling rates of 2 K min-1 using He as the pressure-transmitting medium. Fig. 30B shows pressure-temperature (P, 7) phase diagram determined from the isobaric HP-DSC experiments. Phase boundaries were determined for both heating (red) and cooling (blue), with the transition width highlighted in the shaded area. Note that the minimum pressure required to drive a reversible isothermal entropy change (Pev, 31 bar) and a reversible adiabatic temperature change (Prev.ad, 130 bar) are indicated by vertical lines. Figs. 31A-31 D: Entropy curves for (DA)2CuCl2Br2. Figs. 31A and 31B show isobaric entropy change (△Sb) associated with the phase transition of a powder sample of (DA)2CuCl2Br2, as a function of temperature in the pressure range of 1 bar to 150 bar on (Fig. 31 A) heating and (Fig. 31B) cooling. Figs. 31C and 31D shows isothermal entropy changes (ASt), calculated by the quasi-direct method, for (Fig. 31C) decompression to ambient pressure and (Fig. 31 D) compression from ambient pressure, obtained from heating and cooling data, respectively. Figs. 32A and 32B: Evaluation of barocaloric effects for (DA)2CuCl2Br2. Fig. 32A shows isothermal entropy changes (ASt) calculated by the quasi-direct method for (DA)2CuCl2Br2. The shaded area indicates the reversible isothermal entropy change (ASt,rev) that is accessible at each operating pressure. Fig. 32 shows the maximum reversible isothermal entropy change (ASt,rev,max) and reversible refrigeration capacity (RCrev) are plotted as a function of operating pressure. Note that the barocaloric strength (ASt,rev / AP) is 1391 J K-1 kg-1 kbar-1 and the pressure dependence of RCrev is 2723 J K-1 kg-1 kbar-1. Figs. 33A and 33B: Phase Diagram for (NAo.5DAo.5)2CuCl2Br2. Fig. 33A shows DSC measurements for (NAo.5DAo.5)2CuCl2Br2 under applied hydrostatic pressure with heating and cooling rates of 2 K min-1 using He as the pressure-transmitting medium. Fig. 33B shows a pressure-temperature (P, T) phase diagram determined from the isobaric HP-DSC experiments. Phase boundaries were determined for both heating (red) and cooling (blue), with the transition width highlighted in the shaded area. Note that the minimum pressure required to drive a reversible isothermal entropy change (Rev, 21 bar) is indicated by a vertical line. Note that Prev,ad is 160 bar. Figs. 34A-34D: Entropy curves for (NAo.5DAo.5)2CuCl2Br2. Figs. 34A and 34B show isobaric entropy change (ASb) associated with the phase transition of a powder sample of (NAo.sDAo.5)2CuCl2Br2, as a function of temperature in the pressure range of 1 bar to 150 bar on (Fig. 34A) heating and (Fig. 34B) cooling. Figs. 34C and 34D show isothermal entropy changes (ASt), calculated by the quasi-direct method, for (Fig. 34C) decompression to ambient pressure and (Fig. 34D) compression from ambient pressure, obtained from heating and cooling data, respectively. Figs. 35A and 35B: Evaluation of barocaloric effects for (NAq.sDAo.s^CuC^B^. Fig. 35 shows isothermal entropy changes (ASt) calculated by the quasi-direct method for (NAo.sDAo.s)2CuCl2Br2. The shaded area indicates the reversible isothermal entropy change (ASt,rev) that is accessible at each operating pressure. Fig. 35B shows the maximum reversible isothermal entropy change (ASt,rev,max) and reversible refrigeration capacity (RCrev) are plotted as a function of operating pressure. Note that the barocaloric strength (ASuev / AP) is 1085 J K~1 kg~1 kbar~1 and the pressure dependence of RCrev is 1626 JK’1 kg~1 kbar-1. Fig. 36 Energy-dispersive X-ray spectroscopy measurements and scanning electron microscope (SEM) for (DA)2CuClsBr. The SEM image is shown on the left. Elemental maps of Br (top right) and Cl (bottom right) show an even dispersion of halides on the crystal surface. The magnification is 1,300x and the electron accelerating voltage is 4.0 kV. These results show that Cl and Br are uniformly mixed in the crystal. Figs. 37A and 37B show halide quantification from elemental analysis. Molar bromide content for (NA)2CuCl4-xBrx (Fig. 37A) and (DA)2CuCl4-xBrx (Fig. 37B) was found through elemental analysis. These percentages were determined by oxygen flask combustion and potentiometric titration. The lines delineate what the bromide content would be if all of the reagents in solution were incorporated into the crystal structure. Deviation from expected concentration is likely due to solubility differences between bromide and chloride perovskites. All mixed-halide / chain compounds listed herein are referred to by their expected (nominal) molar ratios (i.e., concentration in solution) for the sake of consistency. Fig. 38 shows a depiction of how dialkylammonium (organic) salts can be used to drive a barocaloric cooling cycle. The order-disorder transitions in the organic bilayers are pressure-dependent. First, an adiabatic compression induces a transition from the expanded, disordered phase of the material to a contracted, ordered phase. Heat that is released during this exothermic process is rejected to a heat sink, returning the material to its original temperature but at a lower entropy. Then, the pressure is adiabatically decreased to reverse the phase transition and take in heat from a heat source. Fig. 39 Structural characterization of (CeHishN^Br. XRD experiments were performed on (CeHi3)2NH2Br. The single-crystal structure obtained at 100 K (left, viewed along b-axis) features a layered structure, where each organic cation is confined by charge-balancing Br anions. We have also successfully carried out variable-temperature PXRD experiments under 300 bar of He (right). The data was collected during cooling from 360 K to 220 K, with an X-ray wavelength of 0.45185 A. Notably, these data show that, even at 300 bar pressure, the compound undergoes a single (disorder-to-order) phase transition that is associated with a large change in volume. Fig. 40 Structural characterization of (Ci2H25)(CHs)NH2Br “(Ci2-Ci)Br”. XRD experiments were performed on (Ci2H2s)(CH3)NH2Br. The single-crystal structure obtained at 100 K (left, viewed along b-axis) features a layered structure, where each organic cation is confined by charge-balancing Br anions. Fig. 41 Structural characterization of (Ci2H2s)(CH3)NH2CI “(Ci2-Ci)CI”. We have carried out preliminary XRD experiments on (Ci2H25)(CHs)NH2Br. The single-crystal structure obtained at 100 K (left, viewed along b-axis) features a layered structure, where each organic cation is confined by charge-balancing Br anions. Figs. 42A and 42B show data from high-pressure differential scanning calorimetry for (Ci2-Ci)Br. Fig. 42A shows DSC measurements for (Ci2H25)(CH3)NH2Br “(C12-Ci)Br” under applied hydrostatic pressure with heating and cooling rates of 2 K min-1 using He as the pressure-transmitting medium. Fig. 42B shows a pressure-temperature (P, 7) phase diagram determined from the isobaric HP-DSC experiments. Phase boundaries were determined for both heating and cooling. Figs. 43A and 43B show data from high-pressure differential scanning calorimetry for (C12-Ci)CI. Fig. 43A shows DSC measurements for (Ci2H25)(CH3)NH2CI “(C12—Ci)CI” under applied hydrostatic pressure with heating and cooling rates of 2 K min 1 using He as the pressure-transmitting medium. Fig. 43B shows a pressure-temperature (P, 7) phase diagram determined from the isobaric HP-DSC experiments. Phase boundaries were determined for both heating and cooling. Figs. 44A and 44B show data from high-pressure differential scanning calorimetry for dCeBr. Fig. 44A shows DSC measurements for (C6His)2NH2Br “dCsBr” under applied hydrostatic pressure with heating and cooling rates of 2 K min-1 using He as the pressure-transmitting medium. Fig. 44B shows a pressure-temperature (P, 7) phase diagram determined from the isobaric HP-DSC experiments. Phase boundaries were determined for both heating and cooling. Fig. 45 shows thermal properties of organic barocaloric materials for a selected group of dialkylammonium salt compounds (left). Entropy changes associated with the order-disorder phase transition (measured by ambient-pressure DSC) are plotted (right) as a function of transition temperatures. Importantly, these materials undergo reversible phase transitions accompanied by colossal entropy changes (>200 J K~ kg-1) near ambient temperature. Figs. 46A and 46B show pressure dependence of phase transition temperature is highly sensitive to the pressure-transmitting medium. Pressure-temperature (P, T) phase diagram determined under He (red), Na, and Ar environments for (Fig. 46A) (DA)2MnCk and (Fig. 46B) (NA)2CuBr4 via high-pressure differential scanning calorimetry (HP-DSC). The pressure sensitivity of the order-disorder phase transition (dT / dP) decreases as the polarizability of gas medium increase (from He to N2 to Ar). The phase boundaries and dT / dPvalues predicted from the Clausius- Clapeyron relationship (dT / dP = △ WAS) are shown in diamonds. Figs. 47A and 47B show entropy of transitions measured from isobaric HP-DSC experiments under He, N2, and Ar for (Fig. 47A) (DA)2MnCl4 and (Fig. 47B) (NA)2CuBr4. The identity of pressure-transmitting medium has minimal impacton the magnitudes of transition entropy. Figs. 48A and 48B show results for how Ar gas as pressure-transmitting medium induces inverse barocaloric effects in (NA)2CuBr4. Fig. 48A shows isobaric high-pressure differential scanning calorimetry (HP-DSC) measurements for (NA^CuBu under Ar environments reveal that the increase in Ar pressure leads to decrease in transition temperature, without noticeable changes in transition enthalpy and entropy. Fig. 48B is a (P, 7) phase diagram under Ar, with transition temperatures determined from heating and cooling. Figs. 49A and 49B show direct evaluation of Ar pressure-induced inverse barocaloric effects in (NA)2CuBr4 via quasi-isothermal HP-DSC. Fig. 49A shows a pressure-temperature phase diagram. In Fig. 49B heat flow signals were measured as a function of time during 3 cycles of applying and removing a hydrostatic pressure of 150 bar at 301.6 K with Ar as the pressure-transmitting medium. As the phase diagram shown in Fig. 49A indicates, the 150-bar pressure swing at 301.6 K, compression induces an endothermic transition from ordered (low-temperature, LT) phase to disordered (high-temperature, HT) phase. Decompression induces an exothermic transition from disordered / HT phase to ordered / LT phase. The area under the heat flow peaks in Fig. 49B correspond to compression-induced endotherms and decompression-induced exotherms is 23.3 and 22.5 J / g, respectively. Fig. 50 shows how manipulating the pressure sensitivity (dT / dP) via pressure-transmitting medium provides a mechanism for pressure-tunable thermal energy storage. Transition temperatures for (NA)2CuBr4 can be increased to 309 K (at increasing He pressure) or lowered to 300 K (at increasing Ar pressure), which creates the temperature window of 9 K at 150 bar pressure. This phenomenon can be utilized for tuning the transition temperatures “on-demand” for thermal energy storage at easily accessible pressure. Thermal energy storage (TES) cycles at low temperatures can be realized under high-pressure Ar environments, whereas TES cycle at high temperatures can be accessed under high-pressure He. DETAILED DESCRIPTION OF THE INVENTION Barocaloric effects—thermal changes driven by hydrostatic pressure—offer particularly simple and energy-efficient ways to achieve solid-state cooling. As first-order phase transitions involve a latent heat, large barocaloric effects are expected to occur near the phase transition temperature when the first-order transition is induced by applied hydrostatic pressure. To exhibit a large barocaloric effect, a material must meet the following three requirements: 1) first-order phase transition with large latent heat (Qr), large entropy change (AStr), and transition temperature Ttrclose to a desired operational temperature; 2) high sensitivity of the phase transition to applied pressure (i.e., high barocaloric coefficient 5Ttr / 6P); and, 3) low thermal hysteresis. As cooling devices operate cyclically, the barocaloric effects must be driven reversibly upon a sequence of application and removal of external pressure; therefore, thermal hysteresis dramatically affects the cooling performance, determining the minimum pressure needed to achieve reversible barocaloric effects (pwv). Usually, prev is proportional to the thermal hysteresis width. Since it is practically beneficial to have low operating pressure (prev), identifying barocaloric materials with low thermal hysteresis is highly desirable. Note, additionally, that for a first-order phase transition, the barocaloric coefficient can be calculated using the Clausius-Clapeyron relation 5Tr / 6F,=AWr / AStr where AW = volume change of the phase transition. Thus, a material must have a high AW / ASir to have a high barocaloric coefficient. The invention provides highly generalizable approaches to realizing a new class of materials that display colossal—yet tunable—barocaloric effects at relatively low operating pressures. Specifically, this invention describes the use of reversible, solid-solid, order-disorder phase transitions, e.g., in layered, two-dimensional (2D) organic-inorganic hybrid materials for barocaloric cooling (Fig. 3A). In these newly identified hybrid barocaloric compounds, long-chain organic molecules (e.g., long alkyl chain CnH2n+i, e.g., where n >3, e.g., >4) are templated by inorganic layers, and the hybrid materials exhibit pressuresensitive phase transitions based on order-disorder transitions of the confined chains—a so-called “chain-melting” process. We believe that any phase-change material for which a solid-state phase transition results from a structural transitions of long-chain organic molecules confined within inorganic components is likely to exhibit large barocaloric effects. The propensity for confined chain melting to drive large barocaloric effect is based on: ( / ) the wide range of organic phase-change materials that undergo phase transitions near ambient temperature with a large volume change (A W), latent heat (Qr), and entropy change (ASr); ( / / ) the organic phase-change materials, when templated with inorganic substances, remain solid-state during the phase change, exhibiting reversible, solid-solid phase transitions with all beneficial phase-change properties (i.e., high A4 Qr, ASr) retained. Unlike magnetocaloric, electrocaloric, and elastocaloric effects, the barocaloric effect is not system-selective and in principle can be observed in any materials, as the free energy of a system always depends on pressure. In summary, this invention reports that order-disorder transition of normal, branched, or functionalized organic chains—on or within inorganic structural templates—can be used as a new mechanism to achieve large barocaloric effects relevant to solid-state cooling. Layered materials such as two-dimensional (2-D) metal-halide perovskites of the form (R-NHs)2MX4 (R = CnH2n+i; n >3 (e.g., >4); M = Mn, Fe, Cu, Cd, Pb; X = F, Cl, Br, or I) can undergo chain-melting transitions in the solid state. In these compounds, sheets of corner-sharing MXe octahedra create anionic pockets— defined by the axial halides of four adjacent metal centers—that template the arrangement of bilayers of alkylammonium cations through charge-assisted hydrogen bonds. When long-chained hydrocarbon molecules (n> 3, e.g., >4) are incorporated, many layered perovskites undergo thermally induced, first- order phase transitions between ordered and disordered states driven by what is effectively a partial melting transition of the hydrocarbon bilayers. As such 2-D perovskites can serve as a highly tunable solid-state platform to leverage the large changes in entropy and enthalpy that accompany hydrocarbon chain-melting transitions for barocaloric cooling (Figs. 3A-3B). Moreover, since the inorganic layers and organic bilayers of 2-D perovskites can be independently manipulated, phase transition hysteresis could be minimized through careful control of the organic-inorganic interfaces. In one embodiment, this invention describes barocaloric effects in 2D hybrid perovskites, with a general chemical formula of (R-NHs)2MX4, which contain layers of first-row transition metal halides [MX4]2' (M = Mn, Fe, Co, Cu, Zn; X = Cl, Br, or I) connected by bilayers of ammonium cations (R-NFV). In these compounds, organic bilayers are confined by metal-halide inorganic layers. Inorganic layers can assemble (and confine organic layers) via, e.g., hydrogen bonds (e.g., between R-NHs^-X groups), electrostatic attraction, or a combination thereof. Van der Waals interactions between R groups (see, e.g., Figs. 3A and 5E-5H) may also contribute to the assembly of layers and confinement of the organic layers. Depending on the identity of the divalent transition metal cation (M2+), the inorganic layers of the 2D layered perovskites have two different structure types. For M = Mn, Fe, Cu, the inorganic layer is composed of corner-sharing MXe octahedra. Each organic molecule is contained within a cavity defined by the terminal halides from four adjacent corner-sharing octahedra. For M - Co, Zn, the inorganic layer consists of planes of isolated MX4 tetrahedra. In all cases, the bilayers of organic chains (R-NHs+) are confined by the inorganic layers. Many 2D perovskites with long-chain organic molecules (R = CnH2n+i, n >4) are known to undergo thermally-induced, reversible, solid-solid phase transitions near room temperature (20-90 °C) due to the ordering and disordering the organic molecules. As these solid-solid transitions are often accompanied by a large latent heat (> 60 kJ kg-1) and entropy change (> 200 J kg-1 K-1), layered hybrid perovskites may be employed as solid-solid phase-change materials for passive thermal management and thermal energy storage. The main phase transition of these compounds involves disordering of organic chains, often referred to as a “chain-melting” transition. The mechanism for “chain melting”—defined as the rapid diffusion of a kink (one or more gauche bonds) up and down along the C-C bonds within an organic chain—has been extensively studied at ambient pressure by various structural, thermal, and spectroscopic techniques, including powder and single-crystal X-ray diffraction, differential scanning calorimetry, dielectric measurements, and infrared and Raman spectroscopies. The dynamics of the ammonium chains have been further investigated at ambient pressure by solid-state NMR techniques and inelastic neutron scattering. In the low-temperature, ordered phase, the confined chains are tilted because their cross-sectional area is less than the area of the halide square (~5 x 5 A2) afforded by the 2D inorganic lattice. In the high-temperature, disordered phase, the chains are disordered and effectively occupy the whole cross-sectional area available to them. This results in a large expansion of the interlayer spacing. As the intralayer distances are essentially unchanged due to the robust inorganic templates, this directly leads to large increase in volume (Al / Wo = 7-10 %). These studies show that the large latent heat, entropy change, and volume change of main phase transition observed in the organic-inorganic hybrid materials originate from confined chain melting process. A representative layered perovskite (CioH2iNHs)2MnCl4 undergoes solid-solid, reversible phase transition near room temperature (35 °C) with large entropy change (e.g., ~221 J kg-1 K-1) and volume expansion (e.g., ~7.3 %). Based on thermodynamics calculations (Clausius-Clapeyron relation), we identified that the phase transition is expected to be highly sensitive to applied pressure (e.g., 6Ttr / 6P ~ 28 K kbar-1). As such, inducing the disorder-to-order transition by adiabatically applying pressure is expected to result in adiabatic temperature increase, e.g., (ATad) of ~30 K. Taken together, this analysis suggested that (CwH2iNH3)2MnCl4 should exhibit colossal barocaloric effect. To experimentally confirm the existence of large barocaloric effects in layered perovskites, we measured powder X-ray diffraction (PXRD) patterns as a function of temperature and applied pressure for the 2D layered perovskites (CioH2iNH3>2MnCl4 to evaluate the pressure dependence of the transition temperature (Ttr) between ordered and disordered phases of this material. As the thermally induced order-disorder phase transition leads to a clear shift in powder diffractions peak positions (Figs. 1A-1B), we were able to identify Ttr as a function of applied pressure. Excitingly, variable-temperature PXRD data obtained under applied pressures up to 360 bar clearly indicate that applying hydrostatic pressure shifts the phase transition to higher temperature (Figs. 2 and 6A-6J). Compositions of the invention thus exhibit colossal barocaloric effects and are very competitive with the best current barocaloric materials (see, e.g., Figs. 7A and 7B). More broadly, the results described herein indicate that the thermodynamic and structural properties afforded by confined chain melting transitions are generally beneficial for barocaloric effects. The class of existing and potential 2D layered perovskites provide access to a tremendous structural and chemical diversity through the judicious selection of the inorganic and organic moieties that constitute each material. As such, we may control the confined chain melting in these materials leading to not only colossal but also highly tunable barocaloric effects. Indeed, the thermodynamics and kinetics of these pressure-induced phase transitions are controllable, e.g., by modifying: 1) the molecular interactions between the inorganic layers, 2) the flexibility of the organic chains, and 3) the free volume within the organic bilayers. For instance, we have synthesized a series of new layered perovskites—containing Cu, Mn, and Fe metal centers ligated to Cl- anions—with organic molecules incorporated as bilayers between the metal-chloride sheets that include oxygen-substituted alkyl chains (C3OC4), functionalized phenylalkylamines (C4Ph and CePh), alkyl chains incorporating an ester group (Cn-COO-C2; n = 9, 10, 11), and alkyl chains functionalized with alcohols (CnOH; n = 5, 6, 8) that create hydrogen bonding networks within the bilayers (see, e.g., Fig. 3 and Table 1 and Tables 20-25). c>oc4 Compound 0, ¢0 (J kg-' K -’) (Ul-9 Go [TPrAWWcaU 330 42.5 52.7 17.3 C-. (CH^qCH-OHk 313 390 390.0 1221 o (C^Mn 28? 