BACKGROUND

[0001] Cylindrical tool rolls are useful in diverse industrial operations, especially in roll-to-roll manufacturing. Micro-structured cylindrical tool rolls including structured patterns with length scales on the order of single micron and above can be made with diamond turning machines, which use a diamond tipped tool to cut copper on a precision lathe. However, this method is fundamentally a turning operation, which limits the size of the structures and the pattern geometry that can be reproducibly cut into a nonplanar substrate like the surface of a cylindrical tool roll.

[0002] To make nanosized (greater than about 100 nm and less than about 1 micron) features and patterns on a nonplanar surface, lithography and laser ablation can be used, but these techniques produce excessively large features, offer limited options for pattern geometry, or require unacceptably long patterning times.

[0003] Microcontact printing can be used to transfer a two-dimensional nanoscale pattern of structures to a nonplanar substrate at a relatively low cost. Microcontact printing transfers to the substrate a pattern of functionalizing molecules, which include a functional group that attaches to the substrate surface or a coated substrate surface via a chemical bond to form a patterned self- assembled monolayer (SAM). The SAM is a single layer of molecules attached by a chemical bond to a surface and that have adopted a preferred orientation with respect to that surface and even with respect to each other.

[0004] A basic method for microcontact printing SAMs includes applying an ink containing the functionalizing molecules to a relief-patterned elastomeric stamp (for example, a

poly(dimethylsiloxane) (PDMS) stamp) and then contacting the inked stamp with a substrate surface, usually a metal or metal oxide surface, so that SAMs form in the regions of contact between the stamp and the substrate. The metallic surface may then be further processed to remove metal that is not protected by the SAM to form a two-dimensional nanoscale pattern on the manufacturing tool.

[0005] The functionalizing molecules should be reproducibly transferred from the elastomeric stamp to the metal substrate surface in the desired high-resolution patterned SAM with a minimum number of defects. Pattern defects such as line blurring and voids should be minimized to ensure accurate SAM pattern resolution and reproducibility. SUMMARY

[0006] In general, the present disclosure is directed to a process for printing a microstructured or a nanostructured pattern on at least a portion of a tool having a nonplanar surface, such as a cylindrical roll suitable for use in a roll-to-roll manufacturing processes. The pattern on the tool acts as an etch mask for subsequent processing steps to transfer the printed nanostructured pattern into the nonplanar metal surface of the tool. The size of the relief-patterned stamp used in the printing process may vary greatly in size, and in some embodiments a stamp is tiled on the nonplanar print layer in a step and repeat process to create many individual prints that can be stitched together to cover a selected region of the tool surface. The printing process of the present disclosure is described with respect to a microcontact printing process, but could be used with any type of printing process in which a flat stamp is used to transfer a pattern to a nonplanar surface of a tool.

[0007] In various embodiments of the printing process of the present disclosure, the relative position of the relief-patterned stamp and the nonplanar surface of the tool are controlled during the printing process.

[0008] In one aspect, the present disclosure is directed to a method of applying a pattern to a nonplanar surface, wherein at least a portion of the nonplanar surface has a radius of curvature.

The method includes providing a stamp with a major surface including a relief pattern of pattern elements extending away from a base surface, wherein each pattern element comprises a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns; applying an ink on the stamping surface, the ink including a functionalizing molecule with a functional group selected to chemically bind to the nonplanar surface; positioning the stamp to initiate rolling contact between the nonplanar surface and the major surface of the stamp; contacting the stamping surface of the pattern elements with the nonplanar surface to form a self-assembled monolayer (SAM) of the functionalizing material on the nonplanar surface and impart the arrangement of pattern elements thereto; and controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface.

[0009] In another aspect, the present disclosure is directed to an apparatus for applying a pattern to a nonplanar surface having a least one portion with a radius of curvature. The apparatus includes a stamper with an elastomeric stamp having a first major surface, wherein the first major surface of the stamp has a relief pattern of pattern elements extending away from a base surface, and wherein each pattern element has a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns. An ink is absorbed into the stamping surfaces of the stamp, the ink including a functionalizing molecule with a functional group selected to chemically bind to the nonplanar surface. The apparatus further includes a first motion controller supporting the stamper and configured to move the stamp with respect to the nonplanar surface; and a second motion controller configured to move the nonplanar surface; wherein the first motion controller and the second motion controller move the stamp and the nonplanar surface to control a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface.

[0010] In another aspect, the present disclosure is directed to a method of applying a pattern to an exterior surface of a roller. The method includes: absorbing an ink into a major surface of a stamp, the ink including a functionalizing molecule with a functional group selected to chemically bind to the exterior surface of the roller, wherein the major surface of the stamp has a relief pattern of pattern elements extending away from a base surface, and wherein each pattern element comprises a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns;

contacting the stamping surface of the pattern elements with the surface of the roller to bind the functional group with the surface of the roller to form a self-assembled monolayer (SAM) of the functionalizing material on the surface of the roller and impart the arrangement of pattern elements thereto; translating the major surface of the stamp with respect to the surface of the roller, wherein translating the major surface of the stamp includes controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface; and repositioning the stamp a plurality of times in a step and repeat fashion to transfer the arrangement of pattern elements to a plurality of different portions of the surface of the roller and form an array of pattern elements, wherein a stitch error between adjacent pattern elements in the array is less than about 10 pm.

[0011] In another aspect, the present disclosure is directed to a method of making a tool, the method including: providing a cylindrical roller including a metal substrate, a tooling layer on the metal substrate, and an external metal print layer on the tooling layer; imparting an arrangement of pattern elements on the metal print layer, wherein each pattern element has a lateral dimension of greater than 0 and less than about 5 microns; and translating the major surface of the stamp with respect to the metal print layer, wherein translating the major surface of the stamp includes controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface; and imparting the pattern elements a plurality of times in a step and repeat fashion to transfer the arrangement of pattern elements to a plurality of different portions of the print layer and form an array of pattern elements thereon, wherein a stitch error between adjacent pattern elements in the array is less than about 10 pm; and etching away portions of the metal print layer uncovered by the pattern elements, exposing portions of the tooling layer. [0012] The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

[0013] FIGS. 1A-1C are schematic side views of a microcontact printing process in which a cylindrical roller with a nonplanar metallic surface makes rolling contact with an elastomeric stamp inked with a SAM forming molecular species, and the SAM forming molecular species are transferred from a stamping surface of the stamp to the nonplanar metallic surface to form a nanoscale pattern thereon.

[0014] FIG. 2A is a schematic perspective view of an apparatus for microcontact printing (MCP) on a nonplanar substrate according to the present disclosure.

[0015] FIG. 2B is a schematic side view of a stamp module of the MCP apparatus of FIG. 2A.

[0016] FIG. 2C is a schematic perspective view of an embodiment of a cylindrical roll that has been patterned using the MCP apparatus of the present disclosure.

[0017] FIG. 2D is a schematic perspective view of a parallelepiped stamp with a

parallelogrammatic cross-section.

[0018] FIG. 2E is a schematic overhead view of a helical stamp pattern made on a non-planar substrate using the stamp of FIG. 2D.

[0019] FIG. 3 is a schematic cross-sectional view of an embodiment of a stamp for microcontact printing.

[0020] FIGS. 4A-4B are schematic cross-sectional views of a process for forming a self-assembled monolayer (SAM) on a substrate using a high-aspect ratio stamp in a microcontact printing process.

[0021] FIGS. 4C-4D are schematic cross-sectional views of a process for making a tool using the SAM of FIGS. 4A-4B.

