SYSTEM AND METHOD OF LOW-WASTE MULTI-MATERIAL RESIN PRINTING

Abstract

A multi-material 3-D printing system and method including at least two printing heads each with a transparent window circumscribed by an ejection nozzle. Each ejection nozzle is coupled to a respective pump that pumps resin from a respective vat onto a respective window. The resin is cured from below the window by exposure to a digital image displayed by a micro display chip. To switch resins, the sample is moved across a plurality of suction nozzles towards a second printing head. A respective one of the suction heads is coupled to a vacuum that effectuates the intake of residual resin from the underside of the sample.

Claims

1. A 3-D printing system, comprising: at least one micro display chip coupled to a light source and adapted to display a digital image received from a computer; three precision stages adapted to move a sample, affixed to a sample platform, in lateral (X and Y) and vertical (Z) directions relative to at least two printing heads and at least two suction nozzles; at least two printing heads, each disposed below the sample, above a respective one of at least two collection vats, and defining an upward-facing frustum comprising a flat, sealed, optically transparent, and gas-permeable window circumscribed by an ejection nozzle fluidically coupled to a respective collection vat; at least two lenses, each disposed below a respective window and adapted to focus the digital image onto a layer of resin coating a top surface of the respective window; and at least two suction nozzles, each disposed below the sample, adjacent to a respective collection vat, fluidically coupled to the respective collection vat, and fluidically couplable to a vacuum source, wherein application of a vacuum to a respective suction nozzle effectuates a suction at an upward-facing opening thereof.

2. The system of claim 1 wherein the opening of each suction nozzle is circumscribed by a rim having a tall edge opposite a short edge, the tall edge being adjacent to the collection vat to which the suction nozzle is fluidically coupled.

3. The system of claim 1 further comprising at least two suction reservoirs, each fluidically coupled to a respective suction nozzle and to a manifold that is fluidically coupled to the vacuum source, wherein the manifold diverts the application of the vacuum to a respective suction reservoir one at a time.

4. The system of claim 3 further comprising at least two storage reservoirs and at least two fluid pumps adapted to pump resin from a respective storage reservoir to a respective printing head, wherein each storage reservoir is disposed below a respective collection vat and fluidically coupled thereto via an orifice, and each storage reservoir is disposed adjacent to a respective suction reservoir and fluidically coupled thereto via a valve.

5. The system of claim 1 further comprising: at least two shutters, each adapted to allow or prohibit the digital image from reaching a respective lens; a beam splitter adapted to partially reflect the digital image towards a first shutter and to partially transmit the digital image towards a mirror; and a mirror adapted to reflect the partially transmitted digital image towards a second shutter.

6. The system of claim 5 further comprising a charge coupled device (CCD) adapted to monitor the digital image focused by a respective one of the lenses, wherein the CCD is disposed on a side of the beam splitter opposite the respective lens.

7. The system of claim 1 wherein each collection vat is at least twice as long as the sample platform in a first lateral direction and at least twice as long as the sample platform in a second lateral direction.

8. A method of printing a 3-D sample, comprising: displaying at least one digital image by a micro display chip coupled to a light source; positioning a sample, affixed to a sample platform, above a flat, sealed, optically transparent, and gas-permeable first window circumscribed by a frustoconical first ejection nozzle fluidically coupled to a first collection vat; coating the first window with a first resin pumped from the first collection vat and exposing the first resin to a first digital image focused by a first lens; and moving the sample past an upward-facing opening of a first suction nozzle that is fluidically coupled to a first suction reservoir while applying a vacuum to the first suction reservoir.

9. The method of claim 8 further comprising: positioning the sample above a flat, sealed, optically transparent, and gas-permeable second window circumscribed by a frustoconical second ejection nozzle fluidically coupled to a second collection vat; coating the second window with a second resin pumped from the second collection vat and exposing the second resin to a second digital image focused by a second lens; and moving the sample past an upward-facing opening of a second suction nozzle that is fluidically coupled to a second suction reservoir while applying a vacuum to the second suction reservoir.

10. The method of claim 9 wherein the opening of each suction nozzle is circumscribed by a rim having a tall edge opposite a short edge, the tall edge being adjacent to the collection vat to which the suction nozzle is fluidically coupled.