219.? 263.6 73.0 CstCOOjCa 308 220.7 264.8 62.1 Cr.(COO)C2 G;(COO)Ck 0 308 / 311 215.5 274.4 842 SwW (CxiCu 309 / 312 944.4 293.3 986 chsif'S 318 2?0.$ 324.? 103.1 h.S- — >- X X (C:^ 332 / 338 285 342 118.1 .x V V v « C,O(C« HiX' x" XX-‘ (GiihCu 328 / 334 252.9 303,5 95.3 Gpb <csoc.,}5Cu 243 •m? 183.0 44.5 L (GAt^Cu 338 82.7 70.8 239 GOH (GOA.<\?Cu 398 134 162 64 GOH (GGHhCu 309 105.9 148.3 45.8 Fuftclisx'.aUxexi ch&ns {CsOHhCu 341 145.8 204.1 69.6 342 223.8 305.0 104 2 0,00.:08 0 ^(COOjC-JjfCu 355 252-? :131.0 117.5 GOPb Table 1 shows a library of long-chain ammonium cations incorporated into layered perovskites. Structures of long-chain ammonium cations studied in our laboratory (left) and thermal properties of layered perovskites incorporating the ammonium cation chains (right). Ttr, transition temperature; AStransition, entropy of phase transition; Qr, latent heat of phase transition. (R)zM denotes layered perovskite (R-NH3)2MCl4. These newly synthesized 2D hybrid perovskites exhibit reversible, thermally-induced phase transitions driven by chain melting. Most notably, the synthetic modifications of the organic chain enabled the tuning of transition temperature between -30 °C to 120 °C without compromising beneficial thermodynamic properties (e.g., large latent heat and entropy change). These results demonstrate that the barocaloric properties of layered perovskites can be readily tuned through synthetic modifications. Barocaloric effects of the functionalized perovskites synthesized in our laboratory are summarized in Table 5. In addition, we have synthesized compositionally engineered mixed halide 2D metal-halide perovskites, e.g., replacing all—or a portion—of Cl anions with Br anions for mixed-halide systems, e.g., having formula [(R1)x(R2)i-x]2MXyX'4-y, where R1 and R2 are long chain alkylammonium species(e.g., CnH2n+iNH3+, where n >3, e.g., >4, e.g., NA or DA) and where X and X' are different halides, e.g., selected from Cl, Br, or I, e.g., (R-NH3)zMCl4-yBry (0 <y< 4), e.g., where M is a transition metal (e.g., Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Rh, Rd, Cd, Re, Pt, or Hg) and R is NA or DA. Mixed halide compounds may also be “double mixed”, e.g., containing two halides (e.g., Cl and Br) and two different alkylammonium species. The different alkylammonium species may be in non-integer ratios, relative to the metal center (e.g., [(NA)o.75(DA)o.25]2CuCl4, [(NA)0.5(DA)0.5]2CuCl4, or [(NA)0.25(DA)0.75]2CuCl4, [(NA)0.25(UA) o^CuCU, [(NA)o.s(UA) o.s]2CuCl4, or [(NA)o.s(DA) o.5]2CuCl2Br2). In compounds of the formula [(R1)x(R2)i-x]2MXyX'4-y, ‘y’ may be 0-4 (e.g., 0,1,2, 3, or 4) and ‘x’ may be between 0-1, e.g., about 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, or 0.95. Thermal and structural data on the mixed 2D metal-halide perovskite materials in shown in Tables 21-25. Some mixed 2D metal-halide perovskite materials are compared to non-mixed 2D metal-halide perovskite materials in Figs. 12A and 12B. In addition, additional functionalized layered perovskites may be formed by ( / ) combining two different modifications in a single chain (e.g., C3OC4OH) ( / 7) fluorinating the chain, ( / 77) synthesizing layered halide double perovskites of the form (R-NHs^MM'Xs where M is a monovalent cation such as Na+ and M' is a trivalent cation such as Fe3+, X = Cl’, Br-. In some embodiments, one or more Cl, Br, or I halides may be replaced by F. In addition, additional functionalized layered perovskites may be formed from non-halide anions, e.g., CN_, HCOO-, Ns-, N(CN)2‘, BF<, BFk, PFe-, SCN-, OCN-. Incorporation of the larger anions can increase the pocket size for cations (e.g., the alkylammonium species), thus relatively larger cations e.g., the largest cations of Table 1, or even dialkylammonium cations described herein. In addition to synthetic tunability and chemical diversity, layered halide perovskites display a number of other properties that are advantageous for practical solid-state cooling. First, the “soft” nature and high solution processability of layered halide perovskites enables thin films to be easily fabricated. The high processability not only presents rich opportunities for the design of miniaturized cooling devices but may also allow the invention to take advantage of microscopic mechanisms for barocaloric effects across various length scales (from bulk powders to thin films to atomically thin layers) and materials forms (from single crystals to microcrystalline powders to thin films). Second, phase transitions in appropriately designed layered perovskites display small thermal hysteresis (< 4 K). Thus, reversible barocaloric effects can be achieved at small operating pressure prev. Given that these layered perovskites display high barocaloric coefficients (> 20 K kbar-1), this suggests that colossal reversible barocaloric effects can be realized at easily accessible pressures (< 100 bar) (Fig. 6). For comparison, organic plastic crystals—another class of colossal barocaloric materials—require relatively high operating pressure of 500-1,000 bar for reversible barocaloric effects. These two features—high processability and low operating pressure—allow various device architectures with minimal design constraints. The confined chain melting described herein is a general mechanism to achieve colossal barocaloric effects because large latent heat, entropy change, and volume expansion—prerequisites to colossal barocaloric effects—can simultaneously emerge when long-chain molecules are forced to undergo large conformational changes in confined space. Note that the analysis and experiments described in this invention are readily applicable to other types of layered materials beyond hybrid perovskites. Any organic and inorganic materials that can be assembled into layers of organic material between layers of inorganic material are suitable to be used in the invention. Alternatively or in addition, organometallic materials including a layer-forming inorganic component and an organic component including long, optionally substituted alkyl chains may be used, for example, the following barocaloric materials: di- / 7-alkylammonium salts (e.g., compounds of formula (CnH2n+i)2NH2X (n >3 (e.g., >4, e.g., C4-36 alkyl chains) or compounds of formula (CnH2n+i)(CmH2m+i)NH2X, where rt is 1-3 or 4-36 and rn is 4-36, e.g., where n — m, or where n = 1-3 (e.g., 1) and m = 4-36 (e.g., 6, 8, 10, or 12); where X is a monoanionic species, e.g., a halide (e.g., F, Cl, Br, or I) or a non-halide anion, such as NO3-, CIO3-, CIO4-, H2PO4-, HSO4-, CN-, HCOO , N3 , N(CN)2, BF4, BH4, PFe, SCN , or OCN ), see Figures 38-45 and Tables 26-29), alkylammonium-modified layered silicates, and layered metal-alkylphosphonate salts may also be used in 24 systems, devices, and methods of the invention (see, e.g., Table 20). These compounds all undergo reversible, solid-solid, phase transition near room temperature with large entropy and volume change. Alkylammonium species may have odd or even numbered main chains. Alkylammonium species may have main chain lengths of greater than 36 carbons (e.g., up to 38, 40, 45, 50, 60, 75, or 100 carbons). Alkylammonium species of the invention may be quaternary ammonium species (e.g., Me3N(CnH2n+i)X or Me2N(CnH2n+i)2X, where n is >3, e.g., >4, e.g., 4-36, and where X is a monoanionic species, e.g., a halide). Dialkylammonium species of the invention may be asymmetric, e.g., having formula (CnH2n+i)(CmH2m+i)NH2X where n and m are both >3 (e.g., 4-36) but are not the same length. Chain-melting phase transitions and their pressure sensitivity (d7tr / dP), discussed here in the context of barocaloric cooling (using the 2-D perovskites as proof-of-concept examples), offer a new mechanism to realize highly efficient and tunable thermal energy storage, whereby application of hydrostatic pressure can be used to tune the storage temperature, Tstor, and release temperature, Trei (Figs. 8A and 8B). The difference between the barocaloric cooling and pressure-tunable thermal energy storage (PT-TES) lies in the specific operating cycle that is employed. During a typical PT-TES cycle—where thermal energy is stored and released by a change in temperature—the pressure change, AP, can occur outside of transition. Here, the pressure change does not drive phase transitions and is only used to tune the transition temperatures for thermal energy storage and release at different temperatures. Due to the simplicity of the operation, we anticipate that PT-TES can be readily implemented in various environments, with a low actuator-to-material volume ratio that will contribute to high volumetric working capacity. We also note that, once the materials are thermally charged, application or removal of the pressure, can directly induce phase transitions, leading the on-demand release of stored thermal energy. This process, despite its simplicity, does not require strict maintenance of isothermal conditions, as long as the pressure change is sufficiently high. The material properties required for efficient PT-TES are similar to those required for efficient barocaloric cooling. Materials for PT-TES should undergo solid-state phase transitions with high thermal changes (△Str), high sensitivity to pressure (dTtr / dP), and small hysteresis (AThys), because the temperature span of the PT-TES operation (ATspan), defined here as the difference between Trei and Tstor, is calculated by, ATspan = (dTtr / dP) x AP - AThys. Note that PT-TES materials will benefit from having large ATspan and small AP, and materials with high dTtr / dPand low AThys, as well as large AStr and AHr, will be suitable for this. Another difference is, unlike barocaloric cooling (which requires phase transition temperatures near or below ambient temperature), thermal energy storage materials are needed across a broad temperature range. In this context, compositions of the invention, e.g., the two-dimensional metal-halide perovskites—first highlighted here in the context of barocaloric cooling due to their large thermal changes (AStr and AHr), high pressure sensitivity (dTtr / dP), and small hysteresis (AThys)— provide a versatile platform to achieve efficient the PT-TES in the broad temperature range, as their transition temperatures and sensitivity to pressure can be readily manipulated by changing the length of hydrocarbon chains to cover a wide temperature range (from 250 K to 400 K) (Tables 2 to 5). Layered compounds of the invention, e.g., with long-chain hydrocarbons, will be highly competitive PT-TES materials, due to their beneficial phase-change properties, synthetic tunability, and pressure dependence, similar to those of the 2-D perovskites (Table 20) exemplified herein. As shown in Fig. 9, we believe that this biggest impact of PT-TES approach is to adjust the phase-change temperature of the TES material on demand, such that the working temperature can be optimized for changing demands of the thermal energy storage and thermal management. Effect of Pressure Transmitting Medium The invention also includes methods of enhancing barocaloric cycles based on the properties of the pressure-transmitting medium. The pressure transmitting medium (PTM) can affect the properties of the phase transitions of the barocaloric cycles in materials including long-chain hydrocarbons. The effects include inverse barocaloric effects for compounds (e.g., with long-chain hydrocarbons) that undergo reversible chain-melting transitions. Gaseous PTMs may induce changes in thermal properties of materials with long alkyl chains (e.g., those of the invention) by permeating into and interacting with the materials of the composition, e.g., by permeating into free volume in the organic layer. Gases that can permeate into the composition are preferably inert gases that can also interact with the composition at the microscopic level (e.g., non-covalently interact, e.g., via Van der Waal’s-type interactions, e.g., via dispersion forces). Both the extent of permeation (e.g., amount of gas molecules in the free volume / interacting with the composition) and degree and nature of interaction (e.g., strength of interaction, e.g., determined by a molecule or atom’s size, shape, polarizability, etc.) can determine the effect of the PTM on thermal transitions of the composition. Exemplary PTM gases include nitrogen, argon, krypton, xenon, methane, ethane, propane, butane, sulfur hexafluoride, or carbon dioxide. Gases that permeate and interact sufficiently with the composition (e.g., argon into (NA)2CuBr4)) can cause the barocaloric effect of the composition to be inverted. In our recent studies, we discovered that the pressure sensitivity (d T / dP) of chain-melting transitions in representative 2-D perovskites —(DA^MnCk and (NA^CuBu— depends on the identity of pressuretransmitting medium (PTM). Specifically, as shown in Figs. 46A and 46B, high-pressure differential scanning calorimetry (HP-DSC) experiments revealed that the use of polarizable gas (such as Ar) lowers the d 77dP values, from 22 K / kbar under He to 4 K / kbar under Ar for (DA^MnCk; from 27 K / kbar under He to -29 K / kbar under Ar for (NA^CuBu. We also note that the pressure-transmitting medium appears to influence only transition temperatures with minimal impact on transition entropy (Figs. 47A and 47B). Most notably, under Ar environments, (NA)2CuBr4 displays inverse barocaloric effects, where the increase in pressure leads to a decrease in transition temperature (i.e., d T / dP <0), as indicated by heat flow traces and phase diagram obtained from Ar HP-DSC experiments (Figs. 48A and 48B). To directly evaluate the magnitudes of the PTM-driven inverse barocaloric effects, we used quasi-isothermal HP-DSC experiments, where phase transitions are induced by pressure changes under isothermal conditions (see Figs 49A and 49B). This experiment demonstrated that the compression induces an endothermic transition from ordered (low-temperature) phase to disordered (high-temperature) phase, whereas the decompression induces an exothermic transition from disordered phase to ordered phase. Note that the sample temperature was held at 301.6 K because the (P, 7) phase diagram shown in Fig. 49A indicates that the pressure swing of 150 bar is sufficient to induce full phase change at that set temperature. Although these phenomena were unexpected, and the microscopic origin of these phenomena remains to be investigated, we hypothesize that the inverse barocaloric effects in (NA^CuBu originates from its large free volume that enables facile absorption of (or interactions with) the polarizable Ar gas molecules in disordered organic bilayers. These results fully confirm the validity of this phenomenon and establish that (NA)2CuBr4—and other related barocaloric compounds (e.g., with long-chain hydrocarbons), e.g., those described herein, more broadly— displays highly reversible, giant inverse barocaloric effects under a pressure-transmitting medium that can interact with hydrocarbon chains (and the lattice). Most inverse barocaloric effects arise from a decrease in volume upon increase in a degree of freedom (during thermally-induced phase transitions). The mechanism described herein is unique for the following reasons. First, the material (i.e., the host lattice, e.g., a barocaloric material of the invention) still undergoes a volume expansion upon the thermally-induced order-to-disorder transition, and the inverse barocaloric effect is entirely driven by the permeation and absorption of the PTM into the lattice. Second, the magnitude of inverse barocaloric effects can be tuned via judicious selection of pressure medium. As shown in Figs. 46A and 46B, the use of N2 as PTM lowers the pressure sensitivity (d T / dP); but still the dT / dPis positive (i.e., normal barocaloric effects). We anticipate that the mixing of two different PTM (e.g., via gas exchange mechanisms) will allow us to continuously access a wide range of pressure sensitivity (from -33 K / kbarwith non-interacting / non-permeating PTM to <-29 K / kbarwith interacting / permeating PTM). Third, to the best of our knowledge, the phenomenon shown here is the first case, where a single material reversibly displays both normal and inverse barocaloric effects. Methods and systems of the invention can make use of these tunable and “on-demand” inverse barocaloric effects, which we expect will play a very important role in realizing practical barocaloric cooling devices, methods and systems. For instance, in response to compression, a normal barocaloric material will increase its temperature, whereas an inverse barocaloric material will decrease its temperature. By utilizing these two materials in series, it may be possible to increase the temperature span and facilitate heat transfer processes for barocaloric cooling cycle. Additionally, as described in Fig. 50, we expect that this PTM effect and inverse barocaloric effects can provide a new mechanism for tunable thermal energy storage (TES). Methods Methods of