Thermal circuits embedded in liquid crystal elastomers

Abstract

Provided herein are liquid crystal polymers and liquid crystal elastomers configured to include a thermal circuit for creating a thermal path between various nodes of the thermal circuit including a heat source, a heat sink, and an insulated area or body. The liquid crystal elastomers described herein can be configured to include portions of the thermal circuit with modified conductivities that meet specifications for heat flow along the thermal path and temperature of nodes in the thermal circuit. The liquid crystal elastomers described herein include modifiable thermal conductivities based on selected alignment of the director of the liquid crystal elastomer. Described herein are methods for designing the alignment of the directors of several different portions of the liquid crystal elastomer, and methods for utilizing liquid crystal elastomers and liquid crystal polymers to create various thermal circuits.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This patent application claims priority to U.S. Provisional Patent Application No. 63 / 138,788, filed January 18, 2021, the entire disclosure of which is incorporated by reference.

[0002] The present disclosure relates generally to liquid crystal elastomers (LCEs) and more particularly, but not exclusively, to thermal circuits integrated into LCEs. [Background technology]

[0003] This section provides background information to facilitate a better understanding of the various aspects of the present disclosure. It should be understood that statements in this section of this document are to be read in this light, and not as admissions of prior art.

[0004] Generally, polymers and elastomers are isotropic and good thermal insulators. They can be used as thermal insulators for sensitive electronic devices. While these materials have been used in electronic devices and other systems, their inherent insulating properties pose various challenges. For example, current methods and designs for modulating and controlling the thermal conductivity of the thermal path through a polymer or liquid crystal elastomer body remain limited. Furthermore, current methods generally rely on adding composite materials to the polymer or elastomer matrix to adjust the thermal conductivity, which can hinder overall performance and increase costs. Summary of the Invention

[0005] This Summary is provided to introduce a selection of concepts that are further described below in the Detailed Description. This Summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0006] In one embodiment, the present disclosure relates to a liquid crystal elastomer composition having a liquid crystal elastomer body configured to include a thermal circuit connecting a heat source to a heat sink via a plurality of first thermal paths from the heat source through the liquid crystal elastomer body to the heat sink. In some embodiments, the plurality of first thermal paths include a shortest first thermal path configured to be aligned with more than a first majority of directors along the shortest first thermal path. In some embodiments, the thermal circuit of the liquid crystal elastomer body is further configured to connect the heat source to the insulated body via a plurality of second thermal paths from the heat source through the liquid crystal elastomer body to the insulated body. In some embodiments, the plurality of second thermal paths include a second thermal path configured to be orthogonal to more than a second majority of directors along the shortest second thermal path. In some embodiments, the thermal circuit of the liquid crystal elastomer body is further configured to connect the insulated body to the heat sink via a plurality of third thermal paths from the insulated body through the liquid crystal elastomer body to the heat sink. In some embodiments, the plurality of second thermal paths includes a shortest third thermal path configured to be orthogonal to more than a third majority of directors along the shortest third thermal path.

[0007] In additional embodiments, the present disclosure relates to a liquid crystal elastomer composition having a liquid crystal elastomer body configured to include a thermal circuit with an insulated body node contact surface portion of the liquid crystal elastomer body, in some embodiments, the insulated body node contact surface portion includes a director configured to align parallel to a contact surface edge of the insulated body node contact surface portion.

[0008] In further embodiments, the present disclosure relates to a method for making a liquid crystal elastomer body having a heat sink-contacting edge that is orthogonal to the director orientation of the liquid crystal elastomer body. Generally, the method includes extruding a portion of a liquid crystal ink through a nozzle. In some embodiments, the extrusion thereby applies a shear force to the liquid crystal ink, i.e., (1) the shear force is sufficient to align the director orientation of the liquid crystal ink, and (2) the shear force is oriented orthogonal to the heat sink-contacting edge of the liquid crystal elastomer body. In some embodiments, the method further includes crosslinking the extruded portion of the liquid crystal ink to a portion of the liquid crystal elastomer having the director orientation by illuminating the extruded portion of the liquid crystal ink with ultraviolet light after the liquid crystal ink exits the nozzle.

[0009] In an additional embodiment, the present disclosure relates to a method for making a liquid crystal polymer body having a heat sink contact edge that is orthogonal to the director orientation of the liquid crystal polymer body. Generally, the method includes placing a liquid crystal mesogen mixture prepared with a non-stoichiometric ratio of functional groups for a Michael addition reaction in contact with a heat sink contact molding surface, reacting the liquid crystal mesogen mixture while the liquid crystal mesogen mixture is in contact with the heat sink contact molding surface until the reaction stops due to the non-stoichiometry, thereby creating a midpoint liquid crystal polymer body having excess unreacted functional groups with a heat sink contact edge in contact with the heat sink contact molding surface, straining the liquid crystal polymer body away from the heat sink contact edge, and exposing the midpoint liquid crystal polymer body having excess unreacted functional groups to a crosslinking stimulus configured to react a population of the excess unreacted functional groups, thereby creating a liquid crystal polymer body having a heat sink contact edge.

[0010] In another embodiment, the present disclosure relates to a method for making a liquid crystal polymer body having an insulation-contacting edge aligned with the director orientation of the liquid crystal polymer body. Generally, the method includes placing a liquid crystal mesogen mixture prepared with a non-stoichiometric ratio of functional groups for a Michael addition reaction in contact with an insulation-contacting molding surface, reacting the liquid crystal mesogen mixture while the liquid crystal mesogen mixture is in contact with the insulation-contacting molding surface until the reaction stops due to the non-stoichiometry, thereby creating a midpoint liquid crystal polymer body having an insulation-contacting edge in contact with the insulation-contacting molding surface, straining the liquid crystal polymer body in a direction parallel to the insulation-contacting edge, and exposing the midpoint liquid crystal polymer body having an excess of unreacted functional groups to a crosslinking stimulus configured to react a population of the excess unreacted functional groups, thereby creating a liquid crystal polymer body having an insulation-contacting edge.

[0011] In a further embodiment, the present disclosure relates to a method for making a liquid crystal polymer body having a heat sink contact edge that is orthogonal to the director orientation of the liquid crystal polymer body. Generally, the method includes applying an anchoring agent to a heat sink contact molding surface, placing a liquid crystal mesogen mixture prepared with a non-stoichiometric ratio of functional groups for a Michael addition reaction in contact with the heat sink contact molding surface, reacting the liquid crystal mesogen mixture while the liquid crystal mesogen mixture is in contact with the heat sink contact molding surface until the reaction stops due to the non-stoichiometry, thereby creating a midpoint liquid crystal polymer body having excess unreacted functional groups that includes a heat sink contact edge in contact with the heat sink contact molding surface, and exposing the midpoint liquid crystal polymer body having excess unreacted functional groups to a crosslinking stimulus configured to react a population of the excess unreacted functional groups, thereby creating a liquid crystal polymer body having a heat sink contact edge.

[0012] A more complete understanding of the subject matter of the present disclosure can be obtained by reference to the following detailed description in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0013] [Figure 1] 1 illustrates the layout of a liquid crystal elastomer (LCE) body made as described herein to include a thermal circuit between a heat source, an insulated body, and a heat sink. [Figure 2A]

[0033] Figure 2A shows an embodiment of thermal anisotropy created by controlling the director orientation of a portion of the LCE along a thermal path, where Kz > Kx = Ky. [Figure 2B] Various configurations of LCEs are shown. The polydomain configuration is demonstrated by mesogens that have no global alignment and form randomly oriented liquid crystal domains. Conversely, the mesogens in monodomain LCEs are oriented along the director. [Figure 2C] 1 shows thermal conductivity and temperature plots measured in two orthogonal directions for a monodomain LCE (parallel), a monodomain LCE (perpendicular), and a polydomain LCE. [Figure 3] A heat transfer specification including general terms for describing heat transfer and the thermal circuits created thereby is presented. [Figure 4] 1 shows a flow chart of a method for making an LCE composition described herein. [Figure 5] 10 illustrates an embodiment of a thermal circuit integrated into an LCE configured for use in an embodiment where the heat source is closer to the heat sink than the body to be insulated. [Figure 6] 10 illustrates an embodiment of a thermal circuit incorporated into an LCE body configured for use in an embodiment in which the heat source is located a distance away from the heat sink similar to the distance to the body or area to be insulated. [Figure 7] 1 illustrates an embodiment of a thermal circuit integrated into an LCE configured for use in an embodiment where the insulated object is disposed between a heat source and a heat sink. [Figure 8] 1 shows a flow chart of a method for making a liquid crystal polymer (LCP) body as described herein. [Figure 9] 1 shows a flowchart of a method for surface anchoring as described herein. DETAILED DESCRIPTION OF THE INVENTION

[0014] The following description and drawings are illustrative and should not be construed as limiting. Numerous specific details are set forth to provide a thorough understanding. However, in some instances, well-known or conventional details are not described to avoid obscuring the description. References to one embodiment or embodiments in this disclosure do not necessarily refer to the same embodiment, and such references mean at least one. References herein to "one embodiment" or "embodiment" or the like mean that the particular feature, polymer composition, design structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. The appearances of phrases such as "in one embodiment" in various places in this specification do not necessarily all refer to the same embodiment, nor are they separate or alternative embodiments mutually exclusive of other embodiments. Furthermore, various features are described that may be exhibited by some embodiments but not by other embodiments.