11. The method of claim 9 wherein: applying the vacuum to the first suction reservoir comprises controlling a manifold to divert the vacuum to only the first suction reservoir; and applying the vacuum to the second suction reservoir comprises controlling the manifold to divert the vacuum to only the second suction reservoir.

12. The method of claim 9 wherein: exposing the first resin comprises opening and subsequently closing a first shutter that optically precedes the first lens; and exposing the second resin comprises opening and subsequently closing a second shutter that optically precedes the second lens.

13. The method of claim 9 further comprising monitoring at least one digital image focused by the first lens via a charge coupled device (CCD).

14. The method of claim 13 wherein each collection vat is at least twice as long as the sample platform in a first lateral direction and at least twice as long as the sample platform in a second lateral direction.

15. A method of printing a 3-D sample, comprising: displaying at least one digital image by a micro display chip coupled to a light source; performing a first exposure, comprising: positioning a sample, affixed to a sample platform, at a first lateral location above a flat, sealed, optically transparent, and gas-permeable first window circumscribed by a frustoconical first ejection nozzle fluidically coupled to a first collection vat, and coating the first window with a first resin pumped from the first collection vat and exposing the first resin to a first digital image focused by a first lens; and performing a second exposure, comprising: positioning the sample at a second lateral location above the first window, and coating the first window with the first resin pumped from the first collection vat and exposing the first resin to a second digital image focused by the first lens.

16. The method of claim 15 wherein the first image and the second image may be identical.

17. The method of claim 15 wherein the first image and the second image may comprise sub-images of a larger image.

18. The method of claim 15 wherein the first lateral location overlaps the second lateral location by 5-20 μm.

19. The method of claim 15 wherein the first collection vat is at least twice as long as the sample platform in a first lateral direction and at least twice as long as the sample platform in a second lateral direction.

20. The method of claim 15 further comprising: moving the sample past an upward-facing opening of a first suction nozzle that is fluidically coupled to a first suction reservoir while applying a vacuum to the first suction reservoir; and performing a third exposure comprising: positioning the sample at a third lateral location above a flat, sealed, optically transparent, and gas-permeable second window circumscribed by a frustoconical second ejection nozzle fluidically coupled to a second collection vat, and coating the second window with a second resin pumped from the second collection vat and exposing the second resin to a third digital image focused by a second lens.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] A more complete appreciation of the present disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings.

[0019] FIG. 1 shows a schematic of a low-waste multi-material PμSL system.

[0020] FIG. 2 shows a schematic of a printing head for a PμSL system.

[0021] FIGS. 3A-3E show alignments of exposures during stitch printing.

[0022] FIGS. 4A-4C show single-, stitch-, and array-exposure printing modes, respectively.

[0023] FIG. 5 shows a schematic of a vacuum nozzle between vats of resin.

[0024] FIGS. 6A-6C show a schematic of a low-waste multi-material PμSL system at various stages during material switching.

DETAILED DESCRIPTION

[0025] The present disclosure may be understood more readily by reference to the following detailed description of the disclosure taken in connection with the accompanying drawing figures, which form a part of this disclosure. It is to be understood that this disclosure is not limited to the specific devices, methods, conditions, or parameters described and/or shown herein, and that the terminology used herein is for the purpose of describing particular embodiments by way of example only and is not intended to be limiting of the claimed disclosure. Also, as used in the specification and including the appended claims, the singular forms “a,” “an,” and “the” include the plural, and reference to a particular numerical value includes at least that particular value, unless the context clearly dictates otherwise.

[0026] The following numerals are used to describe various features of the embodiments. [0027] 5 printing apparatus [0028] 10 sample [0029] 20 sample platform [0030] 30a,b first and second vat [0031] 40a,b first and second storage reservoir [0032] 50a,b first and second resin [0033] 60a,b first and second printing head [0034] 70a,b first and second tip [0035] 80a,b first and second gas-permeable window [0036] 90a,b first and second ring-shaped nozzle [0037] 100a,b first and second resin pool [0038] 110a,b first and second liquid pump [0039] 120a,b first and second suction nozzle [0040] 130a,b first and second suction reservoir [0041] 140a,b first and second valves [0042] 150a,b first and second lens [0043] 160a,b first and second shutter [0044] 170 vacuum chamber [0045] 180 manifold [0046] 190 computer [0047] 200 DLP and light source [0048] 210 beam splitter [0049] 220 mirror [0050] 230 XYZ stage assembly [0051] 240 charge-coupled device (CCD) [0052] 250a,b first and second tall blade [0053] 260a,b first and second short blade

