Polyelectrolyte complexes for critical mineral recovery

Abstract

A method for extracting one or more cations from a solution may include forming a polyelectrolyte complex by mixing a polycation and a polyanion. An aqueous solution including the one or more cations may be obtained. The polyelectrolyte complex and the aqueous solution may be mixed such that the one or more cations may associate with the polyelectrolyte complex. The polyelectrolyte complex including the one or more cations may be separated from the aqueous solution. The one or more cations may be extracted from the polyelectrolyte complex.

Description

POLYELECTROLYTE COMPLEXES FOR CRITICAL MINERAL RECOVERYCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This patent application claims priority to U.S. Provisional Application No. 63 / 656,834 filed June 6, 2024, which provisional is incorporated herein by specific reference in its entirety.BACKGROUNDField:

[0002] The present disclosure relates to polyelectrolyte complexes and / or materials prepared from polyelectrolyte complexes for use in extraction of critical minerals (e.g., lithium) from various sources, whether natural, industrial, or recyclable sources. of Related Art:

[0003] Critical minerals are essential natural resources that play a crucial role in various industries, particularly in the domains of technology, energy, and defense. These minerals are considered critical due to their significant economic and strategic importance, as well as their limited availability and potential supply chain vulnerabilities. Critical minerals may be defined under the US Department of Energy (DOE) designation, which at the time of filing of this application includes aluminum, cobalt, copper, dysprosium, electrical steel, fluorine, gallium, iridium, lithium, magnesium, natural graphite, neodymium, nickel, platinum, praseodymium, terbium, silicon, and silicon carbide, where strontium also may be considered a critical even though it is not on the official list.

[0004] Lithium is one of the important critical minerals. Lithium, a highly reactive alkali metal situated in the s-block of the periodic table, has become a critical component in numerous commercial applications. Lithium is particularly indispensable in the manufacturing of lithium-ion batteries (LIBs), which are widely used in electric vehicles, portable electronics, and renewable energy storage systems and other industries such as glass, ceramics, lubricants, and pharmaceuticals. However, the extraction of lithium ions is not without its challenges, both technical and environmental.

[0005] A Lithium ion (Li+) is a positively charged ion, belonging to the alkali metal group on the periodic table. It has the lowest density of all metals, making it highly lightweight. Lithium ions exhibit exceptional electrochemical performance, producing high energy density and extending battery life, which is the key reason for their wide application. Additionally, lithium is highly reactive and can store and release large amounts of energy with remarkable efficiency.

[0006] Two prominent and available source of critical minerals like Lithium are continental brines and critical-mineral containing ores. Due to increasing demand for critical minerals, the supply of critical minerals are increasingly constrained and concerns have been raised regarding the security and sustainability of the supplies from these resources. For example, just eight areas provide more than 60% of the world’s lithium production: The Clayton Valley in the United States, Salar de Atacama 1 and 2 in Chile, Salar del Hombre Muerto and Salar de Olaroz in Argentina, Lake Zabuye, Dongtai Salt Lake, and Xitai Salt Lake in China. Ensuring a secure and sustainable supply of critical minerals like lithium has become a priority for many countries, especially those heavily reliant on technologies and industries that require these resources. Efforts are being made to diversify the sources of lithium and invest in advanced extraction technologies to optimize production. Additionally, recycling and recovery initiatives are being promoted to minimize resource depletion and waste generation.

[0007] Thus, more attention is being drawn to other sources of Li, such as spent LIBs, geothermal waters, and oilfield brines. These waters may include critical minerals in large enough concentrations for economically feasible extraction. For example, the USA has commercially viable oilfield brines with concentrations high enough for economic extraction. For instance, brines from the Jurassic Smackover Formation in Texas and Arkansas have a lithium concentration ranging from 50 to 572 mg / L, brines from Texas Cretaceous reservoirs have a lithium concentration ranging from 132-333 mg / L, and brines from the Devonian formations in the Williston Basin (North Dakota) have lithium concentrations ranging from 100 and 288 mg / L of Li+.

[0008] Currently, the primary technologies for concentrating lithium from brine sources include techniques like solvent extraction, evaporation precipitation, membrane separation, lithium-ion sieve adsorption, and electrochemical recovery. However, these techniques may not achieve low energy consumption, pollution-free operation, and / or high-efficiency production. The evaporation precipitation method is time-consuming and energy-intensive; solvent extraction generates waste and is susceptible to fire risks; the ion sieve adsorption method faces issues with the powder material dissolving; membrane separation suffers from permeability and selectivity trade-off, and is challenging to scale; and electrochemical methods consume high energy and are susceptible to electrode fouling.

[0009] Accordingly, there is a need to develop an efficient and economically feasible technique of extraction to meet the increasing global demand for critical minerals, such as lithium. The present disclosure focuses on critical mineral extraction from brines usingpolyelectrolyte complexes such as those formed from a polycation such as polyethyleneimine and polyanions such as dextran sulfate and using nanoparticles made from polyelectrolyte complexes. Furthermore, the polyelectrolyte complexes described throughout this disclosure may be utilized in conjunction with membranes to improve the selectivity of the membranes.SUMMARY10010J In some embodiments, a method for extracting one or more cations from a solution may be provided. The method may include obtaining an aqueous solution including the one or more cations. The method may include forming a polyelectrolyte complex by mixing a polycation and a polyanion. The method may include mixing the polyelectrolyte complex and the aqueous solution, wherein the one or more cations may associate with the polyelectrolyte complex. The method may include separating the polyelectrolyte complex including the one or more cations from a supernatant portion. The method may include extracting the one or more cations from the polyelectrolyte complex.

[0011] In some embodiments, the one or more cations may include at least one of a monovalent metal ion, a divalent metal ion, or a trivalent metal ion. In some aspects, the one or more cations may be selected from the group consisting of: aluminum, cobalt, fluorine, gallium, iridium, lithium, magnesium, natural graphite, neodymium, nickel, platinum, praseodymium, terbium, silicon, bromine, manganese, sodium, potassium, boron, zinc, tungsten, lanthanum, cerium, cesium, strontium, barium, promethium, samarium, europium, gadolinium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or combinations thereof.

[0012] In some embodiments, the polycation may be selected from chitosan, polyethyleneimine, poly(di allyldimethylammonium halide), poly(diallyldimethylammonium chloride), poly D-Lysine, poly allylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof. In some aspects, the polyanion may be selected from dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of polymethacrylic acid, an alkali metal salt of 3-sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

[0013] In some embodiments, the polycation may include polyethyleneimine and the polyanion may include dextran sulfate. In some aspects, the one or more cations may include lithium, and the lithium may be entrapped in the polyelectrolyte complex nanoparticle via interactions between the lithium and -NH2 groups of thepolyethyleneimine and -SO3’ groups of dextran sulfate. In some embodiments, the one or more cations may be entrapped in the polyelectrolyte complex nanoparticle via interactions between positive groups of the polycation and negative groups of the polyanion.

[0014] In some embodiments, the aqueous solution may include a brine. In some aspects, the brine may have a lithium content of less than about 1000 mg / L. In some aspects, the brine may be produced from a geologic reservoir.

[0015] In some embodiments, at least one of: the polyelectrolyte complex may have a mass ratio of the polycation to the poly anion between about 0.1 and about 20; the aqueous solution may have a pH between about 3 and about 10; a concentration of the poly cation in the aqueous solution may be between about 0.01% (w / w) and about 20% (w / w); a concentration of the polyanion in the aqueous solution may be between about 0.01% (w / w) and about 20% (w / w); the polyelectrolyte complex may form a nanoparticle having a zeta potential with an absolute value between about 0 mV and about 50 mV; or the nanoparticle may have a diameter of less than about 1000 nm.

[0016] In some embodiments, at least one of: the polycation to polyanion mass ratio may be between about 1 and about 20; the concentration of the polycation in the aqueous solution may be between about 0.01% (w / w) and about 10% (w / w); or the concentration of the polyanion in the aqueous solution may be between about 0.01% (w / w) and about 10% (w / w).

[0017] In some embodiments, nanoparticles may be formed by mixing the polycation with the polyanion, the nanoparticles having a polydispersity of between about 0.1 and about 4.00. In some aspects, the method may further include, after mixing the polyelectrolyte complex and the aqueous solution, recovering no excess poly electrolytes, or at least one of an excess polycation or an excess polyanion from the supernatant portion.

[0018] In some embodiments, the polyelectrolyte complex may be formed in solution or on a surface to form monolayer or multi-layer complexes. In some aspects, the supernatant portion may include an excess of the one or more cations, and the method may further include: forming a second polyelectrolyte complex by mixing a second polycation and a second polyanion; mixing the second polyelectrolyte complex and the supernatant portion, wherein at least a portion of the excess of the one or more cations in the supernatant portion may associate with the second polyelectrolyte complex; separating the second polyelectrolyte complex including the portion of the excess from a second supernatant portion; and extracting the portion of the excess from the second polyelectrolyte complex.

[0019] In some embodiments, the method may further include contacting the aqueous solution with a membrane, the membrane configured to extract at least one of the one or more cations, or one or more additional cations from the aqueous solution. In some aspects, the method may further include removing divalent cations from the aqueous solution before mixing the polyelectrolyte complex and the aqueous solution.

[0020] In some embodiments, the one or more cations may be extracted from the polyelectrolyte complex via gas separation. In some aspects, the polyelectrolyte complex may be formed in the aqueous solution. In some embodiments, the one or more cations may include lithium ions, and the lithium ions may be entrapped by the polyelectrolyte complex at an extraction efficiency between about 5% and about 82%.

[0021] In some embodiments, a polyelectrolyte complex nanoparticle for extracting one or more cations from an aqueous solution may be provided. The polyelectrolyte complex nanoparticle may include a polycation. The polyelectrolyte complex nanoparticle may include a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0. 1 and about 20. The polyelectrolyte complex nanoparticle may include one or more association sites. In some embodiments, at least a first association site of the one or more association sites may electrostatically associate with at least one of the one or more cations from the aqueous solution. In some embodiments, the one or more association sites may include a plurality of association sites that each electrostatically associate with at least one of the one or more cations from the aqueous solution. In some aspects, the cations may be sterically entrapped in the polyelectrolyte complex nanoparticle.

[0022] In some embodiments, the polycation may be selected from the group consisting of: chitosan, polyethyleneimine, poly(diallyldimethylammonium halide), poly (diallyldimethylammonium chloride), poly D-Lysine, poly allylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof. In some aspects, the polyanion may be selected from the group consisting of: dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, poly acrylic acid, an alkali metal salt of poly methacrylic acid, an alkali metal salt of 3- sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

[0023] In some embodiments, the polycation may include polyethyleneimine and the polyanion may include dextran sulfate. In some aspects, the one or more cations may include lithium ions, and wherein the lithium ions may be entrapped in the polyelectrolyte complex nanoparticle via interactions between the lithium ions and at least one of NH2 groups of the polycation or SCh groups of the polyanion.

[0024] In some embodiments, the one or more cations may be entrapped in the polyelectrolyte complex nanoparticle via interactions between positive groups of the polycation and negative groups of the polyanion. In some aspects, the polyelectrolyte complex nanoparticle may have a mass ratio of the polycation to the polyanion between about 1 and about 10.

[0025] In some embodiments, the polyelectrolyte complex nanoparticle may have at least one of: a diameter of less than about 1000 nm or a zeta potential with an absolute value between about 0 mV and about 50 mV.

[0026] In some embodiments, a polyelectrolyte complex nanoparticle may be provided. The polyelectrolyte complex nanoparticle may include a polycation. The polyelectrolyte complex nanoparticle may include a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0.1 to about 20. The polyelectrolyte complex nanoparticle may include one or more cations associated with one or more association sites of the polyelectrolyte complex nanoparticle formed by the complexation of the polycation and the polyanion.

[0027] In some embodiments, the one or more cations may be entrapped in the polyelectrolyte complex nanoparticle (1) sterically and / or (2) via interactions between positive groups of the polycation and negative groups of the polyanion.

[0028] The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.BRIEF DESCRIPTION OF THE FIGURES

[0029] The foregoing and following information as well as other features of this disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several embodiments in accordance with the disclosure and are, therefore, not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings.

[0030] Fig. 1A illustrates an example critical mineral extraction process using a polyelectrolyte complex.

[0031] Fig. IB illustrates transmission electron microscopy (TEM) images of a polyelectrolyte complex formed by PEI and DS prepared in the presence of reverse osmosis-deionized (RO-DI) water (left) and prepared in lithium chloride brine (right).

[0032] Fig. 2A illustrates a workflow for determining PEI or DS concentration from total organic carbon (TOC) and total organic nitrogen (TON) of a supernatant of a polyelectrolyte complex solution.

[0033] Fig. 2B illustrates a TON vs. TOC calibration chart that may be used in determining the TOC of PEI in the workflow of Fig. 2A.