the invention may include providing heat energy (e.g., from a room, an AC system, heat transfer medium, heat pump, heat sink, etc.) to a composition of the invention (e.g., a 2D perovskite). The heat energy may cause alkyl chains in the composition to undergo a phase transition (e.g., from an ordered to a disordered state, e.g., in a thermal energy storage system) or there may be no phase transition until pressure is applied (e.g., in a barocaloric cooling system). Methods may be for refrigeration or heating. In a barocaloric cooling system or method, providing compression to the composition releases latent heat in the composition, which may be removed, e.g., via a heat sink, e.g., a high surface area, high conductivity medium in thermal contact with the composition which may be itself cooled by, e.g., a fan. Removal of the heat is performed while the composition is still compressed, and removal of the compression allows the composition to return to a disordered state, cooling the composition as the endothermic transition occurs. At this point the cycle may be repeated with input of new heat energy. In a barocaloric thermal energy storage system heat energy is provided to a composition of the invention causing it to undergo a phase transition to a disordered state. The disordered state is then modified by the application of compression in order to change the temperature at which heat is released. Methods of the invention may also include selecting or otherwise controlling the pressure transmitting medium to modulate the barocaloric cycle. For example, selecting a gas (e.g., a high polarizability gas) that sufficiently permeates and interacts with the composition at the microscopic level as the PTM to change the temperature of phase transitions in the barocaloric material, or to induce inverse barocaloric effects such as described herein. Methods may include modulating the barocaloric cycle by altering a ratio of polarizable and on-polarizable gases used as a mixed in a PTM. Methods may include selecting a gas as the PTM that does not interact, or minimally interacts, with the composition (e.g., He), e.g., to not induce changes in thermal properties, or to revert changes caused by an interacting gas. Systems and Additional Components Systems of the invention may include components to provide compressive force to the composition, e.g., pumps, pistons, actuators (e.g., mechanical, hydraulic, or pneumatic, etc., actuators), presses (e.g., mechanical, hydraulic, or pneumatic, etc., presses), piezoelectric actuators, levers, etc. Systems may also include components to transfer or remove heat energy, e.g., pumps, heat sinks, thermoelectrics, fans, chiller pumps, etc. A system of the invention may also include a power source, e.g., to power the source of compressive force, the cooling or heat transfer components, etc. Systems of the invention may include a pressure transmitting medium (PTM), e.g., a gas. The PTM may be a non- or minimally-interacting gas (e.g., a low polarizability gas, e.g., He) or a polarizable gas (e.g., N2, Ar, Kr, Xe, methane, ethane, propane, butane, sulfur hexafluoride, or carbon dioxide). Systems of the invention may include a pump for controlling a pressure transmitting medium (e.g., a mixture of gases), such as pumps, gas reservoirs (e.g., tanks, cylinders, etc.), pressure sensors, actuators, valves, etc. The PTM may not be a gas, for example, the PTM may be an oil, e.g., a fluorocarbon oil, silicone oil, etc.). EXAMPLES The 2-D perovskite (DA)2MnCl4 (DA = decylammonium) was selected as a barocaloric material because of its large phase-transition entropy (AStr = 230 J kg- K~1) and enthalpy (AMr = 71 kJ kg~1), near-ambient phase transition temperature (Ttr = 310 K), and lightweight, nontoxic elemental composition. At ambient temperature and pressure, (DA)2MnCl4 adopts an ordered monoclinic structure (low-temperature, LT, phase) with bilayers of hydrocarbon chains—each of which contain a single gauche C-C bond (C2-C3) and seven trans C-C bonds—aligned parallel to one another and tilted 48.3(1)° with respect to the Mn-CI plane (Fig. 5E, Table 10). Upon heating above 310 K, the compound undergoes a first-order phase transition to an expanded orthorhombic lattice (high-temperature, HT, phase) with dynamically disordered 28 hydrocarbon chains that have liquid-like conformational degrees of freedom. The large increase in entropy during the transition is due to both flipping of the alkylammonium cations between two favorable orientations within the Mn-CI pockets and internal rotations of C-C bonds that create dynamically disordered conformational defects within the hydrocarbon chains. Note that 90% of the overall molar entropy change results from conformational disorder, with approximately six C-C bonds freely converting between three rotameric states—gauche+, gauche-, and trans—in the HT phase. Differential scanning calorimetry (DSC) measurements (Figs. 5A-5C) at ambient pressure show that the hydrocarbon chain-melting transition is sharp and fully reversible with a thermal hysteresis, AThys, of just 1.4 K at a scan rate of 2 K min-1 (Fig. 5A). Variable temperature single crystal X-ray diffraction structures (e.g., Figs. 5E-5H) at ambient pressure show that the phase transition is accompanied by an increase in interlayer distance of 2.115(2) A as the alkylammonium cations tilt further away from the Mn-CI plane to create additional space between disordered hydrocarbon chains in the HT phase (Fig. 5F, Table 10). This uniaxial expansion leads to an 8.0% increase in the volume of the compound (△ 14 = 65.1 cm3 kg-1) during the phase transition (Fig. 10C). Based on the measured volume and entropy changes, the Clausius-Clapeyron equation, dTMP = AWAStr, can be used to predict a barocaloric coefficient for (DA)2MnCl4 of 28.3 K kbar1, which would represent one of the highest values reported for a barocaloric material with a AStr above 20 J kg-1 K-1 (Table 18). To directly evaluate the pressure dependence of the phase transition temperature, isobaric DSC experiments were performed under applied hydrostatic pressures of up to 150 bar using He as the pressure-transmitting medium. The phase transition shifts to higher temperatures as the pressure is increased, with a measured dTtr / dPof 22.1 ± 0.7 K kbar1 during heating and 20.6 ± 0.8 K kbar1 during cooling (Fig. 6A). Importantly, the application of pressure does not lead to any significant changes to the phase transition width. Moreover, AStr remains within 97% of its ambient pressure value at 150 bar and does not decrease upon repeated thermal cycling at 150 bar. Variable temperature and pressure powder X-ray diffraction (PXRD) experiments confirm that structural phase transitions with similar volume changes still occur at pressures up to at least 360 bar (Fig. 6G), and the dTtr / dP of 18.6 ± 1.0 K kbar-1 during cooling over this extended pressure range is in close agreement with that measured by HP-DSC (Fig. 6H). However, the d7tr / dP values determined by PXRD and HP-DSC are lower than those predicted using the Clausius-Clapeyron equation. To investigate the origin of the different experimental and predicted barocaloric coefficients, we used helium pycnometry to directly measure the volume change of (DAjsMnCk during the phase transition (Fig. 5C). In particular, we expected that He might permeate into the disordered organic bilayer of the HT phase—owing to its increased free volume—while being excluded from the denser, crystalline organic bilayer of the LT phase. This would lead to a lower effective volume change during the phase transition since He permeation would reduce the amount of additional volume that was occupied by the expanded phase. Indeed, the volume change measured by pycnometry is 16 cm3 kg-1 lower than that determined by crystallography, and this lower effective volume change yields a predicted dTtr / dPof 21.4 ± 1.5 K kbar1 that matches the HP-DSC and PXRD values (Table 9). Although effects of the pressure-transmitting medium are not typically considered when evaluating barocaloric materials, this result provides a pathway to realizing a higher dTtr / dP by preventing the pressure-transmitting medium from entering the disordered phase through, for instance, encapsulation, the use of a larger fluid, or the application of mechanical pressure. Regardless, the dTtr / dPthat can be achieved using He to transmit hydrostatic pressure is higher than many barocaloric materials, which, along with the large AStr and small hysteresis, presents considerable advantages for barocaloric cooling. Under the cyclic operating conditions of a barocaloric cooling system, the lowest possible operating pressure is set by the pressure that must be applied to induce a reversible entropy change, Prev, when cycling to and from ambient pressure. For a conventional barocaloric effect, P-ev corresponds to the pressure at which the onset temperature of the exothermic phase transition is equal to the onset temperature of the endothermic phase transition at 1 bar. As such, Prev is proportional to the thermal hysteresis at 1 bar and inversely proportional to the barocaloric coefficient for the exothermic transition, with Prev = AThys / (d7tr / dP)Cooiing {16). Owing to its low AThys and high d 7tr / dP, (DA)2MnCl4 has a predicted Prev of just 66 bar. This low Prev was further confirmed by calculating the isothermal entropy changes (ASt). To do so, we first obtained isobaric entropy changes (ASb) associated with the chain-melting transition as a function of temperature and pressure by integrating the HP-DSC heat flow signal, Q, obtained at a scan rate of t over the temperature range from 7i to Tc ASt curves were then calculated as the difference between ASb at ambient pressure and ASb at elevated pressure, with ASb values obtained from heating data corresponding to the disordering transition induced by a decrease in pressure (ASt >0) and ASb values from cooling data corresponding to the ordering transition induced by an increase in pressure (ASt <0). Excitingly, these ASt curves show that a non-zero reversible entropy change can be induced below 80 bar, and the full entropy of the phase transition can be induced irreversibly by applying a pressure of just 100 bar (Fig. 6B). Moreover, a reversible entropy change of 75 J kg -1 K~1 can be accessed at a driving pressure of 150 bar, and the full entropy of the chain-melting transition would become reversible at only 270 bar. To the best of our knowledge, inducing a reversible entropy change of more than 200 J kg ~1 K~1 through a pressure change of less than 300 bar is unprecedented in barocaloric materials. By assuming an average specific heat capacity, cP, of 1550 J kg~1 K~1 for the LT and HT phases that does not vary substantially with pressure, the equation A Tad, max = TASt / cP can be used to estimate a maximum adiabatic temperature change of 42 K, which ranks among the highest values yet reported for barocaloric materials (Table 18). Although quasi-direct methods of calculating isothermal changes—as well as adiabatic ones—from isobaric experiments are commonly used to evaluate barocaloric materials due to the challenge of maintaining isothermality—or adiabaticity—during direct variable pressure measurements, we performed quasi-isothermal HP-DSC experiments to more directly evaluate P-ev by measuring pressure, rather than thermal, hysteresis. Specifically, we measured heat flow signals while cycling the pressure between 1 bar and 150 bar at 311 K. Note that isothermality is maintained until the phase transition onset pressure, which allows us to accurately determine pressure hysteresis. By comparing the onset pressures for compression-induced exotherms and decompression-induced endotherms, we were able to directly measure a pressure hysteresis for (DA^MnCk of 70 bar, which is in excellent agreement with the predicted value of 73 bar at 311 K (Fig. 5C). To the best of our knowledge, the Bev value of (DA)2MnCk is the lowest reported for a barocaloric material with ASr >45 J kg~1 K~1 (Fig. 7B). Note that three-dimensional metal-dicyanamide perovskites, [(C3H?)4N][M(dca)3] (M = Mn and Cd) display low Prev of 40 bar, due to their high d TMP (23 K kbar1 and 38 K kbar1 for Mn and Cd compounds, respectively) and low hysteresis (1 K) (Table 18). These compounds, however, have low ASr and undergo transitions well above room temperature. In an effort to target barocaloric materials with large reversible entropy changes at even lower pressures, we searched for a 2-D perovskite that undergoes a chain-melting transition with a thermal hysteresis of less than 1 K. Unlike (DA^MnCk, however, the total entropy of the chain-melting transition in most 2-D perovskites is partitioned across one or more minor—lower entropy—phase transitions in addition to the principal transition (Fig. 3B, Tables 2 to 4). The presence of multiple successive transitions at different temperatures, although not necessarily detrimental to barocaloric cooling performance, complicates the evaluation of barocaloric properties because each minor and major transition has an independent hysteresis loop with a different pressure dependence. With a lack of suitable existing compounds, we synthesized a new 2-D perovskite that features a sharp chain-melting transition near ambient temperature with ultralow hysteresis and a high sensitivity to pressure. In particular, we expected that altering the inorganic-organic interface of 2-D perovskites through the substitution of different metal cations and halide anions might provide a pathway to reducing the hysteresis associated with the confined phase transition and increasing its sensitivity to pressure. More specifically, we hypothesized that larger Br anions would increase the distance between ammonium headgroups of hydrocarbon chains to provide more free volume, reducing the activation energy barrier for nucleation of an ordered bilayer phase during cooling or compression and increasing the sensitivity of the phase transition temperature to pressure. Since Br anions can be more readily accommodated within Cu, rather than Mn, 2-D perovskites, we targeted a (CnH2n+iNH3)2CuBr4 compound with alkylammonium cations of appropriate length to place the chain-melting temperature near ambient temperature. We found that the new 2-D perovskite (NA)2CuBr4 (NA = nonylammonium) undergoes a chain melting transition at 303 K with a high ASr (78 J kg-1 K-1), hysteresis of only 0.4 K, and no minor phase transitions within at least 60 K of the principal transition (Fig. 5B). Variable-temperature PXRD experiments reveal that the phase transition involves a 4.0% increase in volume (A 14 = 24.9 cm3 kg~1), and crystal structures of the LT and HT phases show that the phase transition leads to an increase in interlayer distance of 1.630(2) A, which is consistent with conformational disordering of the chains (Fig. 5H, Table 11). The crystallographic volume change yields a predicted barocaloric coefficient of 32 K kbar1 using the Clausius-Clapeyron equation, while the volume change determined by He pycnometry (A 14 = 20.0 cm3 kg-1)—which accounts for He permeation into the HT phase—yields a predicted barocaloric coefficient of 25.6 K kbar1 (Fig. 5D, Table 9). Isobaric HP-DSC experiments confirmed that (NA)2CuBr4 features a high barocaloric coefficient with dTtr / dPof 26.9 ± 0.4 K kbar1 and 26.5 ± 0.5 K kbar1 during heating and cooling, respectively (Fig. 6D). In fact, these values represent one of the highest sets of barocaloric coefficients ever measured among barocaloric materials with AStr >20 J K-1 kg-1. In addition, variable pressure PXRD experiments show that the structural transition persists to at least 300 bar with a similar volume change and average barocaloric coefficient (25.9 ± 1.0 K kbar-1) (Figs. 61 and 6J). As a result of its high barocaloric coefficient and ultralow hysteresis, (NA)2CuBr4 has a record-low Bev of 16 bar, which is within the pressure range already accessed during commercial vapor-compression refrigeration cycles (Table 18). The low value of Prev was confirmed through quasi-isothermal pressure cycling experiments at 307 K, where we directly measured a pressure hysteresis of 25 bar (Fig. 6F). Moreover, a reversible entropy change of 68 J kg -1 K-1 (90% of AStr at 1 bar) can be accessed at a driving pressure of just 150 bar (Fig. 6E). Based on an average heat capacity of 800 J kg 1 K 1, (NA)2CuBr4 is predicted to have a maximum adiabatic temperature change of 21 K. To provide additional insight into the structural and chemical factors that influence barocaloric effects in 2-D perovskites, we used X-ray crystallography and IR spectroscopy to compare the nature of the chainmelting transition in (NA)2CuBr4 and (DA)2MnCl4. In particular, we hypothesized that the increased size of the halide pocket in (NA)2CuBr4 (30.5 A2) relative to (DA)2MnCl4 (26.3 A2)—coupled with weaker N-H--Br hydrogen bonds at the organic-inorganic interface—would lead to more conformational disorder in the LT phase of the Cu compound. This would reduce the entropy difference between the LT and HT phases and explain the 56% lower molar entropy change of (NA)2CuBr4, as well as the lower entropy changes generally observed across longer-chain (CnH2n+iNH3)2CuBr4 (n= 11-16) compounds compared to (CnH2n+iNH3)2MCl4 (M = Mn, Cu, Cd) compounds of the same lengths (Tables 2 to 4). As anticipated, the atoms in the NA chains of (NA)2CuBr4 have much larger atomic displacement parameters in the LT phase than those in the DA chains of the LT phase of (DA)2MnCl4 (Figs. 5E and 5G). This is consistent with the smaller increase in chain flexibility and number of rotatable C-C bonds modelled for conversion to the HT phase of (NA^CuBu. Note that NA chains adopt two conformations— alternating between chains with a gauche C2-C3 bond and those with a gauche C1-C2 bond, each modeled with two-part disorder—in the LT crystal structure of (NA)2CuBr4, and average displacement parameters are similar for both chain conformations. The residual motion and configurational disorder in the LT phase of (NA)2CuBr4 is further corroborated by variable-temperature IR spectra, which show a band near 1360 cm~1 assigned to CH2 wagging from gfen+irX-type kinks that is present below the phase transition temperature for (NA)2CuBr4 but is only present above the phase transition temperature for (DA)2MnCl4. The IR spectra also suggest that the local environment around the chain ends (CH3) and headgroups (NHs+) is more similar in the LT and HT phases of (NA)2CuBr4 than in those of (DA)2MnCl4 (Tables 7 to 8). Although conformational disorder in the LT phase leads to a decreased entropy change, it also likely contributes to the enhanced reversibility of the (NA)2CuBr4 chain-melting transition through two primary effects. First, the higher degree of disorder in the alkylammonium chains in the LT phase—along with the softer nature of Br anions—should make the (NA^CuBu lattice more compressible than the (DA)2MnCk lattice. Since the barocaloric coefficient dTtr / dPof a solid tends to increase with increasing compressibility (43, 44), this would be expected to make the phase transition in (NA)2CuBr4more sensitive to pressure. Indeed, dTtr / dPfor the transition to the LT phase of (NA)2CuBr4 is 29% higher than for (DA)2MnCl4. Second, the presence of certain configurational degrees of freedom, such as kinks, in both the LT and HT phases should render the two phases more compatible, lowering both isobaric and isothermal hysteresis. In any case, both compounds display, near room temperature, large and reversible barocaloric cooling, represented by their materials properties 7tr, AStr, and Prev, and are highly competitive with other leading barocaloric