[0054] FIG. 1 shows an embodiment of a multi-material resin printing apparatus 5 for printing a 3-D sample 10 on the underside of a sample platform 20. The sample platform 20 may be coupled to a precision XYZ stage assembly 230 that can move the sample platform 20 laterally in the X and Y directions and vertically in the Z direction relative to each of a first printing head 60a and a second printing head 60b. In some embodiments, relative motion between the printing heads 60 and the sample platform 20 may be enabled by coupling each stage of the XYZ stage assembly 230 to various parts of the printing apparatus 5 such as the printing heads 60.

[0055] Each printing head 60 may be disposed in a respective vat 30 and partially or completely submerged in and/or coated by a respective resin 50. Each vat 30 is above and fluidically coupled to a respective storage reservoir 40 such that liquid resin 50 in the vat 30 may drain into the storage reservoir 40. The vat 30 may collect liquid resin 50 as it drips off of a sample 10 during printing.

[0056] A multi-material printing process may begin by generating (or otherwise obtaining) a digital 3-D model via a computer 190. The 3-D model may be an assembly of multiple models each representing different materials. The 3-D model may be sliced, or divided, into layers approximately 5-20 μm thick. Each layer may be represented by one or more 2-D digital images, where any given digital image corresponds to a single material. In other words, if a given layer comprises two materials, then there would be at least two digital images for that layer.

[0057] A sample 10 may be printed in layers, one at a time, by projecting and focusing a series of optical images onto a selected one of the printing heads 60. To print a given layer, the computer 190 may send a digital image to a DLP and light source 200 where it may be transformed into an optical image. The DLP and light source 200 may project the optical image towards a selected one of the printing heads 60, for example, towards a first printing head 60a for printing a first resin 50a or towards a second printing head 60b for printing a second resin 50b. Each printing head 60a or 60b may be selected (or deselected) by opening (or closing) a respective shutter 160a or 160b. A lens 150a or 150b may be disposed between each respective shutter 160a or 160b and the respective printing head 60a or 60b to focus the optical image(s).

[0058] In some embodiments the optical image projected by the DLP and light source 200 may encounter a beam splitter 210 that partially reflects the optical image towards the first shutter 160a and partially transmits the optical image therethrough towards a mirror 220 that reflects the optical image towards the second shutter 160b. In some embodiments a charge-coupled device (CCD) 240 may be aligned with an optical axis of the first lens 150a to monitor the projection of the optical image onto the first printing head 60a. The CCD 240 may be positioned on a side of the beam splitter 210 opposite the first shutter 160a.

[0059] As shown in FIG. 2, a printing head 60 may be frustoconical with a flat tip 70 at the frustum. The tip 70 may comprise a transparent gas-permeable window 80 through which an optical image may be transmitted. The gas-permeable window 80 may have lateral dimensions to accommodate an entire optical image projected by the DLP and light source 200. For example, a DLP and light source 200 that utilizes a DLP chip having 1920×1080 resolution with 10×10 μm pixels may project an optical image with a 22 mm diagonal dimension (via Pythagorean's theorem). Thus, a circular gas-permeable window 80 may be chosen to have a diameter of 25 mm.

[0060] The gas-permeable window 80 may be referred to as a membrane or a film, and it may be constructed from or coated by any suitable material, preferably those with superior optical clarity such as DuPont Teflon AF2400 or polydimethylsiloxane (PDMS). Gas permeability helps to prevent the gas-permeable window 80 from sticking to resin 50 that cures during photo polymerization due to exposure to an optical image. Oxygen permeability is especially advantageous because oxygen inhibits photo-crosslinking. The gas-permeable window 80 may have a thickness of 130 μm.