[0034] Fig. 2C illustrates a TOC vs. PEI concentration chart that may be used in determining the PEI concentration in the workflow of Fig. 2A.

[0035] Fig. 2D illustrates a TOC vs. DS concentration chart that may be used in determining the DS concentration in the workflow of Fig. 2A.

[0036] Fig. 3 illustrates a scale of observed cloudiness for different PELDS Mass Ratios solutions.

[0037] Fig. 4A is a chart illustrating polydispersity index for different PELDS mass ratios of a 10 wt.% PELDS paired concentration solution.

[0038] Fig. 4B is a chart illustrating polydispersity index for different PELDS mass ratios of a 9 wt.% PELDS paired concentration solution.

[0039] Fig. 4C illustrates a 2D contour plot of polydispersity index as a function of PELDS mass ratio and PELDS pairwise concentration (wt.%) at a pH of 4.5.

[0040] Figs. 5A-5G illustrate scatter-plots of nanoparticle size vs. PELDS mass ratio at varying wt.% of PEI and DS.

[0041] Figs. 6A-6E are charts illustrating nanoparticle size and extraction efficiency of lithium as a function of nanoparticle composition for different pHs. For each figure, the first digit is the PELDS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation;

[0042] Fig. 7 is a chart showing PEI and DS TOC data in the supernatant as a function of nanoparticle composition for different PELDS mass ratios at a pH of 5 and a PELDS pairwise concentration of 9 wt.%. For each composition, the first digit is the PELDS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation.

[0043] Figs. 8A-8C are charts illustrating nanoparticle zeta potential as a function of PELDS mass ratio at varying paired PELDS concentrations.

[0044] Fig. 8D is a chart illustrating zeta potential as a function of nanoparticle size at the paired PELDS concentration of Fig. 8C.

[0045] Figs. 8E and 8F are 2D contour plots illustrating zeta potential as a function of PELDS mass ratio and PELDS pairwise concentration (wt.%) at a pH of 4.5 respectively for positively charged particles and negatively charged particles.

[0046] Fig. 9 is a chart illustrating unprotonated nitrogen of PEI as a function of pH.

[0047] Figs. 10A-10D are charts illustrating extraction efficiency of lithium in the aqueous solution as a function of PELDS mass ratio at varying concentrations of PEI and DS and varying pH.

[0048] Fig. 11 is a chart illustrating extraction efficiency of lithium in the aqueous solution as a function of nanoparticle size.

[0049] Figs. 12A-12D are charts illustrating extraction efficiency of lithium as a function of nanoparticle compositions. For each figure, the first digit is the PEEDS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation.

[0050] Figs. 13A is a chart illustrating extraction efficiency as a function of DS:PEI ratio in the supernatant.

[0051] Fig. 13B is a chart illustrating extraction efficiency as a function of PELDS ratio in the supernatant.

[0052] Fig. 14 illustrates an example process of sequential critical mineral extraction using a polyelectrolyte complex.

[0053] Fig. 15 is a chart illustrating a normal distribution of extraction efficiency for different polyelectrolyte complexes.

[0054] The elements and components in the figures can be arranged in accordance with at least one of the embodiments described herein, and which arrangement may be modified in accordance with the disclosure provided herein by one of ordinary skill in the art.DETAILED DESCRIPTION

[0055] In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are explicitly contemplated herein.

[0056] Polyelectrolyte complexes form when oppositely charged polyelectrolytes interact through electrostatic forces. The poly electrolyte complexes discussed throughout the disclosure may be formed by the interaction of cationic polyelectrolytes (e.g., polycations) and anionic polyelectrolytes (e.g., polyanions), each polyelectrolyte contributing distinct groups that interact electrostatically. For example, the polycation may include positively charged groups, such as amine groups, while the polyanion may include negatively charged groups, such as sulfate or carboxylate groups. The formation of these complexes may be influenced by various factors including the molecular weight of the polymers used, the charge density of the polyelectrolytes, the mass ratio of polycation to polyanion, the pH of the environment, the presence of salts or other ionic species in the solution, among others.

[0057] Polyelectrolyte complex nanoparticles (PECNP) represent a specific morphological form of a polyelectrolyte complex where the polyelectrolyte complex assembles into discrete particles at the nanoscale, typically ranging from 10 to 1000 nanometers in diameter. These nanoparticles form through controlled mixing of oppositely charged polyelectrolytes under specific conditions that favor particulate formation rather than bulk precipitation or gel formation. The size, charge, stability, and internal structure of these nanoparticles may be tailored by adjusting parameters such as the polyelectrolyte mass ratio, the polyelectrolyte concentration, pH, ionic strength, and mixing protocol.

[0058] PECNP are charged nanoparticles formed by mixing anionic and cationic polyelectrolytes in non-stoichiometric ratios. Using polyelectrolyte complexes for critical mineral extraction may lead to advantages such as cost-efficiency, the absence of a need for specialized equipment, production of a high-purity final product, simple phase separation, minimal operational costs, suitability for solutions with low concentrations of critical minerals, and / or the elimination of the need for inorganic materials and various organic solvents that are susceptible to fire risks.

[0059] Generally, the present technology relates to critical mineral (e.g., lithium) extraction from aqueous media using polyelectrolyte complexes (e.g., polyelectrolyte complex nanoparticles). The polyelectrolyte complexes may be present in compositions and systems adapted for extraction of the critical mineral from a source material. The polyelectrolyte complexes may electrostatically associate with critical mineral cations to entrap the critical mineral cations in the polyelectrolyte complexes. The complex may then be separated out of the extraction system, such as by centrifugation, precipitation, or filtration, among other techniques. Then, the critical element ions may be extracted from the polyelectrolytecomplexes, such as by adding counter anions to compete with and dissociate the polyelectrolyte complex from the critical element cations.

[0060] For example, in lithium extraction, the lithium ions (Li+) in an aqueous solution may interact with sulfate (SO3 ) groups of dextran sulfate and the amine (NH2 or charged ammonium ion NH3+) groups of polyethyleneimine. This may result in the formation of a stable complex wherein the lithium ions are effectively entrapped within the polyelectrolyte complex and / or the polyelectrolyte complex may otherwise electrostatically associate with the lithium ions.

[0061] In practical applications, such as in the recovery of critical minerals from brines, the polyelectrolyte complexes may be introduced into the critical mineral-containing solution. During and / or after mixing, the critical mineral ions may associate with the polyelectrolyte complex and may later be separated from the solution, such as by centrifugation, filtration, or precipitation, among other techniques. The critical mineral- loaded polyelectrolyte complexes may then be processed to extract the critical mineral ions, which may be further purified and used in various applications. For example, lithium ions may be extracted from the polyelectrolyte complex and used in lithium ion batteries.

[0062] Thus, critical minerals may be recovered from brines produced from geologic reservoirs, such as oil and gas reservoirs or geothermal reservoirs using polyelectrolyte complexes. These produced brines have typically been considered as a waste byproduct from extraction of other resources. However, by utilizing polyelectrolyte complexes to extract critical minerals from produced brines, a new source of critical minerals may be unlocked, which may enhance critical mineral supply and recovery and mitigate the environmental impact of industrial waste. By leveraging the properties of polyelectrolyte complexes, these brines can be transformed from waste to resource, providing a cost- effective and environmentally friendly solution to mineral extraction challenges.

[0063] Moreover, the complex formation between lithium ions and poly electrolyte complexes like PECNPS may be utilized in the preparation of secondary compositions. The resulting complex may serve as a precursor for the preparation of useful materials. This approach may provide a sustainable and economically viable method for obtaining lithium- based secondary compositions, which may find applications in diverse fields, including energy storage, catalysis, and materials science.

[0064] Fig. 1A illustrates an example critical mineral extraction process 100. The example critical mineral extraction process 100 is shown as having a first stage 102a, a second stage 102b, and a third stage 102c for illustrative purposes. Although the stages 102a, 102b, andstages, various stages may be divided into additional stages, expanded, and / or consolidated.

[0065] An aqueous solution 104 may be obtained. In some embodiments, the aqueous solution 104 may include one or more critical mineral cations 112. In some embodiments, the aqueous solution 104 may be a brine. In these and other embodiments, the aqueous solution 104 may be a produced brine such as a brine produced from a geologic reservoir (e.g., an oil and gas reservoir, a geothermal reservoir, or other geologic reservoirs). In some embodiments, the critical mineral cations 112 may be lithium cations (Li+) and the aqueous solution 104 may have a lithium content of less than about 1000 mg / L.

[0066] In some embodiments, the aqueous solution may have a pH between about 3 and about 10, between about 3 and about 8, between about 3 and about 6, between about 5 and about 10, between about 4 and about 5, among other ranges of pH. In these and other embodiments, the pH may be about 4.5. In some embodiments, the pH of the aqueous solution 104 may be adjusted to within the previously described ranges in response to the pH being outside of these ranges.

[0067] The critical mineral cations 112 may be monovalent, divalent, and / or trivalent ions. In some embodiments, the critical mineral cations 112 may be metal ions. In some embodiments and as illustrated in Fig. 1A, the critical mineral cations 112 may be lithium ions. In some embodiments, the critical mineral cations 112 may be aluminum, cobalt, fluorine, gallium, iridium, lithium, magnesium, natural graphite, neodymium, nickel, platinum, praseodymium, terbium, silicon, bromine, manganese, sodium, potassium, boron, zinc, tungsten, lanthanum, cerium, cesium, strontium, barium, promethium, samarium, europium, gadolinium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or combinations thereof.

[0068] A polycation 108 (e.g., a cationic polyelectrolyte) and a polyanion 110 (e.g., an anionic polyelectrolyte) may be introduced to the aqueous solution 104. In some embodiments, the polycation 108 may be chitosan, polyethyleneimine, poly(diallyldimethylammonium halide), poly(diallyldimethylammonium chloride), poly D-Lysine, polyallylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof. In some embodiments, the polyanion 110 may be dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of poly methacrylic acid, an alkali metal salt of 3- sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

[0069] In some embodiments, the polycation 108 and the polyanion 110 may be prepared in separate solutions before being added to the aqueous solution 104 and / or the prepared polycation 108 solution and poly anion 110 solution may be mixed before being added to the aqueous solution 104. In these and other embodiments, the concentration of the polycation 108 and the polyanion 110 in the aqueous solution may be between about 0.01% (w / w) and about 20% (w / w), between about 0.1% (w / w) and about 10% (w / w), or between about 1% (w / w) and about 10% (w / w), among other concentration ranges.

[0070] In some embodiments, the polycation 108 is polyethyleneimine (PEI) and the polyanion 110 is dextran sulfate (DS).

[0071] As illustrated in Fig. 1A, the aqueous solution 104 may be mixed with a mixer 106 during the first stage 102a. As illustrated, the mixer 106 is a magnetic stirrer that may be used in a lab-setting, but other mixers 106 may be used depending on the size and / or scale of the critical mineral extraction process 100. For example, in some embodiments, the mixer 106 may be a stirred tank mixer (e.g., an agitated tank), a propeller driven mixer, a magnetic stirrer, a paddle mixer, a vortex mixer, a static mixer, a jet mixer, or any other mixer capable of mixing the aqueous solution 104. In some embodiments, divalent cations may be removed from the aqueous solution 104 before mixing.

[0072] As illustrated in the second stage 102b, the mixing of the aqueous solution 104 may form one or more poly electrolyte complexes 114. The mixer 106 may facilitate the effective interaction between the polycation 108 and the polyanion 110, leading to the formation of polyelectrolyte complexes 114. In some embodiments, the polyelectrolyte complexes 114 may be formed in a different solution than the aqueous solution 104 and may be introduced to the aqueous solution 104 after already having been formed. For example, the polyelectrolyte complexes 114 may be formed in a separate container than the aqueous solution 104 and may be added to the aqueous solution 104 after having been formed.

[0073] The polyelectrolyte complexes 114 may be formed when the positively charged groups of the polycation 108, such as amine groups, interact electrostatically with the negatively charged groups of the polyanion 110, such as sulfate or carboxylate groups. The efficiency of this interaction and the stability of the resulting complexes may be influenced by several factors, including the molecular weight of the polymers, the charge density of the polyelectrolytes, the mass ratio of the polycation 108 to the polyanion 110, and the environmental conditions such as pH of the aqueous solution 104, the pH of the polycation 108 solution, the pH of the polyanion 110 solution, and / or the ionic strength of the solution.

[0074] In some embodiments, the polyelectrolyte complexes 114 may be PECNPs. In these and other embodiments, a zeta potential of the formed PECNPs may have an absolute value of between about 0 mV and about 100 mV, between about 0 mV and about 70 mV, between about 0 mV and about 50 mV, between about 0 mV and about 30 mV, among other ranges of zeta potential. In some embodiments, the PECNPs may have a diameter of less than about 1000 nm, less than about 900 nm, less than about 800 nm, less than about 700 nm, less than about 600 nm, less than about 500 nm, less than about 400 nm, less than about 300 nm, less than about 200 nm, less than about 100 nm, or less than about 50 nm. In some embodiments, the PECNPs may have a polydispersity index (the smaller the PDI the more uniform the dimensions of the nanoparticles) between about 0.1 and about 4.00, between about 0 and about 0.75, between about 0 and about 0.5, between about 0.1 and about 0.5, between about 0. 1 and about 0.3, among other ranges.

