Abstract:
A method and system for constructing structures by self-assembly of objects. The method and system include providing a first object having a first selected shape and providing a second object having a second selected shape, the shape of the first and second objects interacting to form an alignment which has only a simple stable state arising from minimization of interaction energy for the single stable state.

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATION 
       [0001]    This application claims priority from U.S. Provisional Application No. 61/299,636 filed Jan. 29, 2010, which is hereby incorporated by reference herein. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention is directed to a method and system for self-assembly construction of a structure. More particularly, the invention is directed to providing a first object with a first shape and a second object with a second shape with symmetry such that the first and second objects interact to align in a stable state arising from minimization of interaction energy. 
       BACKGROUND OF THE INVENTION 
       [0003]    Creating 3D structures by self assembly with specific architecture remains a scientific and technological goal far from being achieved. Inducing the spontaneous association of microscopic building blocks into macroscopic structures has been a promising way to create these new materials for a variety of useful applications. Such fabrication processes typically require interactions between microscopic building blocks. Many kinds of interactions have been investigated so far; including, for example, electrostatic, magnetic, Van der Waals, depletion, and DNA interactions. For many of these interactions, especially Van der Walls, depletion, and DNA interactions, the attractive energy between the particles is proportional to the overlapping surface between the colloids. Controlling the relative positions and orientations of the microscopic building blocks is a critical issue in such processes. However, to date there has been no efficient or reliable process that enables such spontaneous assembly and orientation of building blocks. 
       SUMMARY OF THE INVENTION 
       [0004]    A method and system are provided herein to create a particular building block shape, hereinafter “universal alignment patches”. Universal alignment patches that have the ability to align in only a single configuration when they interact face to face. The “universal alignment patches” can be attached to any structures, forcing two such structures to join in a particular configuration. The shape of the patches must be such that the aligned configuration corresponds to the only existing minimum in the energy landscape. Thus, the shape has to be carefully chosen such that the energy landscape does not exhibit any metastable configurations. For example, in one nonlimiting embodiment a flat eccentroid shape has a hole therethrough or a recessed region, which provides a desired shape meeting the stability requirements. In other embodiments, the two or more objects can have different shapes so long as the objects interact to form only one stable aligned state with the energy overlap minimized by the maximization of their face-to-face contact area. Such a method and system therefore enables exploitation for a variety of useful applications, particularly at the colloidal, ˜1 μm, scale. For example, methods and systems can be used in conjunction with biotechnology in related application U.S. Ser. No. 12/482,823 which is incorporated in its entirety by reference herein. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0005]      FIG. 1A  shows two objects positioned apart;  FIG. 1B  shows the two such objects interacting to align;  FIG. 1C  shows a first interaction and overlap configuration of the two objects; and  FIG. 1D  shows a second configuration which is a metastable state of overlap of the two objects; this is therefore a system that does not meet the desired criteria; 
           [0006]      FIG. 2A  shows a top view of two overlapping objects, each being circular with an off-center hole therethrough or surface recess on each object;  FIG. 2B  shows another type of shape embodiment similar to  FIG. 2A ;  FIG. 2C  shows yet another embodiment of shape;  FIG. 2D  shows still another embodiment of the invention;  FIG. 2E  shows the energy landscape for the embodiment of  FIG. 2A  and  FIG. 2F  shows yet another embodiment with a groove therein. 
           [0007]      FIGS. 3A-3G  shows a time lapse set of freeze frames at different times for interactions of the eccentric hole shaped objects. 
           [0008]      FIG. 4A  shows placement of one alignment patch on the face of an “L” shaped object and another at an angle on a cube (or a square cross section) with interaction causing the cube (or a square cross section) and “L” to come together;  FIG. 4B  shows the alignment of three objects, a block having an alignment patch, a cylinder having an alignment patch on each end face, and a plate having an alignment patch, which all assemble to form an assemblage through interaction of universal alignment patches. 
           [0009]      FIG. 5  shows two disk patterns with a spiral cut out or indentation, designed so that particles rotate primarily in one direction as they align. 
           [0010]      FIGS. 6A-6C  shows two disks with spiral patterns, aligned face to face showing overlaps as they rotate. 
           [0011]      FIG. 7  shows energy as a function of angle for the spiral shaped patterns in  FIGS. 6A-6C . 
           [0012]      FIG. 8A  shows an electron micrograph of a set of colloidal particles fabricated with the eccentric hole motif and  FIG. 8B  shows an enlarged electron micrograph image of two overlapping particles of the shape of  FIG. 8A . 