[0015] Described herein are methods and designs for modulating and controlling the thermal conductivity of multiple thermal pathways through a liquid crystal polymer (LCP) or liquid crystal elastomer (LCE) body that creates a thermal circuit therein. As described herein, LCE is used as a specific embodiment of LCP, which may include an incompletely crosslinked network, such as excess unreacted functional groups in the LCP. For example, as described herein, an LCP with controlled conductivity may include reduced thermal conductivity between an insulated body and a heat source or heat sink designed to provide or receive heat through the thermal circuit. As further described herein, the LCE body is designed to promote heat transfer along the thermal pathways between a heat source and a heat sink by modulating the thermal conductivity along these various thermal pathways, while limiting heat transfer to the insulated body via the thermal circuit (e.g., to limit heat received from the heat source and / or provided to the heat sink).

[0016] Described herein are embodiments having longer thermal paths with higher conductivity than shorter thermal paths by creating specific arrangements of directors within the LCE material. Additionally, described herein are embodiments having thermal paths with higher conductivity adjacent to thermal paths with low or relatively no conductivity. Additionally, described herein are embodiments of mapped thermal paths through the LCE body created by novel arrangements of directors, where each portion contains directional anisotropy of thermal conductivity to create these thermal paths.

[0017] FIG. 1 illustrates the layout of an LCE body 110 fabricated as described herein to include a thermal circuit between a heat source 120, an insulated body 160, and a heat sink 130. In one embodiment, the heat source 120 is packaged inside the LCE body 110, including the thermal circuit, and the heat source can be a light-emitting diode (LED) chip package with specific requirements for transparency through the LCE and / or low-distortion transmission of light on a particular side of the LCE body. For example, the bottom of the LCE may be a particularly important light output direction; therefore, the bottom side of the LCE package must be particularly transparent and / or have low optical distortion or optical dispersion. In some embodiments of the heat source 120, the heat source is sensitive to heat generation and must also have a specific heat flow to maintain the correct operating temperature of the heat source 120. One such example is an LED chip package that may overheat if there is no specific heat flow from the heat source 120 to the heat sink 130. These and other boundary requirements may define the design of the thermal circuit within the LCE body 110.

[0018] This embodiment illustrates a thermal circuit design having a heat source 120, such as an LED package, inside an LCE body 110, which covers the heat source 120. The thermal circuit can be defined by equivalent thermal resistors 150, 152, 154, and 156 between the heat source 120 and the heat sink node contact surface 132 and between the heat source 120 and three different edges of the insulator node contact surface 162, respectively. As described further herein, portions of the LCE 110 can include portions that are more transparent or have lower optical distortion than other portions of the LCE. Each of the equivalent thermal resistors 152, 154, and 156 connects to the environment 160 surrounding the LCE. In one embodiment, the requirement to keep thermal resistances 152, 154, 156 high and heat flow from heat source 120 to environment 160 through interface 162 low means that thermal resistance 150 should be kept low to facilitate heat flow from heat source 120 to heat sink 130 through interface 132. According to some embodiments described herein, heat flow can be directed through many equivalent thermal resistances by selection of LCE director alignments for many of the critical thermal paths between nodes on the thermal circuit.

[0019] The physical boundary requirements for the LCE may include, for example, that the LCE should fill all of the space between the heat source 120 and the heat sink 130, as well as a defined outer envelope 162 that serves as an interface with the external environment 160 (e.g., air). In the embodiment shown herein, there is a requirement that the interface 162 with the external environment 160 receives only a low heat flow, and thus the embodiment treats the environment 160 as an insulated body and the interface 162 as an insulated node interface edge. In an example where the heat source 120 is an LED light source, the requirement that the interface 162 receive no heat flow may be based on an optical requirement that the interface remain distortion-free over the operating temperature range, operating power dissipation range, or operating output range of the heat source 120.

[0020] Thus, thermal paths are designed into the thermal circuit of the LCE, generally represented by thermal resistors 150, 152, 154, and 156, which represent the respective resistances to heat flow between the heat source 120, the heat sink 130, and the insulated body 160 (or area / environment). These different thermal resistances can be matched to the operating requirements of the heat source 120 and the heat flow requirements of the nodes of the thermal circuit, such as the interface surfaces 132 and 162 and the heat sink 130. For example, resistor 150 strongly influences the heat flow between the heat source 120 and the heat sink 130 across interface surface 132, and this heat flow establishes the operating parameters that can be maintained by the thermal circuit, such as the operating temperatures of the heat source and the heat sink, respectively, and the heat flow through resistor 150 between those two nodes when they are at their operating temperatures. The thermal resistance characteristics of the thermal paths between the nodes of the thermal circuit built within the LCE enable novel configurations of thermal resistance paths, which can create low-resistance paths with longer thermal path lengths than high-resistance paths. Thermal circuits incorporated into the LCEs described herein can alter their thermal properties within their homogeneous LCE material using techniques of selective director alignment within the LCE body to create these different thermal conductivities. The effect of these alignments on the thermal paths can be described in standard terms for thermal conductivity, which can be compared directly or inversely as resistivity, as shown for equivalent thermal resistors 150, 152, 154, and 156 in Figure 1.

[0021] FIG. 2A shows one embodiment of anisotropy of thermal conductivity (K) created by controlling the director orientation of a portion of an LCE body. Methods for modulating an LCE to create specific thermal pathways with different properties are described herein. Thermal conductivities K are shown in the diagram along three directions: Kx along the X axis, Ky along the Y axis, and Kz along the Z axis. These different conductivities are related to the director orientation of the mesogens in the LCE aligned along the Z axis, as shown in FIG. 2A. Thus, this mesogen director alignment along the Z axis is orthogonal to the heat flow (and thermal pathways) along the X axis and the Y axis, and parallel to the heat flow along the Z axis. As described herein, modulation of conductivity along thermal pathways is created herein by modulating the director orientation relative to those heat flows. In this embodiment, calamitic, i.e., rigid-rod, mesogens are used to form a nematic liquid crystal elastomer. In other embodiments, other mesogens, such as discotic, or liquid crystal phases, such as smectic, may be used.

[0022] For example, a director orientation shown aligned with the Z axis is parallel to both thermal interface surfaces parallel to the XZ plane and thermal interface surfaces parallel to the YZ plane. This minimizes thermal conductance along the X and / or Y axes. A director orientation can be parallel to two coordinate planes and orthogonal to a third coordinate plane. As another example, a thermal interface surface parallel to the XY plane is orthogonal to a director orientation shown aligned with the Z axis. A thermal interface surface can be any surface that connects a thermal node of a thermal circuit to an interface portion of a thermal circuit created within an LCE, as described herein. Thus, there can be many interface edges contained within any interface surface, and director orientations are further described herein with respect to both interface surfaces and interface edges.

[0023] The conductivity exhibited by the LCE body in the Kz direction is significantly different from the conductivity exhibited in the Ky and Kx directions. In one embodiment, including an LCE synthesized from a functionalized mesogen of 4-(3-acryloyloxypropyloxy)benzoic acid 2-methyl-1,4-phenylene ester; 2-methyl-1,4-phenylene-bis[4[3(acryloyloxy)propyloxy]benzoate], the thermal conductivity anisotropy exhibited by the LCE includes a 100% increase in conductivity along the director orientation compared to the conductivity perpendicular to the director orientation. Other embodiments of LCE materials may provide greater thermal conductivity anisotropy based on the director orientation and a measure of director alignment, such as the order parameter of the LCE material from 0 to 1. As described herein, by creating LCEs with different alignments, different thermal conductivities can be achieved with orthogonal and parallel orientations relative to the thermal path. Similarly, intermediate conductivity values ​​can be achieved by orienting the director at an angle (e.g., 0-90 degrees) relative to the thermal path. As described further herein, different anisotropies exhibited by different LCE materials can influence different patterns of directors within the LCE thermal circuit when those properties are combined with other requirements, such as heat flow to and from the node contacts of the LCE.

[0024] As described herein, different complex strains can be applied to the LCP. Different strain rates, as described herein, can create different order parameters for the director within the LCP. The order parameter of an LCP is a measure of the average director orientation of the liquid crystal molecular axes with a preferred or measured direction (e.g., the thermal path being evaluated through the LCP). As described further herein, this measurement of the order parameter can also be described herein as the percentage of directors aligned along the measured direction. The greater the strain, the greater the order parameter created for the direction of the strain, and many different percentages of director orientation and order parameters that can be created by using complex and different strains within the LCP are described herein.