materials (Figs. 7A and 7B, Tables 18 to 19). In addition to its influence on operating pressure, hysteresis, which leads to dissipative heat losses, adversely impacts the second-law efficiency and coefficient of performance (COP) of any caloric cooling cycle. The impact of hysteresis on efficiency can be quantified by calculating the idealized thermodynamic efficiency, 77, of a caloric material—relative to the Carnot efficiency—using a simple material model that integrates the dissipative losses in a Carnot-like cycle: COP _ 1 COPcarnot AThys ATad max Based on this model, caloric materials with AThys / ATad,max of less than 10% will have second-law efficiencies competitive with those of conventional vapor compression-based systems (-85%). Excitingly, (DA)2MnCl4 and (NA^CuBu display second-law efficiencies of 88 and 93%, while the values found in most barocaloric compounds range between 40 and 65% (Table 19), either because of large AThys or a low AStr that leads to a small ATad,max. Additionally, both compounds display the largest values of barocaloric strength—the reversible isothermal entropy change ASt, rev normalized by the driving pressure—than have been realized for barocaloric materials (Table 19). These results highlight exciting opportunities to exploit the tunability of 2-D perovskites to independently manipulate phase-change hysteresis, entropy, and sensitivity to pressure for improved barocaloric performance. For instance, it should be possible to realize chain-melting transitions with even higher entropy changes through functionalization of the organic bilayers—such as by introducing aromatic groups or hydrogen bond donor-acceptor pairs—and even lower hysteresis through modification of the organic-inorganic interface—such as by incorporating mixtures of different halide anions or introducing defects—or through leveraging multicaloric effects. In addition, the anisotropic nature of the chainmelting transition in (DA)2MnCl4 and (NA)2CuBr4—wherein an increase in interlayer spacing along a single direction accounts for -80% of the volume change—suggests that uniaxial stress, which can be readily applied through mechanical actuation, may be able to drive large elastocaloric effects in 2-D perovskites. The results and materials discussed herein were obtained according to the following methods. Experimental Methods All manipulations were conducted in air unless otherwise noted. Anhydrous diethyl ether was obtained from a Pure Process Technology anhydrous solvent system. Anhydrous methanol and ethanol were purchased from a commercial vendor and used as received. All other reagents were purchased from commercial vendors and used as received. Single crystal diffraction data was collected using a Bruker D8, SMART APEX II, or APEX DUO instrument. IR spectra were obtained on a Bruker ALPHA II Platinum ATR with a variable temperature stage. Thermogravimetric analysis (TGA) experiments were performed using a TA Instruments TGA550. Abbreviation used: DA - decylammonium, (CioH2iNHs)2MnCl4 = (DA)2MnCl4, (NA) = nonylammonium, (CgHigNHs^CuBu = (NA)2CuBr4. Synthesis of two-dimensional perovskites (DA)2MnCl4.: Decylamine (> 99.0%) and hydrochloric acid (HCI) solution (37 wt%) were purchased from Sigma Aldrich and used without further purification. C10H21NH3CI was first synthesized by adding HCI solution (550 pL, 6.6 mmol) into decylamine (1.1 mL, 5.5 mmol) in ca. 5 mL ethanol in a cold-water bath. After evaporating the solvent at reduced pressure, the resulting white powder of (DA)CI was washed with diethyl ether and vacuum dried at room temperature for a day. Crystalline powders of (DA)2MnCl4 were prepared by the cooling of an ethanol solution containing a stoichiometric quantity of the manganese(ll) chloride and (DA)CI, as previously reported (e.g., in M. R. Ciajolo, et al., Comparative Studies of Layer Structures: The Crystal Structure of Bis(Monodecylammonium)tetrachloromanganate(ll). Gazzetta Chimica Italiana. 106, 807 (1976), and H. Arend, et al., Layer perovskites of the (CnH2n+iNHs)2MX4 and NH3(CH2)mNHsMX4 families with M = Cd, Cu, Fe, Mn or Pd and X = Cl or Br: Importance, solubilities and simple growth techniques. J. Cryst. Growth. 43, 213-223 (1978)). (DA)CI (96.9 mg, 0.5 mmol) was dissolved in 4.0 mL of ethanol. After several minutes of stirring, MnCl2'4H2O (49.5 mg, 0.25 mmol) was added to the solution, and the solution was heated to 65 °C. After the cooling this solution to room temperature at a rate of 4 K h~1, pale pink crystals were obtained. The crystals were filtered and washed with diethyl ether (5x10 mL) and held at reduced pressure for 6 h to afford 45.2 g (35.2% yield) of product. Crystals suitable for structure determination were obtained by slow cooling at a rate of 2 K h-1. (NA)2CuBr4: Nonylamine (> 99.5%) and hydrobromic acid (HBr) solution (48 wt%, 8.8 M) were purchased from Sigma Aldrich and used without further purification. CgHigNHsBr was first synthesized by adding HBr solution (545 pL, 4.8 mmol) into nonylamine (733 pL, 4.0 mmol) in ca. 5 mL ethanol in a cold-water bath. The solvent was removed at reduced pressure to yield colorless powder of (NA)Br. The powder was washed with diethyl ether and vacuum dried at room temperature for a day. CuBr2 (402 mg, 1.8 mmol) and CgHigNHsBr (807 mg, 3.6 mol) were dissolved in 2 mL of ethanol. The solution was slowly cooled from 65 °C to room temperature at a rate of 4 K h-1. The saturated solution was then stored at below ambient temperature (5 °C) for 1 hour. The resulting dark purple precipitate was filtered and washed with diethyl ether (5x10 mL). The dark purple crystalline powder was held at reduced pressure for 12 h to remove moisture. Crystals suitable for structure determination was obtained by slow evaporation of a 1 -mL solution of (NA)2CuBr4 (202 mg, 0.3 mmol) in methanol. Anal. Calcd. for (CgHigNH3)2CuBr4: C: 32.19%, H: 6.60%, N: 4.17%, Br: 47.58%. Found: C: 31.84%, H: 6.69%, N: 4.43%, Br: 47.76%. Differential scanning calorimetry (DSC) DSC at ambient pressure: A Discovery 2500 DSC with an RCS 90 cooling system (TA Instruments) was used to measure the transition temperatures and gravimetric enthalpies for all compounds. The DSC baseline and cell thermal parameters were calibrated using sapphire discs. The temperature and cell constant were calibrated using an indium standard. All DSC samples were prepared in air using 3-15 mg of sample and were hermetically sealed in aluminum pans (purchased from TA instruments). The sample was scanned under a dynamic flow of N2 (50 mL min-1). An empty, hermetically sealed aluminum pan we used as a reference. Determination of Ttr and gravimetric AHtr and AStr: Transition temperatures, 7tr, and enthalpies of transition, AHtr, were determined using the TA Instrument TRIOS or Netzsch Proteus software. Peaks were selected for analysis by defining a temperature range containing the peak of interest. The lower bound and upper bounds of the temperature range were chosen to encompass the phase transition, which starts with a deviation from the baseline and ends with a return to baseline. Prior to determination of Ttr or AHtr, a baseline, which models the heat flow in the absence of transition, must be generated to approximate the baseline in the transition region in the absence of a transition. A baseline is generated within the defined temperature range using various option that determine the slope of the lower and higher temperature limits and shape of the baseline. When possible, baselines were generated using mutual tangent slopes at both the upper and lower temperature limits with a sigmoidal baseline, which we found to produce most physically reasonable baselines. The extrapolated onset temperature was reported as the transition temperature, as is standard in DSC data analysis, because the onset temperature—unlike the peak temperature—is relatively independent of experimental parameters like the heating rate or sample mass. The onset temperature is determined by identifying the region of the onset melting peak that has the highest slope, defining a tangent to that region, and then extending the tangent to the generated baseline. The intersection between the baseline and the tangent is the onset temperature. Endotherms were integrated between the upper and lower temperature limits with the baseline subtracted to provide AHtr, and AStr was calculated through AStr = AHtr / Ttr. If physically reasonable limits were chosen, the onset transition temperatures and AHtr did not depend strongly on the choice of the temperature limits, and such variations were within the error of the measurements, which is estimated to be <0.5% for Ttr and <2% for AHtr. Note that volumetric AHtr were calculated from gravimetric quantities using crystallographic densities at ambient temperature. DSC at applied hydrostatic pressure: High-pressure DSC measurements at the pressure range between 1 to 150 bar were carried out in a DSC 204 HP Phoenix (Netzsch). The temperature and heat flow were calibrated at each pressure using an indium standard. The temperature and cell constant were calibrated at each pressure using an indium standard. Helium gas was used as a pressure-transmitting medium. All DSC samples were prepared in air using 3-10 mg of sample and were sealed in aluminum pans (purchased from Netzsch) with a pierced lid. An empty, aluminum pan with a pinhole was used as a reference. All measurements were carried out in a dynamic gas environment with a 50 ml min-1 He. Otherwise noted, heating and cooling rates of 2 K min-1 were used during isobaric measurements. During the pressure cycling experiments, heat flow signals were measured over time under the repeated application and removal of a hydrostatic pressure of 150 bar at 311 K for (DA)2MnCk and 307 K for (NA)2CuBr4. The pressure linearly increased at a rate of 6 bar min 1 and asymptotically decreased at an 35 average rate of 13 bar min-1. During the pressure change, quasi-isothermal conditions were maintained, where a small change in temperature (<1 K) induced by gas compression and decompression is compensated by external thermal control measures. The pressurization and depressurization processes are associated with average temperature fluctuations of 0.3 K and 0.7 K, respectively. To distinguish the heat flow signals associated with pressure-induced phase transitions of samples from those associated with compression and decompression of pressure transmitting medium (He gas), (Ci2H25NH3)2MnCk, prepared from the previously reported procedure (G. F. Needham, et al., J. Phys. Chern. 88, 674-680 (1984), was used as a blank sample because it undergoes transitions at temperatures (Ttr, major = 331 K and 7tr, minor = 335 K) well above the set temperatures for (DA)2MnCl4 and (NA)2CuBr4. The heat flow signals measured from the blank during the pressure change at the set temperature were modeled as a baseline for the sample data. By subtracting the features in the heat flow associated with the gas compression and decompression from the sample data, we were able to determine the onset pressure associated with the pressure-induced transitions during compression and decompression processes. Because maintaining isothermal conditions becomes challenging once the phase transition is induced and both pressure and temperature change drive the endothermic and exothermic transitions to completion, we did not integrate the heat flow signals and focused only on using the information to determine the onset pressures for transitions. On the barocaloric effects outside the transition: We note that the ASt values obtained through our HP-DSC experiments do not include the contributions from the additional barocaloric effects (AS+) that arise from each phase. This additional contribution can be estimated through AS+ = -[(3 V73T)fto]AP, where AP and (dV / dT)p=o denote a driving pressure and a thermal expansion at the ambient pressure, respectively. Note that the isothermal entropy contribution is derived from the Maxwell relation (3V / dT)p = -(3S / 3P)7-with an assumption that the volume expansion is independent of pressure. The AS+ values are estimated to be ~3 and ~4 J kg-1 K~1 at the ordered and disordered phases, respectively, under 150 bar driving pressures. Although these values are small in comparison with AStr, these contributions can be large at higher driving pressure, such as ~# at 400 bar, because of large thermal expansion coefficients (~1 O’4 K-1) Helium Pycnometry Sample density was determined using an InstruQuest Inc. jj.-ThermoPyc variable temperature He pycnometer. In a typical measurement, ca. 150 mg of crystalline sample were transferred to the sample holder, and the sample mass obtained. The holder was then placed in the instrument test chamber and the headspace evacuated and refilled five times to obtain a pure He atmosphere. The sample was then cycled multiple times through the order-disorder transition with the chamber volume determined every 2-5 °C away from the transition and every 0.5-1.0 °C close to the transition. For each point, the temperature was fully equilibrated with a standard deviation of no more than 0.2 °C prior to volume measurement. At each temperature, the chamber volume was measured five times to obtain good statistics. Sample volume was then determined by subtracting the average observed chamber volume from the volume of the empty sample holder which had been measured previously. The sample mass was redetermined after the measurement and found to have decreased by no more than 0.5 mg, likely due to loss of adsorbed water. Uncertainties of the reported densities were determined by propagation of the standard deviations of the empty and filled chamber volumes and the sample mass. X-ray Crystallography X-ray diffraction analyses were performed on a single crystal coated with Paratone-N oil and mounted on a MITeGen microloops, at different temperatures (100 to 335 K) controlled by an Oxford Cryostreams nitrogen flow apparatus. Crystals were mounted at 270 K, and 270 K data sets were collected. Crystals were then cooled to 100 K for 100 K data collection. After 100 K data sets, high-temperature data sets were collected, 330 K for (DA)2MnCl4 and 335 K for (NA)2CuBr4. The temperature was manipulated at a rate of 60 K hr1. The intensities of the reflections were primarily collected by a Bruker D8 diffractometer with CMOS area detector (MoKa radiation, A = 0.71073 A). The collection method involved 0.5° scans in a>at 23° in 26? with a detector distance at 9 cm for (DA)2MnCl4 and 8 cm for (NA^CuBu. Data integration down to 0.84 A resolution was carried out using SAINT V8.37A with reflection spot size optimization (9). Most crystals were either single or merohedrally twinned and absorption corrections were made with the program SADABS. All single crystal structures were solved by the Intrinsic Phasing methods and refined by least-squares methods again F2 using SHELXT-2014 and SHELXL-2018 with OLEX 2 interface. Thermal parameters were refined anisotropically for all non-hydrogen atoms. Hydrogen atoms were placed geometrically and refined using a riding model for all structures. Crystal data as well as details of data collection and refinement are summarized in Tables 15 and 16, and geometric parameters are shown in Tables 10 to 14. Notes on data quality, twining, and disorders: The phase transition from low-temperature phase to high-temperature (HT) phase during heating often resulted in fracturing and twining of the crystals, giving rise to the decay of crystal quality. Due to the large thermal motions of the long alkyl ammonium cations, the geometric parameters calculated for the HT phase structures should be treated as estimates, as pointed out in the literature. Synchrotron in situ Powder X-ray Diffraction (PXRD) studies. Powder X-ray diffraction data for (DA)2MnCl4 and (NA)2CuBr4 were collected on beamline 17-BM-B at the Advanced Photon Source (APS) at Argonne National Laboratory. All X-ray wavelengths were between 0.24A and 0.45A, and are specified for each experiment in the relevant figures and tables. For variable temperature and pressure experiments, approximately 10 mg of samples was loaded into a sapphire capillary (1.524 mm x 1.07 mm x 50.8 mm, Saint-Gobain Crystals). Each capillary was attached to a custom-designed flow cell equipped with a gas valve, which was mounted onto the goniometer head and connected to a syringe pump that the applied the hydrostatic pressure of Helium (80-360 bar). Sample temperature was controlled by an Oxford Cryostream (Oxford Cryostream 800+). Prior to measurement, samples were evacuated by flowing ambient pressure of He gas for 10 minutes and annealed by heating 20 K above 7tr and cooling back to ambient temperature, at a rate of 6 K min-1 in the cryostream. The internal sample temperature was monitored via a K-type thermocouple (TC) that maintained the thermal contact with the powder sample within the capillary. Otherwise noted, the samples were heated and cooled by the cryostream at a rate of 6 K min-1, which resulted in the rate of ca. 3 K min-1 in the TC temperature due to the temperature gradient. Diffraction patterns were analyzed using the software TOPAS-R (Bruker AXS, version 3.0, 2005). Diffraction patterns at select temperature were indexed, and Le Bail refinements were performed to extract unit cell parameters. Conformational disorder in two-dimensional metal-halide perovskites Conformational entropy: For an alkylammonium chain CnH2n+iNH3+, there are n-2 rotatable C-C bonds that can contribute to formation of different conformers. Note that the conformation of alkylammonium chains can be described through a sequence of dihedral angles often referred to as Hoffmann’s notation, with the terms g*, g~, and t denoting dihedral angles of approximately +60 (gauche), -60 (gauche), and 180° (trans), respectively. In principle, each C-C bond should be able to equally access these three rotameric states that correspond to local energy minima, and the change in solid-state configurational entropy can be described as AScontiguration = R In 1 / ½ where Wis the ratio between the number of configurations in the disordered and ordered chains (That is, W= A / disorder / A / order). Thus, the entropy change associated with the conformational disordering of an alkylammonium chain can be estimated as R In 3n 2. However, depending on how chains are packed and how neighboring chains influence one another in each phase, the average number of “accessible” rotameric states for each C-C bond—defined as the chain flexibility number 0-can deviate from 3. Note that, in linear organic molecules, the flexibility number depends on the energetic difference between each conformer and a flexibility number of 2.85 has been used to predict the melting thermodynamics. In two-dimensional perovskites, a few structural features— steric restrictions (imposed by halide pockets and neighboring chains), correlations between torsions, and residual degrees of freedom present in C-C bonds in the ordered phase—can partially limit conformational degrees of freedom, reducing the number of C-C bonds associated with the chain melting processes by a restriction parameter / 3. The number of accessible conformations at the disordered phase can then be approximated as (¢)^-^, which includes the conformers arising from kink {gtg1} formation and cooperative torsion along the chain axis. Here, we assume that the two parameters 0 and p are independent. Note that the entropy change associated with a reorientational motion (flipping) of the entire alkylammonium chains between two energetically equivalent orientations within the metal-halide pocket can be accounted for by adding the term R In 2. This chain-flipping can occur as an isolated minor transition or be coupled to the major order-disorder transition. In addition to the flipping, the major conformation disordering can be often distributed across multiple, successive transitions, and the total number of structural transitions of a compound is here referred to as m. The contributions from both flipping (ASiipping) and chain melting (ASmeiting) to the total entropy change, ASotai, are multiplied by 2, because 2 mole of CnH2n+iNH3+chains are present in 1 mole of perovskite. The contribution from any change in entropy associated with the MXg octahedra is assumed to be negligible. Thus, the total difference in entropy associated m structural transitions in 2-D perovskites between low-temperature (LT) “ordered” and high-temperature (HT) “disordered” phases can be expressed through the following relationship: AStotai = △^tr, i = ASflipping + △ Smelting = 2R In 2 4- 2R In (0)°-2-^ (1 ) By fitting AStotai as a function of chain length n, we were able to determine the flexibility number 0 and the restriction parameter j8 for two-dimensional perovskite (CnH2n+iNH3)2MX4 (M = Mn, Cu, Cd; X = Cl, Br). AStotai values are tabulated in Tables 2 to 4, and fitting parameters are summarized in Table 6. With the expectations that odd and even chain lengths should exhibit different thermodynamic trends, odd-numbered and even-numbered analogs were fit separately. We note that, somewhat surprisingly, the structural origins of odd-even effects of the phase-change thermodynamics in 2-D perovskites are not fully understood and require further investigations. (DA^MnCh: From the fitting parameters (<p = 3.0 and / ?