[0075] In some embodiments, the polyelectrolyte complexes 114 may have a polycation 108 to polyanion 110 mass ratio between about 0.1 to about 20, between about 0.1 and about 10, between about 0.5 and about 10, between about 1 and about 7, or between about 4 and about 5, among other ranges.

[0076] During the second stage 102b and / or the third stage 102c, the polyelectrolyte complexes 114 may associate with the critical mineral cations 112 present in the aqueous solution 104. This association may be driven by electrostatic interaction between the critical mineral cations 112 and the polyelectrolyte complexes 114, where groups within the polyelectrolyte complexes 114 attract and associate with the charged critical mineral cations 112. For example, unprotonated NH groups of the polycation 108 and / or SO4"2or SO3" groups of the polyanion 110 may associate with the critical mineral cations 112.

[0077] For instance, unprotonated amine groups of PEI may serve as association sites for lithium ions, and the sulfate or sulfonate groups of dextran sulfate (DS) may interact with lithium ions through electrostatic interactions. These unprotonated amine groups may associate with Li+ ions through the lone pair of electrons on the nitrogen atom. This coordination may be represented as NH2 + Li-i- — NFE- • • Li+, where the nitrogen's lone pair donates electrons to the lithium ion. The coordination between unprotonated NH2 groups and Li+may be stronger than the hydration of Li+in aqueous solutions, which may contribute to the extraction efficiency of the polyelectrolyte complex 114. The sulfate (SO4"2) groups of dextran sulfate and / or or sulfonate (SO3 ) groups of other similar polyanions may interact with lithium ions through electrostatic interactions. These negatively charged groups may attract the positively charged lithium ions, forming ion pairs. This interactionmay be represented as SO4’2+ Li+— SO42- ■ -Li+or SO3’ + Li+— > SO3 ■ • -Li+. The strength of these electrostatic interactions may depend on various factors including the ionic strength of the solution, the pH, and the presence of competing ions. When both unprotonated NH2 groups and SO4-2 / SO3" groups are present in the polyelectrolyte complex 114, these groups may work simultaneously to extract the critical mineral cations 112. For example, FTIR analysis of the polyelectrolyte complexes 114 with and without lithium reveal shifts in the vibrational frequencies of both amine and sulfate / sulf onate groups, indicating that both are involved in lithium binding.

[0078] During the second stage 102b and / or the third stage 102c, the polyelectrolyte complexes 114 may be formed and one or more critical mineral cations 112 may be associated with the polyelectrolyte complexes 114. For example, the critical mineral cation 112 may be lithium as illustrated, and the lithium may be entrapped in the polyelectrolyte complex via interactions between the lithium and the amine groups of the PEI and the sulfonate groups of DS. Thus, one or more of the critical mineral cations 112 may be extracted from the aqueous solution 104.

[0079] As illustrated in the third stage 102c, the mixer 106 may be stopped. In some embodiments, the polyelectrolyte complexes 114 may form precipitates and may settle in the container after the mixer 106 has been stopped. For example, in the third stage 102c the polyelectrolyte complexes 114 are shown as having settled in the aqueous solution 104 to the bottom of the container leaving a supernatant 116 above the settled poly electrolyte complexes 114. As the magnified view of one of the poly electrolyte complexes 114 illustrates, the polyelectrolyte complexes 114 may entrap one or more critical mineral cations 112.

[0080] However, in some embodiments, the extraction efficiency of the critical mineral cations 112 may not be 100%. Thus, in some embodiments, the supernatant 116 may include excess critical mineral cations 122. For example, the supernatant 116 may include excess lithium ions that have not been associated with a polyelectrolyte complex 114. Furthermore, some of the polycations 108 and the polyanions 110 may not form polyelectrolyte complexes 114. As a result, one or more excess polycations 118 and / or one or more excess polyanions 120 may be present in the supernatant 116. For example, the supernatant 116 may include excess PEI and / or excess DS that have not formed polyelectrolyte complexes 114. In some embodiments, the polyanion 110 may be the limiting reactant, and there may be less excess polyanions 120 than excess polycations 118.

[0081] In some embodiments, the polyelectrolyte complexes 114 may be separated from the aqueous solution 104 and / or the supernatant 116. In some embodiments, separation may be achieved via centrifugation, precipitation, filtration, charged membrane separation, and / or gas separation among other techniques for separating polyelectrolyte complexes 114 from a solution. These techniques utilize different physical principles to isolate the polyelectrolyte complex 114, providing flexible options to meet a variety of separation needs. Centrifugation relies on the application of centrifugal force to separate particles in a liquid according to their density. Centrifugation may effectively separate the poly electrolyte complexes 114 based on the different mass and buoyancy properties of the polyelectrolyte complexes 114. By subjecting the aqueous solution 104 to high speeds of rotation, the heavier poly electrolyte complexes 114 may be forced to sediment, while the lighter supernatant 116 may be removed and collected.

[0082] In some embodiments, precipitation separation techniques may be employed. Precipitation involves the formation of insoluble solid particles from a solution. By manipulating the chemical environment of the aqueous solution 104, formation of a solid phase may be induced as illustrated in Fig. 1A, effectively separating the polyelectrolyte complexes 114 with the entrapped critical mineral cations 112 from the remaining solution. Subsequent filtration may then be used to isolate the precipitate.

[0083] For example, filter membranes with specific pore sizes may selectively retain the polyelectrolyte complexes 114 while allowing the clear filtrate to pass through, ensuring a high degree of separation and purity. In some embodiments, charged membrane separation, a technique leveraged when the separation is based on the electrical charge of the polyelectrolyte complex 114 may be employed. This technique uses a membrane with specific charge properties to selectively bind and retain the poly electrolyte complex 114, while allowing the other components to pass through. By manipulating the electrostatic interactions between the polyelectrolyte complexes 114 and the charged membrane, separation may be achieved. In some embodiments, the poly electrolyte complexes 114 may be part of the charged membrane, such as being formed into the membrane, or may be attached to a membrane, which may form a charged membrane due to the charge of the polyelectrolyte complexes 114.

[0084] After the polyelectrolyte complexes 114 have been separated from the aqueous solution 104 and / or supernatant 116, the one or more captured critical mineral cations 112 may be extracted from the polyelectrolyte complexes 114. For example, lithium ions may be removed from the polyelectrolyte complexes 114. There are several techniques that havebeen developed to facilitate the extraction of critical mineral cations from polyelectrolyte complexes 114. Precipitation methods involve the addition of reagents to the polyelectrolyte complexes 114 in order to form insoluble compounds that can be easily separated, thereby facilitating the extraction of critical mineral cations 112 such as lithium. Another technique to extract critical mineral cations 112 from the poly electrolyte complexes 114 is by utilizing secondary compositions. These secondary compositions may be designed to possess anions with a higher affinity towards the captured critical mineral cations 112 than the polyelectrolyte complexes 114. By introducing such secondary compositions, the critical mineral cations 112 may be extracted from the polyelectrolyte complexes 114, allowing for the separation and recovery of the critical mineral cations 112. The polyelectrolyte complexes 114 may also be subjected to different conditions, such as changes in pH or temperature, to disrupt the polyelectrolyte complexes 114 and release the critical mineral cations 112.

[0085] In some embodiments, the critical mineral cations 112 may be extracted from the polyelectrolyte complexes 114 via gas separation. In these embodiments, a gas may be introduced to the polyelectrolyte complex 114 with the entrapped critical mineral cations 112. The gas may disrupt the electrostatic interactions between the critical mineral cations 112 and the polyelectrolyte complex 114 such that the critical mineral cations 112 may be released from the polyelectrolyte complexes 114.

[0086] As a result, critical mineral cations 112 may be extracted from an aqueous solution through the use of polyelectrolyte complexes 114. Thus, brines including critical minerals such as lithium may be processed to extract the critical minerals, which may unlock a viable resource of critical minerals in a resource constrained landscape.

[0087] Modifications, additions, or omissions may be made to the critical mineral extraction process 100 without departing from the scope of the present disclosure. For example, in some embodiments, the critical mineral extraction process 100 may be performed sequentially as is described in more detail with reference to Fig. 14. In these and other embodiments, at least one of the excess polycations 118 and / or the excess polyanions 120 may be recovered from the supernatant 116 of the aqueous solution 104 and may be used to create additional polyelectrolyte complexes 114 in another aqueous solution. In some embodiments, a second poly electrolyte complex may be formed by mixing a second polycation (not shown) and a second polyanion (not shown). In some embodiments, the second poly cation may be an excess polycation 118 and the second polyanion may be an excess polyanion 120.

[0088] After separating the supernatant 116 and the polyelectrolyte complex 114, the second polyelectrolyte complex and the supernatant may be mixed. One or more excess critical mineral cations 122 in the supernatant 116 may associate with the second polyelectrolyte complex such that the second poly electrolyte complex includes one or more of the excess critical mineral cations 122. The association of the excess critical mineral cations 122 with the second polyelectrolyte complex is as discussed previously with reference to the critical mineral cations 112 and the polyelectrolyte complexes 114.

[0089] After the entrapment of one or more of the excess critical mineral cations 122, the second polyelectrolyte complex may settle such that a second supernatant is created from the supernatant 116. The second polyelectrolyte complex with the excess critical mineral cations 122 may be separated from the second supernatant in a similar manner as described previously, and the excess critical mineral cations 122 may be extracted from the second polyelectrolyte complex in a similar manner as described previously. In some embodiments, the above extraction process may be repeated one, two, three, four, five, six, seven, eight, nine, ten, or more times to enhance the extraction of the critical mineral cations 112.

[0090] In some embodiments, the critical mineral extraction process 100 may be different than that illustrated in Fig. 1A. For example, in some embodiments, the polyelectrolyte complexes 114 may be formed before being added to the aqueous solution 104 with the critical mineral cations 112. In some embodiments, the polyelectrolyte complexes 114 may be formed separately from the aqueous solution 104 and conjugated to a surface of a substrate (e.g., membrane, bead, flow channel, separation member, column filer, etc.). As such, the polyelectrolyte complexes 114 may be linked to a substrate. The linkage can be by any linking agent, such as a crosslinking agent. The polyelectrolyte complex-bound membranes may be used to separate the target critical material (e.g., lithium) by injecting the aqueous solution 104 through the membrane. For example, a produced brine may be injected through the membrane, and the membrane, charged with the polyelectrolyte complexes 114, may remove critical mineral cations 112 from the produced brine. In some embodiments, a charged membrane may be used in addition to the critical mineral extraction process 100 described with respect to Fig. 1A.

[0091] In some embodiments, the poly electrolyte complexes 114 may be formed in a solution such as the aqueous solution 104 described with respect to Fig. 1A or other solutions. In some embodiments, the polyelectrolyte complexes 114 may be conjugated to a surface (e.g., a membrane) to form monolayer, bilayer, or multilayer complexes.

[0092] In various embodiments, the polymers can be characterized by one or more molecular weight parameters, including number average molecular weight (Mn), weight average molecular weight (Mw), Z-average molecular weight (Mz), and peak molecular weight (Mp). The molecular weight of the poly anion may fall within a broad range of about 1 kilodaltons (kDa) to about 1000 kDa, within a narrower range of about 15 kDa to about 40 kDa, or within a more specific range of about 20 kDa to about 30 kDa. In certain embodiments, the polymer has a molecular weight centered around approximately 25 kDa. The number average molecular weight (Mn) represents the total weight of all polymer chains divided by the total number of chains, while the weight average molecular weight (Mw) gives greater emphasis to heavier chains, and the Z-average molecular weight (Mz) further amplifies the influence of high-molecular-weight species. The peak molecular weight (Mp) corresponds to the most abundant molecular weight in the distribution. The polymer may also be characterized by a polydispersity index (PDI), defined as the ratio of Mw to Mn, which may range from about 1.1 to about 2.5, indicating the breadth of the molecular weight distribution. Molecular weights may be determined using gel permeation chromatography (GPC), optionally in combination with multi-angle light scattering (MALS) or refractive index detection, as appropriate for the application.