[0025] The unit volume of the LCE shown in FIG. 2A may represent a unit portion of a thermal path length. As described further herein, these unit lengths can be very short and include a small portion of the LCE body. As described further herein, multiple thermal paths can exist parallel to one another, each capable of transmitting heat between node interface edges through the LCE body. The shortest thermal path between node interface edges can be specifically designed to be thermally insulating or thermally conductive. As described herein, the thermal path created by designing the orientation of the director along the thermal path through the LCE body can include multiple three-dimensional thermal paths, such as expansion of a particular area, including through a thickness dimension. This thickness dimension can be added to the two-dimensional representation of the LCE body shown herein. These embodiments of the LCE shown in the figures include two-dimensional representations of three-dimensional LCE bodies. The descriptions of two-dimensional figures herein can be understood to include variable thicknesses, which also affect the thermal resistance of a particular thermal path between nodes in a thermal circuit.

[0026] By creating specific arrangements of directors within the LCE material, longer thermal paths have been created that have higher conductivity than shorter thermal paths. Additionally, thermal paths with higher conductivity have been created adjacent to thermal paths with low or relatively no thermal conductivity. Furthermore, by creating LCE bodies with novel arrangements of directors, thermal circuits have been created through which heat can flow, with each portion of the LCE body containing a directional portion of the thermal circuit between nodes.

[0027] Figure 2B shows various configurations on the LCE. The polydomain sample has no global alignment, while the monodomain sample has global alignment of the mesogens. The two configurations were then tested for thermal properties, some of which are shown in Figure 2C.

[0028] Tests demonstrated that polydomain LCE samples lacking long-range directional orientation (i.e., a global director) possess uniform thermal conductivity in both measured directions. Thermal conductivity remained nearly constant with increasing temperature. Conversely, monodomain samples exhibited directional dependence. Parallel to the director, thermal conductivity was approximately twice as high as perpendicular. Thermal conductivity decreased slightly with increasing temperature for both tested directions. This may be due to the fact that monodomain samples tend to contract slightly along the director when heated (and slight changes in geometry can affect readings). It should be noted that while various methods exist for fabricating monodomain samples, this property is not inherent to LCEs. To induce a monodomain structure, the LCE must be programmed and synthesized in a specific manner; otherwise, a polydomain structure would inherently form. Therefore, this property is not inherent to the materials chemistry; it depends on the method or the orientation of the liquid crystals (or mesogens) during synthesis.

[0029] The thermal conductivity, diffusivity, and / or specific heat per unit volume were measured in (1) an LCE monodomain (21 mm × 16 mm × 1 mm) aligned along the width direction, (2) an LCE monodomain (21 mm × 16 mm × 1 mm) aligned along the length direction, and (3) an LCE polydomain (21 mm × 16 mm × approx. 1.5 mm). The results for the LCE monodomain are as follows: thermal conductivity parallel to the director alignment = 0.35 W / mK; thermal conductivity perpendicular to the director = 0.18 W / mK; thermal diffusivity parallel to the director alignment = 0.167 W / mK. 2 / sec; thermal diffusivity perpendicular to director orientation = 0.087 mm 2 The thermal transport properties of the LCE polydomains are shown in Table 1 below. TIFF0007810712000001.tif29170

[0030] Additionally, the thermal conductivity, thermal diffusivity, and / or specific heat per unit volume were measured for (1) an LCE monodomain (21 mm × 16 mm × 1 mm) aligned along the width direction (i.e., perpendicular to the director), (2) an LCE monodomain (21 mm × 16 mm × 1 mm) aligned along the length direction (i.e., parallel to the director), and (3) an LCE polydomain (21 mm × 16 mm × 1.5 mm). The thermal transport properties of the LCE monodomain sample are listed in Table 2 below, and the thermal transport properties of the LCE polydomain sample are listed in Table 3 below. TIFF0007810712000002.tif37170TIFF0007810712000003.tif32170

[0031] Figure 3 illustrates a heat transfer specification, including common terminology for describing heat transfer, and the thermal circuit created thereby. Figure 3 illustrates standard terminology for describing heat flow governed by thermal conductivity (K), which is equal to the heat flow (H) multiplied by the thickness (t) of the conductor through which the heat flows, divided by the product of the area (A) of the conductor (e.g., the area of ​​the contact surface) and the temperature difference (ΔT) between the two contact surfaces. The two contact surfaces represent a unit portion of the thermal circuit, estimated for purposes of calculation and / or operation, capable of handling the heat flow H while maintaining a consistent temperature between the nodal contact surfaces.

[0032] Because any thermal path includes a non-zero cross-sectional area, each thermal path described herein includes a unit area. Thus, the shortest thermal path includes the associated unit area of ​​the surrounding LCE body when determining the thermal conductivity of that path. Along the thermal path, the portion of the LCE body that is within the unit polygon or unit area associated with and around the shortest path connecting two nodes of the thermal circuit is included.

[0033] While thicknesses and unit areas classically described in heat transfer describe length scales in meters, embodiments described herein relating to thermal circuits can include thermal paths having much smaller length scales, such as tens of micrometers, hundreds of micrometers, millimeters, tens of millimeters, and other short length scales. Thus, while the thermal paths described herein include small cross-sectional areas, the discussion relating to these cross-sectional areas and actual thermal paths includes the cross-sectional areas through which heat flows, as further described and illustrated herein. While multiple thermal paths are included in the drawings, individual specific thermal paths may be described and are readily envisioned. Thus, the specific director designs shown in the figures define different embodiments of the thermal paths, including real-world thicknesses of the designs shown in cross section. Each description herein of the director orientations of an LCE body and their associated thermal paths of thermal circuits created within the LCE body includes a complete and relevant description of various general alternative embodiments of created thermal paths that can be combined between portions of different embodiments of the LCE body.

[0034] Even in a small cross-sectional area through any material, including an LCE, there are numerous thermal paths. For example, a heat dissipation circuit for a heat source, which is an electronic circuit that must diffuse heat from a source with a specific input area to a heat sink with another specific area. The length scale of an LCE body can be very small, including as small as about 10 micrometers to several millimeters (e.g., 10 micrometers to 10 millimeters), and the length of a portion of the thermal path may be only a fraction of the length scale. Furthermore, the thickness of an LCE body can be as small as 10 or 100 micrometers.

[0035] Despite the very short length scales of the thermal paths, the heat flow differentials achieved by the selectively oriented LCEs described herein can create a strong, directional thermal circuit and support the maintenance of desired temperatures at the nodes of the circuit. As further described herein, short thermal paths can still be highly thermally resistant due to the insulating properties of the LCE along those short thermal paths. Thus, the unit of measure for the area of ​​the smallest thermal path can potentially be a small area, such as 10 micrometers by 10 micrometers, i.e., 100 square micrometers, for similarly short thermal paths of 10 micrometers or 100 micrometers. In one such embodiment, the LCE body is a thin film of LCE that provides directional thermal protection and heat flow for a thermal circuit having a heat source, a heat sink, and an insulated area.

[0036] Thus, the length scales of these thermal paths, further described herein with respect to director orientation, can be very short. Certain measurement techniques, such as probing with polarized light or X-ray diffraction (e.g., wide-angle X-ray scattering, small-angle X-ray scattering), can be used to identify director orientation. These can involve samples of one millimeter or more to produce results with discernible director orientation from samples of portions of the LCP body. Thus, in some embodiments with very small length scales, if the length scale of a single thermal path is too short to identify the director orientation along the thermal path using certain techniques for examining director orientation, additional copies of the thermal path can be used to multiply or replicate the effect of the director along the thermal path (e.g., X-ray diffraction), such as by stacking multiple units of the thermal path.

[0037] Embodiments described herein include definitions of majority director orientations oriented relative to a particular thermal pathway, such as having a director orientation of the majority director of 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95%, 97%, 99%, and 99.5% of the director, as measured by measurement techniques including using polarized light or X-ray diffraction. In some embodiments, the measurement techniques can indicate a percentage, an order parameter, or other measurement data that can be converted or interpreted as another measure of director orientation within the LCE samples described herein. In some embodiments, these majority directors can be defined as having a monodomain along that majority director orientation.

[0038] For purposes of calculations in thermal circuits, a node is considered to have sufficient thermal conductance within the node such that the temperature of the node boundary is consistent across the node contact surface. The node contact surface (e.g., boundary) of an LCE described herein includes the portion of the LCE configured to contact the node at the node contact surface. Thus, the description of a node contact surface or node contact boundary of a thermal circuit incorporated in an LCE does not include the node itself. In some cases, a single physical object can be treated as an ideal thermal node, providing heat at a single, consistent temperature to all contact surfaces of the node body. In other instances, such as when extreme heat transfer can cause temperature differences along different points of the node contact surface, a node can be modeled as one or more nodes. For example, a heat sink with sufficient thermal conductance between portions of the heat sink (e.g., made of a thermally conductive metal) to withstand the absorbed heat flow can, under certain conditions, be modeled as having a single thermal contact surface and a single node in the thermal circuit.

[0039] Under other operating conditions, a heat sink can include more than one node. For example, in response to extreme heat transfer to one portion of the heat sink, the heat sink interface can heat up around that portion of the heat sink, causing a temperature increase compared to other portions of the heat sink. In these cases where heat flow (e.g., from the heat source, to the heat sink, or in either direction to the insulated body) overloads the node requirements for heat flow, multiple nodes can be created because the overloads on those different thermal paths cause temperature changes to separate portions of the node. In this case, a second node can be created, allowing excess heat flow to or from that portion of the node and allowing the circuit to be modified to accommodate that flow as needed by creating new LCE director orientations and thermal circuits between all nodes.