[0022] FIG. 5 is a plot of percent area fill of printed and etched samples as a function of d _tange m in Example 1.

[0023] FIG. 6 is a plot of the measured contact force as a function of time for each value of d _tange m in Example 1.

[0024] FIGS. 7A-7C are photographs of the leading edge of the printed and etched samples for different values of d _tange m from Example 1.

[0025] FIG. 8 is a plot of d _tange m variation trajectory along with contact force variation as a function of horizontal position for Example 2. [0026] FIG. 9 is a photograph of the leading edge of the printed and etched sample for different values of d _ta ngcm of Example 3, showing no stamp feature collapse.

[0027] Like symbols in the drawings indicate like elements.

DETAILED DESCRIPTION

[0028] Referring to FIG. 1A, a cylindrical roll 10 has a nonplanar surface 12, which is on a thin metal layer 14. A major surface 19 of a stamp 18 includes a relief pattern of pattern elements 17, which form a stamping surface 16 containing a SAM forming molecular species (not shown in FIG. 1A) that is to be applied to the nonplanar surface 12 to form a corresponding pattern thereon (pattern elements 17 are not shown to scale on the major surface 19 of the stamp 18). In FIG. 1A, the nonplanar metallic surface 12 is about to be patterned by rolling contact with the stamping surface 16 of the stamp 18. To achieve the rolling contact, the roll 10 is rotated in direction“R” while stamp 18 is translated in direction“D” along a trajectory to initiate printing contact between the stamping surface 16 and the nonplanar metallic surface 12 at an initial point of contact 20. The speed of rotation in direction“R” is controlled such that the tangential surface speed of metallic nonplanar surface 12 substantially equals (± 5%) the speed of motion in direction“D” to minimize or eliminate slippage at the initial point of contact 20. The stamping surface 16 and the nonplanar metallic surface 12 remain in substantially steady-state contact such that only a portion of each surface is in contact with only a portion of the other surface at any given time, but the portion of each surface that is in contact with the portion of the other surface changes continuously.

[0029] Referring to FIG. 1B, the cylindrical roll 10 rolls over the stamping surface 16 to maintain contact between the stamping surface 16 and the nonplanar metallic surface 12, and the stamping elements 17 impart the pattern of SAM forming molecular species 22 to the nonplanar metallic surface 12. As the stamp 18, which in some embodiments is made of an elastomeric material, moves in rolling contact relative to the nonplanar metallic surface 12 to form the pattern 22, the contact area between the stamping surface 16 and the nonplanar metallic surface 12 continuously changes, resulting in changes in contact pressure. For example, the stamp 18 is compressed at the initial point of contact at a leading edge 20 of the stamp 18, and the contact interface 24 between the stamp 18 and the nonplanar metallic surface 12 gradually increases as rolling progresses to some approximately steady contact area. As contact interface 24 approaches the terminal point of contact at the trailing edge 26 of the stamp 18, the contact area is reduced to an infinitesimally narrow line.

[0030] The present disclosure relates to apparatus and methods for controlling initiation, engagement, and disengagement of the stamp 18 from the nonplanar surface 12 during the microcontact printing process to reproducibly form nanosized features in a pattern 22 on the nonplanar surface 12 in patterns with high resolution.

[0031] In various embodiments, the apparatus and methods of the present disclosure include controlling a relative position of the stamping surface 16 of the stamping elements 17 on the stamp 18 with respect to the nonplanar surface 12 while the major surface of the stamp contacts the nonplanar surface 12 to form the pattern 22.

[0032] Referring to FIG. 1C, after the position of the initial contact point between the stamping surface 16 and the nonplanar metallic surface 12 is determined at the leading edge 20 of the stamp 18, the stamp 18 and the cylindrical roll 10 are translated with respect to one another to control a vertical position d _tange m of the stamping surface relative to a plane of tangency 50 at a constantly varying interface 52 between the stamping surface 16 and the nonplanar surface 12 while the stamping surface 16 and the nonplanar surface 12 are in contact with each other.

[0033] Referring to FIG. 2A, a microcontact printing apparatus 100 includes a rigid roller support 102 having mounted thereon an air bearing spindle 104. A roller 110 mounted to rotate on a rotation shaft 113 of the air bearing spindle 104 includes a nonplanar surface 112 on a metal support roll 114.

[0034] The microcontact printing apparatus 100 further includes a stamp module 150 mounted on a stage apparatus 152. Using the stage apparatus 152, the stamp module 150 may be moved in any direction along the x and z axes with respect to the roller 110. The apparatus 100 further includes a confocal distance sensor 154, which can be used to monitor the surface topography of a stamp (not shown in FIG. 2A) mounted on the stamp module 150. Metrology data for a stamp mounted on a surface 160 of the stamping module 150 can then be used to correct for tip-tilt misalignment as well as confirm accurate lateral dimensions of the stamp to set indexing positions with respect to the nonplanar surface 112. A laser triangulation sensor 156 can be used to, for example, map runout errors of the nonplanar surface 112 and can be input into a compensation table for setting a pre-contact position for a stamp mounted on the surface 160.

[0035] Referring to FIG. 2B, a cylindrical roll 110 has a metallic nonplanar surface 112 on a support roll 114, which rotates about an axis R. The nonplanar surface 112 can be patterned by rolling contact between the nonplanar surface 112 and a stamping surface of an elastomeric stamp (not shown in FIG. 2B) mounted on a support station 155 of a stamping module 150. In some embodiments, the support station 155 is a vacuum chuck configured to hold a selected elastomeric stamp. Prior to mounting the stamp on the testbed, the compliant elastomeric stamp can optionally be bonded to a rigid or semi-rigid support substrate to provide dimensional stability (e.g. glass, metal, or ceramic shim). [0036] To achieve rolling contact, the roll 110 is rotated in direction R while a stamp mounted on the stamping module 150 is translated along the x-direction in FIG. 2B. The speed of rotation of the roll 110 in direction R is controlled such that the angular velocity w _GO p in degrees/second times the radius (FIG. 1C), which provides the surface speed of the metallic nonplanar surface 112 in mm/second, equals the speed of motion of the stamping module along the x-direction v _sta mp (FIG. 1C). Matching the roll surface speed with the speed of the stamp, while accounting for variations in the radius of the roll 110, ensures that there is a minimal amount of slippage (or substantially no slippage, or no slippage) at the point of contact between a stamping surface of the stamp and the metallic nonplanar surface 112.

[0037] The stamp module 150 includes a stage 162 that can be configured to tip, tilt, or rotate an elastomeric stamp attached to the surface 160. The stage 162 is mounted on a platform 163, which is slideably mounted using an air bearing in housing 164 and move along shafts 184. The platform 163 is attached to at least one pneumatic counterbalance 165. The position of the platform 163 controlled by a voice coil actuator 166, which is also used to implement force control between a stamping surface of a stamp and the nonplanar surface 112 of the roll 110. Closed-loop force control at the interface between the stamping surface of the stamp and the nonplanar surface 112 is achieved with a set of two force sensors 168, 170 to provide feedback. Positive (upward) force along the y-direction is balanced between force sensors 168, 170. When a stamp mounted on the surface 160 is not in contact with the nonplanar surface 112, the force control loop is balanced completely with force sensor 170.