[0093] In various embodiments, the polyanionic polymer is characterized by one or more molecular weight parameters, including number average molecular weight (Mn), weight average molecular weight (Mw), Z-average molecular weight (Mz), and peak molecular weight (Mp). The molecular weight of the polycation polymer may fall within a broad range of about 600 daltons (Da) to about 1000 kDa, within a narrower range of about 100 kDa to about 1000 kDa, or within a more specific range of about 250 kDa to about 1000 kDa. In certain embodiments, the polymer has a molecular weight centered around approximately 500 kDa. The Mn represents the arithmetic mean of the molecular weight distribution, while Mw gives greater emphasis to higher-mass species, and Mz further accentuates the contribution of the largest molecules. The Mp refers to the most prevalent molecular weight species in the sample. The polyanionic polymer may also be characterized by a polydispersity index (PDI), defined as the ratio of Mw to Mn, which may range from about 1.2 to about 4.0, indicative of the molecular weight heterogeneity typical of high- molecular-weight synthetic or natural polymers.

[0094] In some embodiments, a method for extracting one or more cations from a solution may be provided. The method may include obtaining an aqueous solution including the one or more cations. The method may include forming a polyelectrolyte complex by mixing apolycation and a polyanion. The method may include mixing the polyelectrolyte complex and the aqueous solution, wherein the one or more cations may associate with the polyelectrolyte complex. The method may include separating the polyelectrolyte complex including the one or more cations from a supernatant portion. The method may include extracting the one or more cations from the polyelectrolyte complex.

[0095] In some embodiments, the one or more cations may include at least one of a monovalent metal ion, a divalent metal ion, or a trivalent metal ion. In some aspects, the one or more cations may be selected from the group consisting of: aluminum, cobalt, fluorine, gallium, iridium, lithium, magnesium, natural graphite, neodymium, nickel, platinum, praseodymium, terbium, silicon, bromine, manganese, sodium, potassium, boron, zinc, tungsten, lanthanum, cerium, cesium, strontium, barium, promethium, samarium, europium, gadolinium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or combinations thereof.

[0096] In some embodiments, the polycation may be selected from chitosan, polyethyleneimine, poly(di allyldimethylammonium halide), poly(diallyldimethylammonium chloride), poly D-Lysine, poly allylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof. In some aspects, the polyanion may be selected from dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of polymethacrylic acid, an alkali metal salt of 3-sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

[0097] In some embodiments, the polycation may include polyethyleneimine and the polyanion may include dextran sulfate. In some aspects, the one or more cations may include lithium, and the lithium may be entrapped in the polyelectrolyte complex via interactions between the lithium and -NH2 groups of the polyethyleneimine and -SOf groups of dextran sulfate. In some embodiments, the one or more cations may be entrapped in the polyelectrolyte complex via interactions between positive groups of the polycation and negative groups of the polyanion.

[0098] In some embodiments, the aqueous solution may include a brine. In some aspects, the brine may have a lithium content of less than about 1000 mg / L. In some aspects, the brine may be produced from a geologic reservoir.

[0099] In some embodiments, at least one of: the polyelectrolyte complex may have a mass ratio of the polycation to the poly anion between about 0.1 and about 20; the aqueous solution may have a pH between about 3 and about 10; a concentration of the polycation inthe aqueous solution may be between about 0.01% (w / w) and about 20% (w / w); a concentration of the polyanion in the aqueous solution may be between about 0.01% (w / w) and about 20% (w / w); the poly electrolyte complex may form a nanoparticle having a zeta potential with an absolute value between about 0 mV and about 50 mV; or the nanoparticle may have a diameter of less than about 1000 nm.

[0100] In some embodiments, at least one of: the polycation to polyanion mass ratio may be between about 1 and about 20; the concentration of the polycation in the aqueous solution may be between about 0.01% (w / w) and about 10% (w / w); or the concentration of the polyanion in the aqueous solution may be between about 0.01% (w / w) and about 10% (w / w).

[0101] In some embodiments, nanoparticles may be formed by mixing the polycation with the polyanion, the nanoparticles having a polydispersity of between about 0.1 and about 4.00. In some aspects, the method may further include, after mixing the polyelectrolyte complex and the aqueous solution, recovering no excess polyelectrolytes, or at least one of an excess polycation or an excess polyanion from the supernatant portion.

[0102] In some embodiments, the polyelectrolyte complex may be formed in solution or on a surface to form monolayer or multi-layer complexes. In some aspects, the supernatant portion may include an excess of the one or more cations, and the method may further include: forming a second polyelectrolyte complex by mixing a second polycation and a second polyanion; mixing the second polyelectrolyte complex and the supernatant portion, wherein at least a portion of the excess of the one or more cations in the supernatant portion may associate with the second polyelectrolyte complex; separating the second polyelectrolyte complex including the portion of the excess from a second supernatant portion; and extracting the portion of the excess from the second polyelectrolyte complex.

[0103] In some embodiments, the method may further include contacting the aqueous solution with a membrane, the membrane configured to extract at least one of the one or more cations, or one or more additional cations from the aqueous solution. In some aspects, the method may further include removing divalent cations from the aqueous solution before mixing the polyelectrolyte complex and the aqueous solution.

[0104] In some embodiments, the one or more cations may be extracted from the poly electrolyte complex via gas separation. In some aspects, the polyelectrolyte complex may be formed in the aqueous solution. In some embodiments, the one or more cations may include lithium ions, and the lithium ions may be entrapped by the polyelectrolyte complex at an extraction efficiency between about 5% and about 82%.

[0105] In some embodiments, a polyelectrolyte complex nanoparticle for extracting one or more cations from an aqueous solution may be provided. The polyelectrolyte complex nanoparticle may include a polycation. The polyelectrolyte complex nanoparticle may include a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0.1 and about 20. The polyelectrolyte complex nanoparticle may include one or more association sites. In some embodiments, at least a first association site of the one or more association sites may electrostatically associate with at least one of the one or more cations from the aqueous solution. In some embodiments, the one or more association sites may include a plurality of association sites that each electrostatically associate with at least one of the one or more cations from the aqueous solution. In some aspects, the cations may be sterically entrapped in the polyelectrolyte complex nanoparticle.

[0106] In some embodiments, the polycation may be selected from the group consisting of: chitosan, polyethyleneimine, poly(diallyldimethylammonium halide), poly(diallyldimethylammonium chloride), poly D-Lysine, poly allylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof. In some aspects, the polyanion may be selected from the group consisting of: dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of poly methacrylic acid, an alkali metal salt of 3- sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

[0107] In some embodiments, the polycation may include polyethyleneimine and the polyanion may include dextran sulfate. In some aspects, the one or more cations may include lithium ions, and wherein the lithium ions may be entrapped in the poly electrolyte complex nanoparticle via interactions between the lithium ions and at least one of NH2 groups of the polycation or SO3 groups of the polyanion.

[0108] In some embodiments, the one or more cations may be entrapped in the polyelectrolyte complex nanoparticle via interactions between positive groups of the polycation and negative groups of the polyanion. In some aspects, the polyelectrolyte complex nanoparticle may have a mass ratio of the polycation to the polyanion between about 1 and about 10.

[0109] In some embodiments, the polyelectrolyte complex nanoparticle may have at least one of: a diameter of less than about 1000 nm or a zeta potential with an absolute value between about 0 mV and about 50 mV.

[0110] In some embodiments, a polyelectrolyte complex nanoparticle may be provided. The polyelectrolyte complex nanoparticle may include a polycation. The polyelectrolyte complex nanoparticle may include a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0.1 to about 20. The polyelectrolyte complex nanoparticle may include one or more cations associated with one or more association sites of the polyelectrolyte complex nanoparticle formed by the complexation of the polycation and the polyanion.

[0111] In some embodiments, the one or more cations may be entrapped in the poly electrolyte complex nanoparticle (1) sterically and / or (2) via interactions between positive groups of the polycation and negative groups of the poly anion.MATERIALS

[0112] As an example of the critical mineral extraction process 100, Polycationic branched PEI (Catalog # 408727), with an approximate molecular weight of 25 kDa, was procured from Sigma- Aldrich® and utilized without further purification. Anionic Dextran Sulfate sodium salt (Catalog # 9011-18-1, Lot # 116614) with a molecular weight of about 500 kDa, was obtained from Fischer Scientific® and used as received.

[0113] LiCl salt (Catalog # 31,046-8) was sourced from Aldrich Chemical Company, Inc. to prepare Li brine solution. 37% Hydrochloric acid (HC1) (CAS # 7647- 02-0) was acquired from Aqua Solutions, Inc., and sodium hydroxide (NaOH, CAS # 1310- 73-2) from Fischer Scientific® was used to adjust the pH of PEI. Nitric acid (HNO3, 70%; Catalog # A483-212) was purchased from Fisher Scientific ®.PREPARATION OF PEI SOLUTION

[0114] 20 grams of PEI was added to 180 grams of reverse osmosis-deionized (RO-DI) water (18.2 mQ) with continuous stirring at 600 rpm, resulting in a 10 wt.% PEI stock solution after 30 minutes. This stock solution was then diluted to create 9, 8, 7, 6, 5, 4, 3, 2, and 1 wt.% PEI solutions. The pH of these solutions was lowered from around 11 to a pH of 3 by adding 37% HC1 or IM NaOH solution if the target pH was overshot. These stock solutions were utilized to generate the polyelectrolyte complexes described below. PREPARATION OF DS SOLUTION

[0115] 20 grams of DS was gradually added into the vortex of 180 grams of RO-DI water with continuous stirring at 600 rpm, forming a 10 wt.% DS stock solution after 40 minutes. This stock solution was then diluted to produce 9, 8, 7, 6, 5, 4, 3, 2, and 1 wt.% DS solutions. These stock solutions were utilized to generate the polyelectrolyte complexes described below.PREPARATION OF POLYELECTROLYTE COMPLEXES

[0116] Various compositions of polyelectrolyte complex nanoparticles were prepared by the dropwise addition of polyanionic solution into the polycation cationic solution in the presence of 150 ppm Li as detailed in Table 1, at 1200 rpm magnetic stirring5 speed and 25°C. In all formulations, equal concentrations of PEI and DS were paired for the complexation reactions (e.g., 10 wt.% PEI with 10 wt.% DS). This was also done for 9, 8, 7, 5, 3, and 1 wt.% paired systems while varying the PEI and DS mass ratio. The order of addition was PEI first, followed by DS, and then the addition of the 28,401 ppm LiCl solution into a 20 ml glass vial. A 10-minute interval allowed PEI and DS to mix entirely 10 and form nanoparticles before adding LiCl to the glass vial. After adding the LiCl, another 15 -minute interval was allowed for thorough mixing with the poly electrolyte complex solution. However, it is acknowledged that the order of addition, above, may be changed.

[0117] The pH of the complex was recorded, and approximately 0.2 ml was measured into a cuvette. The cuvette sample was further diluted by a factor of 1 lx by15 adding 2 ml of RO-DI water. The new pH was recorded for nanoparticle size and zeta potential measurements using the Nanobrook® Omni particle size and zeta potential analyzer (Brookhaven Instruments® Corporation). The nanoparticle sizes were measured by detecting light scattering at 90° angle. The equipment automatically calculated the electrophoretic mobility of the nanoparticles for zeta potential measurements through the 20 Smoluchowski equation (Sze et al. , 2003). An average of three readings was taken for each size and zeta potential measurement.

[0118] Approximately 1.5 mL of the prepared polyelectrolyte complex solution was transferred into a 2 mL centrifuge tube and centrifuged at 10,000 rpm with a Fisherbrand® accuSpin® 17R Microcentrifuge for 90 minutes. The filtrate deposited in the centrifuge tubes was freeze-dried at 40°C for 24 hours, after which the interaction of complexes with Li was investigated with attenuated reflectance Fourier transform spectroscopy via the Shimadzu® IRSpirit® spectrophotometer. The average transmittance of 32 scans was recorded in the range of 400 and 4000 cm'1wavenumbers.

[0119] After centrifuging, about 1 mL of the supernatant of the complexes was collected from the centrifuge tubes and diluted 10 times with a 5% HNOs(aq) solution to a final volume of 10 mL. The diluted supernatant was then filtered through a 0.2 pm Millipore syringe filter and analyzed for concentration using Agilent® 5800 ICP-OES equipment. An average of three concentration readings were taken for each sample at 670.783 nm wavelength. The extraction efficiency or the ability of nanoparticles to capture Li was calculated using the formula:

[0120] Ci represents the concentration of three 150 ppm baseline Li samples, and Cf denotes the concentration of lithium in the supernatant following centrifugation of the complexation at 10,000 rpm for 90 minutes at 25°C. A calibration curve between 0 and 20 ppm was developed from a Perkin Optima multielement standard solution to correlate Ci and Cf. The Agilent® 5800 equipment uses an axially viewed plasma with multiple viewing modes, allowing ions to be detected radially (perpendicular to plasma) or axially (parallel to plasma). This equipment can identify metals and metalloids within a 167-785 nmwavelength range. It features a Charge Coupled Device (CCD) detector with anti-blooming protection for each pixel at a constant temperature of -40°C. This ensures that electron backscattering to neighboring pixels is minimal, even when a pixel is saturated by an intense ion beam, allowing for precise detection of neighboring wavelengths with substantial intensity differences. This device can measure metal concentrations as low as 50 - 100 ppb, even in the presence of dominant matrix components. The emission intensity at a specific wavelength depends on the concentration of the element(s) corresponding to that wavelength, the efficiency of nebulization and ionization, and the rate of sample introduction. The standard operating conditions for ICP-OES are provided in Table 2.