[0040] Thus, from the thermal circuits incorporated into the LCEs described herein, including generalized heat sources, generalized heat sinks, and generalized insulated bodies, any number of designs can be created to include any thermal circuit that can be created using resistive materials and any of the several boundary constraints described herein. In additional embodiments, the LCE bodies described herein can incorporate and include more complex thermal circuits that include multiple nodes, poorly defined or distributed nodes such as parasitic heat sources or heat sinks, or interfaces and thermal paths for non-direct heat sources such as radiation absorption.

[0041] In additional embodiments, the thermal circuit incorporated in the LCE may include fewer node interfaces, such as only two nodes, such as a heat source node interface and a heat sink node interface, without a defined insulated body / insulated area node interface to protect against heat flow within the thermal circuit. In other embodiments, such as in embodiments where the heat source is unknown or distributed within the body of the LCE, the thermal circuit within the LCE may include only two node interfaces, including an insulated body node interface and a heat sink node interface. As described herein, many ambient node interfaces exist, for example, via air contact around the interface edges of the LCE body. As further described herein, these node interfaces with the ambient or external environment may include requirements associated with thermal requirements, including optical transparency and uniform heating requirements.

[0042] In other embodiments, the LCE body can have directors oriented to create thermal insulation only in the portions of the LCE adjacent to the node contact edges of the LCE body. In alternative embodiments, based on the requirements of the thermal circuit and the anisotropic properties of the LCE material, the directors of the remaining portions of the LCE body between the node contacts may be oriented in a direction that further insulates the node contact edges from each other. As an example of an LCE body with insulating node contact surfaces, the LCE body can include opposing surfaces (e.g., top and bottom, left and right) necessary to insulate from heat flow through the surfaces and into and out of the remainder of the LCE. In this embodiment, the portions of the LCE proximal or adjacent to the node contact edges have directors oriented parallel to those contact edges. Based on the insulating properties of the LCE, the remaining portions of the LCE body may have directors configured in an adiabatic orientation relative to those node contact edges, or may be oriented in another direction due to other properties of the LCE.

[0043] FIG. 4 shows a flowchart of a method for making the LCE compositions described herein. Method 400 describes a method for creating a specific arrangement of director orientation within an LCE by extruding 402 a portion of liquid crystal ink through a nozzle and applying shear force 404 to the liquid crystal ink while extruding the ink through the nozzle, thereby controlling the orientation of the director within the LCE to align with the direction of the shear force. The shear force is sufficient to align 404 the director of the liquid crystal ink along the direction of the force before exposing 406 the ink to a crosslinking stimulus, such as light in embodiments of liquid crystal inks that include a photoinitiator. In one embodiment, crosslinking 406 is induced by exposing the liquid crystal ink to ultraviolet (UV) light. This exposure can be configured to crosslink 406 the liquid crystal ink into the LCE while orienting 404 the director along the direction of the shear force applied by the nozzle as the ink is extruded 402.

[0044] After crosslinking 406 by initiating crosslinking (e.g., by exposure to UV light), the method may include a step of second-extruding 408 a second portion of the liquid crystal ink through a nozzle. This second-extruded 408 second portion of the liquid crystal ink may contact the previously crosslinked 406 first portion of the LCE. After extruding 408 the second portion of the liquid crystal ink through the nozzle, the second portion of the liquid crystal ink may be exposed to a crosslinking initiator, such as UV light 410. When the second portion of the liquid crystal ink is in contact with the first portion of the LCE, in some embodiments, a second illumination 410 chemically bonds the second portion of the liquid crystal ink and the first portion of the LCE. In some embodiments, the first illumination of the first portion of the liquid crystal ink with UV light is adapted to leave unreacted portions of the first portion of the liquid crystal ink. In these embodiments, these unreacted portions of the first portion of the liquid crystal ink allow additional chemical bonding between the first portion of the LCE and the second portion of the liquid crystal ink by the method step of second-illuminating both with UV light.

[0045] Following the second extrusion of the second portion of the liquid crystal ink through the nozzle (step 408), multiple subsequent portions of the liquid crystal ink may be extruded, including portions of the liquid crystal ink that remain incompletely crosslinked, to increase chemical bonding between different portions of the LCE created by the multiple crosslinking steps. Thus, the extrusion step 408 and chemical bonding step 410 may be repeated over multiple iteration cycles to create larger, more complex LCE bodies. The direction of the shear force applied in each extrusion step applies a shear force to each of the portions of the liquid crystal ink, thus controlling the director orientation in the portions of the liquid crystal ink as they are extruded through the nozzle. As described further herein, an entire body of LCE material can be created with individual director orientations applied to the smallest portion of the LCE ink available for extrusion through the nozzle (steps 404, 408). These portion sizes of the liquid crystal ink and LCE can contain very small monodomains of director orientation, which may have orientations aligned or perpendicular to the thermal pathways of the LCE, as described further herein. For example, in the embodiments shown herein of thermal circuits integrated into LCE bodies, director orientation can be controlled over large areas and gradually constructed by additive manufacturing techniques such as extruding liquid crystal ink from a nozzle to control the director on small length scales controllable by a printing nozzle.

[0046] In some embodiments, the method includes a third illumination step 412 in which the LCE body is illuminated with UV light after multiple portions of the liquid crystal ink have been extruded 402, 408 and chemically bonded 410 to one another. In many embodiments, the LCE bodies described herein have multiple portions of the liquid crystal ink chemically bonded to one another. This third illumination step 412 with UV light can be designed as a final curing phase for the entire LCE body, including the multiple portions. The third illumination step 412 can be performed over the entire LCE body at a higher UV light intensity or energy for an extended period of time (e.g., one hour, several hours) to ensure that any remaining unreacted or uncrosslinked mesogen populations of the LCE are fully crosslinked by the third illumination step.

[0047] FIG. 8 shows an embodiment of a flowchart of a method 800 for making an LCP body, as further described herein. The method includes step 802 of placing a liquid crystal mesogen mixture in contact with a contact molding surface, thereby defining a contact edge in the liquid crystal mesogen mixture. The method then reacts the liquid crystal mesogen mixture (804) until reaction ceases due to non-stoichiometry of functional groups in the mesogen mixture, thereby creating an LCP body with excess unreacted functional groups. The method then distorts the LCP body in a direction (e.g., perpendicular, parallel, or at an oblique angle) relative to the contact edge (806). The method then exposes the LCP body with excess unreacted functional groups to a crosslinking stimulus, thereby reacting the unreacted functional groups and creating an LCP body with a contact edge (808).

[0048] In one embodiment, the liquid crystal mesogen mixture 802 placed in contact with the contact molding surface is a liquid crystal mesogen mixture containing a non-stoichiometric ratio of functional groups (e.g., a functional group with an excess of thiol functional groups over acrylate functional groups). Such limited reaction can be explained by a Michael addition reaction. In one embodiment, these functional groups of the mesogen mixture can be thiol groups and electron-deficient groups (e.g., acrylate groups), and the non-stoichiometric ratio can include an excess of acrylate groups. In this embodiment, the mesogen mixture can be first reacted so that the thiol groups and acrylate groups react until the thiol groups have reacted with the acrylate groups (e.g., until completion, after a certain period of time), thereby creating an LCP body 804 with additional unreacted acrylate functional groups. In other embodiments, other chemistries for liquid crystal mesogen mixtures containing different functional groups, including different secondary crosslinking stimuli, can be used.

[0049] Other Michael addition reactions can be used herein. Other ways of creating non-stoichiometric functional groups (e.g., thiol groups, acrylate groups) can be used with these described methods, including, for example, solutions containing a single composite mesogen containing both thiol and acrylate functional groups. The reactions described herein have been demonstrated with non-stoichiometric acrylate group to thiol group ratios greater than 1:1 and less than 2:1. In particular, solutions with a non-stoichiometric ratio of 1.15:1 were used in many of the examples herein.

[0050] The method 800 then continues by reacting the liquid crystal mesogen mixture until the Michael addition reaction has stopped due to the reaction of all or nearly all of one of the stoichiometrically matched functional groups in the mixture, thereby creating an LCP body having some unreacted functional groups 804. For example, reacting the liquid crystal mesogen mixture in contact with a contact molding surface 804 creates a contact surface (e.g., including the contact edge) of the LCP body in contact with (e.g., pressed against) the contact molding surface and having excess unreacted functional groups.

[0051] In one embodiment, the contact molding surface is a solid surface. In other embodiments, the contact molding surface may be a flexible surface, such as a pliable bladder or a fluid (e.g., air). In one embodiment, a pressure (e.g., force, stress) is maintained between the contact molding surface and the mesogenic mixture while reacting 804 to maintain contact with the molding surface.

[0052] In one embodiment, the LCP body having unreacted functional groups remains in contact with the interface molding surface after the first stage of the Michael addition reaction (e.g., after completion of the first reacting step 804). In another embodiment, the LCP body may be removed from contact with the interface molding surface after completing the reacting step 804.