[0038] The pre-contact stamp position can therefore be set using a wide variety of techniques. For example, in the embodiment of FIG. 2B, which is not intended to be limiting, the pre-stamp position can be set using a coarse manual height adjustment screw 172 and a fine adjust piezo actuator 174 with positional feedback from a capacitance distance sensor 176. Once contact between a stamp and the nonplanar surface 112 has developed, the force control loop is balanced completely with force sensor 168. The transition between the force sensors 168, 170 occurs during contact initiation/separation, and in some preferred embodiments the stamp module 150 can be calibrated to ensure that the transition between force sensors occurs smoothly without rebound, particularly since the stamp contacting the nonplanar surface has elastomeric properties.

[0039] The counterbalance 165 is mounted on a linear motion stage 180 of the moveable stage 152. Drivers control the roll spindle motion (C-axis in FIG. 2A) and move the rotation shaft 113 to coordinate with the tangential linear motion along the x-direction of the linear motion stage 180. During microcontact printing, these motions are coordinated to initiate rolling contact between the nonplanar surface 112 and the stamping surface of the stamp mounted on the surface 160. [0040] In some embodiments, speed of rotation of the roll 110 in direction R is controlled such that the angular velocity w _GO ii in degrees/second times the radius (FIG. 1C), which provides the surface speed of the metallic nonplanar surface 112 in mm/second, equals the speed of motion of the stamping module along the x-direction v _sta mp (FIG. 1C). Matching the roll surface speed with the speed of the stamp, while accounting for variations in the radius of the roll 110, ensures that there is a minimal amount of slippage (or substantially no slippage, or no slippage) at the point of contact between a stamping surface of the stamp and the metallic nonplanar surface 112.

[0041] In some embodiments, prior to contacting the stamping surface of the stamp with the nonplanar surface 112, the stage 180 moves the stamp module 150 to place the mounted stamp on a trajectory that initiates a path to a predetermined point of initial contact between the pattern elements on the major surface of the stamp and the nonplanar surface 112. The position of the surface may be determined, for example, by the manual height adjustment screw 172 for coarse adjustments and the piezo actuator 174 for finer adjustments, or a combination thereof. The point of initial printing contact between the stamp and the nonplanar surface may be determined by a detector or combination of detectors such as, for example, the force sensor 168 or the capacitive displacement sensor 176.

[0042] The stage 162 may also be adjusted to tune the relative positions of the stamping surface and the nonplanar surface and determine an initial point of contact or plot a trajectory of the stamping surface to contact the nonplanar surface at a predetermined point or region.

[0043] In various embodiments, after initiating rolling contact between the stamping surface and the nonplanar surface, the stamping surface is contacted with the nonplanar surface for a print time sufficient to chemically bind a functional group with the nonplanar surface to form a self- assembled monolayer (SAM) of a functionalizing material on the nonplanar surface and impart an arrangement of nanoscale pattern elements thereto.

[0044] The stamping surface of the stamp is translated with respect to the nonplanar surface of the roll to control a vertical position d _tange m of the stamping surface 16 relative to a plane of tangency 50 at an interface 52 between the stamping surface 16 of the stamp 18 and the nonplanar surface 12 of the roll 10 while the stamping surface 16 and the nonplanar surface 12 are in contact with each other (FIG. 1C).

[0045] Referring again to FIGS. 1A-1C, in one embodiment d _tange m is held constant while the major surface 19 of the stamp 18 contacts the nonplanar surface 12. However, the contact area along the major surface 19 of the stamp varies throughout the rolling contact printing operation, and is particularly evident at the leading and trailing edges 21, 23 of stamping elements 17, wherein high contact pressures at the rolling interface can cause the elastomeric stamping elements 17 to collapse. The contact area can vary based on, for example, the shape of the stamp, the dimensions of the stamping elements 17 and the stamping surface 16, the arrangement of the stamping elements 17, the composition and the compliance of the stamp, and the like. If d _ta n _S em is held constant, in some cases it can be difficult to balance the relative effects of the collapse of the stamping elements 17 at the leading edge 20 and the trailing edge 26 of the stamp 18, which can cause printing large voids on the non-planar surface 12 due to non-flatness of the stamp 18. At small values of dtangent, there is a high likelihood of printing large voids on the non-planar surface 12. At high values of d _tangent , the stamping elements 17 may collapse due to excessive contact forces between the stamping surfaces 16 and the non-planar surface 12, particularly at the leading edge 20 and trailing edge 26 of the stamp 18. At these transitions, a combination of inertial forces and varying contact area at the interface 52 may cause the stamping elements 17 to collapse.

[0046] To more effectively transition stamp position at selected horizontal positions along the major surface 19 of the stamp 18 such as, for example, at the leading edge 20 and the trailing edge 26, in another embodiment d _ta ngent can be varied as a function of time while the major surface 19 of the stamp 18 contacts the nonplanar surface 12.

[0047] In another embodiment, d _ta ngent can be varied as a function of a horizontal position of the interface 52 while the major surface 19 of the stamp 18 contacts the nonplanar surface 12. For example, the in some embodiments d _tan gent may be selected and varied with respect to horizontal position of the interface 52 to substantially prevent collapse of the pattern elements 17. In another embodiment, d _tan gent is selected or varied to substantially prevent collapse of the pattern elements 17 at selected horizontal positions along the major surface of the stamp 18 such as, for example, one of a leading edge 20 or a trailing edge 26 of the stamp 18, or both.

[0048] In yet another embodiment, dt _an gent is selected or varied such that a predetermined surface area of the stamping surfaces 16 contact the nonplanar surface 12. For example, dt _ang ent can be selected such that at least about 90%, or about 95%, or about 99%, or about 100%, of the stamping surfaces 16 contact the nonplanar surface 12 and transfer pattern to the nonplanar surface 12 over a print cycle (all measurements are ±1%). In some embodiments, for example, a maximum dt _ang ent was set to a value that exhibited zero voids when the dt _ang ent was held constant.

[0049] In another embodiment, dt _ang ent is selected to: (1) substantially prevent collapse of the pattern elements at one or both of a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp; and (2) such that at least about 90%, or 95%, or 99% of the stamping surfaces transfer pattern to the nonplanar surface over a print cycle.

[0050] In some embodiments, a plot of contact force vs. time in which the stamping surfaces contact the nonplanar surface for a selected value of d _t ^ _ge m follows an arbitrary trajectory. In some embodiments, the trajectory is a non-linear trajectory. In some embodiments, the trajectory includes, but is not limited to, a substantially trapezoidal trajectory, or a smoothed trapezoidal trajectory.

[0051] Trajectories over which dtangent is varied, as well as maximum and minimum values of dtangent, can be determined using a variety of methods. For example, experimental data can be used to determine where the onset of collapse occurs at the leading edges 21 and the trailing edges 23 of the stamping features 17. This value can serve as a target nominal interference at these horizontal positions on the major surface 19 of the stamp 18 where contact between the nonplanar surface 12 and the stamping surfaces 16 on the stamping features 17 is initiated or terminated. The same or a similar dataset can also be used to show where sufficient nominal interference is required to make full conformal contact between the stamping surfaces 16 on the stamping features 17 and the nonplanar surface 12 over a center portion of the major surface 19 of the stamp 18. Combining these two positions provides a template to generate a suitable trapezoidal trajectory. In the horizontal trajectory, an inflection point between the ramps and the plateau would be expected to occur at the position of the first and last peaks as this signifies the locations where contact areas between the stamping surfaces 16 of the stamping features 17 and the nonplanar surface 12.

[0052] In various embodiments, the resulting interference between the nonplanar surface and the stamping surface at the unloaded point of contact is less than about 25 microns, or less than about 5 microns, or even less than about 1 micron.