[0121] Fig. IB illustrates transmission electron microscopy (TEM) images of a polyelectrolyte complex formed by PEI and DS prepared in the presence of reverse osmosis-deionized (RO-DI) water (left) and prepared in lithium chloride brine (right). Specifically, Fig. IB illustrates TEM images of PEI:DS mass ratio of 4, initial pH of 4.5, PEI and DS pairwise concentration of 10 wt.% prepared in the presence of RO-DI water (left) and LiCl salt (right) at different magnifications of 15, 30 and 60kx. The scale bar indicates that the samples are macroscopic gels because the scale bar in the nanometer range only occupies small portions of the gels, regardless of the magnification level employed forimaging. The images for samples in the presence of RO-DI water showed different morphology relative to those prepared in LiCl. The sample with RO water appeared to lack a well-defined morphology. According to Mesic et al. , (2025), the introduction of salts such as LiCl results in charge screening. The charge screening in this case is the interaction between protonated polyethylenimine and Cl" via bridging and or overlapping of hydration shells of counterions and polycation. Similarly, Li+also interacts with the SOf groups on the dextran sulfate. However, the extent of counter-ion polyelectrolyte binding is greater for Cl" than Li+because Li+is more hydrated, which reduces its polarity (Wong et al. , 2009). Regardless, the contribution of Li+is not negligible in the screening process. The effect of counter-ion screening on morphology is the coiling of polymer chains, which yields rough and layered morphology, as illustrated in the PEI-DS-LiCl sample shown in Fig. IB.

[0122] For TEM, 10 pL of polyelectrolyte complex with and without lithium was deposited onto a 300-mesh support carbon film and 400-mesh Cu lacey carbon grid, respectively. Excess liquid was gently removed by blotting with filter paper. A 10 pL aliquot of filtered 2% (w / v) uranyl acetate was then added for negative staining and allowed to stand for 5 minutes. Excess stain was blotted off, followed by rinsing with 10 pL of RO- DI water. After final blotting, grids were left to air dry for 5-10 minutes. Imaging was conducted with a Hitachi® H-8100 Transmission Electron Microscope (Hitachi® High- Tech; RRID: SCR_020012) with a lanthanum hexaboride (LaB6) electron gun and an AMT BioSpirit 16 mega-pixels CCD camera (Woburn, MA; 4896 x 3264 pixels) and probe size of 3. The instrument was operated under the following parameters: 200 kV, the condenser aperture at 1, and the objective aperture at 0, Gain: 1, Bin: 1, Gamma: 1, no sharpening, and normal contrast. The areas containing polyelectrolyte clusters were selected and imaged at magnifications ranging from 15,000x to 80,000x (15kx to 60kx shown in Fig. IB).

[0123] Fig. 2A illustrates a workflow 200 for determining PEI or DS concentration from total organic carbon (TOC) and total organic nitrogen (TON) of a supernatant of a polyelectrolyte complex solution.

[0124] The supernatants of samples were collected for TOC-TON analysis with a Shimadzu® TOC-L Total Organic Carbon Analyzer, which includes a TOC-L total organic carbon analyzer and a TNM-L total nitrogen unit for analysis of TOC and TON, respectively. The samples were diluted with RO-DI water to achieve the desired concentrations in the carbon and nitrogen calibration curves range. PEI and DS calibration curves (illustrated in Figs. 2B-2D) were developed to calculate the concentration of PEIand DS in supernatants. The measurement conditions are detailed in Error! Reference source not found..

[0125] At block 202 of the workflow 200, the TON and TOC of the supernatant (e.g., the supernatant 116) were measured. The TOC measurement employed the non- purgeable organic carbon (NPOC) method, which involves the initial acidification of samples to convert all inorganic carbon (IC) into dissolved CO2, which is then removed via sparging. The remaining total carbon (TC) is then measured to determine the TOC value. Concurrently, TN is measured alongside TOC. A two-point calibration curve was established for TC measurements using potassium hydrogen phthalate solutions at concentrations of 0 and 10 mg C / L to calibrate the analyzer. Similarly, potassium nitrate solutions at concentrations of 0 and 10 mg N / L were utilized for TN measurements. The calibration curve origin points were adjusted to correct any inherent TOC and TN in the pure water used to prepare the standard solutions.

[0126] Furthermore, as illustrated in Figs. 2B-2D, PEI and DS calibration curves were created from the two-point calibration curves to analyze the TOC-TON in the supernatants of polyelectrolyte complex solutions.

[0127] At block 204, the measured TON representing the PEI concentration is correlated to the TOC of the PEI to determine PEI’s contribution to the TOC in the supernatant. For example, the calibration chart illustrated in Fig. 2B may be used to determine the TOC of PEI in the workflow 200 from the TON representing PEI concentration. For instance, the TON may be read on the calibration curve to determine the fraction of total TOC that is PEI.

[0128] At block 206, the determined TOC is correlated to a PEI concentration. For example, the TOC vs. PEI concentration chart illustrated in Fig. 2C may be used in determining the PEI concentration (wt. %) in the supernatant.

[0129] At block 208, the TOC fraction representing PEI is then subtracted from the Total TOC to determine the amount of the TOC representing DS (e.g., to determine if there is excess DS at block 210).

[0130] If there is excess DS, at block 214 the TOC fraction representing DS may be correlated to a DS concentration. For example, the TOC vs. DS concentration chart illustrated in Fig. 2D may be used in determining the DS concentration (wt. %) in the supernatant. If there is no excess DS, the workflow 200 ends at block 212.

[0131] Table 3 below illustrates the TOC-TON measurement conditions.VISUAL OBSERVATIONS AND POLYDISPERSITY INDEX

[0132] Visual observations of the produced nanoparticles and the particles' polydispersity index (PDI) were measured to analyze the nanoparticles' yield and degree of uniformity. Upon addition of polyanion into the cation solution, a color change to whitish cloudy formulations is observed. Cloudy suspensions confirm the formation of nanoparticles during the mixing of PEI and DS polyelectrolytes. The cloudiness intensity differed for each polymer mass ratio.

[0133] Fig. 3 illustrates a scale of observed cloudiness for different PELDS Mass Ratios solutions at a pH of 4.5. Cloudiness intensity was ranked on a scale of 0.5 - 5, with 5 indicating the highest turbidity and 0.5 the least. It is noted that these are initial observations of freshly prepared nanoparticles. For PELDS mass ratios 0.5, 1, and 2, the appearance changed with time due to the settling of nanoparticles. For mass ratios between 3 and 7, the opacity decreased as mass ratio increased and fewer gel precipitates were formed in these as compared to mass ratios of 1 and 2. Moreover, the polyelectrolyte complexations looked more viscous and gel-dominated as compared to the particle- dominated sections of mass ratios 1 and 2. Mass ratios 0.5 to 0.2 with higher DS content were extremely whitish but the opacity decreased as mass ratio decreased. Mass ratio 0.5 precipitated heavily until little to no polymers could be observed in the solution. Mass ratios 0.33, 0.25, and 0.2 also looked viscous with viscosity appearing to increase with decreasing mass ratios. However, the viscosity kept the particles suspended in solution as compared to mass ratios 1 and 0.5.

[0134] Thus, generally, the cloudiness of the nanoparticle solutions decreased further from the PELDS mass ratio 1:1 towards both extreme ends (e.g., for higher PELDSmass ratios and for lower PEI:DS mass ratios), with extreme precipitations occurring around the 1:1 PELDS mass ratio. Higher or lower PELDS mass ratios yielded more viscous solutions and formed gel-like precipitates that settled to the bottom of the vials slowly, as compared to PELDS mass ratios closer to the 1:1 formulation. While the PEI to DS 1:1 ratio settled earlier, many nanoparticles were generated that kept themselves relatively suspended in solution, a concept called hindered settling (Te Slaa et al., 2015). Lower mass ratio formulations away from 1: 1 PEI to DS formulations appeared more viscous than the higher PEI to DS mass ratios away from the 1:1 ratio. The increased viscosity at lower mass ratio formulations preserved the nanoparticle sizes and prevented them from settling relative to those at the higher PEI to DS mass ratios.

[0135] Polydispersity describes the degree of uniformity of colloidal particles in solutions (Danaei et al., 2018). The smaller the PDI, the more uniform the dimensions of the nanoparticles. Fig. 4A is a chart illustrating polydispersity index for different PELDS mass ratios of a 10 wt.% PELDS paired concentration solution. Fig. 4B is a chart illustrating polydispersity index for different PELDS mass ratios of a 9 wt.% PELDS paired concentration solution.

[0136] The PDI was high at a mass ratio of 1:1 for both 10 and 9 wt.% PELDS paired concentrations. The severe precipitation and more stoichiometric formation of particles at a mass ratio of 1 : 1 yielded more nanoparticles that were suspended due to the high concentration of particles. The large number of suspended particles caused high readings in the PDI. At mass ratios 2 and 3, there were fewer nanoparticles formed and particles could settle to the bottom of the vial. Thus, smaller nanoparticles were left suspended. This improved the monodispersity as the larger nanoparticles had already settled. A similar trend was observed for mass ratios 0.5 and 0.33. At high mass ratios (5 and 7) or extremely low mass ratios (0.25 and 0.20), the particles were kept in solution as samples looked more viscous so there was more uneven distribution because both smaller and larger nanoparticles were kept suspended.

[0137] Fig. 4C illustrates a 2D contour plot of polydispersity index as a function of PELDS mass ratio and PELDS pairwise concentration (wt.%) at a pH of 4.5. Fig. 4C was generated by fitting a polynomial with a bisquare robustness to the PDI data at a pH 4.5. The visualization shows that the effect of mass ratio on polydispersity was more pronounced at PEI and DS pairwise concentration between 1 and 3 wt.%. At these concentrations, the nanoparticles were suspended in solution. However, 3 wt.% began the transition of nanoparticles that settled and those that stayed in solution, resulting in a higherpolydispersity index. At higher PELDS concentrations, the nanoparticles coagulated and flocculated into gels, leaving behind some uncomplexed PEI and DS. The poly dispersity was dependent on the end-to-end dimensions of these polymers in solution. There was less variation in PDI at higher concentrations.EFFECT OF PEI:DS MASS RATIO ON NANOPARTICLE SIZE

[0138] Numerous studies have demonstrated that the size of the nanoparticles may enhance extraction efficiency for various materials targeting specific molecules (Attallah et al., 2020; Rathore et al., 2020; Tiyaboonchai et al., 2001). Understanding how the mass ratio of polyethyleneimine (PEI) to dextran sulfate (DS) affects nanoparticle size helps in creating formulations that enhance critical mineral (e.g., lithium) extraction.

[0139] Figs. 5A-5G illustrate scatter-plots of nanoparticle size vs. PELDS mass ratio at varying wt.% of PEI and DS. As the PELto-DS mass ratio increases from 1 to 7, nanoparticle size generally decreases, while lower ratios (1 - 0.20) produce larger nanoparticles. Specifically, mass ratios above 2 typically yield particles smaller than 100 nm. Critical analysis through visual observation and comparison of nanoparticles measured at high concentrations of PEI and DS and a high PELDS mass ratio to just pure PEI solution revealed similar nanoparticle diameters under 20 nm. At a high PELDS mass ratio (2 - 7) and high concentration of PEI and DS (5 - 10 wt.% (Figs. 5A-5E)), the nanoparticle readings taken were mostly that of PEI because dextran had been precipitated into PELDS nanoparticles, which had settled to the bottom of the vials while leaving behind excess PEL Slight variations in the PEI measurements may have been due to the final pH of the complexation or minute amounts of DS left in the solution, which influenced the reading. Moreover, the nanoparticle size generally decreased with increasing PELto-DS ratio at lower PEI and DS concentrations (1 and 3 wt.%). However, the particles are larger than those at higher concentrations due to the particles being suspended. High concentrations of polyelectrolytes may have promoted the extent of nanoparticle flocculation, resulting in lots of particle deposition onto the bottom of the vials.

[0140] Mass ratios below 1 often resulted in particles larger than 100 nm due to more significant amounts of DS and the formation of suspended nanoparticles due to the more viscous nature of the aqueous media. This trend suggests that higher concentrations of PEI promote the formation of gel-like macroparticles, whose phases separate to leave behind small PEI molecules whose morphology is pH-dependent. In contrast, increased DS concentrations lead to larger-sized nanoparticles that appear suspended. The balance between PEI and DS highlights the delicate molecular interactions in nanoparticlesynthesis, emphasizing the importance of precise mass ratios in achieving nanoparticle sizes for enhanced extraction.EFFECT OF PH ON NANOPARTICLE SIZE

[0141] Figs. 6A-6E are charts illustrating nanoparticle size and extraction efficiency of lithium as a function of nanoparticle composition at varying pHs. For each figure, the first digit is the PEI:DS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation.