[0053] The method 800 then strains the liquid polymer body relative to the interface edge 806. The LCP, which has excess unreacted functional groups, can be strained 806 to align the director orientation of the polymer with the direction of strain. The unreacted functional groups can then be exposed to a crosslinking stimulus 808 while maintaining the strain (e.g., at the same strain, at a different strain), to fix and lock the director orientation in that direction. This newly locked orientation of the director can be referred to as shape fixing in the LCP, as described herein.

[0054] For example, the macroscopic property of shape fixation is another measure (e.g., percentage) of the fixed director orientation created by the exposing 808 step (e.g., crosslinking step). Shape fixation can be defined as the ratio of fixed strain to applied strain. The fixed strain remains after the exposing 808 step and after releasing the strain from the LCP (e.g., removing the LCP from the straining device). The applied strain used in the calculation is the constant strain applied during the straining 806 step. In some embodiments, the applied strain during the straining 806 step used in the calculation is the average applied strain or the midpoint of the applied strain. In other embodiments, the applied strain is the maximum applied strain during the straining 806 step.

[0055] Shape fixity after the exposing step can reach 90%, 95%, or even more, such as when the LCP maintains a strain of 270% or more after the release of a straining device (e.g., removing the LCP from the fixture) that imposes a constant 300% strain. As described further herein, the LCP herein can have aligned strains in multiple directions and / or multiple strain rates around the node contact surface edges, as well as throughout the LCP body. Therefore, these post-strain shape fixities must be considered when sizing the initial creation 804 of the node contact surfaces of the LCP body before straining 806, as the node contact surface surfaces will retain the majority of the strain applied by the method.

[0056] The strains 806 applied herein are described as being perpendicular, parallel, and oblique to the contact surface edges with the thermal circuit nodes. As further described herein, the conductivity of an LCP is greatest for heat flow along or parallel to the director orientation, while the conductivity is lowest for heat flow perpendicular to the director orientation. Additionally, there is an intermediate conductivity for heat flow at an oblique angle to the director orientation (e.g., between perpendicular and parallel to the director orientation).

[0057] To create a complex thermal circuit through the LCP, strains in multiple directions can be applied to different portions of the LCP (806), including complex maps of director orientations as described further herein. Similarly, thermal circuit node contacts (e.g., heat sink contacts, insulation contacts, heat source contacts) may have node contacts with complex geometries, thus requiring complex equipment or fixtures to maintain the LCP straining 806 step. In some embodiments, the LCP straining 806 step continues throughout the LCP exposing 808 step. In other embodiments, the straining 806 step may be released before the exposing 808 step is completed. In still other embodiments, the straining 806 step can include applying different levels of strain and / or applying different stresses during the exposing 808 step.

[0058] The complex distortions and complex shapes of the node contact surfaces required for different embodiments herein can be created using appropriately designed fixtures or drawing devices. In alternative embodiments, the LCP can be strained with complex distortions (806) to create complex patterns of director orientation, as described further herein. For example, certain thermal circuit nodes are shown herein having circular or curved contact surface surfaces; these curved surfaces may require a curved fixture or curved drawing device to apply distortion in specific directions relative to the node contact surface edges. For example, a circular node contact surface can be strained circumferentially (e.g., around the circumference of the curved contact surface edge) by being pressed against a device that expands the circumference. The shapes of the contact surface edges described herein can be regular or irregular. For example, a conical device can be used to expand the circumference of a circular node contact surface, thereby distorting the LCP at each point tangential to the circle and therefore parallel to the contact surface edge (e.g., creating an insulating node contact surface).

[0059] Complex stretching devices can create different strains (e.g., different amounts, different directions) along the interface edge. As an example, the heat source 702 node interface edge shown in FIG. 7 can create different strain concentrations around portions of the circumference of the interface edge depending on the device used to strain the LCP portion of the heat source node interface. As another example, a thin film having two broad surfaces and a small height dimension of the film can be stretched in one or more directions along the surface of the film (e.g., orthogonal to the height dimension of the thin film), thus creating a director orientation parallel to the surface of the film, which can also function as an insulation interface node interface.

[0060] In alternative embodiments, the LCP can be strained away from the interface edge to create a director orientation that is orthogonal to the interface edge 806. In some embodiments, orientations at angles other than orthogonal or parallel to the thermal circuit node interface edge can be used to create different conductivities adjacent that interface edge, as described further herein.

[0061] In some embodiments, a device or fixture for straining the LCP can be attached to an attachment aid portion of the LCP body. This attachment aid portion can be used in the straining 806 step (e.g., to transmit strain and equalize strain along the interface edges) and may be intended to be removed after the straining 806 step is no longer needed. For example, a thin film can have an attachment aid portion attached to its thin dimension to allow the thin film to be strained along its thin dimension for processing, with the attachment aid portion later removed (e.g., after the straining 806 step is completed, when the straining step is reduced). As another example, before segmenting a large LCP thin film into many smaller thin films, a larger LCP thin film portion with excess unreacted functional groups can be created (804), strained (806), and exposed to a crosslinking stimulus (808). In this embodiment, many of these thin films serve as attachment aid portions for other smaller thin films. The attachment portion can be modified based on the straining 806 step to create different strain concentrations across the contact surface edge of the LCP, including increased strain concentration or equalized strain near the contact surface edge.

[0062] The method 800 then exposes the LCP with excess unreacted functional groups to a crosslinking stimulus 808 configured to react the excess unreacted functional groups in the LCP. As further described herein, this exposure 808 and the resulting crosslinking create a lock in the director orientation. In some embodiments, the partial exposure 808 of the LCP with excess unreacted functional groups results in both partial crosslinking of the excess unreacted functional groups and partial shape locking of the resulting LCP. The lack of shape locking of the unreacted functional groups in an LCP portion can affect the order parameter of the portion and the conductivity of the portion, potentially creating an intermediate value between maximum and minimum conductivity. In one embodiment, the crosslinking stimulus described herein includes exposing the LCP to UV light to react the excess unreacted functional groups. In one embodiment, a crosslinking initiator is included in the mesogen mixture to react the unreacted functional groups.

[0063] Different embodiments of the Michael addition reaction and mesogen mixture can include different cross-linking initiators to drive the Michael addition reaction to completion and fix the director orientation in alignment with the applied strain 806. For example, in the case of a thiol-acrylate mesogen mixture containing an excess of acrylate, a cross-linking photoinitiator can be used to react any unreacted acrylate functional groups remaining in the LCP. The thiol-acrylate chemistry described herein is one example of many potential liquid crystal mesogen mixtures that can use the Michael addition process reaction described herein to create complex maps of director orientation within the LCP.

[0064] In various embodiments, thin layers of LCE and / or LCP can be used to create flexible electronics (e.g., thermal circuits, flexible displays). In such embodiments, the bending strain of the thin films is inherently low, so that the bending strain of the thin films has minimal effect on the overall director orientation. In some embodiments, the flexible electronics is a display and the LCE and / or LCP materials are transparent. In other embodiments, the flexible electronics is a thermal circuit.

[0065] FIG. 9 illustrates a method 900 for surface anchoring according to an embodiment of the present disclosure. Method 900 begins with step 902 of applying an anchoring agent to a molding surface. In some embodiments, the anchoring agent is homeotropic to create alignment perpendicular to the mold surface. In some embodiments, the anchoring agent is flat to create alignment parallel to the mold surface. In some embodiments, the anchoring agent is a polyimide or polyamide. After applying 902 the anchoring agent, a liquid crystal mesogen mixture is placed in contact with the molding surface 904. The mesogen mixture is allowed to align with the anchoring agent 906. Following step 904 of contacting the liquid crystal mesogen mixture with the molding surface and step 906 of aligning, the mixture is exposed to UV light for curing 908. In some embodiments, the flat anchoring agent is rubbed with a felt to induce a director profile in the thermal circuit.

[0066] 5 shows an embodiment of a thermal circuit integrated into an LCE configured for use in embodiments where the heat source is closer to the heat sink than the insulated body. The LCE body 510 is an enclosure for a heat source 520, which in some embodiments can be a solid-state device or light source such as an LED. For example, the solid-state device can be a microprocessor or integrated circuit that sits in thermal contact with the heat sink, separate from the rest of an electronic circuit board, which can contain heat-sensitive equipment and is therefore an insulated body or area node in the thermal circuit.

[0067] LCE body 510 exhibits director orientations within the LCE for several different portions of the thermal circuit and for effective thermal paths from heat source 520 through LCE body 510 to various interfaces with the environment, such as interface 540 with heat sink 530 and primary window interface 548 with an external environment, such as air or another fluid. In one embodiment, heat source 520 may be an LED, and primary window interface 548 may be a relatively transparent, undistorted opening through which radiation from the LED can exit.

[0068] This embodiment showing a thermal circuit integrated into an LCE includes parallel director orientations of the LCE along three adjacent portions of heat source interface edges 524, 526, and 528. In the illustrated embodiment, the parallel director orientations to the interface edges remain uninterrupted along the shortest thermal path between the heat source 520 and the portions of the LCE interface with the external environment, such as interface portions 544 and 548. In one embodiment, the parallel director orientations are formed as a monodomain within the LCE, creating relative permeability or transparency through the portions of the LCE interface with the external environment, including interface portions 544 and 548.