           [0013]      FIGS. 9A and 9B  show two schematic time lapse sequences of the centering and alignment of disks with off-center holes. The interaction between the disks is proportional to their overlap area. Independent of the initial configuration as the disks first touch, they are drawn together and rotate until their centers are coincident and their holes are completely overlapped. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0014]    For alignment of particles, in fact alignment of any particles or structures that are desirable to self-assemble, a shape with unique physical and mathematical properties has been identified for accomplishing this desired goal. An interaction between universal alignment patches, such as flat patterned surfaces, can be established which depends principally on the overlap area of two patterns. Examples of useful attractions are surface tension, Van der Waals forces, depletion forces or the forces between DNA covered surfaces. Self-assembly into a desired geometry can then be achieved using a shape which forces the surfaces to come together in only one configuration with no unwanted trapped metastable orientations. This is the same as achieving a landscape with only one energy interaction minimum. The patterns can be designed on any object and produced as “patches” which can be affixed to any object. For example, in one embodiment a circular patch having a hole therethrough or and indented region provides such a shape. A schematic example to illustrate the problems of self-assembly is shown in  FIGS. 1A and 1B  with two objects of the same complex shape interacting in a sequence.  FIGS. 1C and 1D  show a stable configuration and a metastable configuration, respectively. When the two objects (universal alignment patches) overlap, they interact and orientate in order to maximize the overlapping surface and therefore minimizing the interaction energy. The shape chosen in  FIG. 1  is, however, not a good one as that configuration has an obvious metastable position (FIG  1 D) in which the two objects may be trapped. This shape is therefore a typical example of an undesirable shape. 
         [0015]    There are, however, various shapes which meet the criterion of having only one stable alignment state (with no metastable states). The overall shape can be the assembly of two or more discontinuous shapes, and while the most preferred embodiment has shapes that are the same, in other embodiments shapes can be different as long as they meet the requirement that they interact to align in only one stable state. In one example embodiment, the sets of different shapes in  FIGS. 2A-2D  and  2 G illustrate various shapes which meet the requirements of the invention. The simple shapes are circular disks with various illustrated holes, including truncated holes, inside; and the hole must be off centered. The hole radius cannot exceed a certain critical ratio of the outer circle diameter. These shapes have only one stable point in their energy landscape which is obtained when the outer circumference of the disks are aligned and the inner holes are aligned. 
         [0016]    Considering the shape of  FIG. 2A  which shows a disk with an off-centered hole in it, one can readily show by conventional, well-known methods that two identical particles having such shapes translate and rotate to find a single minimum of energy when they interact. In this case, both objects will translate and rotate until their energy is minimized.  FIG. 2E  illustrates the normalized minimum energy as a function of angular displacement from perfect alignment. It should be appreciated that one of ordinary skill can calculate energy states of objects typically based upon a conventional numerical calculation approach. 
         [0017]    These methods and systems for achieving an object shape which meets the above requirements should therefore be valid for any kind of interactions at any scale as long as the attraction is proportional to the overlapping area. Macroscopic measurements were performed to confirm the validity of these calculations. Actual disks with eccentric holes were constructed of plastic, and were about 1 cm in radius. Silicon oil was applied to the disks; therefore, capillary forces which are also proportional to the overlapping area should drive their alignment. For these examples, the shapes are attached to a cylinder, which is held on a vibrating table. The vibrating table is used in order to overcome any solid friction effects between the disks.  FIGS. 3A-3G  show the sequential, freeze frame motions of two such disks. One disk is attached, the other disk is held to the first disk above by capillarity. When the vibrating table is turned on, both shapes stay aligned and come back to their alignment position when they are moved to a position where they are not perfectly aligned. Without the holes the disks have been observed to undergo random motion. 
         [0018]    The methods and systems described herein can be used for a variety of commercial purposes. For example, as shown in  FIG. 4A , if you place one object on a face of an “L” shaped object and another at an angle on a cube(or a square shape), then the cube (or a square shape) and “L” will come together at the set orientation. Such a universal alignment patch can be used to create arbitrary shapes from building blocks using any of the various herein described surface attractive interaction methodologies. In one embodiment, more than one universal alignment patch can be placed on a shaped object, allowing for selective orientation of the shaped object, for example, as seen in  FIG. 4B .  FIG. 4B  shows the alignment of three objects, a block having an alignment patch, a cylinder having an alignment patch on each end face, and a plate having an alignment patch, which all assemble to form an assemblage through interaction of universal alignment patches. Further, in another embodiment, three-dimensional structures may be assembled via interaction among multiple building blocks connected via the described universal alignment patches. It should be appreciated that a plurality of different universal alignment patches may be used so as to provide for unique combinations of the building blocks to achieve a desired structure. As a nonlimiting example, at least a third object and a fourth object are present wherein the first object is attached to the third object via interaction of the described universal alignment patches and the second object is attached to a fourth object via the described universal alignment patches so as to achieve a selectable orientation of the third object relative to the fourth object when the first object and the second object form and align. In one embodiment, the universal alignment patches have a three dimensional shape, such as, but not limited to a dome or cone, as a protrusion or recess where the face of the alignment patch has rotational symmetry to allow alignment as described herein. Further, additional features may be included on the universal alignment patches to encourage or strength the interaction or selectiveness of interaction of the patches, such as but not limited to the use of DNA or chemical functional groups. 