= 2.1, R2 >0.99) for (CnF^n+iNHs^MnCk, (n = 8-15), we can estimate that each decylammonium chain can access 359 (-650) distinct configurations as a result of conformational disorder at the HT phase. In addition, the total entropy change associated with the single-step transition at 310 K can be calculated as AStotai, caic = ASttipping + ASmeiting = 2R In 2 + 2R In (3)59 = 119 J K1 mol-1, which agrees with the experimentally measured AStotai, exp of 118 J K-1 mol-1. This estimation is further supported by the single-crystal structure of (DA)2MnCl4 at the HT phase (330 K), where each alkylammonium chain is disordered over two energetically equivalent positions and has a conformation with six C-C dihedral angles of 150-166° that deviate from the ideal trans dihedral angle of 180° and two C-C dihedral angles (C1-C2, 174°; C3-C4, 180°) close to the trans angle. (Table 13). This deviation may indicate fast “trans-gauche" rotations around C-C bonds and / or cooperative torsion along the chain axis. It is worth emphasizing that the chain length dependence of AStotai does not display a pronounced odd-even effect in 2-D Mn-CI perovskites. We also note that the conformational disordering is likely to be associated with the formation of one {gtg1} kink per chain (on average) near the chain ends and the most probable conformer is [Ugtg'Q, as suggested by incoherent neutron scattering experiments and intramolecular energy calculations. At higher temperature, some chains could adopt energetically less stable forms, in which the kink defects are located near the polar head groups, such as {hgtg'k} and {bgtsg'ty. These proposed conformers are shown in the conceptual illustration in Fig. 3A. Note that the change in interlayer distance measured from X-ray diffraction experiments also indicates that each chain is likely to favor the formation of one kink on average. More specifically, when chains are positioned perpendicular to the metal-halide layers, the formation of a kink within a chain requires additional lateral space and reduces its projected chain length by 1.27 A. Thus, the changes in interlayer distance, when combined with measurements on vibrational and dynamics of the chains, provide information about chain conformations. The single-crystal structure at the HT phase also supports the proposed model that formation of kink is favored near the chain ends. In Fig. 5E-, equivalent isotropic displacement parameters (t / equiv) of N and C atoms in the decylammonium chain are shown for both LT and HT phases. Note that the atomic displacement parameters obtained from the crystal structure refinement process represent how the atoms deviate from their equilibrium positions and contain information about residual motion (such as rotations and vibration) and static, configurational disorder. The transition from LT phase to HT phase results in a large increase in L / equiv values, and the magnitude of the increase in L / equiv increases from the NHs-polar head to the methyl end group along the chain. This result indicates that the chain melting transition gives rise to a large increase in dynamic disorder, and there is a gradient of disorder along the chain, which also supports that the kink formation is favored near the chain end. The gradient of dynamic disorder, which was also observed in the LT phase data as well, likely originates from the difference in intermolecular interactions between the polar chain head (charge-assisted hydrogen bonding) and the methyl end (weak van der Waals interactions). (NA)2CuBr4: We note that the transition entropy of (NA)2CuBr4 is about 48% and 56% of AStotaiof (Cg)2MnCl4 and (Cg^CuCk, respectively. This trend is also observed in the previously reported thermal data of (Cn)2CuBr4 (n = 11-16), which shows that the transition entropies of 2-D Cu-Br perovskites are only 40-60% of those reported in Cu-CI and Mn-CI analogs. Fitting AStotai with chain length n results in <p = 2.1 and 2.2 and / 3 = 5.1 and 5.5, for odd-numbered and even-numbered chains, respectively (Table 6). The lower value of 0 and higher value of / 3, compared to those obtained from Mn-CI and Cu-CI series, indicate that the difference in solid-state conformational entropy between LT and HT phases is smaller in (CnhCuBu, and the difference likely originates from the smaller difference in the flexibility of the chain and the number of newly rotating C-C bonds. The LT phase crystal structure indicates that the smaller difference in solid-state entropy between LT and HT phase may result from the higher degree of disorder present in the nonylammonium chains at the LT phase. In the LT phase, each of the two chain conformations (chain A with C1-C2 gauche bond and chain B with C2-C3 gauche bond) is modeled with two-part disorder (Table 14). Note that the atomic positions in chain A and chain B were refined to 35 / 65% and 53 / 47% occupancies, respectively. The analysis on the chain conformations shows that ( / ) the chains are distorted near the methyl ends with C7-C8 dihedral angles of and +1597-170° in chain A (Part 1 / Part 2) and +1647-164° in chain B and (if) the chain A displays additional distortion in the C3-C4 bond (-1597+169°). These results illustrate that configurational disorder is present in the LT phase of (NA^CuBu. In addition, the chains also display L / equiv values higher than those in decylammonium chain of (DA)2MnCl4 at the LT phase, whereas the L / equiv values at the HT phase were similar in both compounds (Figs. 5E and 5G). In addition, there is a gradient of disorder along the nonylammonium chain, similar to that present in (DA)2MnCl4. As a result, the difference in L / equiv values between LT and HT phase is smaller in (NA)2CuBr4. These trends collectively demonstrate that the higher degree of disorder present in nonylammonium chains at the LT phase—which result from both configurational disorder and residual motion—give rise to the lower AStr in (NA)2CuBr4 compared to those in M-CI analogs. We also note that the existence of 2nd order phase transition can be ruled out based on the previously reported heat capacity measurements on the 2-D Cu-Br perovskites (25). Comparison with 2-D Cd-CI and Cu-CI perovskites. Although the chain length dependences of ASotai in 2-D Cd-CI and Cu-CI perovskites exhibit similar trends to that observed in the Mn-CI series, with 0 ~ 3 and / 3-2, the trends slightly deviate from linearity and / or display pronounced odd-even effects. Even with the same chain length, these analogs display different phase transition behaviors, depending on the identity of metals. For example, unlike (Cio)2MnCl4, both (Cw)2CuCl4 and (Cio)2CdCl4 display two-step transitions, and the major transition in (Cio)2CuCl4 is followed by a minor transition, whereas the major transition in (Cw^CdCk is preceded by a minor transition. These compounds also display differences in chain conformations at room temperature: (Cw)2MnCl4 with B conformer (C2-C3 gauche), (Cw^CdCk with both A conformer (C1-C2 gauche) and B conformer), and (CioJaCuCk with A, B, and all trans {fe} conformers. As expected, these changes translate to the most probable conformational disorder at the HT phase. Overall, these observations indicate that ( / ) the trends in thermodynamics of chain melting transitions are sensitive to chain packing and metals and ( / 7) the stepwise conformational disordering transitions observed in most compounds are complex. To fully describe the trends and the impact of the phase transition behaviors on barocaloric effects, detailed investigations into the structural changes and microscopic motions associated with each transition are required, both at ambient and applied pressures. Comparison with melting of n-alkane: For the melting transition of n-alkane and solid-solid transitions of 2-D metal-halide perovskites and related systems, the relationships among transition entropy (ASr), chain length (n), and temperature of transition (Ttr) have been investigated, where AStotai normalized by chain length n is fit with Ttr. Although this approach, often referred to as SnTanalysis, can provide insights into the trends in series of 2-D perovskites and related compounds, we did not include the temperature of transition as a fitting parameter because most 2-D perovskites undergo stepwise transitions and the nature of molecular motions associated with each transition is not fully understood. However, both approaches provide similar insights into the conformational degrees of freedom of alkylammonium chains of 2-D perovskites during the phase transition. For example, the SnTanalysis indicates that the total transition entropy increases by 9.1 J K 1 mob1 per carbon in (Cn^MnCk ( / 7 = 7, 11— 17) and 13.5 J K~1 mol-1 per carbon in n-alkane. The chain length dependence of 9.1 J K-1 mol-1 in 2-D Mn-CI perovskites can be translated to the flexibility number of 3, which agrees with our analysis. As previously pointed out, the ratio between the chain length dependences of AStotai in (Cn^MnCk and n-alkane is 2:3 and correlates to the ratio between their dimensionalities. This interesting relationship is supported by a theoretical prediction based on kink-block transitions, where the melting entropy of alkyl chains confined in two-dimensional layers was shown to exhibit similar chain length dependence of 9.1 J K-1 mol-1. We also note that this value is close to the pressure dependences of melting transitions of n-decane (21 K kbar1) and n-nonane (20 K kbar1) (29). (nonane, with a dTdP solid-solid transition also similar). Notes on dynamics: In addition to the kink formation (gauche defect), the cooperative torsion along the chains is coupled to the overall molecular motion at the HT phase. According to incoherent neutron scattering experiments, molecular motion corresponding to kink formation and cooperative torsion occurs over 1-5 ps timescale. However, due to the relatively low Q-values explored in the measurements, overall molecular motions, cooperative torsions, and kink formations were not accurately distinguishable. We also note that further studies are needed to fully model the microscopic details of the chain melting processes, both for fast motions (e.g., kink motion within a chain) and slow processes (e.g., the formation of “clusters” with similar chain conformations), at ambient and applied pressures. Differences in phase transition behaviors between (DA^MnCU and (DA^CdCU: First of all, their transition behaviors are qualitatively similar, with the chains at HT phase adopting approximately one kink conformation per chain. Neutron scattering experiments indicates, however, that the diffusion of kink, which was previously observed in (Cio)2CdCl4 with -1000 ps time scale by proton NMR and 35CI and 14N quadrupole resonance spectroscopies, is unlikely to occur in (Cw)2MnCl4, because no cooperative conformational interconversion within a chain with a time scale greater than 20 ps was observed. This indicates that, unlike in (Cio)2CdCl4, in (Cio)2MnCl4, some kink formations are energetically more dominant. For the diffusion of the kinks to occur, several conformers with similar energies need to be in equilibrium. From the spectroscopic studies , it was revealed that (DA)2CdCl4 does have multiple conformers with similar energy levels. We also note that vibrational studies revealed that {tgtttg'tf} is the most probable conformer in (Cio)2CdCk, which is more flexible in the middle of the chain and does not have an end-gauche conformation. Infrared spectroscopy analysis Note that the IR signals used for conformational analysis are summarized in Tables 7 and 8. C-H stretching: In the compounds containing long alkyl chains, shifts in C-H stretching peaks to higher wavenumbers are correlated with an increase in the number of gauche C-C bonds, a change in chain packing, and presence of order-disorder transitions. For example, in the melting transitions of n-alkanes, Vsymmetric(C-H) and Vanti-symmetric(C-H) shift from 2920 to 2928 cm-1 and 2850 to 2856 cm-1, respectively. 2-D perovskites also display similar trend, with the shifts Av of 2-3 cm-1. The temperature dependence of these peaks can be either abrupt or gradual depending on metal and chain packing. Overall, this feature provides indirect evidence on the changes in the disorder in 2-D perovskites. CH2 rocking and bending: For well-ordered chains in a monoclinic or orthorhombic lattice, CH2 rocking and bending bands split into doublets near 720 and 1470 cm respectively, because of the factor group splitting that arises from directional intermolecular interactions between the chains. Generally, these features have been observed across materials with long hydrocarbon chains, including n-alkanes, layered silver thiolates, and 2-D metal-halide perovskites. The frequencies, shapes, and separations of these signals are correlated with orientations between neighboring chains and conformational disorder within the chain. In 2-D perovskites, the disappearance of the splitting can be used to determine if the chain undergoes conformational disordering, because it is correlated with the emergence of CH2 wagging bands specific to defect conformations {e.g., gtg' kink) and indicative of the re-orientational motion of whole chain. However, we note that understanding specific microscopic motions associated with these features requires further investigations. CH2 wagging: CH2 wagging bands, which provide insights into vibrational modes localized on a few CH2 units pinned in specific conformation sequences, are weakly coupled with the host lattice and independent of chain length. Thus, they provide characteristic signals of specific conformational defects. In 2-D perovskites, these modes are readily mixed with internal modes of chain end (CH3) and head (NH3+), and this coupling enhances the intensity of some CH2 wagging modes. Through normal-mode calculations on (Cw^CdCk and related compounds, the key peaks have been assigned. These signals appear at 1310 cm-1 (in-plane, two CH2 units, kink), a shoulder near 1370 cm-1 (out-of-plane, two CH2 units, kink), 1350 cm-1 (gg conformation), 1340 cm-1 (tg conformation near the chain end). The kink refers to gt2n+ig'-type conformational defects. NH3 and CH3 bending: In 2-D M-CI perovskites, the signal from NH3 symmetric bending modes appears around 1490 cm-1 at the LT phase and are often split into doublet due to the crystal field effect. The degree of the peak splitting highly depends on the identity of metals, with Mn-CI and Cd-CI perovskites displaying very small and often negligible splitting and Cu-CI perovskites showing clear doublet (1492-1480 cm-1). At the HT phase, the peak splitting disappears, often accompanied by noticeable broadening, and this indicates the reorientational motion of the polar head within the halide pocket. The NH3 antisymmetric bending mode is associated with a strong singlet peak near 1580 cm~1 and red-shifts by 6-8 cm-1, as a compound undergoes a structural transition. This feature can be correlated with the decrease in the strength of N-H---CI hydrogen bond. As these features are associated with the onset of chain melting transitions, vibrational spectra from NH3 bending can provide insights into the motions of chains within the halide pocket. The CH3 symmetrical bending mode, which appears near 1376 cm-1 at the LT phase, blue-shifts (Av ~ 3 cm-1) as the chains undergo structural transitions. This feature is correlated with the change in inter-lamellar interactions within the organic bilayers. Comparison of vibrational spectra related to chain conformations: IR spectra of (DA)2MnCl4 and (NA)2CuBr4 are summarized in Figs. 10A-10D. In (DA)2MnCl4, CH2 rocking and bending signals at ~720 and -1470 cm-1 are doublet at the LT phase, due to the factor group splitting that arises from directional, inter-chain interaction in the monoclinic unit cell (Figs. 10B an 10D). The splitting disappears at the HT phase as a result of chain disordering. In (NA)2CuBr4, however, the factor group splitting is not observed, presumably because the chains are arranged in a triclinic unit cell (Figs. 10A-10D). Both CH2 rocking and bending bands appear at the frequencies similar to those of (DA)2MnCl4 and do not display a noticeable change in peak shape after transition. Thus, these signals do not provide useful information about the difference in the disordering processes of the alkylammonium chains. For symmetric C-H stretching peaks, both compounds display blue-shifts (-2 cm~1) after the transitions, which supports that the phase transition introduces disorder in the alkylammonium chains (Fig. 10A). Symmetric CH3 bending peaks can also provide insights into the difference in molecular motions of both compounds at each phase, as the layer-layer interactions between the chain ends within the organic bilayer are also correlated with the chain disorder. Although the peaks blue-shift in both compounds, the degree to which the peak shifts is smaller in (NA)2CuBr4 (Av - 1 cm-1) than in (DA)2MnCl4 (Av - 4 cm-1) (Fig. 10B). The peak shifting in (NA^CuBu was even smaller than those measured in Cu-CI analogs (Av ~ 2 cm-1), as shown in Table 8. This result indicates the difference in the local environments around the methyl ends are smaller in (NA)2CuBr4 than in (DA)2MnCL. Both compounds show pronounced differences in the progression of CH2 wagging bands, as shown in Fig. 10C. In (DA)2MnCI4, CH2 wagging bands associated with {gtzn+i^} kink formation emerge near 1310 and 1367 cm-1 at the HT phase. The appearance of these peaks is also accompanied by broadening and decrease in intensity of a few other bands associated with other wagging / twisting motions in the range (1400-1300 cm-1). In addition, no signal at 1350 cm-1 was observed, which indicates that the highly distorted {gg} conformation is not formed at the HT phase. Note that these trends are similar to those observed in (CuJzMnCk. Interestingly, (NA^CuBu displays a very different trend. At the LT phase, a shoulder peak at 1360 cm-1 (near the CH3 symmetric bending peak at 1378 cm-1) is observed, which indicates that