[0053] Suitable values of dtangent are dependent on various factors such as, for example, the stamp material, stamp thickness, roll diameter and the like. However, in various embodiments, which are provided as examples and not intended to be limiting, for a polydimethylsiloxane (PDMS) stamp, suitable values of d _tangent have been found to be less than about 50 microns, or less than 25 microns, or less than 15 microns, or less than 10 microns, or less than 5 microns, or less than 2 microns, or less than 1 micron, with all measurements ± 0.1 micron. In various embodiments, which are provided as examples and not intended to be limiting, for a

polydimethylsiloxane (PDMS) stamp, suitable values of d _tangent have been found to be greater than about 0.5 microns, or greater than about 1 micron, or greater than 2 microns, or greater than about 3 microns, or greater than about 4 microns, or greater than about 5 microns, or greater than about 10 microns, or greater than about 12 microns, or greater than about 15 microns, or greater than about 25 microns, with all measurements ± 0.1 micron.

[0054] Referring again to FIGS. 2A-2B, in some embodiments the linear motion stage 180 is itself mounted on a second linear motion stage 182 oriented to translate linear motion stage 180 and the rest of the apparatus 150 it supports along the z-direction, and perpendicular to the x- and y- directions. This allows additional instances of the pattern on the stamping surface to be applied in a step-and-repeat fashion onto the nonplanar surface 112 not only circumferentially, but also in a direction parallel with the axis of the cylindrical roll 110. The distance sensor 156 may be used to measure the distance from itself to the nonplanar surface 112, which can in turn be used to map the run-out on the cylindrical roll 110.

[0055] For the step and repeat procedure, in one embodiment, the stamp and tool diameter are sized such that an integer number of printed stamp tiles will exactly wrap around the

circumference of the tool. The stamp tiling progresses in a grid pattern on the roll and forms a patterned area that is continuous around the circumference of the roll. This embodiment is illustrated in FIG. 2C, a perspective view of cylindrical roll 110 in isolation with nine instances of a pattern 167 laid down in a step-and-repeat fashion in a three by three array on the nonplanar surface 112. The nine instances in the depicted embodiment are separated by a certain distance in either the circumferential direction or the axial direction, or both, which is referred to herein as a stitch error. However, it is contemplated in this disclosure that the instances of the pattern 167 could be immediately adjacent, or even deliberately overlapping. It is possible to regulate a gap between adjacent instances of pattern 167 on the nonplanar surface 112 with great accuracy, even to less than 2 pm.

[0056] Also seen in FIG. 2C are fiducial marks 169, each of which bear a specific positional relationship of one of the patterns 167. It is contemplated that fiducial marks 169 could be applied by the same stamp and at the same time as the pattern is applied. It is also possible that fiducial marks 169 could be applied in a separate operation. Such fiducial marks 169 are known in the art, and can in some cases be convenient when cylindrical roll 110 is used after patterning in, e.g., a roll-to-roll operation on a web and it is desirable to accurately register some secondary operation with the results of the cylindrical roll 110 upon that web.

[0057] In another embodiment shown in FIG. 2D, the stamp 118 is made as a parallelogram prism (parallelepiped) having a length /, a width w, and an angle Q selected to provide a cross-section 119 having the shape of a parallelogram. Referring to FIG. 2E, the parallelepiped stamp 118 of FIG. 2D can be used to transfer a pattern 140 to a non-planar circumferential tool surface 132 with parallelogrammatic tile-like pattern elements 139. As shown schematically in FIG. 2E, to form the tiled pattern 140, each successive parallelogram tile 139 (numbered 1-9 in order of application) is serially applied to the surface 132 and offset both circumferentially along the circumferential direction CD and axially along the axial direction AD on the surface 132 of the non-planar surface 132 such that the tiles are printed on the surface 132 in a helical configuration. In this arrangement, the circumference of the roll does not have to be an integer multiple of the stamp length / (FIG. 2D). While this relaxes the absolute size tolerance on the stamp length, there are additional constraints on the parallelogram angle that can be controlled to ensure the pattern area is continuous around the circumference of the roll. For example, if the width w of the stamp 118 of FIG. 2D is known, and the circumference TC of the non-planar surface 132 of the tool is known, the angle Q of the stamp can be determined by tan Q = TC lw .

[0058] In various embodiments, the presently described microcontact printing process can impart an array of nanoscale pattern elements, each with a lateral dimension of less than about 5 microns, to a nonplanar surface of a roll. The array includes a plurality of tile-like elements arranged such that adjacent tile-like elements are separated by less than about 10 pm, less than 5 pm, less than 1 pm, or less than 0.1 pm, or even less than 0.02 pm, or overlapping by a predetermined amount of less than about 10 pm, less than 5 pm, less than 1 pm, or less than 0.1 pm, or even less than 0.02 pm. These small patterns may be applied over a nonplanar surface of a cylindrical roller with a height of about 9 inches (23 cm) and a base with a diameter of 12.75 inches (32.39 cm), which can be used in a roll-to-roll manufacturing process.

[0059] FIG. 3 shows a schematic illustration of a portion of a microcontact printing stamp 210, which includes a substantially planar base surface 212. An array of pattern elements 214 extends away from the base surface 212. In some embodiments, the stamp 210 is a unitary block of an elastomeric material, and in other embodiments may include elastomeric pattern elements 214 supported by an optional reinforcing backing layer 211. The array of pattern elements 214 on the base surface 212 of the stamp 210 can vary widely depending on the intended microcontact printing application, and can include, for example, regular or irregular patterns of elements such as lines, dots, polygons, and combinations thereof.

[0060] The pattern elements 214 in the array on the base surface 212 can be described in terms of their shape, orientation, and size. The pattern elements 214 have a base width x at the base surface 212, and include a stamping surface 216. The stamping surface 216 resides a height h above the base surface 212, and has a lateral dimension w, which may be the same or different from the base width x. In various embodiments, the aspect ratio of the height h of the pattern elements 214 to the width w of the stamping surface 216 of the pattern elements 214 is about 0.1 to about 5.0, about 0.2 to about 3.0, or about 0.2 to about 1.0.

[0061] The methods and apparatuses described herein are particularly advantageous for small pattern elements 214 with a stamping surface 216 having a minimum lateral dimension w of less than about 10 pm, or less than about 5 pm, or less than about 1 pm. In the embodiment shown in FIG. 3, the stamping surface 216 is substantially planar and substantially parallel to the base surface 212, although such a parallel arrangement is not required. The methods and apparatuses reported herein are also particularly advantageous for microcontact printing with pattern elements 214 having a height h of about 50 pm or less, or about 10 pm or less, or about 5 pm or less, or about 1 pm or less, or about 0.25 pm or less. [0062] The patern elements 214 can occupy all or just a portion of the base surface 212 (some areas of the base surface 12 can be free of patern elements). For example, in various

embodiments the spacing / between adjacent patern elements can be greater than about 50 pm, or greater than about 100 pm, or greater that about 200 pm, or greater than about 300 pm, or greater than about 400 pm, or even greater than about 500 pm. Commercially useful arrays of patern elements 14 for microcontact printing cover areas of, for example, about 0.1 cm ² to about 1000 cm ² , or about 0.1 cm ² to about 100 cm ² , or about 5 cm ² to about 10 cm ² on the base surface 212 of the stamp 210.

[0063] In some embodiments, the pattern elements 214 can form a "micropatem," which in this application refers to an arrangement of dots, lines, filled shapes, or a combination thereof having a dimension (e.g. line width) of about 1 pm to about 1 mm. In some embodiments, the arrangement of dots, lines, filled shapes, or a combination thereof have a dimension (e.g. fine width) of at least 0.5 pm and typically no greater than 20 pm. The dimension of the micropattem pattern elements 214 can vary depending on the micropattem selection, and in some embodiments, the micropattem patern elements have a dimension (e.g. line width) that is less than 10, 9, 8, 7, 6, or 5 pm (e.g. 0.5- 5 pm or 0.75-4 pm).

