Deterministic assembly of complex, three-dimensional architectures by compressive buckling

A structure comprising:

• a thin film structure characterized by a plurality of cut-outs configured to allow said thin film structure to form a predetermined three-dimensional shape upon application of a compressive force provided by relaxation of a deformable substrate;
• wherein said predetermined three-dimensional shape is a rigid structure characterized by at least one region with a mode ratio greater than or equal to 0.1;
• wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• and
• the three-dimensional shape is a complex shape characterized as non-linear and helical.

A structure comprising:

• a deformable substrate having a surface;
• and
• a thin film structure supported by said surface;
• wherein said thin film structure is bound to said surface at a plurality of bonding regions and not bound to said surface at a plurality of non-bonding regions;
• wherein relaxation of said deformable substrate provides a compressive force that generates a predetermined three-dimensional form of said thin film structure;
• wherein said predetermined three-dimensional form is characterized by at least one region with a mode ratio greater than or equal to 0.1;
• wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• and
• the thin film structure has a complex shape characterized as non-linear and helical.

A structure comprising:

• a deformable substrate having a surface;
• and
• a thin film structure supported by said surface;
• wherein said thin film structure is bound to said surface at a plurality of bonding regions and not bound to said surface at a plurality of non-bonding regions;
• wherein an overall shape of said thin film structure is non-linear and no bonding region exists at corners of a square or termini of a four-way intersection formed by said thin film structure;
• wherein each of said non-bonding regions physically contacts said deformable substrate when said deformable substrate is in an expanded state and none of said non-bonding regions physically contacts said deformable substrate when said deformable substrate is in a contracted state;
• wherein:
• wherein said overall shape is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• and
• the overall shape is a complex shape characterized as non-linear and helical.

A template for a three-dimensional structure comprising:

• a deformable substrate having a surface;
• and
• a two-dimensional thin film structure substantially parallel with and supported by said surface;
• wherein said two-dimensional thin film structure comprises a pattern of cut-outs configured to allow said two-dimensional thin film structure to convert into a predetermined three-dimensional complex shape upon application of a compressive force provided by relaxation of said substrate;
• wherein:
• the three-dimensional complex shape is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional complex shape is characterized as non-linear and helical.

A structure comprising:

• a thin film structure characterized by a plurality of cut-outs configured to allow said thin film structure to form a predetermined three-dimensional shape upon application of a compressive force provided by relaxation of a deformable substrate;
• wherein:
• the three-dimensional shape is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional shape is a complex shape characterized as non-linear and helical.

A spatially varying structure comprising:

• a deformable substrate having a surface;
• and
• a thin film structure supported by said surface;
• wherein said thin film structure is bound to said surface at a plurality of bonding regions and not bound to said surface at a plurality of non-bonding regions;
• wherein relaxation of said deformable substrate provides a compressive force that generates a predetermined three-dimensional form of said thin film structure having a plurality of buckled regions characterized by an anisotropic distribution of periodicities, amplitudes or both;
• wherein:
• the three-dimensional form is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• and
• the three-dimensional form is a complex shape characterized as non-linear and helical.

A spatially varying structure comprising:

• a deformable substrate having a surface;
• and
• a thin film structure supported by said surface;
• wherein said thin film structure is bound to said surface at a plurality of bonding regions and not bound to said surface at a plurality of non-bonding regions;
• wherein said thin film structure has a spatially varying density along a longitudinal axis;
• wherein each of said non-bonding regions physically contacts said deformable substrate when said deformable substrate is in an expanded state and none of said non-bonding regions physically contacts said deformable substrate when said deformable substrate is in a contracted state;
• wherein:
• the thin film structure is characterized by at least one region with a mode ratio greater than or equal to 0.1 when the deformable substrate is in a contracted state, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• and
• the thin film structure has a complex shape characterized as non-linear and helical when the deformable substrate is in a contracted state.

A method of making a three-dimensional structure, said method comprising:

• providing a prestrained elastic substrate in an expanded state;
• said substrate having a receiving surface;
• providing a two-dimensional thin film structure to said receiving surface, wherein said two-dimensional thin film structure comprises a pattern of cut-outs configured to allow said two-dimensional thin film structure to convert into a predetermined three-dimensional complex shape upon application of a compressive force;
• and
• allowing said prestrained elastic substrate to relax so as to provide said compressive force, thereby generating said three-dimensional structure;
• wherein:
• the three-dimensional complex shape is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the three-dimensional structure is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional complex shape is non-linear and helical.

A method of making a three-dimensional structure, said method comprising:

• providing a prestrained elastic substrate characterized by an anisotropic spatial distribution of strain;
• said substrate having a receiving surface;
• providing a thin film structure to said receiving surface, said thin film structure having a geometry allowing conversion into a predetermined three-dimensional complex shape upon application of an anisotropic compressive force;
• and
• allowing said prestrained elastic substrate to relax, thereby generating said anisotropic compressive force for making said three-dimensional structure;
• wherein:
• the three-dimensional complex shape is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the three-dimensional structure is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional complex shape is non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate having a first state characterized by a first shape;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• and
• transitioning said assembly substrate from said first state into a second state characterized by a second shape different from said first shape;
• wherein transition of said assembly substrate from said first state into a second state generates a nonuniform spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate having a first state characterized by a first shape;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• transitioning said assembly substrate from said first state into a second state characterized by a second shape different from said first shape;
• wherein transition of said assembly substrate from said first state into a second state generates a spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• and
• at least partially embedding said predetermined three-dimensional geometry in an encapsulating material to rigidify said predetermined three-dimensional geometry;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate having a first state characterized by a first shape;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• transitioning said assembly substrate from said first state into a second state characterized by a second shape different from said first shape;
• wherein transition of said assembly substrate from said first state into a second state generates a spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• and
• rigidifying said assembly substrate;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate having a first state characterized by a first shape;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• transitioning said assembly substrate from said first state into a second state characterized by a second shape different from said first shape;
• wherein transition of said assembly substrate from said first state into a second state generates a spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• and
• transferring said predetermined three-dimensional geometry to a rigid secondary substrate;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate provided in a first state characterized by a first nonuniform spatial distribution of tensile strain;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• transitioning said assembly substrate from said first state into a second state characterized by a second nonuniform spatial distribution of tensile strain different from said first nonuniform spatial distribution of tensile strain;
• wherein transition of said assembly substrate from said first state into a second state generates a nonuniform spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.

A method of making a structure having a predetermined three-dimensional geometry, said method comprising:

• providing an assembly substrate having a first state characterized by a first shape;
• wherein said assembly substrate has a receiving surface;
• bonding selected regions of a thin film structure having a planar geometry to said receiving surface of said assembly substrate;
• transitioning said assembly substrate from said first state into a second state characterized by a second shape different from said first shape;
• wherein transition of said assembly substrate from said first state into a second state generates a spatial distribution of compressive forces upon said thin film structure resulting in transformation of said planar geometry into said predetermined three-dimensional geometry of said thin film structure;
• and
• rigidifying said predetermined three-dimensional geometry;
• wherein:
• the three-dimensional geometry is characterized by at least one region with a mode ratio greater than or equal to 0.1, wherein the mode ratio of the at least one region corresponds to a ratio of average twisting curvature of the at least one region to the average bending curvature of the at least one region;
• the thin film structure is characterized by a thickness less than or equal to 300 μm;
• the thin film structure having the three-dimensional geometry is bound to the substrate at a plurality of bonding regions and not bound to the substrate at a plurality of non-bonding regions;
• and
• the three-dimensional geometry is a complex shape characterized as non-linear and helical.