conformational disorder associated with a kink conformation is present even before the transition. At the HT phase, this shoulder peak disappears while another CH2 wagging band, also associated with a kink formation, emerges at 1312 cm-1. This result suggests that the compound, through the phase transition, undergoes a switching in most favorable conformers, each of which contains a kink. The signal associated with {gg} conformation (near 1350 cm-1) is also not detected. In addition, a peak near 1340 cm-1 at the LT phase disappears after the transition, which may indicate the existence of an end-gauche conformation before the transition. In addition, the phase transition in (NA^CuBu does not seem to have much impact on the peak shape in the CH2 wagging region (1400-1300 cm-1). We also note that the possibility of the end-gauche conformer in (NA^CuBu is supported by its smaller shift in symmetric CH3 bending peaks and the higher frequency of the LT phase peak (1378 cm-1) than Vs(CHs)bending of (DA)2MnCk at 1375 cm~1 at the LT phase. Taken together, these results indicates that ( / ) the differences in conformations of and local environments around the chains in (NA^CuBu is smaller than those in (DA)2MnCk and ( / 7) a noticeable degree of conformational disorder is present in (NA)2CuBr4 at the LT phase. These results, qualitatively, agree with our interpretations of single-crystal structures at the HT phase. Although the trends we observed from both compounds are consistent with those measured in other 2-D metal-halide perovskites as shown in Table 8, we note that accurate assignments and quantitative interpretation of IR spectra, particularly of CH2 wagging bands, are challenging, because the signals are relatively weak, coupled with the internal modes of chain end and head, and sensitive to the positions and diffusion of the defects, with the relationships among these factors not well understood. For accurate assignments of chain conformations, particularly those for (NA^CuBu, further investigations using normal-mode calculations and other complementary spectroscopic techniques, such as Raman or sum frequency generation vibrational spectroscopy, will be required. Chemical origin of the difference in the solid-state disorder between (NA)2CuBr4 and (DA)2MnCI4: The difference in the disorder between the two compounds may arise from the difference in the size of metal-halide pocket and the strength of N-H--X (X = Cl, Br) hydrogen-bond interactions within the pocket. In particular, comparisons of IR spectra associated with NH3 bending modes provide useful insights into how the charge-assisted H-bond interactions differ between the two compounds. As shown 44 in Figs. 10A and 10B, the anti-symmetric NH3 bending mode of (NA)2CuBr4 appears at 1570 cm-1 which is 15 cm-1 lower than that of (DA)2MnCl4 (1585 cm-1), as well as lower than other M-CI perovskite analogs (Cu-CI, 1583 cm~1; Cd-CI, 1589 cm-’). In (NA)2CuBr4, the position and shape of vas(NH3)bending peak does not change after the transition, whereas (DA)2MnCk undergoes both noticeable red-shifting (Av ~ -6 cm~1) and peak broadening through the transition. This result suggests that the polar heads (NH3+) in the decylammonium chains displays re-orientational motions accompanied by the weaking of hydrogen bonds, while the local environments around those in the nonylammonium chains remain nearly unchanged after the transition. We also note that the vas(NH3)bending peak of (NA^CuBu displays a very small splitting at the LT phase, which may suggest that its A and B conformers experience slightly different hydrogen bonds at the Cu-Br pockets. . Similar trends are observed in the NH3 symmetric bending modes: the vs(NH3)bending peak of (NA)2CuBr4 was red-shifted by ~16 cm-1 compared to that of (DA)2MnCl4 and the transition-induced peak broadening is observed only in (DA)2MnCk. Note that we do not discuss the peak splitting of Vs(NHs)bending peaks, because ( / ) the degree to which the peak splits in (DA)2MnCk was very small and ( / 7) vs(NH3)bending peak of (NA)2CuBr4 overlaps with its CH2 bending peak at 1470 cm-1. Collectively, these results illustrate that, for (NA)2CuBr4, the weaker N-H-Br hydrogen bonds, in combination with a larger area provided for each chain (from incorporation of larger Br ions and presence of Jahn-Teller distortion), result in the increased degrees of freedom of chains in (NA)2CuBr4 at the LT phase, which contributes to the difference in the chain disorder between LT and HT phase smaller than the difference in (DA)2MnCk. We also hypothesize that the smaller thermal hysteresis observed in (NA)2CuBr4 may arise from this enhancement in the conformational degrees of freedom, as it may lower the energy barrier associated with the formation of nucleation sites (i.e., “clusters” with similar chain conformations). The structure-property relationship between the two compounds provides insights into how conformational disorder in the 2-D perovskites can be controlled through chemical manipulations of the organic-inorganic interfaces. Data tables Table 2. Summary of previous reported chain melting transitions in representative two-dimensional (CnFkn+iNHs^MnCk perovskites. Chemical Formula3 Typeb Tuc (K) AH AS (J mol-1 K-1) AS (J kg1 K-1) (kJ mol-1) AH (kJ kg1) minor 206 5 13 26 64 (C6)2MnCk major 291 10 25 37 93 total 15 38 63 157 major 250 17 39 68 159 (C^MnCk minor 314 10 24 33 76 total 27 63 101 235 (C8)2MnCk major 274 19 42 70 153 minor 302 4 10 14 32 total 24 52 84 185 major 291 26 53 89 183 (Cg^MnCk minor 294 2 5 8 16 total 28 58 97 199 287e 31 63 107 220 (CwjsMnCk 308 35 68 113 221 310 37 72 118 230 major 317 40 74 126 234 (Cn)2MnCl4 minor 321 4 8 13 25 total 44 82 140 258 316e 46 86 147 271 major 331 48 84 145 254 (Ci2)2MnCl4 minor 335 6 10 18 31 total 54 94 162 285 major 331 52 87 158 264 (Ci3)2MnCl4 minor 343 8 13 22 37 total 60 100 180 301 major 345 58 92 167 268 (CujgMnCk minor 357 9 15 26 41 total 67 107 193 309 major 340 63 96 184 282 (Cis)2MnCk minor 362 10 16 28 44 total 73 112 213 325 major 346 60 88 172 253 (Ci6)2MnCl4 minor 364 12 17 32 46 total 71 104 204 299 aCn = CnH2n+iNH3. bWhen a compound displays multiple transitions, the transition with the highest AS was labeled as a major transition. The temperature of transition measured during the first heating scans are tabulated here. dThis compound was synthesized and characterized for the completeness of the 5 series. eClosely spaced transitions were not resolved. These compounds was synthesized and characterized by DSC at a slow scan rate (0.5 K / min) to resolve major and minor transitions. The difference between the previously reported value are within experimental uncertainties; however, the higher 7tr reported here may represent the higher purity of the sample, because some of the long-chain amines used in the previous literature have been shown to contain impurities, such as amines with 10 different chain lengths (n±2), which typically give rise to lowering of 7tr (up to 4-5 K), A / 7 and AS. Table 3. Summary of previous reported chain melting transitions in representative two-dimensional (CnH2n+iNH3)2CuX4 perovskites (X = Cl, Br). Chemical Formula3 Typeb TtrC (K) AH (kJ mol-1) AH (kJ kg-1) AS (J mol-1 K-1) AS (J kg-1 K" 1) major 269 18 39 68 146 (C8)2CuCl4 minor 303 5 11 16 35 total 23 50 84 181 major 294 23 46 78 158 (Cg)2CuCl4 minor 303 5 9 15 31 total total 28 56 93 189 major 309 35 67 113 216 (Cio)2CuCl4 minor 312 5 9 15 28 total 39 75 128 244 major 317® 36 65 112 204 (Cu)2CuCl4 minor 327 6 11 18 33 total 42 76 130 237 major 328 40 69 121 210 (Ci2)2CuCl4 minor 334 8 14 25 43 total 48 83 146 253 major 333® 48 80 145 239 (Cl3)2CllCl4 minor 344 10 16 29 48 total 58 96 174 287 major 334 50 61 150 237 (CuJgCuCk minor 356 11 83 31 48 total 61 144 181 285 major 343 54 82 158 238 (CisJgCuCk minor 358 12 18 33 50 total 66 100 191 288 major 345 36 52 103 150 (C16)2CUCI4 minor 354 8 12 23 33 minor 360 14 20 39 56 total 58 83 165 239 (Cg)2CuBr4 303 16 24 52 78 major 328 19 26 59 80 (Cn)2CuBr4 minor 340 1 1 1 2 total total 20 27 60 82 (Ci2)2CuBr4 337 22 29 64 85 (Ci3)2CuBr4 344 30 38 86 109 (Ci4)2CuBr4 348 28 34 80 98 (Ci5)2CuBr4 354 39 46 110 131 (Ci6)2CuBr4 major 343 2 2 4 5 minor 357 37 43 105 120 total total 39 45 109 125 aCn = CnHan+iNHs. bWhen a compound displays multiple transitions, the transition with the highest AS was labeled as a major transition. cThe temperature of transition measured during the first heating scans are tabulated here. These minor transitions were not resolved in the initial reports. Note that reported full 5 DSC traces of (Cn)2CuCl4 (n = 2-14), are reported without integrated thermodynamic values. Table 4. Summary of previous reported chain melting transitions in representative two-dimensional (CnH2n+iNH3)2CdCl4 and (CnH2n+iNH3)2Pbl4 perovskites. Chemical Formula’ Typeb Tuc (K) AH (kJ mol-1) AH (kJ kg-1) AS (J mol-1 K-1) AS (J kg-1 K- 1) major 250 18 36 71 147 (C7)2CdCl4 minor 317 5 10 16 33 total 23 47 87 180 major 269 15 28 54 105 (C8)2CdCl4 minor 308 5 10 17 32 total 20 38 71 138 minor 308 8 14 25 44 (Cio)2CdCl4 major 313 30 52 95 166 total 38 66 120 210 minor 332 11 17 33 52 (Ci2)2CdCl4 major 334 44 69 130 208 total 54 87 163 260 major 345 40 58 115 168 (Ci4)2CdCl4 minor 351 23 34 66 96 total 63 92 181 264 major 345 40 55 117 158 (Ci6)2CdCl4 minor 352 8 10 22 30 minor 356 32 43 88 120 80 108 227 308 minor 271 7 7 25 26 (C7)2Pbl4 major 286 8 9 29 31 minor 310 3 3 9 10 total 18 19 63 67 (C8)2Pbl4 minor 252 15 15 58 59 major 311 21 22 68 70 total 36 37 126 129 minor 252 7 7 28 28 (Cg)2Pbl4 major 314 24 24 75 75 total 31 31 104 103 minor 259 10 10 39 38 minor 284 8 8 30 29 (Cw)2Pbl4 major 337 32 31 96 93 total 51 49 165 160 minor 315 11 10 35 32 (Ci2)2Pbl4 major 350 44 41 126 116 total 55 51 161 148 minor 329 11 9 32 28 (Ci4)2Pbl4 major 360 55 48 152 133 total 65 57 184 161 minor 340 12 10 34 28 (Ci6)2Pbl4 major 369 63 52 170 142 total 74 62 204 170 aCn = CnH2n+iNH3.bWhen a compound displays multiple transitions, the transition with the highest AS was labeled as a major transition. cThe temperature of transition measured during the first heating scans are tabulated here. Note that 2-D Pb-I perovskites have partially interdigitated organic bilayers. Table 5. Estimated barocaloric coefficients of representative two-dimensional M-CI perovskites (M = Mn and Cu). Note that chain-melting phase transitions of these compounds are also expected to be sensitive to pressure, with minor transitions particularly more sensitive than major transitions. Chemical Formula3 Type Ttr (K) Estimated dTtrdP0 (K kbar1) Ad (A) △V (cm3 kg-1) AS, (J K-1 kg1) 29.7 to (Ci2)2MnCk major 331 31.9; 2.2 (7.4%) 31.9 to 61.7 254 24.3 minor 335 32.2; 0.3 (0.9%) 8.4 31 27.1 33.3 to major 345 35.5; 2.2 56.1 268 20.9 (Cu^MnCk minor 357 (6.6%) 35.5 to 36.4;0.9 (2.5%) 23.0 41 56.0 25.2 to major 309 27.0; 57.1 216 26.4 (Cio)2CuCk minor 312 1.8 (7.1%) 27.0 to 27.6; 0.6 (2.2%) 19.0 28 68.0 28.8 to major 328 30.3; 1.5 43.0 210 20.5 (CizjzCuCk minor 334 (5.2%) 30.3 to 31.1;0.8 (2.6%) 22.9 43 53.3 32.9 to major 334 34.5; 1.6 41.8 237 17.6 (Ci4)2CuCk minor 356 (4.9%) 34.5 to 35.5; 1.0 26.1 48 54.4 (2.9%) aCn = CnHzn+iNHs. bNote that the specific volume of each phase was estimated using the relationship, 1 / = dAcxMw / Nk, where Ac is the area of metal-halide sheet per chain, of is the interlayer distance, is the molecular weight, and Na is Avogadro’s number. We used this estimation because the unit cell 5 parameters of intermediate phases were often not available. The reported mean values of are 26.5 A2 and 27.5 A2 for Mn-CI and Cu-CI perovskites, respectively. Note that this approach is likely to overestimate the volume change. cBarocaloric coefficients were calculated through the Clausius-Clapeyron equation (d7tr / dP= AW / AStr). 10 Table 6. The linear relationship between chain length and total change in entropy (ASiotai) in chain-melting transition of 2-D perovskites. Compound’ Chain length Slope y-intercept R2 Flexibility number 0 Restriction parameter P Area per chain (A2) (Cn)2MnCk odd 19.4 -75.3 0.995 3.2 2.5 26.5 even 18.5 -63.7 0.994 3.0 2.1 (Cn)2CdCk even 18.7 -71.4 0.976 3.1 2.4 27.7 (Cn)2CuCk odd 16.9 -55.8 0.960 2.8 2.0 27.5 even 15.5 -35.2 0.965 2.5 1.0 (Cn)2CuBr4 odd 12.5 -77.2 0.999 2.1 5.1 30.3 even 11.3 -73.2 0.946 2.0 5.5 aCn = CnH2n+lNH3. Table 7. Summary of characteristic infrared signals of (DA)2MnCk and (NA^CuBu. Structure Mode3 (cm-1) (DA)2MnCI4 LT band (cm-1) (DA)2MnCI4 HT band (cm-1) (NA)2CuBr4 LT band (cm-1) (NA)2CuBr4 HT band (cm-1) vas(C-H) 2919 2919 2919 2920 Vs(C-H) 2850 2852 2851 2853 V(CH2)rocking 727-720 doublet 721 singlet 722 singlet 722 singlet V(CH2)bending 1472-1463 doublet 1464 singlet 1467 shoulders (-1440, -1455) 1468 shoulders (-1440, -1455) V(CH2)wagging two units, inplane -1310 (kink} band progression -1310 (shoulder, contribute to broadening) 1306 1306 (broadening) 1312 (new peak) Alkyl chain V(CH2)wagging (CnH2„+1NH3*) two units, out-of-plane -1360 (kink} band progression -1367 (shoulder) 1360 not detected V(CH2)wagging single unit '1350 (gg} not detected not detected not detected not detected (CHgjragging single unit -1340 (tg, chain end) not detected not detected 1340 not detected Vs(CHs)bending -1376 1375 1379 1378 1379 Polar head Vs(NHs)bending 1496 narrow 1496 broad 1480 1480 (C„H2w1NH30 Vas(NH3)bending 1585 narrow 1579 broad 1569-1572 doublet 1569 singlet avs and Vas refer to symmetric and anti-symmetric modes, respectively. previous reports on Cd-CI and Mn-CI analogs revealed that the peak near 1337 cm-1 does not depend on chain conformation (20, 37). 5 Table 8. Summary of characteristic infrared signals of representative 2-D perovskites. Structure Modea (cm~1) (Cio)2CdCl4 (C^CuCU (CtohCuCh (Ci2)2CuCh (CukMnCh Vas(C-H) -2920 not discussed not discussed not discussed 2919 2923 increase not discussed vs(C-H) -2850 2851 2853 increase 2852 2854 increase not discussed 2850 2852 increase not discussed 728-720 727-722 730-725 730-725 729-719 V(CH2)rocking doublet to doublet to doublet to doublet to doublet to singlet singlet singlet singlet singlet V(CH2)bending -1460 doublet to singlet 1471- 1466 doublet to singlet 1472-1467 doublet to singlet 1472-1467 doublet to singlet 1475-1463 doublet to singlet V(CH2)wagging Alkyl chain (CnH2n+iNH3+) two units, inplane -1310 (kinlP) 1306 broad 1310 broad 1308 broad 1310 broad 1305 broad V(CH2)wagging two units, not 1364 1367 1367 out-of-plane -1360 (kinlP) detected shoulder shoulder shoulder V(CH2)wagging single unit -1350 (gg) not detected not detected not detected not detected not detected (CH2)wagging single unit -1340 (to, chain end) not detected 1340 1341 1342 not detected Vs(CH3)bending -1376 1376a not discussed 1376 1378 increase 1377 -+ 1379 increase 1375 -+ 1379 increase 1491- Polar head (C„H2n+iNH3+) Vs(NH3)bending Vas(NH3)bending -1488 1492-1480 doublet to singlet 1583—> 1576 decrease 1492-1480 doublet to singlet 1584—> 1575 decrease -1496 doublet to single? not discussed doublet to singled 1589d 1479 doublet to singlet 1583—> 1575 decrease Ref. (20, 30) (34) (19) (33) (37) avs and Vas refer to symmetric and anti-symmetric modes, respectively. bkink generally refers to gfe+irX-type conformational defects. cthe splitting in Mn-CI and Mn-CI analogs tends to be small and often not discernible. dtemperature-dependent band progression is not discussed Table 9. Comparison of predicted and experimentally determined barocaloric coefficients (dTMP). Note that the barocaloric coefficient were estimated using the Clausius-Clapeyron equation d7tr / dP = AI / tr / AStr, with A l / tr determined through powder X-ray diffraction or Helium pycnometry, and ASr measured at ambient pressure. AStr values for (DA)2MnCh and (NAjsCuBr-i were 230 and 78 J K~1 kg-1, respectively. PXRDa He pycnometry HP-DSC Compound Al / (cm3 kg-1) dTtr / dP (K kbar 1) Al / (cm3 kg-1 dTMP (K kbar- 1) dTMP (K kbar1) heating cooling heatin a cooling heating cooling (DA)2MnCI4 65.07 (7.95 %) 28.3 linear fit nearest 54.7 (6.60% ) 49.3 ± 3.4 (5.9%) 53.06 (6.38% ) 47.5 ± 5.8 (5.7%) 23.8 21.4 + 23.1 20.7 ± 22.1 ± 0.7 20.6 ± 0.8 points 1.5 2.5 linear 19.32 19.25 24.8 25.6 + 24.7 25.3 ± (NA)2CuBr4 24.93 (3.95 %) 32 fit nearest (3.1%) 20.0 ± 1.9 (3.2%) (3.1%) 19.7 ± 2.4 (3.1%) 26.9 + 0.4 26.5 ± 0.5 points 2.4 3.0 10 aPXRD data was obtained during cooling and the volume change was obtained through linear fit away from the transition. Table 10. Selected geometric parameters of (DA)2MnCI4 at 100 K, 270 K, and 330 K. Temperature (K) 100 K 270 K 330 K Space Group PI C2 / m Cccm l / (A3) 672.07(14) 1396.0 (2) 3069.5 (9) Nearest Mn-Mn (A) 5.0548(6) 5.1252 (3) 5.1619(3) Nearest N-N (A) 5.0548(6) 4.9369 (3) 5.0726 (3) Interlayer distance (A) 26.419(3) 26.685 (2) 28.800 (1) Distance between N atoms and [MnCk]2- (A)a 2.325(4) 2.305 (1) 2.262 (1) Chain tilt angle relative to [MnCk]2- sheet normal (°) best line (C1 to C10) [Disordered position] 42.8(10) [42.8(10)] 41.7(1) 25.8 (1) Chain tilt angle relative to [MnCk]2- sheet normal (°) mean plane (C2 to C10) [Disordered position] 65.1(10) [65.4(10)] 70.9 (1) 69.5 (1) Cross-sectional area per chain (A2)b 25.439(6) 26.157(4) 26.635(8) Cross-sectional area per chain (A2)c 25.551(4) 26.268(2) 26.645(2) Calculated as the distance between mean plane of four N atoms and mean plane of [MnCk]2- layer Calculated from V / (Zd), where V is the unit cell volume, Z is the number of molecules in the unit cell, and dis the interlayer distance. estimated by cP, where d is the nearest metal-metal distance. Table 11. Selected geometric parameters of (NA^CuBu at 100 K, 270 K, and 335 K. Temperature (K) 100 K 270 K 335 K Space Group Pt Pt Cmca V (A3) 1330.3(2) 1382.70(7) 2966.0(3) Nearest Cu-Cu (A) 5.4102(4) 5.5173(1) 5.4927(3) Nearest N-N (A) 5.117(7) 5.1667(1) 5.4927(3) Interlayer distance (A) 23.054(2) 23.254(1) 24.578(2) Distance between N atoms and [MnCk]2- (A)a 2.201(4) 2.150(1) 2.138(1) Chain tilt angle relative to [CuBr4]2- sheet normal (°) best line (C1 to C9) [Disordered position] 46.9(2) 46.67(1) [43.37(1)] 35.4 (1) Chain tilt angle relative to [CuBr4]2- sheet normal (°) best line (C11 to C19) [Disordered position] 48.7(2) 48.49(1) [47.00(1)] Chain tilt angle relative to [CuBr4]2- sheet normal (°) 58.9(3) mean plane (C2 to C9) [Disordered position] 64.60(1) [72.16(1)] 68.4 (1) Chain tilt angle relative to [CuBr4]2- sheet normal (°) 54.8(3) mean plane (C12 to C19) [Disordered position] 52.36 (1) [54.72(1)] Cross-sectional area per oo chain (A2)b 28.852(5) 29.730(2) 30.169(4) Cross-sectional area per ovn,os chain (A2)c 29.270(3) 30.440(7) 30.169(2) acalculated as the distance between mean plane of four N atoms and mean plane of [MnCU]2- layer bcalculated from V / (Zd), where V is the unit cell volume, Z is the number of molecules in the unit cell, and dis the interlayer distance. Ccalculated by di x dz, where di and dz are metal-metal distances. 