[0064] In some embodiments, the pattern elements 214 can fomi a "nanopattem," which in this application refers to an arrangement of dots, lines, filled shapes, or a combination thereof having a dimension (e.g. line width) of about 10 nm to about 1 pm. in some embodiments, the arrangement of dots, lines, filled shapes, or a combination thereof have a dimension (e.g. fine width) of about 100 nm to about 1 pm. The dimension of the nanopattem pattern elements 214 can vary depending on the nanopattem selection, and in some embodiments, the nanopattem pattern elements have a dimension (e.g. line width) that is less than 750 nm, or less than 500 nm, less than 250 nm, or less than 150 nm.

[0065] In some embodiments, combinations of micropatem elements and nanopatem elements may be used.

[0066] In some embodiments, the pattern elements are traces, which may be straight or curved. In some embodiments, the pattern elements are traces that form a two-dimensional network (i.e., mesh). A mesh comprises traces that bound open cells. The mesh may be, for example, a square grid, a hexagonal mesh, or a pseudorandom mesh. Pseudorandom refers to an arrangement of traces that lacks translational symmetry, but that can be derived from a deterministic fabrication process (e.g., photolithography or printing), for example including a computational design process that includes generation of the patern geometry with a randomization algorithm. In some embodiments, the mesh has an open area fraction of between 90 percent and 99.75 percent (i.e., density of patern elements of between 0.25 percent and 20 percent). In some embodiments, the mesh has an open area fraction of between 95 percent and 99.5 percent (i.e., density of pattern elements of between 0.5 percent and 5 percent). The pattern elements may have combinations of the aspects described above, for example they may be curved traces, form a pseudorandom mesh, have a density of between 0.5 percent and 5 percent, and have a width of between 0.5 pm and 5 pm. In other embodiments, the pattern elements may have a density of pattern elements of greater than 20%, or greater than 60%, or greater than 80%, or even greater than 90%, and may appear as a dark background with a small open area fraction.

[0067] Referring to FIG. 4A, an ink 320 including a functionalizing molecule is absorbed into a stamp 310, and resides on the stamping surfaces 316 of the stamp 310. The functionalizing molecules in the ink 320 include a functional group selected to bind to a selected surface material 322 on a nonplanar surface. The nonplanar surface is supported by a support layer 324, which in some embodiments may be a portion of a cylindrical roll (not shown in FIG. 4).

[0068] Referring to FIG. 4B, the stamp 310 is positioned and is brought into contact with a tool substrate 335. The tool substrate 335 includes a print layer 322 with a nonplanar surface 326, a tooling layer 323, and a cylindrical roll substrate 324. In various embodiments, which are not intended to be limiting, the tooling layer 323 is a hard, reactive ion etchable (RIE) material such as, for example, metals or metal alloys chosen from, for example, aluminum, tungsten, and alloys and combinations thereof, non-metallic inorganics like glass, quartz, silicon, diamond-like glass (DLG) or diamond-like carbon (DLC). The cylindrical roll substrate 324 is a metal suitable for use in diamond turning operations, and non-limiting examples include copper, aluminum, and alloys and combinations thereof. The cylindrical roll substrate may consist of multiple materials as one skilled in the art would recognize would enable diamond turning of the surface while providing a more robust underlying structure, such as copper on steel. Materials for the print layer 322 will be discussed in more detail below. Additionally, one or more optional adhesion promoter layers may be used to enhance adhesion between layers. The adhesion promoter layers are typically a few nanometers thick and are not shown in FIG 4.

[0069] The stamping surfaces 316 contact a first portion 325 of the surface 326. The

functionalizing molecules in the ink 320 contact the surface 326 for a print time sufficient to allow the functional group to chemically bind thereto (contacting step not shown in FIG. 4B). In various embodiments, the print time is from about 0.001 seconds to about 5 seconds, or about 0.010 seconds to about 1 seconds.

[0070] Then, the stamping surface 316 is removed, and the ink remaining on the surface 326 forms a self-assembled monolayer (SAM) 330 on the portions 325 of the surface 326 according to the shapes and dimensions of the stamping surfaces 316. Portions 327 of the surface 326, contiguous with first portions 325, remain free of the SAM 330. [0071] Referring to FIG. 4C, portions 327 of the print layer 322 not underlying the SAM 330 are removed by any suitable process such as, for example, wet chemical etching, to form pattern elements 352 having a height hi of less than about 500 nm, or less than about 250 nm, or less than about 100 nm, or less than about 50 nm. The etching process further exposes regions 350 of the tooling layer 323.

[0072] Referring to FIG. 4D, the remaining portions of the tool substrate 335 can optionally be further processed by an additional etch using, for example, reactive ion etching (RIE), to remove portions of the tooling layer 323 not overlain by the pattern elements 352. The RIE process produces high aspect ratio pattern elements 360 with an aspect ratio of about 0.1 to about 10, or about 0.25 to about 7, and in some embodiments may optionally expose regions 370 of the cylindrical roll substrate 324.

[0073] In an optional further processing step not shown in FIGS. 4A-D, the tool substrate 335 can be further treated to strip away the SAM 330 and the print layer 322 in the high aspect ratio pattern elements 360, leaving behind portions of the tooling layer 323 on the cylindrical roll substrate 324.

[0074] The stamp 310 used in the MCP processes of the present disclosure should be sufficiently elastic to allow the stamping surfaces 316 to very closely conform to minute irregularities in the surface 326 of the print layer 322 and completely transfer the ink 320 thereto. This elasticity allows the stamp 310 to accurately transfer the functionalizing molecules in the ink 320 to nonplanar surfaces. However, the pattern elements 314 should not be so elastic that when the stamping surfaces 316 are pressed lightly against a surface 326, the pattern elements 314 deform to cause blurring of the ink 320 on the substrate surface 326.

[0075] The stamp 310 should also be formed such that stamping surface 316 includes an absorbent material selected to absorb the ink 320 to be transferred to a surface 326 to form a SAM 330 thereon. The stamping surface 316 can swells to absorb the ink 320, which can include functionalizing molecules alone or suspended in a carrier such as an organic solvent. In some cases, such swelling and absorbing characteristics can provide good definition of an isolated SAM 330 on a substrate surface 326, but in general should be minimized to improve dimensional control over the stamping surface 316. For example, if a dimensional feature of stamping surface 316 has a particular shape, the surface 316 should transfer the ink 320 to the surface 326 of the print layer 322 to form SAMs 30 mirroring the features of the stamping surface 316, without blurring or smudging. The ink is absorbed into the stamping surface 316, and when stamping surface 316 contacts material surface 326, the ink 320 is not dispersed, but the functional groups on the functionalizing molecules chemically bind to the surface 326, and removal of the stamping surface 316 from the surface 326 results in a SAM 330 with well-defined features. [0076] Useful elastomers for forming the stamp 310 include polymeric materials such as, for example, silicones, polyurethanes, ethylene propylene diene M-class (EPDM) rubbers, as well as commercially available flexographic printing plate materials (for example, those commercially available from E. I. du Pont de Nemours and Company, Wilmington, DE, under the trade designation Cyrel). The stamp can be made from a composite material including, for example, an elastomeric material on the stamping surfaces 316 combined with a woven or non-woven fibrous reinforcement 311 (FIG. 4A).

