The design of complex three-dimensional (3D) microstructures is extremely important for the development of novel materials for optics, biotechnology, lab-on-chips, regenerative medicine as well as for micro- and nanoelectronics (1–5). Different techniques such as interference photolithography, 3D printing and two-photon lithography are already used in 3D micro-fabrication. One modern and very attractive approach for the design of 3D structures is based on the folding principle, which is inspired by the Japanese art of paper folding – origami. In its traditional fashion, folding is realized through the application of an external mechanical force to form objects with size ranging from tens of meters down to millimeters (http://quentinbaur.weebly.com/origami-world-records.html; accessed 24 November 2013). Substitution of the manpower with pneumatics (6) and magnetic fields (7) allows for controlled folding at the micrometer scale. More advanced and attractive approaches are based on the effect of self-folding, which is provided by internal actuation caused by thermal and shape memory alloy actuation (8), internal stress (9), surface forces, swelling (10, 11), etc.
Recently, self-folding polymer films have attracted considerable interest owing to their unique properties. In fact, a variety of polymers sensitive to different stimuli such as pH, temperature and light (12) allow the design of self-folding films (13, 14), which move in response to various external signals. Next, many polymers are able to change their properties under physiological conditions. There are also plenty of biocompatible and biodegradable polymers. These properties make polymer-based self-folding films highly attractive for biotechnological applications. Moreover, polymers undergo considerable, reversible and fast volume changes upon swelling/deswelling that allow the design of systems with reversible folding. Last, fabrication of folded 3D structures from nano- to macroscale is possible.
The main actuation principle, which is used by us for the design of self-folding polymer films, is reversible swelling of hydrogels (15). In this way, stimuli-responsive hydrogels behave similarly to plant cells, which are able to swell and shrink, and produce macroscopic actuation in response to external stimuli (16–18). In most cases, change of conditions results in homogeneous expansion or contraction of hydrogels in all directions. More complex actuation such as twisting, bending and folding occurs as a result of inhomogeneous expansion/shrinking, which proceeds with different amplitude in different directions (1, 4). In such actuating schemes, inhomogeneous deformation caused by structural inhomogeneity of polymer materials is used. This can be, for example, lateral inhomogeneity in swelling behavior, which was actively investigated by Kumacheva et al. (19, 20) and Kim et al. (21). They demonstrated that, when swelled in an aqueous medium, such films do not bend to the side of the less swelling component as observed in the case of “classical” bilayer but roll into a 3D shape consisting of two nearly cylindrical regions connected by a transitional neck. Another possible geometry is a bilayer, which consists of one hydrophobic polymer and one layer of stimuli-responsive polymer. The deformation of bilayers was first discussed by Timoshenko (22) in his paper about bimetal strips (22). He predicted that the radius of curvature is inversely proportional to the film stress. Moreover, the radius of curvature first decreases and then increases upon increase in the volume of the active component. According to Timoshenko (22), the resultant curvature appears not very sensitive to the difference in stiffness between the two layers, and is predominately defined by the actuation strain and the layer thickness (2, 23). However, Timoshenko’s equation applies to 1D bending and does not predict the folding direction of films. In contrast, the folding behavior of polymer bilayers is highly complex and depends on many parameters such as the radius of curvature, shape and presence of substrate, and does not result in simple unidirectional bending but in the formation of highly complex 3D structures. The goal of this review was to summarize our achievements in understanding of the folding mechanism of polymer bilayers with respect to the design of 3D structures with controlled geometry.
2 General description of the folding films
For most of our experiments, we used polymer bilayers consisting of a hydrophilic thermoresponsive polymer, which was the bottom layer, and a hydrophobic polymer, which was the top layer (Figure 1A). The bilayer was deposited on a solid substrate. The thermoresponsive polymer was typically a copolymer of poly(N-isopropylacrylamide), which swells in water below 33°C and is not swollen above this temperature. The hydrophobic polymer was either poly(caprolactone) or poly(methyl methacrylate). At elevated temperature, the thermoresponsive polymer is not swollen and the bilayer is flattened. Immersion in cold water led to swelling of the thermoresponsive polymer and to deformation of the bilayer (Figure 1B).
Apparently, swelling of the hydrophilic polymer is the first step towards the folding of the bilayer and, in fact, defines how the folding will proceed. In our case, the lower polymer layer is confined between two water-impermeable substances (the substrate and the hydrophobic polymer) that restrict the water diffusion and define the direction of swelling. We qualitatively investigated swelling by observing for changes in the color of the films, which, due to light interference, reflects the change in its thickness and swelling degree (Figure 2) (24). The non-swollen films have a homogenous color. The color of the films started to change immediately after immersion in water at 25°C. The changes in color started from the periphery of the bilayer film and gradually proceeded towards its center in the cases of films with rectangular, elliptical or star-like shapes, which indicates inhomogeneous activation profile in the active layer due to slow water diffusion (23, 24).
The exact scenario of swelling is defined by the shape of the film. This can be seen clearly in the differences in the activation patterns of rectangular (Figure 2A), elliptical (Figure 2B and C) and star-like films (Figure 2D and E). In all cases, swelling starts from the periphery of the bilayer, as this is the only accessible contact region between the active layer and the medium. However, in rectangular films, swelling at the corners is faster than that along the sides. In the case of elliptical films, the swelling front propagates homogenously towards the center. For star-like bilayers, the tips of the triangular-like arms swell faster than both their base and the polygonal central part they are attached to. This can be explained by the fact that the diffusion fronts on either side of the star-like arms/corners of the rectangles intersect, resulting in faster swelling.