5 Table 12. Donor-acceptor (N--CI) distances and bond angles for LT and HT phases in (DAJzMnCL and (NA)2CuBr4. Tilt of NH3 Compound T(K) N-H-X H-A (A) D-A (A) z(DHA) (°) Occupancy group (°)a Equatorial 2.4213(34) 3.291(37) 166.12(44) 61.4 270 Axial 1 2.4668(14) 3.3310(75) 164.12(42) (16) (DA)2MnCI4 Axial 2 2.3544(15) 3.226(66) 165.2(26) Equatorial 2.6051(17) 3.384(20) 146.53(74) 67.66 330 Axial 1 2.7753(4) 3.622(29) 158.8(17) iqo\ Axial 2 2.7215(22) 3.3332(84) 127.02(52) Equatorial 2.7385(5) 3.5262(45) 148.22(31) Chain A 50.682 Axial 1 3.0803(7) 3.9226(54) 158.73(35) Part 1 (0.35) (60) Axial 2 2.7546(6) 3.4350(48) 134.20(31) Equatorial 2.5836(6) 3.431(5) 159.52(31) Chain A 57.37 Axial 1 2.6022(6) 3.4350(48) 156.18(31) (NA)2CuBr4 270 Axial 2 2.9046(7) 3.7516(55) 159.55(35) Part 2 (0.65) (39) Equatorial 2.6289(6) 3.4424(55) 152.25(31) Chain B 54.76 Axial 1 2.5648(6) 3.3696(49) 150.76(31) Part 1 (0.53) (41) Axial 2 2.7882(7) 3.6367(55) 159.92(35) Equatorial 2.6929(6) 3.5496(50) 161.86(31) Chain B Axial 1 2.7716(6) 3.3696(49) 125.71(31) Part 2 (0.47) 81.09(8 Axial 2 3.3243(7) 4.0423(54) 139.38(35) 8) Equatorial 2.6419(12) 3.506(21) 162.449(3) 335 Axial 1 3.1158(5) 3.9023(25) 147.952(4) 70.7(15 ) Axial 2 3.1905(10) 3.8858(25) 136.106(1) athe tilt angle is defined as the angle between a line connecting the atoms N and C and a plane through the metal atoms of the inorganic layers. Table 13. Tabulation of dihedral angle <p of alkylammonium chains at 100 K, 270 K, and 330 K for 5 (DA)2MnCl4. T(K) Atoms Part 1a Part 1 Occupanc Occupancy Part 2 y Part 1 Atoms Part 2s Part 2 100 N1-C1-C2-C3 179.6 (10) 0.504(13) N1A-C1A-C2A- C3A 178.2 (10) 0.496(13) C1-C2-C3-C4 -68 (2) 0.504(13) C1A-C2A-C3A- C4A 70 (2) 0.496(13) C2-C3-C4-C5 -178.2 (13) 0.504(13) C2A-C3A-C4A- C5A 177.5 (14) 0.496(13) C3-C4-C5-C6 178.0(14) 0.504(13) C3A-C4A-C5A- C6A -178.4 (15) 0.496(13) C4-C5-C6-C7 -179.7 (15) 0.504(13) C4A-C5A-C6A- C7A -179.3 (16) 0.496(13) C5-C6-C7-C8 178.6 (14) 0.504(13) C5A-C6A-C7A- C8A -179.3 (15) 0.496(13) C6-C7-C8-C9 178.4(15) 0.504(13) C6A-C7A-C8A- C9A 177.7 (16) 0.496(13) C7-C8-C9-C10 175.9 (17) 0.504(13) C7A-C8A-C9A- C10A 179.3 (17) 0.496(13) 270 N1-C1-C2-C3 174 (3) C1-C2-C3-C4 -65 (5) C2-C3-C4-C5 179 (3) C3-C4-C5-C6 177 (4) C4-C5-C6-C7 -175 (5) C5-C6-C7-C8 180 (5) C6-C7-C8-C9 -174 (5) C7-C8-C9-C10 -169 (8) 330 N1-C1-C2-C3 174 (3) C1-C2-C3-C4 -166 (3) C2-C3-C4-C5 -180 (3) C3-C4-C5-C6 163 (4) C4-C5-C6-C7 154 (4) C5-C6-C7-C8 160 (4) C6-C7-C8-C9 165 (5) C7-C8-C9-C10 -151 (5) aPart 1 and part 2 refer to the sets of disordered positions of the alkylammonium chains conformer B (C2 - C3 gauche bond) Table 14. Tabulation of dihedral angle (p of alkylammonium chains at 100 K, 270 K, and 335 K for 5 (NA)2CuBr4. T(K) Atoms Part 1a vn Part 1 Occupancy Part 1 Atoms Part 23 Part 2 Occupancy Part 2 100 N1-C1-C2-C3 -175.0(6) C1-C2-C3-C4 -65.7 (9) C2-C3-C4-C5 -177.4(7) C3-C4-C5-C6 178.8 (7) C4-C5-C6-C7 179.9(6) C5-C6-C7-C8 179.0(7) C6-C7-C8-C9 177.9 (7) N2-C11-C12-C13 70.0 (7) C11-C12-C13-C14 -177.6 (6) C12-C13-C14-C15 174.1 (6) C13-C14-C15-C16 178.6(6) C14-C15-C16-C17 -179.5 (6) C15-C16-C17-C18 -175.1 (6) C16-C17-C18-C19 -177.3 (7) 270 N1-C1-C2-C3 -173.0 (17) 0.528(9) N1A-C1A-C2A- C3A 172 (2) 0.472(9) C1-C2-C3-C4 -39 (3) 0.528(9) C1A-C2A-C3A- C4A -178 (3) 0.472(9) C2-C3-C4-C5 -176 (3) 0.528(9) C2A-C3A-C4A- C5A 174 (3) 0.472(9) C3-C4-C5-C6 178 (3) 0.528(9) C3A-C4A-C5A- C6A 180 (4) 0.472(9) C4-C5-C6-C7 178 (4) 0.528(9) C4A-C5A-C6A- C7A 173 (4) 0.472(9) C5-C6-C7-C8 168 (4) 0.528(9) C5A-C6A-C7A- C8A -174 (4) 0.472(9) C6-C7-C8-C9 164 (4) 0.528(9) C6A-C7A-C8A- C9A -164 (4) 0.472(9) N2-C11-C12-C13 -67 (5) 0.350(15) N2A-C11A- C12A-C13A 77 (2) 0.650(15) C11-C12-C13-C14 173 (4) 0.350(15) C11A-C12A- C13A-C14A -176.9 (19) 0.650(15) C12-C13-C14-C15 -159 (5) 0.350(15) C12A-C13A- C14A-C15A 169 (2) 0.650(15) C13-C14-C15-C16 -175 (5) 0.350(15) C13A-C14A- C15A-C16A -180 (2) 0.650(15) C14-C15-C16-C17 -173 (6) 0.350(15) C14A-C15A- C16A-C17A 175 (3) 0.650(15) C15-C16-C17-C18 -177 (6) 0.350(15) C15A-C16A- C17A-C18A 176 (3) 0.650(15) C16-C17-C18-C19 159 (6) 0.350(15) C16A-C17A- C18A-C19A -170 (3) 0.650(15) 335 N1-C1-C2-C3 156 (3) C1-C2-C3-C4 44 (7) C2-C3-C4-C5 156 (4) C3-C4-C5-C6 -128 (8) C4-C5-C6-C7 160 (7) C5-C6-C7-C8 174 (6) C6-C7-C8-C9 -142 (10) aPart 1 and part 2 refer to the sets of disordered positions of the alkylammonium chains conformer conformers A (C1 - C2 gauche) and B (C2 - C3 gauche bond) Table 15. Crystallographic data for (DA)2MnCl4 collected at 100 K, 270 K, and 330 K. (DA)2MnCI4 (DA)2MnCI4 (DA)2MnCI4 Formula C2oH4sCl4MnN2 C2oH4sCl4MnN2 C2oH4sCI4MnN2 Temperature (K) 100(2) 270(2) 330(2) Crystal System Triclinic Monoclinic Orthorhombic Space Group P? C2 / m Cccm a (A) 5.0548 (6) 7.1857 (6) 7.3264 (5) b(A) 5.0626 (6) 7.3100 (6) 57.601 (15) c(A) 26.419(3) 26.685 (2) 7.2735 (6) or(°) 95.516(4) 90 90 / 3(°) 92.683 (4) 95.150 (1) 90 Y(°) 90.904 (4) 90 90 1 / (A3) 672.07(14) 1396.0 (2) 3069.5 (9) z 1 2 4 Radiation, / (A) MoKa, 0.71073 MoKa, 0.71073 MoKa, 0.71073 / j (mm-1) 0.90 0.86 0.79 Crystal Size (mm) 0.18 x 0.12 x 0.08 0.18 x 0.12 x 0.08 0.18 x 0.12 x 0.08 Max. and min. transmission 0.767 and 0.635 0.767 and 0.492 0.801 and 0.478 Completeness to 98.6% 98.5% 97.1% 20 (20 = 25.123°) (20= 25.191°) (20 = 25.607°) No. of measured, independent and observed [ / > 2o( / )] reflections 8898, 2353, 1872 11186, 1345, 1062 18017, 1533, 928 Hint 0.055 0.061 0.100 (sin B / A)max (A 1) 0.597 0.599 0.608 Data / Restraints / Parameters 2353 / 134 / 238 1345 / 0 / 124 1533 / 170 / 116 Goodness of Fit on F2 1.10 1.05 1.08 FF, wF?2b [ / > 2o< / )] 0.066, 0.171 0.061,0.181 0.097, 0.259 Largest Diff. Peak and Hole (e A-3) 1.32 and -0.65 1.64 and -0.77 0.78 and -0.41 = Z||Fo| - |Fc|| / E|F0|. bwRz = {Z[w(F02 - F=2)2] / Z[w(Fc2)2]}12. Table 16. Crystallographic data for (NA)2CuBr4 collected at 100 K, 270 K, and 335 K. (NA)2CuBr4 (NA)2CuBr4 (NA)2CuBr4 Formula CisH44Br4CuN2 Ci8H44Br4CuN2 CisH44Br4CuN2 Temperature (K) 100(2) 270(2) 335(2) Crystal System Triclinic Triclinic Orthorhombic Space Group Pl Pl Cmca a (A) 7.4107 (7) 7.6549 (2) 49.155 (3) b(A) 7.9092 (8) 7.9674 (2) 7.7844 (5) c(A) 23.054 (2) 23.2541 (7) 7.7512 (5) a(°) 82.835 (2) 80.4332 (9) 90 / 3(°) 82.901 (3) 81.4664 (9) 90 / (°) 89.808 (2) 89.8532 (8) 90 1 / (A3) 1330.3 (2) 1382.70 (7) 2966.0 (3) Z 2 2 4 Radiation, / (A) MoKa, 0.71073 MoKa, 0.71073 MoKa, 0.71073 jU(mm“1) Crystal Size (mm) 6.83 0.24 x 0.12 x 0.06 6.58 0.24 x 0.12 x 0.06 6.13 0.24 x 0.12 x 0.06 Max. and min. transmission 0.646 and 0.428 0.801 and 0.658 0.694 and 0.290 Completeness to 99.3% 99.4% 96.8% 20 No. of measured, (20 = 25.092°) (20 = 25.026°) (20 = 25.004°) independent and 20830, 4693, 15136, 4857, 17040, 1291,790 observed [ / > 2o( / )] reflections 3569 3313 Hint 0.065 0.042 0.112 (sin qM)max (A-1) Data / Restraints / 0.597 0.595 0.595 Parameters Goodness of Fit 4693 / 0 / 233 4857 / 988 / 399 1291 / 151 / 103 on F2 Ra, wRzb 1.05 1.03 1.09 [ / > 2o( / )] 0.040, 0.104 0.042, 0.099 0.104, 0.261 Largest Diff. Peak and Hole (e A-3) 1.21 and -0.78 0.58 and -0.61 0.46 and -0.47 aRi = Z||Fo| - |Fc|| / Z|F0|. bwRz = {Z[w(Fo2 - Fc2)2] / ^^2)2]}1''2. Table 17. Comparison of crystallographic unit cell data for ordered phase of (DA)2MnCI4. (DA)2MnCI4 experimental (DA)2MnCI4 experimental (DA)2MnCI4 reported (1) Formula C2oH4sCl4MnN2 C2oH4sCl4MnN2 C2oH48Cl4MnN2 Temperature (K) 100(2) 270(2) 298(3) Crystal system Triclinic Monoclinic Monoclinic Space Group Pl C2 / m F2i / a a (A) 5.0548 (6) 7.1857 (6) 7.213(8) b(A) 5.0626 (6) 7.3100 (6) 7.337(2) c(A) 26.419(3) 26.685 (2) 26.747(21) or(°) 95.516(4) 90 90 92.683 (4) 95.150 (1) 94.64(5) Y(°) 90.904 (4) 90 90 l / (A3) 672.07(14) 1396.0 (2) 1411(2) Z 1 2 2 Radiation, >1 (A) MoKor, 0.71073 MoKor, 0.71073 CuKa, 1.5418 No. of measured, independent and observed [ / > 2o(f)] reflections 8898, 2353, 1872 11186, 1345, 1062 No. of independent reflections 1393 Hint 0.055 0.061 0.086 (for 1204 reflections) (sin qM)max (A-1) 0.597 0.599 R[ / =2 >2(7( / =2)]. 0.066, 0.171, 0.061,0.181, wR(P), S 1.10 1.05 Data / Restraints / Parameters 2353 / 134 / 238 1345 / 0 / 124 Largest Diff. Peak and Hole (e A-3) 1.32 and -0.65 1.64 and -0.77 Table 18. Phase-change properties and barocaloric effects of representative barocaloric materials. Type Chemical Formula3 T b *1r AS / (J kg-1 K- 1) dTtr / dP heating (K kbar dTtr / dP cooling (K kbar AThysd (K) P™' (bar) A Sit, rev1 (J kg-1 K- 1) AP (bar) Ref (DA)2MnCI4 310 230 22.1 20.6 1.4 66 75 150 This 2-D perovskite (NA)2CuBr4 303 78 26.9 26.5 0.4 16 68 150 work 3-D hybrid [(CH3)4N][Mn(N3)3] 305 80 123 7 583 70 900 {59) [TPrA][Mn(dca)3] 330 43 23.10 0.9 39 31 70 {60) perovskite [TPrA][Cd(dca)3] 386 16 38.2° 1.4 37 11.5 70 {61) (CH3)2C(CH2OH)2 314 389 11.3 9.3 14 1505 445 2500 {62. 63) Organic (CH3)C(CH2OH)3 354 485 7.9 9.4 3.7 394 490 2400 {64) plastic crystal (CH3)3C(CH2OH) 232 204 22 11.9 20.3 1706 290 2600 {64) 32 1000 Ceo 259 27 16.7 17.2 3 174 (42) (4100) {65) (NH4)2SO4 222 65 -5.7 -4.5 1 175 60 1000 {66) Agl 420 64 -14 -12.8 25 1786 60 1000 {67) Inorganic Fe43Rh5i 310 13 5.4 6.4 10 1563 13 2500 {68) Nio.85Feo.i5Sh 303 53 -7.5 11.5 1533 (69) Spin 80 550 Fe3(bntrz)6(tcnset>6 318 80 25 25 2 80 (120) (2600) {70) crossover complex [FeL2](BF4)2h. 262 86 101 10i 4 400 {71) aDA = decylammonium; NA = nonylammonium; TPrA = tetrapropylammonium; bntrz = 4-(benzyl)-1,2,4- triazole; tcnset = 1,1,3,3-tetracyano-2-thioethylepropenide; L = 2,6-di(pyrazol-1-yl)pyridine. bTransition 5 temperatures measured during heating are tabulated here. cEntropy of transition AStr measured at ambient pressure are tabulated here. dA7hys refers to the difference between Ttr, heating and Ttr, cooling at ambient pressure. ePrev is calculated through = AThys / |dTtr / dP|, and dTtr / dP values for exothermic and 61 endothermic transitions are used for conventional and inverse barocaloric materials, respectively. Note that inverse barocaloric materials refer to the compounds with d 7tr / dP <0. 'The reversible isothermal entropy changes, ASt, rev, at the driving pressure AP are tabulated here. Note that these values were derived from quasi-direct measurements. At high pressure (typically above 1 kbar), the additional entropy change outside of the transition, AS+, plays a role and contributes to ASt values, leading to ASt to higher than ASr. The ASt measured at higher pressures are shown in the parentheses, adTMP values were averaged from heating and cooling data. hOnly irreversible ASt value is reported (Nio.asFeo.isS, 53 J kg-1 K~1 at 1000 bar; [FeL2](BF4)2, 68 J kg-1 K-1 at 430 bar), 'an irreversible phase transitions occur at the pressure above 4900 bar. id 7tr / dP values obtained at a pressure range <2 kbar values are shown. Note that (dTtr / dP)heating and (d7tr / dP)cooiing were obtained from calorimetry and SQUID magnetometry, respectively. Table 19. Barocaloric effects and predicted thermodynamic efficiencies for selected barocaloric materials including two of the invention ((DA)2MnCk and (NA^CuBu). Chemical Formula3 Ttrb ASit, rev / AP° (J kg1 K1 kbar1) AT . d n * ad, max (K) △ 7hys / A Tad, e max (%) n1 (%) (DA)2MnCl4 310 500 429 3.3 89 (NA)2CuBr4 303 453 21h 1.9 93 [TPrA][Mn(dca)3] 330 436 51 15.8 61 (CH3)2C(CH2OH)2 314 178 45i 31.1 45 Ceo 259 32 20k 15.0 63 (NH4)2SO4 222 60 81 12.5 67 Nio.85Feo.isSh 303 30m 38.3 40 Fes(bntrz)6(tcnset) 6 318 145 35n 5.7 81 aDA = decylammonium; NA = nonylammonium; TPrA = tetrapropylammonium; bntrz = 4-(benzyl)-1,2,4-triazole; tcnset = 1,1,3,3-tetracyano-2-thioethylepropenide. bTransition temperatures measured during heating are tabulated here. cThe reversible isothermal entropy change ASt, rev normalized by the driving pressure, often referred to as barocaloric strength, are tabulated here. Note that the barocaloric strength values were maximized by choosing the smallest AS values that can capture the full entropy of the transition. dMaximum adiabatic temperature changes tabulated here were predicted by indirect methods, with A Tad, max = TASt / cP, or, by quasi-direct methods. eA7hys values measured at ambient pressure were used. 'The second-law efficiency r), which corresponds to coefficient of performance (COP) of material with hysteresis normalized by COP of Carnot cycle, is estimated using the equation ij = COP / COPcamot = ----. Note that this relation is derived from a phenomenological model that integrates the dissipative ^7"ad, max losses due to hysteresis in a Carnot-like cycle and provides insights into how thermal hysteresis of a material reduces the efficiency. sEstimated through the indirect method, with ASt, rev of 210 J kg-1 K-1 predicted to occur at the driving pressure of 270 bar with 7= 312 K and cP = 1550 J kg~1 K~. hEstimated through the indirect method, with ASt, rev of 68 J kg-1 K- from the pressure change of 150 bar with 7 = 306 K and cP = 800 J kg-1 K-1. 'Estimated through the indirect method, with ASt, rev of 68 J kg-1 K-1 from the pressure change of 150 bar with T = 332 K and cP = 2450 J kg-1 K-1. iEstimated to be around 50 K and later confirmed through quasi-direct measurement to be 45 K at the driving pressure of 5700 bar. kquasi-direct measurements at the driving pressure of 5.9 kbar. 'Estimated through the indirect method, with ASt, rev of 60 J kg~1 K~1 predicted to occur at the driving pressure of 1000 bar with cP = 1700 J kg~1 K~ 5 1. mEstimated through the indirect method, with the irreversible ASt value of 53 J kg-1 K~1 at the driving pressure of 1000 bar. mQuasi-direct measurements at the driving pressure of 2600 bar. Table 20. Phase-change properties and barocaloric effects of compounds with long-chain hydrocarbons. Type Chemical Formula3 V △Strc (J kg-1 K- 1) dTtrd / * (K kbar1) AThysd (K) (OA)2MnCl4e 274 major 153 13 3.0 2-D perovskite (OA)2MnCl4e 303 minor 33 40 0.7 (NA)2MnCke 291 major 183 20 2.2 (n-C6Hi3)2NH2Br 292 291 34e 4.7 (n-C8Hi7)2NH2CI 294 343 (n-C8Hi7)2NH2Br 302 247 Di-n-alkyl ammonium salt1 (n-Ci2H2s)2NH2CI 338 379 (n-Ci2H25)2NH2Br 345 327 (n-CisH37)2NH2CI 366 411 (n-Ci8H37)2NH2Br 370 379 Intercalation FeOCI«Ci4H29NH20 323 327 93 compound Ni(CN)2-C12H25NH2h 214 (first-row transition major metal) Ni(CN)2-Ci2H25NH2h 363 minor 41 (Cl8H37)sNH+l intercalated between Self-Assembled 324 83 montmorillonite Monolayer (smectite) (ClsH37)4N+l Self-Assembled Monolayer 310 63 Layered metal lo-alkylphosphonate Mg(O3PC22H45)j 290- 330 682 10 aDA = decylammonium; NA = nonylammonium. bTransition temperatures measured during heating are tabulated here. cEntropy of transition ASr measured at ambient pressure are tabulated here. The literature values are associated with large uncertainty. dBarocaloric coefficients tabulated here were measured through high-pressure differential calorimetry under Helium gas environment. Thermal 15 hysteresis were measured at ambient pressure. ®Phase-change properties, including the change in volume, was previously reported. Compounds listed here are predicted to display large barocaloric effects, due to high ASr and large volume change (A 14) of ~7%. ^Predicted to display large inverse barocaloric effects due to A14, = -7%. hPredicted to display large barocaloric effects due to large A14 ~ 11%. However, the reversibility of the major transition requires further investigation. iPredicted to display large barocaloric effects due to large A14 of 2% and 5% for (CisH37)3NH+ and (CisH37)4N+, respectively. iFour successive transitions occur at a temperature range between 290 K and 330 K, with a major 5 transition around 305 K. The total entropy change is tabulated here. To probe reversibility and volume change, further investigations are required. Table 21. Summary of both gravimetric and molar thermodynamic properties of the phase transition in mixed-halide 2-D perovskites. The transition temperatures listed are heating values for the principal 10 transition, and the molar values were calculated based on the intended halide ratios. Chemical Formula Tlr (K) AH (kJ mol"1) AH (kJ kg"1) AS (J moF1 K’1) AS (J kg-1 K-1) (NAECuCh 295 26.8 51.7 86.1 174.3 (NAjjCuChBr 290 24 44.6 82.3 153.0 (NAhCuChBr? 286 17.9 30.8 62.5 107.2 (NA)2CuClBr3 292 16.4 26.1 56.1 89.5 (NAhCuBn 302 15 22.3 49.6 73.9 (DAhCuCU 309 34.5 66.2 111.4 213.5 (DAhCuChBr 308 25.6 45.3 83.3 147.1 (DAhCuCEBn 307 25.2 41.2 82.0 134.2 (DABCuCIBr? 309 19.8 30.2 64.2 97.9 (DAKuBn 317 18.1 25.9 57.3 81.9 Table 22. Summary of both gravimetric and molar thermodynamic properties of the phase transition in mixed-cation 2-D perovskites. Chemical Formula rtr (K) AH (kJ moF1) AH (kJ kg1) AS (J moF1 K1) AS (J kg-1 K-1) (NAKuCk 295 26.8 54.3 86.1 174.3 [,(NA)o.75(DA)o.25]2CuC14 290 19.0 44.6 65.5 130.7 [(NA)o.5(DA)o.5]2CuC14 291 22.0 43.2 75.6 148.9 [(NA)o.25(DA)o.75]2CuC14 297 21.7 26.1 72.9 141.6 (DA^CuCk 309 34.5 22.3 111.4 213.5 [(NA)o.5(UA)».5]2CuC14 282 20.6 39.4 72.8 139.4 15 Table 23. Summary of thermodynamic properties of the phase transition in compositionally engineered 2-D perovskites with promising barocaloric potentials. Chemical Formula (K) (kJ moF1) MT (kJ kg’1) AS' (J mol ’ K1) AS’ (J ka1 K1) (DAhCuChBr 308 25.6 45.3 83.3 147.1 (DAhCuChBn 307 25.2 41.2 82.0 134.2 (NAo.sDAos^CuCIj 291 22.0 43.2 75.6 148.9 (NAo.5UAo.5)2CuCl4 282 20.6 39.4 72.8 139.4 (NAo.sDAo.shCuCbBn 285 18.2 31.45 64.0 111.5 5 Table 24. Summary of thermodynamic trends for the five compounds identified as promising barocaloric materials. AThys is defined here as the difference between the peak transition temperature upon heating and the peak transition temperature upon cooling. Chemical Formula Tir (K) MT (kJ kg1) A.S (J kg"1 K1) dTMP (K kbar’) PFtv.aii (bar) VF.. (K) (DA^CuChBr 308 45.3 147.1 24.3 151 2.3 (DAhCuCljBij 307 41.2 134.2 25.8 129 2.3 (NAo.sDAe^’CuClj 291 43.2 148.9 22.4 166 1.6 (N Ao.sUAo shCuClj 39.4 139.4 25.1 176 2 2 (NAo.jDAos^CuChBra 285 31.45 111.5 24.1 161 2.6 10 Table 25. Summary of barocaloric properties for mixed halide and mixed cation perovskites. Here, AP is defined as the operating pressure required to achieve the maximum adiabatic temperature change, and is calculated as ATad,max / (d77dP). Note that cP for the low temperature phase is used for the calculations. Chemical Formula To (K> AS (J kg1 K ’) (W1) (K kbar ‘) (bar) (K) A1 (K) AP (bar) (DA)2CuChBr 308 147 1.50 24.3 151 2.3 27 1103 (DA^CuChBrs 307 134 1.41 25.8 129 23 26 989 (XA..:l>A, w.uCi 291 149 1.50 22.4 166 1.6 26 1163 (NAo.5UAt>.j)2CuCh 282 139 1.51 25.1 176 2.2 23 915 (NAojDAtOjCuChBn 285 112 1.34 24.1 161 2.6 21 866 15 Table 26. Phase-change properties of newly synthesized symmetric dialkylammonium salts. Preliminary characterizations through high-pressure differential scanning calorimetry (HP-DSC) in our lab or the Clausius-Clapeyron equation (dTtr / dP- AWAStr) indicate that these candidate compounds are all expected to display high pressure sensitivity (dTtr / dP) between 10-30 K kbar1. Note that the temperature of transition measured during the first heating scans are tabulated here. Candidates Ttr (°C) major (minor) △Thys AStr (°C) (J kg-1 K1) major (minor) △Str AStr (J L1 K 1) (J mol1 K 1) per chain (total) dTtr / dP (K kbar1) major (minor) (Ci2H25)(CH3)NH2Br 69.6 1.4 300 351 84 23.1 22.2 (Ci2H25)(CH3)NH2CI 61.1 (58.6); 58.6 (48.1) 2.5 350 (10.5) (14) 363 RR (15) 83 23.1 (36) 24.5 (42.7) Chemical Formula rtl (K) \S (kJ kg1) (J K-' kg dT / dP ~‘) (Kkbar1) (C6H!3)2NH2C1 277 59.5 215 (CsHnhNILCl 292 105.5 361 - (C i oil? i )2NH2C1 321 125.0 390 (CsHrOyNHzBr 295 88.3 308 (G^Wr 301 80.1 266 22-27 (C.:.ll 377 103.7 317 (C6Hb)2NH2I 284 56.6 199 (C8Hi2)2NH2I 285 47.7 167 16-25 (CmlfehNHJ 317 81.0 256 5 Table 27. Phase-change properties of newly synthesized asymmetric dialkylammonium salts. Preliminary characterizations through high-pressure differential scanning calorimetry (HP-DSC) indicate that these candidate compounds all display high pressure sensitivity (dTMP) between 20-30 K kbar1. Table 28. Unit cell parameters for (CnH2n+j)2NH2Br (n — 6,8,10) from single-crystal X-ray diffraction at ambient pressure. Compound T(K) *(A) c (A) af) fin 7 (°) l-qA’) Space Group (QHuhNTLBr 100 26.267(2) 5.3453(3) 10.7542(6) 90 98.299(1) 90 1494.14 Q / c <. H ) Kil =3« 100 5.372(2) 33.568(1) 5.279(2) 90 90 90 951.895 P2;2;2 100 5.3475(4) 39.886(3) 5.2758(4) 90 90 90 1125.28 P2;2.2 5 Table 29. Unit cell parameters for (Ci2H2s)N(CH3)H2X (X = Cl, Br) from single-crystal X-ray diffraction at ambient pressure at 100 K. Compound « (A) &(A) c (A) fin ?n Space Group (CuHaKCHONHsCl 4.8858(3) 5.2510(2) 29.585(1) 93.453(4) 94.633(4) 90.810(4) 755.012 / 7 (CJ2H>9(CH5)NH-Br 5 3299(4) 5.3390(4) 28.010(2) 90 90.581(3) 90 797.021 P2! Other embodiments are in the claims. What is claimed is: 21 05 25