[0077] Polydimethylsiloxane (PDMS) is particularly useful as a stamp material, as it is elastomeric and has a low surface energy (which makes it easy to remove the stamp from most substrates). A useful commercially available formulation is available from Dow Coming, Midland, MI, under the trade designation Sylgard 184 PDMS. PDMS stamps can be formed, for example, by dispensing an un-crosslinked PDMS polymer into or against a patterned mold, followed by curing. The master tool for molding the elastomeric stamps can be formed using lithography techniques (e.g. photolithography, e-beam) known in the art. The elastomeric stamp can be molded against the master tool by applying uncured PDMS to the master tool and then curing.

[0078] The print layer 322 and the ink 320 are selected such that the functionalizing molecules therein include a functional group that binds to a surface 326 of the layer 322. The functional group may reside at the physical terminus of a functionalizing molecule as well as any portion of a molecule available for forming a bond with the surface 326 in a way that the molecular species can form a SAM 330, or any portion of a molecule that remains exposed when the molecule is involved in SAM formation. In some embodiments, the functionalizing molecules in the ink 320 may be thought of as having first and second terminal ends, separated by a spacer portion, the first terminal end including a functional group selected to bond to surface 326, and the second terminal group optionally including a functional group selected to provide a SAM 330 on material surface 326 having a desirable exposed functionality. The spacer portion of the molecule may be selected to provide a particular thickness of the resultant SAM 330, as well as to facilitate SAM formation and control transport mechanisms (e.g. vapor transport). Although SAMs of the present invention may vary in thickness, SAMs having a thickness of less than about 50 A are generally preferred, more preferably those having a thickness of less than about 30 A and more preferably those having a thickness of less than about 15 A. These dimensions are generally dictated by the selection of molecular species 20 and, in particular, the spacer portion thereof.

[0079] Additionally, SAMs 330 formed on surface 326 may be modified after such formation for a variety of purposes. For example, a functionalizing molecule in the ink 320 may be deposited on surface 326 in a SAM, the functionalizing molecule having an exposed functionality including a protecting group which may be removed to effect further modification of the SAM 330. Alternately, a reactive group may be provided on an exposed portion of the functionalizing molecule in the ink 320 that may be activated or deactivated by electron beam lithography, x-ray lithography, or any other radiation. Such protections and de-protections may aid in chemical or physical modification of an existing surface-bound SAM 330.

[0080] The SAM 330 forms on the surface 326 of the print layer 322. The substrate surface 326 can be substantially planar and have a slight curvature, or may have a significant curvature like the surfaces of a cylindrical roller described above. Useful materials for the print layer 322 can include an inorganic material (for example, metallic or metal oxide material, including

polycrystalline materials) coating on a metal or glass support layer. The inorganic material for the print layer 322 can include, for example, elemental metal, metal alloys, intermetallic compounds, metal oxides, metal sulfides, metal carbides, metal nitrides, and combinations thereof. Exemplary metallic print layers 322 for supporting SAMs include gold, silver, palladium, platinum, rhodium, copper, nickel, iron, indium, tin, tantalum, aluminum, as well as mixtures, alloys, and compounds of these elements. Gold is a preferred metallic surface 322.

[0081] The print layer 322 on the supporting substrate 324 can be any thickness such as, for example, from about 10 nanometers (nm) to about 1000 nm. The inorganic material coating can be deposited using any convenient method, for example sputtering, evaporation, chemical vapor deposition, or chemical solution deposition (including electroless plating) as well as other methods known in the art.

[0082] In one embodiment, combinations of materials for the print layer 322 and functional groups for functionalizing molecules in the ink 320 include, but are not limited to: (1) metals such as gold, silver, copper, cadmium, zinc, palladium, platinum, mercury, lead, iron, chromium, manganese, tungsten, and any alloys of the above with sulfur-containing functional groups such as thiols, sulfides, disulfides, and the like.

[0083] Additional suitable functional groups on the functionalizing molecules in the ink 320 include acid chlorides, anhydrides, sulfonyl groups, phosphoryl groups, hydroxyl groups and amino acid groups. Additional surface materials for the print layer 322 include germanium, gallium, arsenic, and gallium arsenide. Additionally, epoxy compounds, polysulfone compounds, plastics and other polymers may find use as the material for the print layer 322. Additional materials and functional groups suitable for use in the present invention can be found in U.S. Pat. Nos. 5,079,600 and 5,512,131, which are incorporated herein by reference in their entirety.

[0084] Referring again to FIGS. 4A-4D, in some embodiments, the functionalizing molecules utilized to form SAMs in the presently-described process are delivered to the stamp 310 as ink solutions 320 including one or more organosulf ir compounds as described in U.S. Published Application No. 2010/0258968, incorporated herein by reference. Each organosulfiir compound is preferably a thiol compound capable of forming a SAM 330 on a selected surface 326 of a print layer 322. The thiols include the— SH functional group, and can also be called mercaptans. The thiol group is useful for creating a chemical bond between molecules of the functionalizing compound in the ink 320 and the surface 322 of a metal print layer. Useful thiols include, but are not limited to, alkyl thiols and aryl thiols. Other useful organosulfur compounds include dialkyl disulfides, dialkyl sulfides, alkyl xanthates, dithiophosphates, and dialkylthiocarbamates.

[0085] Preferably the ink solution 320 includes alkyl thiols such as, for example, linear alkyl thiols: HS(CH ₂ ) _n X, wherein n is the number of methylene units and X is the end group of the alkyl chain (for example, X =— C¾,—OH,— COOH,— NFU. or the like). Preferably, X =— CH3. Other useful functional groups include those described, for example, in: (1) Ulman, "Formation and Structure of Self-Assembled Monolayers," Chemical Reviews Vol. 96, pp. 1533-1554 (1996); and (2) Love et ak, "Self-Assembled Monolayers of Thiolates on Metals as a Form of

Nanotechnology," Chemical Reviews Vol. 105, pp. 1103-1169 (2005).

[0086] Useful alkyl thiols can be linear alkyl thiols (that is, straight chain alkyl thiols) or branched, and can be substituted or unsubstituted. The optional substituents preferably do not interfere with the formation of a SAM. Examples of branched alkyl thiols that are useful include alkyl thiols with a methyl group attached to every third or every fourth carbon atom of a linear alkyl chain backbone (for example, phytanylthiol). Examples of mid-chain substituents within useful alkyl thiols include ether groups and aromatic rings. Useful thiols can also include three-dimensional cyclic compounds (for example, l-adamantanethiol).

[0087] Preferred linear alkyl thiols have 10 to 20 carbon atoms (more preferably, 12 to 20 carbon atoms; most preferably 16 carbon atoms, 18 carbon atoms, or 20 carbon atoms).

[0088] Suitable alkyl thiols include commercially available alkyl thiols (Aldrich Chemical Company, Milwaukee, WI). Preferably, the ink solutions 320 consist primarily of a solvent and the organosulfur compound, with impurities including less than about 5% by weight of the ink solution; more preferably less than about 1%; even more preferably less than about 0.1%. Useful inks 320 can contain mixtures of different organosulfur compounds dissolved in a common solvent such as, for example, mixtures of alkyl thiol and dialkyl disulfide.

[0089] Aryl thiols, which include a thiol group attached to an aromatic ring, are also useful in the ink 320. Examples of useful aryl thiols include biphenyl thiols and terphenyl thiols. The biphenyl and terphenyl thiols can be substituted with one or more functional groups at any of a variety of locations. Other examples of useful aryl thiols include acene thiols, which may or may not be substituted with functional groups.