We found that the folding follows the scenario of the swelling. In particular, folding always starts from the periphery of the film, where the film is most swollen. For example, rectangular films start to fold from the corners because swelling of the thermoresponsive layer in these areas is the fastest (water diffuses from orthogonal sides). This leads to the formation of dog-ear shapes in the first moments (Figure 3A). Folding along the long and short sides starts later because swelling in this direction is slower (Figure 3B and C). This specific sequence of folding events leads to the formation of different structures. Specifically, small films (whose length and width are smaller than the radius of curvature) undergo diagonal rolling. In this case, rolling starts either from two adjacent or from opposite corners (Figure 3D).
A more complicated scenario is observed in the case of films with a large aspect ratio (ratio between length and width) (23). Rolling starts at the corners first like before. The long-side rolling starts later (Figure 3B and E) but dominates and leads to the transition of bent corners to a “long-side rolling” scenario. Depending on the width of the film and on the circumference, either incompletely rolled tubes are formed or the two long-side rolling fronts collide into a completely rolled singular or double tubes (Figure 3C) (23).
If the deformed circumference (diameter of the tubes) is considerably smaller than the width and length of the films, then rolling starts first from all corners and then continues along the long and short sides of the film (Figure 3F). The rolling fronts do not collide until several turns are made, which were shown to be almost irreversible (15). Since already rolled fronts are unable to unroll, irreversible all-side rolling is observed.
The observed experimental findings allowed us to plot qualitative phase diagram showing what kind of structures is formed depending on the shape and size of the rectangular films (Figure 4). Diagonal rolling is observed in the case of small bilayer films, where the length and width are smaller than the radius of curvature. Very large films (when the length and width are larger than the curvature radius) fold along all sides. The formed tubes are narrow and long. The fact that the bilayer is located on the solid substrate is very important. For example, narrow bilayer on a substrate folds along the long sides and forms tubes (Figure 3C). The same bilayer, when freely floating in solution, folds along the short sides and forms a scroll.
Similarly to rectangles, folding of rounded shapes such as stars with six or four arms starts from the periphery (24). If the radius of curvature is small, folding results in the formation of multiple short tubes along the periphery of the film. These small tubes merge during their rolling (Figure 5C–E), and the probability of merging depends on the angle between tubes. We found that the critical value of the angle below, where merging of the tubes was not observed, was ca. 120–150°. This observation was defined as the first rule of folding.
It was observed that folding does not stop after the tubes stopped to merge (Figure 6A and B) but proceeds further (24). For example, the arms of the star bend towards their base (Figure 6C). In fact, after the first step of folding, multiple tubes are formed along the perimeter of the bilayer films. The rigidity of these tubes is higher than that of the undeformed films, and the formed polygonal shapes are stiffened by this tube formation. These shapes possess, nevertheless, a number of weak points located at the intersection of the tubes, i.e., at the vertices. These points act like hinges, and folding is only observed along the lines connecting them (dashed line in the inset in Figure 6B). The formation of hinges during folding of homogenous bilayers has not been reported in the literature, and, typically, local deposition of stimuli-responsive materials was used for the generation of hinges (25).
Interestingly, the semi-elliptical film folds further along the lines connecting the vertexes at the base and the top vertex, and no folding along the lines connecting either the vertexes of the middle or the ones at the base is observed. This effect is related to the swelling of hydrogel layer: the folding can proceed only along the lines where the hydrogel layer is swollen, i.e., along the lines, which are closer to the periphery of the film. Interestingly, folding of one arm can result in blocking of the folding of the neighboring arms. In particular, this happens if the angle between the base of the folded ray and the shoulders of the neighboring rays is close to 180° (Figure 6D). Such kind of interactions results, for example, in folding of only three of six arms of the star (Figure 6E) (24).
In the case of large curvature, swelling starts from the periphery as well but the whole arm gradually bends towards the center of the star. In this case, one can say that one tube or a half-folded tube along each arm is formed. As a result, capsules with rounded walls are formed (Figure 7).
The advantage of origami-inspired approaches is that it can be applied not only to thermoresponsive polymers but also to other kinds of polymers and materials. For example, by using this approach, we developed fully biodegradable/biocompatible self-folding films that are particularly suitable for bio-applications (26). The approach is based on the use of polycaprolcactone-polysuccinimide bilayers. Both polymers are biocompatible/biodegradable and hydrophobic. Polysuccinimide, which is obtained by polycondensation of aspartic acid, is able to slowly hydrolyze in physiological buffer and yield hydrophilic polyaspartic acid. As a result, the bilayer rolls and forms a tube. The rolling is, however, irreversible.
In this review, our progress in understanding of the folding of stimuli-responsive polymer bilayers, consisting of a hydrophobic and a stimuli-responsive hydrophilic polymer, is summarized. We found that the bilayers can bend in one direction or undergo multi-step folding to form complex structures. The shape of the formed self-folded structures depends on (a) the initial shape of the film; (b) the radius of curvature, which is determined by the thickness of the layers; and (c) the presence of a substrate. For example, it was found that the same rectangular film folds along different directions when freestanding or located on a substrate. The radius of curvature defines whether the films undergo one- or multi-step folding. A large radius of curvature results in one-step folding and in the formation of rounded shapes such as tubes and capsules. A small radius of curvature leads to multi-step folding of the bilayer and the formation of 3D structures with sharp hinges. These observations open perspectives for the precise programming of the folding scenario and the directed generation of different 3D shapes by varying the initial shape of the film.
The author is grateful to DFG (grant IO 68/1-1) and IPF for financial support. The author is also grateful to Georgi Stoychev for his comments on the manuscript.
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