[0142] At high PEI and DS concentrations of 9 wt.%, nanoparticles formed were unstable and susceptible to coagulation and flocculation, which led to precipitation and settling. Measurements of particle size distribution, especially at PEI:DS mass ratios of 4 and 5 (Figs. 6D and 6E), were an analysis of supernatant PEI hydrodynamic radius, reflecting different levels of protonation- induced morphology, except for pH 10, which had a few nanoparticles in solution due to the low protonation. At pH 10, particles were still suspended in solution, but the low opacity of the solution implied that not many nanoparticles were formed relative to the lower PEI starting pH of the complexations.

[0143] For compositions with mass ratios of 4 and 5 (Figs. 6D and 6E), the nanoparticle sizes seemed to increase with pH up to pH 8, after which there was a slight decrease in the nanoparticle size at pH 10. At these compositions, the pH-dependent particle size distribution was akin to that observed by Curtis et al. (2016), which reported that the hydrodynamic radius of PEI was the lowest and compact between pH 4 and 2 due to interchain repulsion by the highly charged PEI molecules. The hydrodynamic radius increased from pH 4 to 6.8 due to intrachain repulsion. Between pH 6.8 and 9.5, the hydrodynamic radius of free polymer chains was the highest, where aggregates of PEI transition from aggregates to free PEI chains as pH decreases to 7.5. Moreover, the extent of the transition depends on the availability of salts for charge screening. Beyond pH 9.5, aggregates of PEI were the most dominant forms of PEI present. However, the aggregates assumed a more compact structure than neutral pH conformations.

[0144] At lower PELDS mass ratios (1-3 as illustrated in Figs. 6A-6C) larger particle sizes were also seen in more basic pH. However, the presence of more DS in solutions and slight differences in ionic strength due to different extraction efficiency resulted in a shift in the peak particle size from pH 8 to 5. For sample 14-9 (Fig. 6A), particle size distribution may have been taken early before precipitation to the bottom of the vials. Hence, some nanoparticles may have been suspended in the supernatant.SUPERNATANT TOTAL ORGANIC CARBON AND TOTAL ORGANIC NITROGEN

[0145] Fig. 7 is a chart showing PEI and DS TOC data in the supernatant as a function of nanoparticle composition for different PELDS mass ratios at a pH of 5 and a PEI:DS pairwise concentration of 9 wt.%. For each composition, the first digit is the PELDS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation.

[0146] The supernatant of the polyelectrolyte complex systems that showed higher extraction efficiency were analyzed to determine how much PEI and DS were left in solution after complexation. The TOC data illustrated in Fig. 7 shows that most of the supernatant contained PEI TOC fractions which increased as the PELDS mass ratio increased. Relatively small amounts of DS were left in solution. Although DS was a limiting reactant, there was still some excess DS in solution. Since the pH of the aqueous environment was around 5, there may have been some sulfate ions that were still bound to H+or some dextran sulfate may have been released into solution upon addition of LiCl solution.EFFECT OF MASS RATIO ON ZETA POTENTIAL

[0147] Zeta potential measurements may be used to determine the surface charge of colloidal particles, which may provide insight into the stability of the colloidal system. Zeta potential measurements reveal the magnitude of electrostatic repulsion between nanoparticle complexations. Higher absolute values of zeta potential mean repulsion amongst particles of like charges is more likely whilst lower zeta potential infers flocculation amongst nanoparticles is more probable. For Li extraction, stable nanoparticles may inhibit release of captured Li due to interaction with ions in the aqueous medium. According to Barati Ghahfarokhi, (2010), zeta potential values correlate with specific stability levels: values between 0 to ±5 mV indicate rapid coagulation or flocculation, while ±10 to ±30 mV reflect incipient instability. Moderate stability is observed at ±30 to ±40 mV, good stability at ±40 to ±60 mV, and excellent stability occurs when zeta potential exceeds ±61 mV.

[0148] Figs. 8A-8C are charts illustrating nanoparticle zeta potential as a function of PELDS mass ratio at varying paired PELDS concentrations. Figs. 8A-8B illustrate that for mass ratios between 0.5 and 5, especially at higher concentrations of polymer, the nanoparticle sizes may be utilized as an indicator of the magnitude of stability of nanoparticles. It must be noted that the count rate of the nanoparticles for 9 wt.% and 10 wt.% PELDS paired concentration systems was below 100 kcps for mass ratios of 0.5 andabove, which impacted the accuracy of the zeta potential measurements. Hence, the zeta potential measurements were good indicators of the charge but not necessarily the magnitude of the charge.

[0149] Data on zeta potential for lwt% PEI and DS is illustrated in Fig. 8C. The count rate at this PEI-DS paired concentration was always above the 100 kcps threshold for accuracy. Moreover, a plot of zeta potential against the nanoparticle size from PEI:DS mass ratios 1 - 5 revealed an increase in zeta potential as nanoparticle sizes decreased, with an R-squared of 0.63 as shown in Fig. 8D, which is a chart illustrating zeta potential as a function of nanoparticle size at the paired PEI-DS concentration of Fig. 8C.

[0150] This trend was in accord with earlier works (Barati Ghahfarokhi, 2010; Tiyaboonchai, 2002). The zeta potential increasing as nanoparticles sizes decreased may result in excess PEI forming a protective layer over nanoparticle surfaces and causing repulsion amongst nanoparticles. Despite the low count rate, the mass ratios of 9 wt.% and 10 wt.% PEI-DS concentration yielded positively charged nanoparticles that were similar to the 1 wt.% paired system. For mass ratios of below 0.5, across all paired concentrations, the count rates were sufficiently high, so the magnitude of charges was representative of the systems. These lower PELDS mass ratios yielded negatively charged nanoparticles between -24 and -27 mV for the 10wt% paired system and -25 to -29 mV for the 9 wt.% paired system. These zeta potential values of negatively charged particles can be classified as incipiently unstable (Barati Ghahfarokhi, 2010).

[0151] Figs. 8E and 8F are 2D contour plots illustrating zeta potential as a function of PEEDS mass ratio and PELDS pairwise concentration (wt.%) at a pH of 4.5 respectively for positively charged particles and negatively charged particles.

[0152] A linear least squares model with a bisquare robustness was fitted to the zeta potential data for PELDS mass ratios (1 to 7) and PEI and DS pairwise concentrations (1 - 10 wt.%) at pH 4.5 to generate the 2D zeta potential contour plot illustrated in Fig. 8E. At lower concentrations of PEI and DS (1 - 3 wt.%), the zeta potential showed slight changes as the PELDS mass ratio increased. However, beyond 4wt.%, the effect of mass ratio became more visible because the zeta potential decreased as the mass ratio increased. Moreover, irrespective of the PELDS mass ratio, zeta potential decreased as the PEI and DS concentration increased from (1 - 10 wt.%). At higher concentrations exceeding 3 wt.%, the zeta potential was mostly under +30 mV, indicating that the particles were positively charged and incipiently unstable or underwent rapid coagulation or flocculation. Hence, 3 wt.% PEI and DS pairwise concentration may be inferred as the criticalcoagulation concentration where the repulsive forces of the nanoparticles were overcome by the attractive forces between the nanoparticles, increasing the probability of coagulation and flocculation (Hsu & Liu, 1998).

[0153] Likewise, as illustrated in Fig. 8F, a linear least squares model with a bisquare robustness was fitted to the zeta potential data for PELDS mass ratios (0.5 to 0.2) and PEI and DS pairwise concentration between 1 and 10 wt.%. Most areas of the contour plot illustrated in Fig. 8F showed negative zeta potential, indicating that the particles formed at mass ratios below 0.5 were negatively charged. Zeta potential was more negative at PEI and DS pairwise concentrations below 3 wt.%. Also, the zeta potential was negative at all concentrations as the PELDS mass ratio decreased from 0.3 towards 0.2. After PEI was consumed into nanoparticles, these lower mass ratios had excess dextran in the solution. However, the viscous nature of the aqueous media kept the particles suspended in the solution. The excess dextran may have adsorbed to the surface of the nanoparticles to provide negative charges that promote repulsion (Tiyaboonchai et al. , 2001). Generally, the negative nanoparticles were more stable since some of the samples exhibited moderate to excellent stability.ATTENUATED TOTAL REFLECTANCE FOURIER TRANSFORM INFRARED (AFTIR) SPECTROSCOPY RESULTS

[0154] The AFTIR measurements in the wavenumber range of 500-1700 cm1are shown in Table 4. These results present the position and assignment of bands for pure PEI, dextran sulfate (DS) powder, LiCl(aq), and PELDS complexes, both with and without lithium. The complexes were prepared at PELDS mass ratios of 3, 4, and 5, with an initial PEI pH of 4.5 and concentrations of 9 wt.% for both PEI and DS.

[0155] For pure PEI, a significant peak occurs at 1458 cm1that is attributed to N- H bending combined with CH2 scissor motions (Grenda et al., 2022; Zaaeri et al., 2018). The 1113 cm1band corresponds to C-N stretching. Primary amine bands are typically observed in the range of 1500-1650 cmwith peaks at 1515 cm1and 1596 cm1reflecting N-H bending vibrations.

[0156] Dextran sulfate (DS) shows characteristic peaks at 1217 cm1028 cm and 981 cm representing asymmetric S=O stretching, symmetric S=O stretching, and another symmetric S=O stretching vibration, respectively. Peaks at 792 cm1and 574 cm1correspond to asymmetric and symmetric vibrations of O-S-O, respectively. (Cakic et al., 2005). It was observed that sulfo-group vibrations vary with orientation: axial bands appear near 850 cm while equatorial bands occur near 820 cm In the PEI-DS-Li complexes,the bands at 792 cm1and 784 cm1are closer to 820suggesting the equatorial positioning of the sulfate groups. Additionally, the 734 cm1peak represents out-of-plane deformation vibrations of the glucopyranose unit, specifically C-CH, C-O-C, C-C-O, and O-C-O modes (Nikolic et al., 2017). LiCl exhibits a prominent low-wavenumber peak at -200 cm1, attributed to lattice vibrations, which lies outside the measured spectrum range of 400-4000 c100157 J Distinct spectral differences were observed between PE1-DS complexes with and without LiCl. The vas(-O-S-O) bands exhibited higher wavenumbers in Li- bearing complexes. For PELDS mass ratio 3, the vas(-O-S-O) band increased by 29 cm1relative to the same ratio without Li. Similarly, mass ratios 4 and 5 showed increases of 40 cm1and 29 cm respectively. These shifts suggest Li —SCL2complexation, consistent with findings from Nikolic et al., (2017) involving silver (Ag) nanoparticle interactions with dextran sulfate.

[0158] In contrast, the vas(S=O) and vs(S=O) bands exhibited minimal changes. For mass ratios 3, 4, and 5, the Av (cm ') of vas(S=O) between Li-bearing and pristine complexes was 6, 0, and 6, respectively, while the Av of vs(S=O) was 6, 0, and 0, respectively.

[0159] Significant changes were also observed in the unit conformation of the 4Ci a-D-glucopyranose unit. The Av (cm1) was 40, 46, and 52 for mass ratios 3, 4, and 5, respectively, indicating conformational shifts upon lithium complexation. Moreover, the area under the vas(-O-S-O) peak decreased as the PELDS mass ratio increased, reflecting reduced sulfate content in the complexes. The peak areas for mass ratios 3, 4, and 5 were 874, 432, and 170, respectively, suggesting lower sulfate content at higher mass ratios (Korva et al., 2016).

[0160] All pristine samples exhibited amine peaks at 1458 cm1and within the 1500-1650 cm1range. However, these peaks were different in Li-bearing complexes, likely due to new interactions in the 1300-1700 cm1region. The interactions may involve unprotonated or basic amine groups forming coordination complexes with Li1. Furthermore, these amine interactions with Li (N-Li+) weaken and replace N-H bonds. Previous studies (Artigues et al., 2022; Paul et al., 1992) have reported similar amine-Li+interactions, although typically outside the observed wavenumber range (e.g., 3300 cm '). Artigues et al., (2023) is one of the few studies reporting fingerprints within 1300-1650 cm1that shows comparable spectral features.

[0161] Fig. 9 is a chart illustrating unprotonated nitrogen of PEI as a function of pH. As illustrated in Fig. 9, at pH 4.5, approximately 40-50% of the nitrogen in PEI remains unprotonated Suh et al., 1994). These unprotonated fractions likely interact with Li+through coordination, which may explain the improved extraction efficiency observed at higher PELDS mass ratios despite lower sulfate content. Higher mass ratios provide increased concentrations of protonated PEI and unprotonated NH2 groups, facilitating additional interactions with Li+. These findings suggest that both amines and sulfate groups play a role in lithium complexation within the precipitated gel structures, thereby enhancing extraction efficiency.EFFECT OF MASS RATIO ON EXTRACTION EFFICIENCY

[0162] Figs. 10A-10D are charts illustrating extraction efficiency of lithium in the aqueous solution as a function of PELDS mass ratio at varying concentrations of PEI and DS and varying pH.