Claims

1. A barocaloric system comprising:a) a composition comprising an organic layer between first and second inorganic layers or wherein the organic layer comprises a head group capable of hydrogen bonding, halogen bonding, and / or electrostatic interaction with a counterion; wherein the composition is selected from:(i) a 2D perovskite composition, comprising:an organic layer comprising optionally substituted C>4 alkyl chains; anda transition metal halide; and(ii) a di-n-alkylammonium salt composition, comprising:a compound of formula (CnH2n+1)2NH2X wherein n >3 and X is a halide; ora compound of formula (CnH2n+i)(CmH2m+i)NH2X, wherein n = 1-3 or 4-36 and m = 4-36, and X is a halide; andb) a source of compression.

2. The barocaloric system of claim 1, further comprising:c) a pressure transmitting medium (PTM), wherein the PTM is capable of inducing a change in a thermal property of the composition;d) a pump;e) a heat sink; orf) a power source.

3. The barocaloric system of any one of claims 1 or 2, wherein the organic layer of the 2D perovskite composition comprises substituted C>4 alkyl chains.

4. The barocaloric system of any one of claims 1-3, wherein the organic layer of the 2D perovskite composition comprises an alkyl ammonium species selected from:

5. The barocaloric system of any one of claims 1-4, wherein the organic layer is an organic bilayer.

6. The barocaloric system of any one of claims 1-5, wherein the organic layer comprises two different molecular structures.

7. The barocaloric system of any one of claims 1-6, wherein the composition comprises a compound of the following table:Type Chemical Formula (OA)2MnCI4 2-D perovskite (DA)2MnCI4 (NA)2MnCI4 (NA)2CuCI4 (DA)2CuCI4 Mixed 2D perovskites (NA)2CuCI3Br (NA)2CuCI2Br221 05 25(NA)2CuCIBr3 (DA)2CuCI3Br (DA)2CuCI2Br2 (DA)2CuCIBr3 [(NA)o.75(DA)o.25]2CuCl4 [(NA)os(DA) o.5]2CuCl4 [(NA)o.25(DA)o.75]2CuCl4 [(NA)o.25(UA)o.75]2CuCl4 [(NA)os(UA) O5]2CUCI4_____________________________[(NA)q5(DA) o.5]2CuCI2Br2 (n-C6Hi3)2NH2Br (n-C8Hi7)2NH2CI (n-C6Hi3)2NH2CI (n-C6Hi3)2NH2l (n-C8Hi7)2NH2Br (n-Ci2H25)2NH2CI (n-C8Hi7)2NH2lDi-n-alkyl ammonium salt (n-CioH2i)2NH2CI (n-CioH2i)2NH2Br (n-CioH2i)2NH2l (n-Ci2H25)2NH2Br (n-Ci8H37)2NH2CI (n-Ci8H37)2NH2Br (n-Ci2H25)(CH3)NH2Br (n-Ci2H25)(CH3)NH2CI8. The barocaloric system of any one of claims 1-6, wherein the di-n-alklyl ammonium salt composition comprises a compound of formula (CnH2n+i)(CmH2m+i)NH2X, wherein n is 1-3 or 4-36 and m = 4-36; and wherein X is a halide.

9. The barocaloric system of claim 8, wherein n = m and n = 4-36 or wherein n = 1 -3 and m = 4-36.

10. The barocaloric system of any one of claims 1-6, wherein the 2D perovskite composition is of formula [(R1)x(R2)i-x]2MXyX'4-y, wherein R1 and R2 are independently optionally substituted alkylammonium21 05 25species, wherein X and X’ are different halides, wherein x is between 0-1, wherein y is 0-4, wherein M is a transition metal; and wherein if y = 0 or 4, R1 £ R2 and x £ 0 or 1.

11. The barocaloric system of any one of claims 2-10, wherein the pressure transmitting medium (PTM) comprises a fluid.

12. The barocaloric system of any one of claims 2-11, wherein the pressure transmitting medium (PTM) comprises a gas, a liquid, or a vapor.

13. The barocaloric system of any one of claims 2-12, wherein the pressure transmitting medium (PTM) comprises a gas.

14. The barocaloric system of any one of claims 2-12, wherein the pressure transmitting medium (PTM) comprises a liquid.

15. The barocaloric system of any one of claims 2-12, wherein the pressure transmitting medium (PTM) comprises a vapor.

16. The barocaloric system of any one of claims 12 or 13, wherein the gas comprises a non-interacting gas, a minimally interacting gas, ora polarizable gas.

17. The barocaloric system of claim 14, wherein the liquid comprises a hydrocarbon.

18. The barocaloric system of any one of claims 2-17, wherein the pressure transmitting medium (PTM) is able to permeate a free volume of the organic layer.

19. The barocaloric system of claim 18, wherein the permeated pressure transmitting medium (PTM) is able to interact with the composition.

20. The barocaloric system claim 19, wherein an extent of permeation and interaction of the pressure transmitting medium (PTM) into or with the composition together induce a lowering of a phase transition and / or a barocaloric effect inversion.

Images