[0061] Each printing head 60 may be circumscribed by a ring-shaped nozzle 90, e.g., an ejection nozzle having an annular (or polygonal annular) opening, that is fluidically coupled to a respective liquid pump 110 capable of pumping resin 50 from a storage reservoir 40 to the tip 70 of the printing head 60. The ring-shaped nozzle 90 may be frustoconical (or frusto-pyramidal) with an outer wall extending upwards and inwards at an angle of approximately 50 degrees from the horizontal, and the ring-shaped nozzle 90 may have an annular opening adjacent to and circumscribing the tip 70 of the printing head 60 with a gap of approximately 500 μm. Resin 50 may be pumped by the liquid pump 110 into and through the ring-shaped nozzle 90. As the resin 50 exits the annular opening of the ring-shaped nozzle 90, it may flow towards the center of the gas-permeable window 80 due to the inward angle of the outer wall of the ring-shaped nozzle 90, thereby creating a resin pool 100 that covers the top surface of the gas-permeable window 80. The thickness of the resin pool 100 may be controlled by adjusting the flow rate of the liquid pump 110. In some embodiments a thickness of 1-3 mm may be preferred. The liquid pump may be any suitable type, for example a non-contact peristaltic pump or a diaphragm pump, and it may pump at a flow rate of approximately 5-10 ml/s. During printing, excess resin 50 of the resin pool 100 may flow off the tip 70 into a respective vat 30 and reservoir 40. The terms “frustoconical” and “frusto-pyramidal” may be used interchangeably herein, and the terms “annular” and “polygonal annular” may be used interchangeably herein.

[0062] An optical image that is focused on a printing head 60 creates a focused image at or adjacent to the gas-permeable window 80, and therefore, at or adjacent to the resin pool 100 coating the top surface of the gas-permeable window 80. The bright areas of the optical image cause the resin 50 of the resin pool 100 to cure, or polymerize, whereas the dark areas of the optical image do not cause curing or polymerization.

[0063] Due to size limitations of currently available LCD and DLP chips, a single exposure may not be large enough to print an entire layer (of a given material) of a sample 10. For example, a DLP chip having a pixel resolution of 1920×1080 resolution with 10×10 μm pixels creates an optical image of 19.2×10.8 mm. If a cross-section of the sample 10 is larger than 19.2×10.8 mm, then the corresponding layer must be printed with multiple exposures, i.e., in multiple sections.

[0064] In some embodiments multiple-exposure printing may be achieved by dividing a digital image corresponding to an oversized layer into multiple digital sub-images. Each sub-image corresponds to an optical image no larger than the maximum projected image of the DLP or LCD chip at the desired pixel size. For example, a printing apparatus 5 that utilizes a DLP chip having a pixel resolution of 1920×1080 may need to print an oversized layer having a pixel resolution of 3800×2000. In this case, the computer 190 may generate (or otherwise obtain) four digital sub-images for that layer, each having a pixel resolution of 1900×1000. The printing apparatus 5 may then print the oversized layer one section at a time, where each section corresponds to one of the sub-images.

[0065] Adjacent edges of neighboring sections may be printed to overlap one another by 5-20 μm, as indicated by FIGS. 3B-3C, to improve mechanical strength of the resulting layer at the section boundaries. The precise positions and amounts of overlap at section boundaries may be accurately controlled by the XY stage of the XYZ stage assembly 230. However, misalignment elsewhere in the printing apparatus 5 may cause errors in overlapping of section boundaries. As indicated in FIG. 1, there are at least two frames of reference for each printing head 60. A first frame of reference corresponds to alignment between the DLP and light source 200 and the printing head 60, and a second frame of reference corresponds to alignment between the printing head 60 and the sample platform 20. If these two frames of reference are misaligned with each other, then errors in overlapping of section boundaries like those shown in FIGS. 3D-3E may result. Specifically, FIG. 3D represents misalignment in the Y direction and FIG. 3E represents misalignment in the X direction.

[0066] A typical error requirement for PμSL printing may be 10 μm. However, it is not uncommon for an XY stage to have an offset error that is greater than this amount, and further, the offset may be nonlinear with respect to travel distance. Therefore, to counter misalignment errors during multiple-exposure printing, offsets may be measured at a plurality of points distributed in both the X and Y directions of a maximally sized layer. In some embodiments five or more uniformly distributed points may be measured in a maximally sized, square-shaped layer. The measurements may be fit to a second order (or greater) polynomial that may be used to compensate for the observed nonlinear offsets of the XY stage.