[0163] The mass ratio of polyelectrolyte complexes (PECs) plays a role in the formulation of nanoparticles, as the mass ratio may impact extraction efficiency of the critical mineral cations. Previous studies on polyethyleneimine (PEI) and dextran sulfate (DS) nanoparticles demonstrated this effect (Barati et al., 2012; Danso et al., 2024; Tiyaboonchai et al., 2001). =

[0164] As illustrated in Figs. 10A-10D, the effect of the PELDS mass ratio on extraction efficiency was investigated to determine desired mass-ratios for enhanced lithium extraction. The analysis was performed at pH values of 4, 4.5, and 5 using 9 wt.% PEI and DS pairwise concentrations as illustrated in Figs. 10A-10C. The results reveal a distinct mass ratio for each pH condition that corresponds to the highest observed extraction efficiency. Specifically, the PELDS mass ratio for pH 4, 4.5, and 5 that corresponded to the highest extraction efficiencies were 5, 4, and 7, respectively, which respectively yielded Li extraction efficiencies of 38%, 50.3%, and 32%.

[0165] Analysis was also performed on a 10 wt.% PEI and DS paired concentration at a pH of 4.5. The highest extraction efficiency observed was 55% at a PELDS mass ratio of 4. At pH 4.5 and 10 wt.% PEI and DS pairwise concentration, the mean extraction efficiency for PEI to DS mass ratios ranging from 2 to 7 was about 51%, with a standard deviation of 4.1, resulting in a coefficient of variation of approximately 8%. This level of variability is considered acceptable for maintaining the robustness of the extraction process without compromising efficiency.

[0166] Across all pH values, higher PEI to DS mass ratios generally favored improved extraction efficiency. A continuous increase in efficiency was observed as the mass ratio approached the peak extraction efficiency, beyond which a marginal rise or slight decrease in extraction efficiency occurred. Extraction efficiencies were significantly reduced at lower mass ratios but improved progressively as the mass ratio decreased. Polynomial fits to the extraction data showcased both minimum and maximum points across the range of mass ratios evaluated, highlighting the higher PELDS mass ratio region as having increased lithium recovery.EFFECT OF NANOPARTICLE SIZE ON EXTRACTION EFFICIENCY

[0167] Polyelectrolyte complex nanoparticles can be standalone agents in coagulation unit processes to enhance critical mineral recovery. In this context, nanoparticle size can function as a quality control parameter, providing predictive insights into the efficiency of critical mineral extraction. Fig. 11 is a chart illustrating extraction efficiency of lithium in the aqueous solution as a function of nanoparticle size in various compositions.

[0168] As illustrated in Fig. 11, a logarithmic model with an R2value of 0.76 was fitted to the data. A marked increase in extraction efficiency for nanoparticle sizes below 50 nm was observed, whereas particles larger than 50 nm consistently demonstrated lower extraction efficiencies, typically below 20%. This enhanced performance of systems whose supernatants contained smaller nanoparticles may be attributed to the pore structure of the nanoparticles and the higher surface area of the nanoparticles, which may promote Li entrapment.EFFECT OF INITIAL POLYETHYLENEIMINE ON EXTRACTION EFFICIENCY

[0169] Figs. 12A-12D are charts illustrating extraction efficiency of lithium as a function of nanoparticle compositions. For each figure, the first digit is the PELDS mass ratio, the second digit(s) is the pH, and the last digit after the hyphen is the pairwise concentration of PEI and DS in wt.% utilized for the nanoparticle formulation.

[0170] To understand how pH influences extraction efficiency, nanoparticle formulations with a constant PEI and DS concentration of 9 wt.% and fixed PELDS mass ratios (ranging from 2 to 5 (Figs. 12A-12D, respectively)) were prepared at different initial PEI pH levels (4, 4.5, 5, 8, and 10).

[0171] The results revealed that extraction efficiency was sensitive to the initial pH of the PEI solution. The peak extraction efficiency was consistently observed at pH 4.5, followed by pH 4 and pH 5. These results suggest that peak extraction efficiency may be obtained at a pH between about 4 and about 5 or at about 4.5. At pH 4, the extraction efficiency was slightly lower than at pH 4.5, likely due to tighter complexation and smaller pore structures, which may restrict the influx of lithium Li into the complex. Additionally, the FTIR results indicated that at pH 4.5, the base forms of NH2 groups were more abundant, which likely contributed to more efficient Li extraction. Furthermore, at higher pH values, the competition between Li+and H+for binding to SO3" groups decreases, facilitating better complexation of Li+over H+.

[0172] Near- neutral conditions of pH 8 resulted in the lowest extraction efficiency. This may have been due to stoichiometric complexation between PEI and DS, leaving fewer sulfate sites for lithium binding available. A slight increase in efficiency was observed at pH 10, although the extraction efficiency remained below the values obtained at lower pH levels. This suggests that partial deprotonation of PEI at alkaline pH may allow for some lithium-ion capture, though not to the extent seen at acidic pH.

[0173] The extraction efficiency appears to be governed by the extent of PEI protonation and the structural arrangement of the nanoparticle pore network, which may be enhanced for lithium-ion diffusion at lower pH levels. This trend is distinct from the behavior observed in the encapsulation of larger molecules such as amphotericin B (Tiyaboonchai et al., 2001) or pectinase (Barati Ghahfarokhi, 2010), where enhanced entrapment occurred at pH 8. This highlights a fundamental difference in the capture mechanisms for low-charge-density cations like lithium within PECNPs, underscoring the importance of charge density in designing nanoparticle systems for ion extraction.BILAYER EFFECT ON PARTICLE SIZE DISTRIBUTION AND EXTRACTION EFFICIENCY

[0174] Mass ratios 4 and 5 from the 10 wt.% nanoparticle systems were selected for bilayer deposition studies. To achieve bilayer deposition, a PELDS-Li-PEI-DS-Li order of addition was utilized. Table 5 presents the data on nanoparticle size, zeta potential, PDI, and EE% of monolayer and bilayer nanoparticle systems. The stepwise addition of a layer onto the monolayer increased the nanoparticle sizes of samples 45-10 and 55-10 from 8.46 nm and 11.28 to 66.8 and 71.3 nm, respectively. The zeta potential of bilayer systems remained positive and in the same unstable regime for both nanoparticle systems. This is because excess PEI is utilized in these nanoparticle systems, so PEI short-chain molecules are lined up around longer-chain DS molecules in the binding stage. The EE% increased from 37% to 47.23% for samples 45-10 with a PEI: DS mass ratio of 4. Sample 55-10 with PEI: DS mass ratio of 5 also increased in EE% from 43% to 48%. The bilayer system improved the extraction by creating more functionalized pore space within the nanoparticle systems for Li entrapment or diffusion.PELDS RATIO AND DS:PEI RATIO IN SUPERNATANT

[0175] Following the process of nanoparticle complexation and subsequent centrifugation, it was observed that residual polymers remained in the supernatant, as detailed in Tiyaboonchai (2002). Tiyaboonchai documented the presence of residual polymers in the solution post-centrifugation. This residual presence suggests that not all of the polymers were successfully incorporated into the nanoparticles during the complexation process. Therefore, analyzing the concentration of these remaining polymers may serve as a proxy for understanding the efficiency of the nanoparticle formation process. Specifically, it allows researchers to ascertain the extent to which PEI and DS were utilized in the formation of nanoparticles, providing insights into the overall efficiency of the process. Figs. 13 A is a chart illustrating extraction efficiency as a function of DS:PEI ratio in the supernatant. Fig. 13B is a chart illustrating extraction efficiency as a function of PELDS ratio in the supernatant.

[0176] One trend observed in Figs. 13A and 13B is the inverse relationship between extraction efficiency and DS concentration in the supernatant. It was found that extraction efficiency tends to increase as the concentration of DS in the supernatant decreases. This observation suggests that excess DS molecules present in the solution are actively consumed in the formation of nanoparticles. As a result, a lower concentration of DS in the supernatant corresponds to a higher extraction efficiency, indicating a more efficient utilization of the polymer components in the nanoparticle formation process. Conversely, the analysis also unveiled a positive correlation between extraction efficiency and PEI concentration. As the concentration of PEI in the supernatant increases, so does the extraction efficiency. This finding suggests that the presence of higher concentrations of PEI facilitates the formation of nanoparticles, leading to enhanced extraction efficiency. Moreover, it indicates that excess DS molecules present in the solution are utilized moreefficiently in the presence of higher concentrations of PEI, further enhancing the overall extraction efficiency of the nanoparticle system.

[0177] Delving into the underlying mechanisms behind these observed trends, these findings suggest that PEI and DS play crucial roles in the formation and function of the nanoparticles. DS, with its functional SOf groups, is capable of electrostatic interactions with Li, thereby facilitating the extraction process. On the other hand, PEI drives the complexation reaction to completion, ensuring the formation of stable nanoparticles. Therefore, the peak extraction efficiency may be achieved when there is a balanced concentration of both PEI and DS, with higher concentrations of PEI driving the complexation reaction while excess DS molecules provide additional functional groups for enhanced interaction with Li in the nanoparticle.SEQUENTIAL EXTRACTION

[0178] Fig. 14 illustrates an example sequential critical mineral extraction process 1400. As illustrated, the example sequential critical mineral extraction process 1400 may include multiple stages. Each stage may be similar to the example critical mineral extraction process 100 illustrated and described with respect to Fig. 1A. For example, a polycation (e.g., the polycation 108) and a polyanion (e.g., the polyanion 110) may form a first polyelectrolyte complex 1414a in an aqueous solution (e.g. the aqueous solution 104) that includes critical mineral cations (e.g., the critical mineral cations 112). The first polyelectrolyte complex 1414 may be similar to the polyelectrolyte complex 114 described with respect to Fig. 1A. The first polyelectrolyte complex 1414 may be mixed via a mixer 1406 with the aqueous solution such that a critical mineral cation associates with the first polyelectrolyte complex 1414. The mixer 1406 may be similar to the mixer 106 described with respect to Fig. 1 A.

[0179] As illustrated in Fig. 14, the first polyelectrolyte complex 1414a may be formed by PEI and DS in an aqueous solution including lithium, and at least some of the lithium may associate with the first polyelectrolyte complex 1414a. The first polyelectrolyte complex 1414a may be formed as a nanoparticle, which may entrap the lithium and settle in the aqueous solution leaving a first supernatant 1416a above the settled nanoparticles. The first poly electrolyte complex 1414a with the extracted critical mineral cations (e.g., lithium) may be separated from the first supernatant 1416a and the critical mineral cations may be extracted from the first polyelectrolyte complex 1414a as described previously.

[0180] As illustrated in Fig. 14, first supernatant 1416a may include excess critical mineral cations and may be utilized for sequential extraction. In these and other embodiments, the first supernatant 1416a may be mixed with a second polyelectrolyte complex 1414b that may be formed by mixing a second polycation and a second poly anion. The second polycation and the second polyanion may be the same or different than those used to form the first polyelectrolyte complex 1414a. For example, the second polyelectrolyte complex 1414b may be similar to the polyelectrolyte complex 114 described with respect to Fig. 1A. The second polyelectrolyte complex 1414b may be mixed with the first supernatant 1416a such that the excess critical mineral cations in the first supernatant 1416a may associate with the second polyelectrolyte complex 1414b. The second polyelectrolyte complex 1414b may settle in the solution as described previously such that a second supernatant 1416b may be formed, which may include less excess critical mineral cations than the first supernatant 1416a.

[0181] The second polyelectrolyte complex 1414b with the extracted excess critical mineral cations (e.g., lithium) may be separated from the second supernatant 1416b and the extracted excess critical mineral cations may be extracted from the second polyelectrolyte complex 1414b as described previously. Thus, sequential extraction may improve the overall critical mineral extraction in an aqueous solution such as produced brine.

[0182] Although only two stages are illustrated in Fig. 14, it will be appreciated that more stages of extraction may be included in the example sequential critical mineral extraction process 1400. For example, three, four, five, six, seven, eight, nine, ten, or more stages may be included in the example sequential critical mineral extraction process 1400 based on various factors such as the initial concentration of lithium in the aqueous solution, the overall separation efficiency of each stage, costs of separation, among other factors.

[0183] Fig. 15 is a chart illustrating a normal distribution of extraction efficiency for different poly electrolyte complexes. As illustrated in Fig. 15, the example sequential critical mineral extraction process 1400 was tested using the 44.5-10 and 55-10 formulations of the polyelectrolyte complex. This was performed to simulate the stripping of Li from one unit process to another to increase the amount of Li removed. The complexation was first formulated in a 150-ppm aqueous environment, after which the Listripped supernatant is further stripped of Li with more polyelectrolyte complexations in the second stage.