[0069] In the illustrated embodiment, the director orientation of LCE body 510 adjacent contact surface edges 524, 526, and 528 is parallel to those contact surface edges, respectively, thereby creating a high thermal resistivity portion of the LCE around heat source 520. This additional insulation around the three sides 524, 526, and 528 of the heat source requires a greater proportion of the heat flow transport requirements to be carried by the thermal path between contact surface edge 522 with heat source 520 and contact surface edge 540 with heat sink 530. However, in this embodiment, this configuration with reduced heat transport capacity is selected to create a greater region of light transmission and transparency through LCE body 510 for portions of LCE body 510 configured to transmit light from the heat source to the external environment.

[0070] The thermal pathways in the LCE body 510 between the heat source 520 contact edge 522 and the heat sink 530 contact edge 540 are designed with directors oriented nearly perpendicular to the heat source contact edge 522, with a deviation angle from perpendicular in this embodiment designed for the heat spreading portions of the LCE body 510. In these heat spreading regions, the directors deviate from perpendicular by a small angle to spread the heat and accommodate the different lengths of the contact surfaces 522 and 540. These heat spreading portions of the thermal circuit accommodate the difference in length between the heat source top contact edge 522 through the LCE body 510, and the directors create conductive thermal pathways that spread heat across the longer length of the heat sink 530 contact surface 540. Heat spreading through these diffusion thermal pathways can be achieved by spreading in one or more dimensions, as needed, for each portion of the respective contact surfaces 522, 540.

[0071] The degree of deviation from orthogonal relative to the contact surface 522 may be determined by the requirements of the heat source 520 node in the thermal circuit and other requirements of the LCE body 510. As described further herein, other requirements of the LCE, such as the transparency and / or transmittance of the LCE, can further refine the selection of orthogonal directors in particular portions of the LCE body 510. Thus, in some other embodiments, other portions of the LCE body 510 can have all or substantially all of the directors aligned to create transparency in those portions, such as in the embodiment described herein for the portion of the LCE between the heat source contact surface 528 and the primary window contact surface 548 between the LCE body 510 and the external environment. For example, in one embodiment, to increase transparency through the portion of the LCE adjacent the contact surface portion 542, the LCE can eliminate some or all of the shift in director orientation in the portion of the LCE body 510 along the contact surface edge 522 and in the portion of the LCE body 510 between the heat source 520 and the heat sink 530. In some embodiments, the monodomain may be formed from a director adjacent to a contact surface edge of a node contact surface of the LCE body 510, such as a monodomain aligned with the contact surface edge or aligned perpendicular to the contact surface edge.

[0072] In the thermal circuit embodiments described herein, other boundary conditions of the LCE and the thermal circuit may be considered as well. For example, the equal shortest thermal path lengths between the heat source contact surfaces 524, 526, and 528 and the LCE contact surface portions 544 and 548 are an effect of these contact surfaces being parallel and are shown as one embodiment only. Actual contact surfaces may exhibit an array of thermal path lengths, including a single shortest thermal path between the contact surfaces, as shown in the further example of the node contact surface, and thermal paths of different lengths. As another example of a boundary condition, the LCE body 510 may be required to fill the physical space between the insulated body and the heat source and / or heat sink (e.g., no voids, to provide physical support). As another example of a boundary condition affecting the thermal circuit, a limited amount of LCE may be fitted between the heat source and heat sink, thus requiring additional conductive and circuitous thermal paths through the thermal circuit described with respect to different embodiments herein. Other boundary conditions may include an insulated body disposed between the heat sink and the heat source, or an insulated body with a shorter thermal path through the LCE to the heat sink and heat source than the thermal path between the heat sink and the heat source through the LCE. Many potential requirements and design parameters are described herein for designing thermal circuits and LCE bodies to meet both the thermal conduction requirements and other physical requirements of thermal circuits integrated into the LCE.

[0073] The portion of the LCE body 510 that interfaces with the external environment (e.g., air, another fluid) includes certain portions that may have requirements separate from thermal requirements (e.g., transparency based on director orientation) or related to thermal requirements (e.g., transparency related to relative lack of thermal distortion). A primary window LCE interface portion 548 is shown at a portion of the LCE interface with the external environment, with a portion of the LCE aligned to be relatively transparent from the heat source interface 528 through the LCE and out of the interface portion 548. In the illustrated embodiment, the parallel alignment of the directors at the primary LCE interface 548 and the portion of the LCE adjacent the side window 544 ultimately reduces heat dissipation away from the heat source (e.g., through the interface surfaces 524, 526, 528) at the expense of increased transparency in the window portion, thereby interrelating some of the design requirements of this LCE body 510.

[0074] The LCE body 510 shows corner contact surface portions 546 of the interface between the LCE and the external environment. In the illustrated embodiment, there may be additional requirements for heat flow between the heat source and the corner contact surface portions 546; these contact surfaces 546 may not be required to be optically transparent, but may remain insulated to meet the continued low heat flow requirement. For example, the optical path through the LCE to the heat source through the contact surface 546 may include multiple director orientations and thus lack transparency relative to the rest of the LCE. In one embodiment, for example, because the LCE packaging is designed not to heat up or cause thermal warping, the corner contact surface 546 must still receive only a low heat flow from the heat source; therefore, the portion of the LCE between the heat source 520 and the contact surface 546 must still be an insulator-node interface. Thus, despite the lack of optical transparency of the LCE body beneath these interfaces 546, the interfaces themselves can still be insulated based on the tangential orientation of the directors irradiating the interfaces 546 from the corners of the heat source interface edges 524, 526, 528.

[0075] Some embodiments of the LCE body 510 and other LCE bodies shown herein include a substantial thickness dimension that allows for director selection similar to the discussion herein of in-plane thermal paths. Many of the figures showing mesogen orientation herein include only one plane, and the discussion should be understood to include the three-dimensional nature of thermal paths with non-zero cross-sectional areas. Thermal paths can also travel in three dimensions, and the shortest thermal path can be measured as the path that traverses the third dimension.

[0076] 6 illustrates an embodiment of a thermal circuit incorporated into an LCE body configured for use in an embodiment in which a heat source 602 is located a distance from a heat sink 604 similar to the distance to the insulated body or area 606. Each of the nodes is shown with the shortest thermal path 608, 610, 612 through the LCE between the nodes.

[0077] Director orientations around these shortest paths often define the dominant conduction heat path (e.g., conducts the most heat) based on the heat flow equation and the dominance of form factor factors (e.g., path length and area). However, the shortest heat path may not be the dominant heat conduction path due to the conductivity along that path, which is controlled and modulated by the director orientation. These heat paths are further described herein based on how their conductivity is adjusted by the director orientation to control which path is the dominant heat conduction path and utilize longer paths for the conduction of the dominant heat flow.

[0078] The LCE body includes complex thermal circuits that balance heat flow from the nodes based on conductivity and length while also satisfying certain boundary requirements, including the heat flow requirements of the nodes 602, 604, and 606. Additional requirements for the LCE body, as well as the physical requirements of the LCE body's boundary 620, and the requirement that the LCE fill the volume between the node interfaces 602, 604, and 606 (e.g., no voids for thermal insulation), are present. While there are many thermal paths between each of the nodes, for simplicity, only the director orientations along the shortest thermal paths 608, 610, and 612 are described in detail. Other director orientations to create other thermal paths can be inferred from these descriptions, as shown in the figures and described further herein. In some cases, little or no heat flow occurs because the thermal paths are redundant or dominated by other paths, as described further herein. In these dominant paths without significant heat flow, there are no thermal requirements for the LCE body, and other non-thermal requirements may dictate the LCE design for that portion.

[0079] In one embodiment, the shortest thermal path 608 is a straight line. As described herein, the shortest thermal path through an LCE body is the shortest thermal path that includes a perimeter cross-sectional area that can be drawn with the shortest thermal path through the LCE body. Thus, in one embodiment, the shortest thermal path is a curved path that includes a cross-sectional area for heat conduction along that path. For example, the shortest thermal path can be a curved path if there are boundary constraints that limit the ability of the shortest thermal path to be a straight line and force the shortest path to follow a curved path through the LCE body between two nodes (e.g., the edge of the LCE body). While alternative thermal paths can add to the heat-carrying capacity of the thermal circuit between nodes, the shortest thermal paths 608, 610, 612 between those nodes are described herein for the purpose of describing the orientation of the director along those shortest thermal paths. These paths are particularly important because they are likely candidates for the dominant thermal path for heat flow between nodes and therefore, modulating thermal conductivity can significantly affect the operation of the nodes.