         [0019]    In yet another form of the invention, the shapes that overlap each other can also be of a different type of shape. For example,  FIGS. 6A and 6B , show two shapes that differ from each other in that one of the shapes is a mirror image of the other. The two shapes in this figure are disks with a “hole” (white area) in the shape of a widening spiral from the middle to the edge of the disk. For the purposes of future reference the disk of  FIG. 5A  is considered to have a counter-clockwise spiral, and the disk of  FIG. 5B  is considered to have a clockwise spiral. When one of the disks is placed on top of the other, there is never perfect overlap of the two disks, since they are different shapes. Nevertheless, the area of overlap is a function of the relative position and orientation of the two disks, so that under the conditions described hereinbefore for energy minimization, these disks will translate and rotate relative to each other so as to reach a configuration where the overlap between the two disks is a maximum to minimize overlap energy. 
         [0020]      FIGS. 6A-6C  show various relative orientations of the two disks from  FIGS. 5A and 5B , when the disk of  FIG. 5B  is placed on top of the disk of  FIG. 5A . In these  FIGS. 6A-6C , the regions shown in black are where there is overlap between areas on each of the two disks. Regions shown in light gray are where part of the hole on one disk overlaps a region on the other disk that is not part of a hole, and the white areas correspond to regions where the holes in the two disks overlap. The configuration of maximum overlap, or lowest energy, is that configuration noted by inspection of  FIGS. 6A-6C  where the area of the black region is a maximum and thus corresponds to  FIG. 6A . 
         [0021]      FIG. 6B  shows the situation where the disk with clockwise spiral is rotated so that the overlap area between the disks is smaller (smaller area of black region). This is the smallest overlap area possible under conditions that the outer edges of the two disks overlap. Thus,  FIG. 6B  represents the configuration with highest energy under this condition. When the disk with clockwise spiral is rotated further (see  FIG. 6C ), this has slightly lower energy then the configuration of  6 B. Thus, there is a torque tending to rotate the disk with clockwise spiral in a counter-clockwise direction. This disk will rotate all the way around until the configuration of  FIG. 6A  is reached.  FIG. 7  shows a sketch of the expected energy curve from the shapes shown in  FIGS. 6A-6C . Zero degrees in this figure corresponds to the configuration of  FIG. 6A , and increasing angle corresponds to counter-clockwise rotation of the shape with the clockwise spiral while the other shape is held fixed. The significance of this curve is that the shape of the potential is not symmetric, when the direction of rotation is reversed (Angle Θ→−→). In cases where the two shapes are the same, the potential will always be symmetric. 
         [0022]    The following non-limiting Example illustrates several aspects of invention. 
       Example 
       [0023]    To test the feasibility of these ideas on a several micron scale colloidal disks with eccentric holes were fabricated at the Cornell Center for Nanofabrication (CNF). Electron micrographs of the 5 micron disks with 2 micron holes is shown in  FIG. 8A . Note that both disks and holes are circular although the image is distorted. The disks were separated from the substrate and dispersed in water with surfactant. An electron micrograph of two overlapping disks as in  FIG. 8A , which have their holes aligned is shown in  FIG. 8B . 
         [0024]    In  FIGS. 9A  and B illustrates how two disks with off-centered holes will be drawn together and aligned in a unique configuration. Independent of the point and configuration of initial overlap the area monotonically increases with relative displacement and rotation until maximum overlap occurs. The maximum overlap corresponds to the disks being centered on one another and the holes being completely aligned. 
         [0025]    The foregoing description of embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the present invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the present invention. The embodiments were chosen and described in order to explain the principles of the present invention and its practical application to enable one skilled in the art to utilize the present invention in various embodiments, and with various modifications, as are suited to the particular use contemplated.