[0184] To ensure reproducibility of example sequential critical mineral extraction process 1400, the results of the extraction were replicated 6 times. For formulation 44.5-10, about 46% Li was extracted in the first stage, followed by 58% in the second stage. Overall, 75.53% Li was extracted from the initial 150 ppm Li solution via the 44.5-10 formulation on average.

[0185] In the case of formulation 55-10, 42% of the initial Li concentration of 150 ppm was extracted in the first stage. In the second stage, about 58% of the remaining Li was extracted. Overall, 75.89% of the initial Li concentration was extracted from the initial 150 ppm solution by the 55-10 formulation on average.

[0186] For all 6 replicates, a normal distribution (Bell curve) has been presented in Fig. 15 and the mean and standard deviation of the extraction efficiency of the replicates is also presented. Both formulations follow a bell curve distribution with a similar mean extraction efficiency of -76%. However, formulation 55-10 appears to have a smaller standard deviation of 3.54, relative to the 4.05 of formulation 44.5, and a narrower bell curve, indicating more consistency with the extraction efficiency of the 6 replicate samples.

[0187] The above-described results indicate that dextran sulfate and polyethyleneimine polyelectrolytes may be used to develop nanoparticles / gel complexes capable of capturing lithium from single-ion Li aqueous solutions. These results may also be extrapolated to extract other critical mineral cations using the same or different polyelectrolyte complexes. Regardless of pH, the high mass ratio of PELDS produced smaller nanoparticles, whilst lower mass ratios yielded larger nanoparticles. However, at higher concentrations exceeding 3 wt.%, the nanoparticle sizes of the higher PELDS mass ratio were mostly that of excess PEI dimensions after severe precipitation and settling of the complexations. Also, the higher mass ratio of PELDS above 0.5 favored the formation of positively charged complexes, whilst lower mass ratio complexes were negatively charged.

[0188] Peak extraction efficiency generally leaned towards higher PELDS mass ratios and high concentrations of PEI and DS. At a constant formulation composition, pH had an apparent effect on lithium extraction from aqueous media. The order of extraction efficiency at different pH was as follows: pH 4.5 > pH 4 > pH 5 > pH 10 > pH 8, indicating complex pH-induced control of Li into the gel complexation pore networks. Overall, the peak extraction efficiency was approximately 55% in 1 cycle and about 80% in two cycles, achieved with a PELDS mass ratio of 4, a pairwise concentration of 10 wt.% for both PEI and DS, and a pH of 4.5.

[0189] FTIR analysis also shows that both NH2 groups and SO3 groups from the polyelectrolytes play roles in coordinating with Li+from the aqueous environment.Moreover, considerable amounts of polyelectrolytes are left over in supernatant solutions that may be utilized to form more polyelectrolyte complexations. Thus, polyelectrolyte complexes may be used to extract Li from a single ion Li aqueous solution.

[0190] One skilled in the art will appreciate that, for this and other processes and methods disclosed herein, the functions performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and operations are only provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments.

[0191] The present disclosure is not to be limited in terms of the particular embodiments described in this application, which are intended as illustrations of various aspects. Many modifications and variations can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. Functionally equivalent methods and apparatuses within the scope of the disclosure, in addition to those enumerated herein, will be apparent to those skilled in the art from the foregoing descriptions. Such modifications and variations are intended to fall within the scope of the appended claims. The present disclosure is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled. It is to be understood that this disclosure is not limited to particular methods, reagents, compounds compositions or biological systems, which can, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.

[0192] With respect to the use of substantially any plural and / or singular terms herein, those having skill in the art can translate from the plural to the singular and / or from the singular to the plural as is appropriate to the context and / or application. The various singular / plural permutations may be expressly set forth herein for sake of clarity.

[0193] It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding,the following appended claims may contain usage of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles "a" or "an" limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an" (e.g., “a” and / or “an” should be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the bare recitation of "two recitations," without other modifiers, means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “ a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “ a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and / or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”

[0194] In addition, where features or aspects of the disclosure are described in terms of Markush groups, those skilled in the art will recognize that the disclosure is also thereby described in terms of any individual member or subgroup of members of the Markush group.

[0195] As will be understood by one skilled in the art, for any and all purposes, such as in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Anylisted range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, etc. As a nonlimiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, etc. As will also be understood by one skilled in the art all language such as “up to,” “at least,” and the like include the number recited and refer to ranges which can be subsequently broken down into subranges as discussed above. Finally, as will be understood by one skilled in the art, a range includes each individual member. Thus, for example, a group having 1-3 cells refers to groups having 1, 2, or 3 cells. Similarly, a group having 1-5 cells refers to groups having 1, 2, 3, 4, or 5 cells, and so forth.

[0196] From the foregoing, it will be appreciated that various embodiments of the present disclosure have been described herein for purposes of illustration, and that various modifications may be made without departing from the scope and spirit of the present disclosure. Accordingly, the various embodiments disclosed herein are not intended to be limiting, with the true scope and spirit being indicated by the following claims.

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Claims

CLAIMSWhat is claimed is:

1. A method for extracting one or more cations from a solution, the method comprising: obtaining an aqueous solution comprising the one or more cations; forming a polyelectrolyte complex by mixing a polycation and a polyanion; mixing the polyelectrolyte complex and the aqueous solution, wherein the one or more cations associate with the polyelectrolyte complex; separating the polyelectrolyte complex comprising the one or more cations from a supernatant portion; and extracting the one or more cations from the polyelectrolyte complex.

2. The method of claim 1 , wherein the one or more cations include at least one of a monovalent metal ion, a divalent metal ion, or a trivalent metal ion.

3. The method of claim 1, wherein the one or more cations are selected from the group consisting of: aluminum, cobalt, fluorine, gallium, iridium, lithium, magnesium, natural graphite, neodymium, nickel, platinum, praseodymium, terbium, silicon, bromine, manganese, sodium, potassium, boron, zinc, tungsten, lanthanum, cerium, cesium, strontium, barium, promethium, samarium, europium, gadolinium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or combinations thereof.

4. The method of claim 1, wherein the poly cation is selected from chitosan, polyethyleneimine, poly(di allyldimethylammonium halide), polyi di allyldi methyl ammonium chloride), poly D-Lysine, poly allylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof.

5. The method of claim 1, wherein the poly anion is selected from dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of polymethacrylic acid, an alkali metal salt of 3-sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

6. The method of claim 1, wherein the polycation includes polyethyleneimine and the polyanion includes dextran sulfate.

7. The method of claim 6, wherein the one or more cations include lithium, and the lithium is entrapped in the polyelectrolyte complex via interactions between the lithium and -NH2 groups of the polyethyleneimine and -SO f groups of dextran sulfate.

8. The method of claim 1, wherein the one or more cations are entrapped in the polyelectrolyte complex via interactions between positive groups of the polycation and negative groups of the polyanion.

9. The method of claim 1, wherein the aqueous solution includes a brine.

10. The method of claim 9, wherein the brine has a lithium content of less than about 1000 mg / L.

11. The method of claim 9, wherein the brine is produced from a geologic reservoir.

12. The method of claim 1, wherein at least one of: the polyelectrolyte complex has a mass ratio of the polycation to the polyanion between about 0.1 and about 20; the aqueous solution has a PH between about 3 and about 10; a concentration of the polycation in the aqueous solution is between about 0.01 % (w / w) and about 20% (w / w); a concentration of the polyanion in the aqueous solution is between about 0.01 % (w / w) and about 20% (w / w); the polyelectrolyte complex forms a nanoparticle having a zeta potential with an absolute value between about 0 mV and about 50 mV; or the nanoparticle has a diameter of less than about 1000 nm.

13. The method of claim 12, wherein at least one of: the polycation to polyanion mass ratio is between about 1 and about 20;the concentration of the polycation in the aqueous solution is between about 0.01% (w / w) and about 10% (w / w); or the concentration of the polyanion in the aqueous solution is between about 0.01% (w / w) and about 10% (w / w).

14. The method of claim 1, wherein nanoparticles are formed by mixing the polycation with the polyanion, the nanoparticles having a polydispersity of between about 0.1 and about 4.00.

15. The method of claim 1, further comprising, after mixing the poly electrolyte complex and the aqueous solution, recovering no excess polyelectrolytes, or at least one of an excess polycation or an excess polyanion from the supernatant portion.

16. The method of any one of claims 1, 14, or 15, wherein the poly electrolyte complex is formed in solution or on a surface to form monolayer or multi-layer complexes.

17. The method of claim 1, wherein the supernatant portion comprises an excess of the one or more cations, the method further comprising: forming a second polyelectrolyte complex by mixing a second polycation and a second poly anion; mixing the second polyelectrolyte complex and the supernatant portion, wherein at least a portion of the excess of the one or more cations in the supernatant portion associates with the second polyelectrolyte complex; separating the second polyelectrolyte complex comprising the portion of the excess from a second supernatant portion; and extracting the portion of the excess from the second polyelectrolyte complex.

18. The method of claim 1, further comprising contacting the aqueous solution with a membrane, the membrane configured to extract at least one of the one or more cations, or one or more additional cations from the aqueous solution.

19. The method of claim 1, further comprising removing divalent cations from the aqueous solution before mixing the polyelectrolyte complex and the aqueous solution.

20. The method of claim 1, wherein the one or more cations are extracted from the polyelectrolyte complex via gas separation.

21. The method of claim 1, wherein the polyelectrolyte complex is formed in the aqueous solution.

22. The method of claim 1, wherein the one or more cations include lithium ions, and the lithium ions are entrapped by the poly electrolyte complex at an extraction efficiency between about 5% and about 82%.

23. A polyelectrolyte complex nanoparticle for extracting one or more cations from an aqueous solution, the polyelectrolyte complex nanoparticle comprising: a poly cation; and a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0. 1 and about 20; and wherein the polyelectrolyte complex nanoparticle comprises one or more association sites, wherein at least a first association site of the one or more association sites electrostatically associates with at least one of the one or more cations from the aqueous solution.

24. The poly electrolyte complex nanoparticle of claim 23, wherein the one or more association sites comprises a plurality of association sites that each electrostatically associate with at least one of the one or more cations from the aqueous solution.

25. The poly electrolyte complex nanoparticle of claim 23, wherein the cations are sterically entrapped in the polyelectrolyte complex nanoparticle.

26. The poly electrolyte complex nanoparticle of claim 23, wherein the polycation is selected from the group consisting of: chitosan, polyethyleneimine, poly(diallyldimethylammonium halide), poly(diallyldimethylammonium chloride), poly D-Lysine, polyallylamine hydrochloride, poly(4-vinylpyridine), or combinations thereof.

27. The polyelectrolyte complex nanoparticle of claim 23, wherein the polyanion is selected from the group consisting of: dextran sulfate, polystyrene sulfonate, sodium alginate, pectin, carrageenan, hyaluronic acid, fucoidan, polyvinyl sulfonic acid, polyacrylic acid, an alkali metal salt of polymethacrylic acid, an alkali metal salt of 3- sulfopropyl methacrylate, xylan phosphate, dextran phosphate, or combinations thereof.

28. The polyelectrolyte complex nanoparticle of any one of claims 23 to 27, wherein the polycation comprises polyethyleneimine and the polyanion comprises dextran sulfate.

29. The polyelectrolyte complex nanoparticle of any one of claims 24 to 27, wherein the one or more cations comprise lithium ions, and wherein the lithium ions are entrapped in the polyelectrolyte complex nanoparticle via interactions between the lithium ions and at least one of NH2 groups of the polycation or SO3 groups of the polyanion.

30. The polyelectrolyte complex nanoparticle of claim 23, wherein the one or more cations are entrapped in the polyelectrolyte complex nanoparticle via interactions between positive groups of the polycation and negative groups of the polyanion.

31. The polyelectrolyte complex nanoparticle of claim 23, wherein the polyelectrolyte complex nanoparticle has a mass ratio of the polycation to the polyanion between about 1 and about 10.

32. The polyelectrolyte complex nanoparticle of claim 23, wherein the polyelectrolyte complex nanoparticle has at least one of: a diameter of less than about 1000 nm or a zeta potential with an absolute value between about 0 mV and about 50 mV.

33. A polyelectrolyte complex nanoparticle comprising: a polycation; a polyanion complexed with the polycation at a polycation to polyanion mass ratio between about 0.1 to about 20; and one or more cations associated with one or more association sites of the polyelectrolyte complex nanoparticle formed by the complexation of the polycation and the polyanion, wherein the one or more cations are entrapped in the polyelectrolyte complexnanoparticle (1) sterically and / or (2) via interactions between positive groups of the polycation and negative groups of the polyanion.

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