[0080] As described further herein, various thermal requirements of the node (e.g., heat flow, operating temperature) may influence different embodiments of director alignment along the shortest thermal path. For example, these thermal requirements, as described further herein for node heat flow, may influence the decision of whether to include a portion of the LCE having directors parallel to the shortest thermal path at the node interface, or whether to include only directors orthogonal to the shortest thermal path (and tangential to the node interface). Accordingly, several alternative embodiments herein include descriptions based on populations of directors aligned along portions of those paths or the degree of director alignment. Furthermore, director orientation may be described with respect to only the portion of the thermal path adjacent to the interface and / or only the portion of the thermal path that is closer to or further away from the node interface.

[0081] The LCE body along the shortest thermal path 608 between heat sources 602 within the heat source-sink 604 creates a dominant thermal path through the LCE body configured in a director orientation that induces high conductivity along the path. In one embodiment, the director orientation induces high conductivity along the entire thermal path from the edge of the interface with the heat source 602 to the edge of the interface with the heat sink 604. In some embodiments, the director orientation along the shortest thermal path 608 between the heat sources 602 within the heat sink 604 can include a monodomain or multiple portions of a monodomain of director aligned along the shortest thermal path.

[0082] The LCE body along the shortest thermal path 610 between the heat source 602 and the insulated area 606 contains a majority of director orientations orthogonal to the shortest thermal path, thereby creating a thermal path that is largely insulating. However, as described further herein, along the thermal path, specifically in the portion of the LCE adjacent the contact surface edge of the heat source 602, there are portions of the shortest thermal path 610 that contain aligned directors.

[0083] In one embodiment, along a small portion of the shortest thermal path 610 between the heat source 602 interface and the insulated area or body 606, the director orientation of the LCE adjacent the heat source 602 interface edge is perpendicular to the interface edge, thereby creating a highly conductive portion of the LCE along the shortest thermal path. This orientation continues only for some short threshold distance from the heat source 602 interface. Thus, the shortest thermal path 610 can be configured to guide heat away from the heat source, spread the heat (and the thermal path) over a larger area of ​​the LCE, and then shift the director orientation so that it is oriented parallel (e.g., tangential) to the heat source 602 interface and parallel (e.g., tangential) to the insulated body 606 interface. These embodiments of portions of the LCE body near the node interface and having directors orthogonal to the heat source 602 interface edge can be used when heat flow from the heat source requires additional thermal paths to carry heat away from the heat source, such that the directors begin to orthogonal to the heat source interface edge and, after a threshold distance shift, their orientation points away from the insulator and possibly toward the heat sink 604. This orientation of the directors is orthogonal to the heat source 602 interface edge (e.g., around part or all of the boundary of the heat source node in the thermal circuit, a specific portion that increases heat flow near the LCE directly adjacent the heat source). As shown by the map of director orientations, this localized heat flow away from the heat source 602 (e.g., along the shortest thermal path 610 between the heat source and the insulated area 606 over a threshold distance adjacent to the heat source) is only present in the portion of the shortest thermal path 610 directly adjacent to the heat source interface, increasing the area of ​​the shortest thermal path to a practical cross-section required to transport heat from the heat source.

[0084] This embodiment, in which a portion of the directors are oriented perpendicular to the heat source contact surface in the adjacent portion of the shortest thermal path 610, can be used in certain cases, such as when there is a large or significant anisotropy between the thermal conductivity of the LCE between parallel and orthogonal director orientations. For example, this embodiment can be used when there is a large heat flow requirement for heat flow out of the contact surface with the heat source 602 and when there is a large anisotropic thermal conductivity such that heat flow parallel to the director orientation is significantly better than heat flow perpendicular to the director orientation. A director orientation perpendicular to the heat source contact edge can be used for contact surface portions of the LCE to increase local heat flow across the contact surface edge at some portions of the contact surface with the heat sink.

[0085] Thus, this embodiment of director orientation along the shortest thermal path can be used to avoid heat generation in portions of the heat source 602 that could raise the temperature of the heat source outside of operating parameters and / or create two temperatures along the node interface. If the node has a second temperature, the node is split into two effective nodes, thereby creating a new thermal path, and possibly a new dominant thermal path, based on the new node temperature. As shown in the embodiment and described further herein, different decisions can be made about the director orientation along the shortest thermal path between nodes based on the conductivity of the LCE body, the magnitude of the anisotropy in conductivity between heat flow orthogonal to the director orientation and heat flow in the direction of the director orientation, and requirements for reduced heat flow into and out of the insulated area / body 606.

[0086] In some embodiments, the requirements for the shortest thermal path 612 through the LCE body between the heat sink 604 and the insulated body 606 can be designed similar to the shortest thermal path 610. For example, the requirements for constraining heat flow along the shortest thermal paths 610, 612 can be similar, especially if the temperature difference is similar between nodes, there are no asymmetric heat flow requirements (e.g., the insulated body must be insulated more from the heat source than from the heat sink), and / or each of the nodes is arranged as shown with three shortest thermal paths having similar path lengths. While the LCE body includes similar director orientations along the shortest thermal path 610 and the shortest thermal path 612 in the illustrated embodiment, other design decisions can be made based on different heat flow requirements.

[0087] 7 illustrates an embodiment of a thermal circuit incorporated into an LCE body 710 configured for use in an embodiment in which the contact surface with an insulated body 706 is located between the contact surface with a heat source 702 and the contact surface with a heat sink 704. Specific boundary conditions create different parameters for designing the director orientation of the LCE body, including physical boundary conditions of the LCE body, such as physical edges 720 (e.g., the interface edges with the environment). As shown, the contact surface with the insulated body 706 is located between the contact surface portion with the heat sink 704 and the contact surface portion with the heat source 702, but the contact surface with the insulated body is not centered between all portions of the contact surface with the heat source and the heat sink. Thus, there are different portions of the contact surface with the heat source 702 and the contact surface with the heat sink 704 that alternatively have a thermal path through the LCE separated by the insulated body 706, and several different portions of those nodes that have a direct thermal path passing near the contact surface with the insulated body.

[0088] In some embodiments, the physical boundary conditions of the LCE, including the peripheral boundary 720 of the LCE body 710, act to constrain direct thermal paths between the heat source 702 and the heat sink 704. For example, the heat source 702 and the heat sink 704 may have difficult-to-meet heat flow requirements for the number of thermal paths between two nodes that are constrained by the physical limitations of the LCE, whether those limitations are due to the in-plane constraints of FIG. 7 or a combination of those in-plane constraints and the thickness constraint of the LCE body 710. These physical boundary constraints of the LCE may require additional thermal paths that are oriented for conduction but are neither straight nor the shortest thermal path.

[0089] 7 , the direct and shortest thermal paths between the heat source and heat sink do not all include directors that are generally oriented perpendicular to the contact surface edge of the heat source 702 and / or the contact surface of the heat sink 704 (e.g., directors that are all oriented along a direct thermal path). In other words, in embodiments of the LCE body 710, the LCE body includes director orientations selected for each portion of the LCE body as a result of increased requirements for limiting heat flow into and out of the insulated body 706. Thus, in some embodiments of the LCE body 710, a primary design consideration is the amount of insulating LCE that surrounds the insulated body 706. For example, in each of the portions of the LCE body 710 that surround the insulated body along the bottom of the LCE physical boundary 720, all of the directors are oriented tangentially to the insulated body contact surface (e.g., perpendicular to the shortest thermal path between the insulated body and the heat source along the LCE body boundary 720). This director orientation extends from the LCE body portion adjacent to the contact surface with the insulated body 706 along both directions below the LCE boundary 720, thereby extending the insulating configuration to the contact surface portion with the heat source 702 and the contact surface portion with the heat sink 704.

[0090] As shown in the embodiment of Figure 7, the insulation-preferring design constraint is just one embodiment that ensures that the director orientations are always aligned in an adiabatic direction relative to the interface with the insulated body 706 over at least a threshold distance from the insulated body, and that the directors are aligned between the heat source 702 and the heat sink 704 only for portions of the LCE where their orientations are also tangentially aligned with the boundary of the insulated body.

[0091] In other embodiments where the heat flow requirements between the heat source 702 and the heat sink 704 exceed the heat flow requirements into and out of the insulated body 706, or where different anisotropies of thermal conductivity cause those requirements to interact differently with the physical constraints of the LCE body 720, the director orientation layout of the embodiment shown in FIG. 7 can be modified depending on design decisions described further herein.

[0092] For example, without changing the physical boundary constraints 720 or adding additional thickness to the LCE body 710, different embodiments of director orientations and thermal paths within the LCE can be constructed to meet different heat flow requirements, such as aligning more directors with more direct paths between the heat source 702 and the heat sink 704. These different embodiments of director orientations can be further modified if more heat flow is allowed to enter or exit the interface with the insulated body 706. Such different designs of directors can also be obtained in embodiments in which the LCE material has a higher thermal conductivity anisotropy between heat flow in different directions. In these embodiments, more of the direct heat paths can be included that are closer to the interface with the insulator 706, including direct heat paths that are further below the node contact surfaces of the heat source 702 and the heat sink 704. In such embodiments, thermal conduction to or from the insulated body can be significantly reduced due to the greater resistivity embodied in the heat paths orthogonal to the director orientation.