[0090] Useful thiols can include linear conjugated carbon-carbon bonds, for example double bonds or triple bonds, and can be partially or completely fluorinated. [0091] The ink solutions 320 can include two or more chemically distinct organosulfur compounds. For example, the ink can include two linear alkyl thiol compounds, each with a different chain length. As another example, the ink 320 can include two linear alkyl thiol compounds with different tail groups.

[0092] Although microcontact printing has been carried out using neat organosulfur compounds to ink the stamp, the delivery of organosulfur compounds to the stamp can be achieved more uniformly, and with less stamp swelling in the case of linear alkyl thiols and PDMS stamps, if delivered from a solvent-based ink. In some embodiments, the ink includes more than one solvent, but most useful formulations need include only a single solvent. Inks formulated with only one solvent may contain small amounts of impurities or additives, for example stabilizers or desiccants.

[0093] Useful solvents are preferably compatible with PDMS (that is, they do not excessively swell PDMS), which is the most commonly used stamp material for microcontact printing. In microcontact printing, swelling of the PDMS stamp can lead to distortion of the patterned features and poor pattern fidelity. Depending on the inking approach, excessive swelling can also present significant challenges in providing mechanical support to the stamp.

[0094] Ketones can be suitable solvents for the ink solutions. In some embodiments, suitable solvents include, for example, acetone, ethanol, methanol, methyl ethyl ketone, ethyl acetate, and the like, and combinations thereof. In some embodiments, the solvents are acetone and ethanol. The one or more organosulfur compounds (for example, thiol compounds) are present in the solvent in a total concentration of at least about 3 millimoles (mM). As used herein, the "total concentration" refers to the molar concentration of all the dissolved organosulfur compounds taken in aggregate. The one or more organosulfur compounds (for example, thiol compounds) can be present in any total concentration in which the ink solution consists of essentially a single phase. The one or more organosulfur compounds (for example, thiol compounds) can be present in total concentrations of at least about 5 mM, at least about 10 mM, at least about 20 mM, at least 50 mM, and even at least about 100 mM.

[0095] The stamp 310 can be "inked" with the ink solution 320 described herein using methods known in the art (for example, as described in Libioulle et al. "Contact-Inking Stamps for

Microcontact Printing of Alkanethiols on Gold," Langmuir Vol. 15, pp. 300-304 (1999)). In one approach, an applicator (for example, a cotton swab or a foam applicator) impregnated with the ink solution 320 can be rubbed across the stamping surfaces 16 of the stamp 310, followed by drying of solvent from the stamping surfaces 316. In another approach, the stamping surfaces 316 can be pressed against an "ink pad" impregnated with the ink solution, the ink pad optionally being a PDMS slab. In another approach, the stamp can be charged with ink solution from its back side, relative to the printing surface. In the latter approach, the organosulfur compound diffuses through the stamp to reach the relief-patterned face (the face including the planar surface 312 and the pattern elements 314 with the stamping surfaces 316) for printing. In another embodiment, the relief-patterned printing face of the stamp can be immersed in the ink solution, followed by withdrawal and drying ("immersive inking").

[0096] The devices of the present disclosure will now be further described in the following non limiting examples.

[0097]

[0098] EXAMPLES

Example 1

[0099] A silver-coated PET film was wrapped onto a surface of a cylindrical roll. A PDMS stamp was cast against a master roll with generic donut structures of about 2 microns to about 5 microns in diameter. The stamp, which had dimensions of approximately 25 cm x 25 cm, was saturated with a 5-10 mM thiol solution in ethanol, and the solution was allowed to penetrate into the stamp for a time of about 1 hour to about 24 hours.

[00100] The stamp was attached to a vacuum chuck in a stamping module shown schematically in FIGS. 2A-2B. Using optical alignment methods, the tool was aligned to the tool coordinate system. While actively maintaining alignment, the surface speeds of the flat stamp and the tool substrate were coordinated.

[00101] After contact between the stamp and tool substrate was initiated, d _ta ngent was varied throughout the rolling contact printing operation.

[0100] After printing, the silver-coated PET film was wet chemical etched so that printed features could be inspected, and the number of voids printed on the nonplanar substrate of the cylindrical roll were determined for each value of d _ta ngent· The results are shown in FIG. 5, which shows the percent area fill of printed and etched samples as a function of d _tan gent· FIG. 6 shows the measured contact force as a function of time for each value of dt _an gent· It should be noted that print area coverage never reaches 100% due to the presence of dust particulates and/or other stamp defects. The voids are not a function stamp flatness.

[0101] At high values of dt _ang ent, there is a high likelihood of stamping element collapse due to excessive contact forces, particularly at the leading and trailing edges of the stamp. At these transitions, a combination of inertial forces and varying contact area may cause feature collapse. FIGS. 7A-7C show the leading edge of the printed and etched samples for different values of d _t a _ngent , with dtan _gent varying from 2 pm in FIG. 7A, to 8 pm in FIG. 7B, and to 14 pm in FIG. 7C.

Examnle 2 [0102] One method for controlling leading and trailing edge transitions is to vary dtangent as a function of time and/or horizontal position. FIG. 8 provides the dtangent variation along with contact force variation as a function of horizontal position. In this example, a plot of contact force of the stamping surfaces against the nonplanar surface over time for a selected value of d _tangent follows a substantially trapezoidal trajectory, however, it should be noted that many different trajectories are possible. FIG. 8 shows the d _tangent trajectory along with the contact force profile as a function of horizontal position. Also shown is an inset image of the printed and etched with 99.4% area coverage.

Example 3

[0103] FIG. 9 shows the leading edge of the printed and etched sample for different values of dtangent with no stamp feature collapse. For this print trajectory, the maximum dtangent was set to a value that exhibited zero voids in the constant d _ta n _g ent experiment of Example 1 (see FIG. 5). At contact initiation and disengagement, d _ta n _g ent was set to a value that exhibited zero stamp feature collapse (see FIGS. 7A-7C). Note that these parameters are highly dependent on stamp material and geometry.

EMBODIMENTS

Embodiment A. A method of applying a pattern to a nonplanar surface, wherein at least a portion of the nonplanar surface has a radius of curvature, the method comprising:

providing a stamp with a major surface comprising a relief pattern of pattern elements extending away from a base surface, and wherein each pattern element comprises a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns;

applying an ink on the stamping surface, the ink comprising a functionalizing molecule with a functional group selected to chemically bind to the nonplanar surface;

positioning the stamp to initiate rolling contact between the nonplanar surface and the major surface of the stamp;

contacting the stamping surface of the pattern elements with the nonplanar surface to form a self-assembled monolayer (SAM) of the functionalizing material on the nonplanar surface and impart the arrangement of pattern elements thereto; and

controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface. Embodiment B. The method of Embodiment A, wherein controlling a relative position of the stamping surface of the pattern elements comprises controlling a vertical position d _tangent of the stamping surface relative to a plane of tangency at an interface between stamping surface and the nonplanar surface.

Embodiment C. The method of any of Embodiments A-B, wherein the dtangent is held constant while the major surface of the stamp contacts the nonplanar surface.

Embodiment D. The method of any of Embodiments A-C, wherein the dtangent is varied as a function of time while the major surface of the stamp contacts the nonplanar surface.

Embodiment E. The method of any of Embodiments A-D, wherein the dtangent is varied as a function of a horizontal position of the interface while the major surface of the stamp contacts the nonplanar surface.

Embodiment F. The method of E, wherein the d _tangent is selected to substantially prevent collapse of the pattern elements.