[0067] FIGS. 4A-4C shows three printing modes enabled by the XY stage of the XYZ stage assembly 230. In each figure, the maximum layer size is represented by the dotted outer rectangle and the optical-image exposure size is represented by the dashed inner rectangles (nine exposures per layer). FIG. 4A shows “single-exposure” printing, where the printed area fits within a single exposure. In this mode, the XY stages of the XYZ stage assembly 230 do not need to move provided that only one resin 50 is used. FIG. 4B shows “stitch-exposure” printing, where a large image is divided into sub-images each of which is independently printed. In some embodiments each exposure may overlap neighboring exposures by 5-20 μm as described earlier (overlaps are not shown in FIG. 4B). FIG. 4C shows “array-exposure” printing, where the same small image is printed independently multiple times. For low-volume production, array-exposure printing may be faster than single-exposure printing. Array-exposure and stitch-exposure printing may be combined, for example when multiple identical samples need to be printed and each sample has at least one layer that cannot be printed with a single exposure.

[0068] For array-exposure and stitch-exposure printing in both X and Y directions, it may be advantageous to laterally size the vat 30 beneath each printing head 60 to be at least four times larger than the maximum size of a printed layer, e.g., at least four times larger than the sample platform 20. This prevents residual resin 50 from dripping from the sample 10 and/or sample platform 20 outside the vat 30. In other words, the vat 30 should be at least twice as long at the sample platform 20 in the X direction and at least twice as long in the Y direction. In some embodiments the printing head 60 may be moved while the sample 10 is kept stationary, and in other embodiments both the sample 10 and the printing head may be moved.

[0069] When the printing apparatus 5 finishes printing a first layer, the Z stage of the XYZ stage assembly 230 may move the sample platform 20 (and sample 10) up vertically by at least a layer thickness to define a next layer of liquid resin 50 for printing. However, it may be advantageous to move the sample 10 away from the printing head 60 in the X and/or Y directions (laterally) before moving the sample 10 in the vertical direction. This is because the shear fluid force that results between the printing head 60 and the sample 10 when moving the sample laterally is generally much less than the normal fluid force that results between the printing head 60 and the sample 10 when moving the sample 10 vertically. For example, the vacuum pressure (normal force per unit area) caused by separating two surfaces wetted by resin commonly used in PμSL printing can be described by the following equation: σ=−pI+2με, where σ is the fluid stress tensor, p is the pressure, I is the identity tensor, μ is the fluid viscosity and ε is velocity gradient tensor (or fluid strain tensor). A resin viscosity μ=50 cP and a velocity ε=10 mm/s yields a vacuum pressure on the order of 1E5 Pa. In contrast, the same two wetted surfaces sliding past each other with a gap of 20 μm yields a shear pressure of 1E2 Pa—approximately three orders of magnitude lower than the normal vacuum pressure. Thus, separating the sample 10 from the printing head 60 laterally instead of vertically helps to prevent damaging or deforming delicate 3-D printed features of the sample 10. As indicated above, the vat 30 should be at least twice as long at the sample platform 20 in the X direction and at least twice as long in the Y direction (for array or stitch printing in both dimensions) to prevent residual resin 50 from dripping from the sample 10 and/or sample platform 20 outside the vat 30.

[0070] If the printing apparatus 5 needs to switch between resins 50 during multi-material printing, the XY stage of the XYZ stage assembly 230 may move the sample 10 (on the underside of the sample platform 20) between printing heads 60. However, the underside of the sample 10 may be coated with residual first resin 50a that could drip into a second vat 30b meant only for a second resin 50b. To prevent such cross-contamination, the sample 10 may be moved over (slid across) a first suction nozzle 120a to remove any residual resin 50a Similarly, to prevent cross-contamination in the opposite direction, e.g., when switching from resin 50b to resin 50a, the sample 10 may be moved over a second suction nozzle 120b to remove any residual resin 50b. Indeed, the printing apparatus may include one suction nozzle 120 for each different resin 50.

[0071] FIG. 5 shows two suction nozzles 120a and 120b disposed between the first vat 30a and the second vat 30b, where the first suction nozzle 120a may be closer to the first vat 30a and the second suction nozzle 120b may be closer to the second vat 30b. In some embodiments an outer wall of each suction nozzle 120a and 120b may contact or be shared with a respective vat 30a and 30b. Each suction nozzle 120a and 120b may be coupled to a respective suction reservoir 130a and 130b that may in turn be coupled to a vacuum chamber 170 (or any other vacuum source including a vacuum pump) via a manifold 180. Each suction reservoir 130a and 130b may be connected to a respective storage reservoir 40a and 40b via a respective valve 140a and 140b.