[0093] In some embodiments, boundary conditions, such as physical boundary 720, may create portions of the LCE body 710 that are not critical to heat flow along the dominant thermal path between the heat source 702 and the heat sink 704. Such portions are shown in FIG. 7 without director orientation markings. These portions of the LCE body 710 to the left of the heat source 702 and to the right of the heat sink 704, and shown without director orientation indication, may be uncritical to heat flow in the thermal circuit between the heat source 702, the heat sink 704, and the insulated body 706, because the respective lengths and relative thermal resistivities of the thermal paths are so large in these areas that heat flow through these portions of the LCE body is negligible. In other words, in areas of the LCE body 710 without director orientation markings, the thermal paths are necessarily longer and more thermally resistant than other thermal paths that are labeled with boundary condition-based director orientations. Thus, the directors in these areas may be oriented for other conditions, such as to route heat between portions of the heat source 702 or portions of the heat sink 704, thereby thermally stabilizing the node, or to satisfy other boundary conditions, such as the LCE providing physical support for the node at the node interface without using air gaps for thermal insulation.

[0094] The embodiments described herein may include the specification of only a portion of the node contact surfaces shown in FIG. 7 , and some of these embodiments may include other combinations of requirements regarding contact surface edges and associated director orientations. For example, an embodiment may be designed to confine heat flow to the insulated body interface without specific heat source and / or heat sink interface areas; these nodes may instead be dispersed through absorption or emission of radiation from the surrounding environment or may be partially defined. In some embodiments, the LCE body may include a thermal circuit that includes only the requirement for heat flow along a conduction path between the heat source and the heat sink, with limited or no requirement that the insulated body interface within the LCE body have low heat flow to or from the heat source and / or the heat sink. In other embodiments, the insulated body may be modeled as dispersed, requiring containment of heat flow between the heat source and the heat sink. In other embodiments, such as those described with respect to FIGS. 1 and 5 , the insulated body (e.g., air, fluid) may be dispersed around or within a portion of the LCE's boundary.

[0095] In some embodiments, a heat source / heat sink may include portions that have different temperatures when heat flow is at a particular level. These portions may exhibit different temperatures if they have very high and / or very different heat flows across the heat source 702 or heat sink 704. This temperature difference may imply that multiple heat sources or heat sinks are included in the design requirements for a thermal circuit incorporated into an LCE body, as indicated by the dashed portions of the heat source 702 and heat sink 704. The dashed portions of the heat source 702 and heat sink 704 may specify multiple nodes to include in the design solution. Descriptions herein of separate multiple thermal paths between nodes include interactions between these multiple nodes with different temperatures and different heat flow requirements. These general cases are described herein to include descriptions of solutions for multiple nodes, as well as solutions for LCE thermal circuits that include as few as one distributed node, such as an insulating body that is independent of other heat flows around the LCE body.

[0096] In various embodiments, the present disclosure relates to a liquid crystal elastomer composition having a liquid crystal elastomer body with a heat sink-contacting edge that is perpendicular to the director orientation of the liquid crystal elastomer body, the liquid crystal elastomer body being made by a method disclosed herein. For example, in some embodiments, the method includes extruding a portion of a liquid crystal ink through a nozzle, whereby the extrusion applies a shear force to the liquid crystal ink, i.e., (1) the shear force is sufficient to align the director orientation of the liquid crystal ink, and (2) the shear force is oriented perpendicular to the heat sink-contacting edge of the liquid crystal elastomer body. In various embodiments, the method further includes crosslinking the extruded portion of the liquid crystal ink to a portion of the liquid crystal elastomer having the director orientation by illuminating the extruded portion of the liquid crystal ink with ultraviolet light after the liquid crystal ink exits the nozzle.

[0097] In some embodiments, the present disclosure relates to a liquid crystal polymer composition having a liquid crystal polymer body with a heat sink contact edge perpendicular to the director orientation of the liquid crystal polymer body, the liquid crystal polymer body being prepared by the method disclosed herein. For example, in some embodiments, the method includes placing a liquid crystal mesogen mixture prepared with a non-stoichiometric ratio of functional groups for a Michael addition reaction in contact with a heat sink contact molding surface, reacting the liquid crystal mesogen mixture while the liquid crystal mesogen mixture is in contact with the heat sink contact molding surface until the reaction stops due to the non-stoichiometry, thereby creating a midpoint liquid crystal polymer body with excess unreacted functional groups including a heat sink contact edge in contact with the heat sink contact molding surface, straining the liquid crystal polymer body away from the heat sink contact edge, and exposing the midpoint liquid crystal polymer body with excess unreacted functional groups to a crosslinking stimulus configured to react the excess unreacted functional groups, thereby creating a liquid crystal polymer body with a heat sink contact edge.

[0098] In another embodiment, the present disclosure relates to a liquid crystal polymer composition having a liquid crystal polymer body with an insulation-contacting edge aligned with the director orientation of the liquid crystal polymer body, the liquid crystal polymer body being prepared by a method disclosed herein. For example, in some embodiments, the method includes placing a liquid crystal mesogen mixture prepared with a non-stoichiometric ratio of functional groups for a Michael addition reaction in contact with an insulation-contacting molding surface, reacting the liquid crystal mesogen mixture while the liquid crystal mesogen mixture is in contact with the insulation-contacting molding surface until the reaction stops due to the non-stoichiometry, thereby creating a midpoint liquid crystal polymer body with excess unreacted functional groups including an insulation-contacting edge in contact with the insulation-contacting molding surface, straining the liquid crystal polymer body in a direction parallel to the insulation-contacting edge, and exposing the midpoint liquid crystal polymer body with excess unreacted functional groups to a crosslinking stimulus configured to react the excess unreacted functional groups, thereby creating a liquid crystal polymer body with an insulation-contacting edge.

[0099] While various embodiments of the present disclosure are illustrated in the accompanying drawings and described in the above detailed description, it will be understood that the present disclosure is not limited to the embodiments disclosed herein, but is capable of numerous rearrangements, modifications, and substitutions without departing from the spirit of the disclosure set forth herein.

[0100] The term "substantially" is defined as largely, but not necessarily entirely, specified, as understood by one of ordinary skill in the art. In any disclosed embodiment, the terms "substantially," "approximately," "nearly," and "about" can be substituted with "within .about. [percentage]" of what is specified, where percentages include 0.1, 1, 5, and 10 percent.

[0101] The foregoing outlines features of some embodiments so that those skilled in the art may better understand aspects of the present disclosure. Those skilled in the art will appreciate that they can readily use the present disclosure as a basis for designing or modifying other methods and structures that carry out the same purposes and / or achieve the same advantages as the embodiments introduced herein. Those skilled in the art will also appreciate that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and alterations can be made herein without departing from the spirit and scope of the present disclosure. The scope of the present invention should be determined solely by the language of the claims that follow. The term "comprising" in the claims is intended to mean "including at least," such that the list of recited elements in the claim is an open group. The terms "a," "an," and other singular terms are intended to include their plural forms unless specifically excluded.

Claims

1. 1. A method of making a liquid crystal elastomer body having a heat sink contact surface edge perpendicular to the director orientation of the liquid crystal elastomer body, comprising: extruding a portion of the liquid crystal ink through a nozzle; The extrusion thereby applies shear forces to the liquid crystal ink, i.e., The shear force is sufficient to align the director orientation of the liquid crystal ink, Oriented perpendicular to the heat sink contact surface edge of the liquid crystal elastomer body; and and crosslinking the extruded portion of the liquid crystal ink to a portion of the liquid crystal elastomer having director alignment by illuminating the extruded portion of the liquid crystal ink with ultraviolet light after the liquid crystal ink has exited the nozzle. method.

2. extruding a portion of the liquid crystal ink is initially extruding a first portion of the liquid crystal ink; a first crosslinking step of crosslinking the extruded portion of the liquid crystal ink to a portion of the liquid crystal elastomer having director alignment by illuminating the extruded portion of the liquid crystal ink with ultraviolet light, and a second crosslinking step of crosslinking the first extruded portion of the liquid crystal ink to a first portion of the liquid crystal elastomer having director alignment by illuminating a first extruded portion of the liquid crystal ink with ultraviolet light; The method is a second extrusion of extruding a second portion of the liquid crystal ink through the nozzle; a second illumination step of illuminating both the first portion of the liquid crystal elastomer and the second portion of the liquid crystal ink with ultraviolet light after the second extrusion step of extruding the second portion of the liquid crystal ink, thereby crosslinking the second portion of the liquid crystal elastomer to the second portion of the liquid crystal ink; The method of claim 1 further comprising:

3. The method of claim 2 , wherein the second illuminating further chemically bonds the first portion of the liquid crystal elastomer with the second portion of the liquid crystal elastomer.

4. a plurality of extrusion cycles each extruding a plurality of portions of the liquid crystal ink; multiple crosslinking cycles, including creating multiple portions of the liquid crystal elastomer by multiple cycles of illuminating each of the multiple portions of the liquid crystal ink with ultraviolet light; a third illumination, after the multiple cycles of illumination with ultraviolet light, illuminating the multiple portions of the liquid crystal elastomer with ultraviolet light in addition to the first portion of the liquid crystal elastomer and the second portion of the liquid crystal elastomer; The method of claim 2 further comprising:

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