Embodiment G. The method of any of Embodiments E-F, wherein the d _tangent is selected to substantially prevent collapse of the pattern elements at one of a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp.

Embodiment H. The method of any of Embodiments E-G, wherein the d _tangent is selected to substantially prevent collapse of the pattern elements at both a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp.

Embodiment I. The method of any of Embodiments E-H, wherein the d _ta n _g ent is selected such that at least about 95% of the stamping surface of the pattern elements contact the nonplanar surface over a print cycle.

Embodiment J. The method of any of Embodiments E-I, wherein the d _ta n _g ent is selected such that at least about 99% of the stamping surface of the pattern elements contact the nonplanar surface over a print cycle.

Embodiment K. The method of any of Embodiments E-J, wherein the d _ta ngent is selected to: (1) substantially prevent collapse of the pattern elements at one of a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp; and (2) such that at least about 95% of the stamping surface of the pattern elements contact the nonplanar surface over a print cycle.

Embodiment L. The method of any of Embodiments E-K, wherein a plot of contact force between the stamping surfaces and the nonlinear surface over time for a selected value of the d _tangent follows a non-symmetric trajectory.

Embodiment M. The method of any of Embodiments E-L, wherein a plot of contact force between the stamping surfaces and the nonlinear surface over time for a selected value of the d _tangent follows a substantially trapezoidal trajectory. Embodiment N. The method of any of Embodiments A-M, further comprising repositioning the stamp to apply the arrangement of pattern elements to a plurality of different portions of the nonplanar surface in a step and repeat fashion.

Embodiment O. The method of any of Embodiments A-N, wherein the stamping surface comprises a poly(dimethylsiloxane) (PDMS), and wherein the functionalizing molecule is an organosulf ir compound chosen from alkyl thiols, aryl thiols and combinations thereof.

Embodiment P. The method of any of Embodiments A-O, wherein the nonplanar surface is a metal chosen from gold, silver, platinum, palladium, copper, and alloys and combinations thereof.

Embodiment Q. An apparatus for applying a pattern to a nonplanar surface having a least one portion with a radius of curvature, the apparatus comprising:

a stamper comprising an elastomeric stamp having a first major surface, wherein the first major surface of the stamp has a relief pattern of pattern elements extending away from a base surface, and wherein each pattern element comprises a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns,

an ink absorbed into the stamping surfaces of the stamp, the ink comprising a

functionalizing molecule with a functional group selected to chemically bind to the nonplanar surface;

a first motion controller supporting the stamper and configured to move the stamp with respect to the nonplanar surface; and

a second motion controller configured to move the nonplanar surface;

wherein the first motion controller and the second motion controller move the stamp and the nonplanar surface to control a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface.

Embodiment R. The apparatus of Embodiment Q, wherein the first motion controller and the second motion controller control a vertical position d _tange m of the stamping surface relative to a plane of tangency at an interface between stamping surface and the nonplanar surface.

Embodiment S. The apparatus of Embodiment R, wherein the d _tange m is held constant while the major surface of the stamp contacts the nonplanar surface.

Embodiment T. The apparatus of any of Embodiments R-S, wherein the d _tange is varied as a function of time while the major surface of the stamp contacts the nonplanar surface.

Embodiment U. The apparatus of any of Embodiments R-T, wherein the dtangem is varied as a function of a horizontal position of the interface while the major surface of the stamp contacts the nonplanar surface. Embodiment V. The apparatus of Embodiment U, wherein the d _tange m is selected to substantially prevent collapse of the pattern elements.

Embodiment W. The apparatus of any of Embodiments U-V, wherein the d _tange m is selected to substantially prevent collapse of the pattern elements at one of a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp.

Embodiment X. The apparatus of any of Embodiments U-W, wherein the d _tange is selected to substantially prevent collapse of the pattern elements at both a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp.

Embodiment Y. The apparatus of any of Embodiments R-X, wherein the d _tange is selected such that at least about 95% of the stamping surface of the pattern elements contact the nonplanar surface over a print cycle.

Embodiment Z. The apparatus of any of Embodiments R-X, wherein the d _tange is selected such that at least about 99% of the stamping surface of the pattern elements contact the nonplanar surface over a print cycle.

Embodiment AA. The apparatus of any of Embodiments R-Z, wherein the d _ta ngem is selected to: (1) substantially prevent collapse of the pattern elements at one of a leading edge of the major surface of the stamp and a trailing edge of the major surface of the stamp; and (2) such that at least about 95% of the stamping surface of the pattern elements contact the nonplanar surface.

Embodiment BB. The apparatus of any of Embodiments R-AA, wherein a plot of contact force between the stamping surfaces and the nonlinear surface over time for a selected value of the dtangem follows a non-symmetric trajectory.

Embodiment CC. The apparatus of any of Embodiments R-BB, wherein a plot of contact force between the stamping surfaces and the nonlinear surface over time for a selected value of the dtangem follows a substantially trapezoidal trajectory.

Embodiment DD. The apparatus of any of Embodiments Q-CC, wherein the nonplanar surface is the exterior surface of a roller.

Embodiment EE. A method of applying a pattern to an exterior surface of a roller, the method comprising:

absorbing an ink into a major surface of a stamp, the ink comprising a functionalizing molecule with a functional group selected to chemically bind to the exterior surface of the roller, wherein the major surface of the stamp comprises a relief pattern of pattern elements extending away from a base surface, and wherein each pattern element comprises a stamping surface with a lateral dimension of greater than 0 and less than about 5 microns;

contacting the stamping surface of the pattern elements with the surface of the roller to bind the functional group with the surface of the roller to form a self-assembled monolayer (SAM) of the functionalizing material on the surface of the roller and impart the arrangement of pattern elements thereto;

translating the major surface of the stamp with respect to the surface of the roller, wherein translating the major surface of the stamp comprises controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface; and

repositioning the stamp a plurality of times in a step and repeat fashion to transfer the arrangement of pattern elements to a plurality of different portions of the surface of the roller and form an array of pattern elements, wherein a stitch error between adjacent pattern elements in the array is less than about 10 pm.

Embodiment FF. The method of Embodiment EE, wherein the stitch error between adjacent pattern elements in the array is less than about 1 pm.

Embodiment GG. The method of any of Embodiments EE-FF, wherein the stamp is a parallelepiped comprising a parallelogrammatic cross-section, and the pattern elements in the array comprise parallelogrammatic tiles.

Embodiment HH. The method of any of Embodiments EE-GG, wherein the pattern elements are helically arranged on the surface of the roller.

Embodiment II. A method of making a tool, the method comprising:

providing a cylindrical roller comprising a metal substrate, a tooling layer on the metal substrate, and an external metal print layer on the tooling layer;

imparting an arrangement of pattern elements on the metal print layer, wherein each pattern element comprises a lateral dimension of greater than 0 and less than about 5 microns; and translating the major surface of the stamp with respect to the metal print layer, wherein translating the major surface of the stamp comprises controlling a relative position of the stamping surface of the pattern elements with respect to the nonplanar surface while the major surface of the stamp contacts the nonplanar surface; and

imparting the pattern elements a plurality of times in a step and repeat fashion to transfer the arrangement of pattern elements to a plurality of different portions of the print layer and form an array of pattern elements thereon, wherein a stitch error between adjacent pattern elements in the array is less than about 10 pm; and

etching away portions of the metal print layer uncovered by the pattern elements, exposing portions of the tooling layer.

[0104] Various embodiments of the invention have been described. These and other

embodiments are within the scope of the following claims.