[0072] Consider the case when the printing apparatus 5 switches from a first resin 50a to a second resin 50b. As the sample 10 moves away from the first vat 30a it encounters the first suction nozzle 120a. At this time the first valve 140a is closed and the manifold 180 has diverted the vacuum of the vacuum chamber 170 to only the first suction reservoir 130a. In so doing, air (or gas) is sucked into the upwards-facing opening of the first suction nozzle 120a as indicated by the dashed arrows in FIG. 5. This rapid air intake sucks residual resin 50a from the sample 10. As the sample 10 continues to move towards the second vat 30b, no resin 50a is sucked in by the second suction nozzle 120b because there is no vacuum in the second suction reservoir 130b (because the manifold 180 has diverted the vacuum to only the first suction reservoir 130a). The sample 10 may continue moving until it reaches the second printing head 60b. At this time the manifold 180 may divert the vacuum away from the first suction reservoir 120a and the first valve 140a may be opened to recirculate any captured residual resin 50a into the first storage reservoir 50a. Now consider the case when the printing apparatus 5 switches back from the second resin 50b to the first resin 50a. When the sample 10 encounters the second suction nozzle 120a, the second valve 140b is closed and vacuum has been diverted by the manifold 180 to only the second suction reservoir 130b. The second suction nozzle 120b therefore sucks residual resin 50b from the sample 10 while the first suction nozzle 120a does not.

[0073] The side walls (or rim) of each suction nozzle 120 may have different heights. Consider the first suction nozzle 120a. The wall closer to the vat 30a may define a first tall blade 250a and the wall further from the vat 30a may define a first short blade 260a. The first short blade 260a allows greater air flow than the first tall blade 250a as the sample 10 moves past the first suction nozzle 120a. Thus, the dominant flow of air is in a direction towards the first vat 30a and away from the second vat 30b, e.g., opposite the direction of motion of the sample 10. This helps to prevent resin 50a from splashing into or otherwise entering the second suction nozzle 120b and thereby contaminating resin 50b. In some embodiments a gap between the two suction nozzles 120 is open to external air to allow unhindered air supply, which may be important if the sample 10 spans across both suction nozzles 120 during movement of the sample 10 past the suction nozzles 120.

[0074] In some embodiments the difference in height between a tall blade 250 and a short blade 260 may be approximately 1 mm. In some embodiments each suction nozzle 120 may have an opening of approximately 0.5-1.0 mm, resulting in an air (or gas) flow velocity of approximately 1-10 m/s when driven by a pressure difference from the vacuum chamber 170 of approximately 0.2-1.0 atm. In some embodiments the sample 10 may move laterally past (slide above) a suction nozzle 120 at approximately 5 mm/s or less and at a vertical distance of approximately 0.5-1.0 mm. A higher air (or gas) flow rate and a slower movement of the sample 10 may result in more residual resin 50 being sucked from the sample 10 per unit time, especially for resins 50 with viscosities greater than approximately 500 cP.

[0075] FIGS. 6A-6C show an exemplary multi-material printing sequence for the printing apparatus 5. FIG. 6A indicates an optical image being projected through an open first shutter 160a, through a first lens 150a, and onto the first printing head 60a adjacent to the sample 10. Excess resin 50a may be collected by a first vat 30a. FIG. 6B shows the sample 10 moving away from the first printing head 60a in preparation for printing with a second resin 50b. The sample 10 moves laterally past a first suction nozzle 120a, which sucks residual resin 50a from the sample 10. FIG. 6C indicates an optical image being projected through an open second shutter 160b, through a second lens 150b, and onto the second printing head 60b adjacent to the sample 10. Excess resin 50b may be collected by a second vat 30b.

[0076] While several embodiments of the disclosure have been shown in the drawings, it is not intended that the disclosure be limited thereto, as it is intended that the disclosure be as broad in scope as the art will allow and that the specification be read likewise. Therefore, the above description should not be construed as limiting, but merely as exemplifications of particular embodiments.