Swelling-induced instability in a gel. The gel was synthesized using dimethylaminoethylmethacrylate and acrylamide as monomers, N,N′-methylenebisacrylamide as crosslinkers, and ammonium persulfate as initiators. (a) The as-fabricated gel, diameter ∼3 cm. (b) During swelling in water, the surface of the gel formed creases. (c) As the migration of water progressed, the surface pattern coarsened.
Bending-induced instability in a popular Chinese food, Liang Fen (astarch gel). A hot solution was poured into a large tray and was left at room temperature for hours to form a gel. On the top surface of the gel, a thin stiff skin formed due to the evaporation of water. (a) When the gel was bent to compress the top surface, multiple wrinkles formed. (b) When the gel was bent to compress the bottom surface, a single crease formed. (Courtesy of Denian Zhuang).
Schematics of two types of surface instability: (a) wrinkles and (b) creases.
Each element of the network is marked by its coordinate , when the network is in the reference state, which is taken to be the dry polymer. When the network absorbs the solvent and swells, the element of the network moves to a new location of coordinate x. The field of deformation, , and the field of concentration of the solvent, , together describe the state of the gel.
A gel is attached to a rigid substrate. The thickness of the gel is much smaller than the in-plane dimensions. In a homogeneous state, the gel is constrained by the substrate in the in-plane dimensions, and swells in the thickness direction. The amount of swelling depends on the crosslink density , the Flory-Huggins parameter , and the prestretch .
Critical prestretch for the onset of wrinkles. The gel is stable against wrinkling, when the prestretch is greater than the critical value. For large , the critical prestretch approaches 0.666 (the dashed line) as predicted by Biot (1963) for rubber under equal-biaxial compression.
Finite-element calculation of creasing of a gel attached to a rigid substrate. (a) Schematics of a homogeneous state of the swollen gel and a creased state. (b) The deference between the energy of the creased state and that of the homogeneous state is plotted as a function of . ( = 0.1 and = 1.55).
Finite-element simulation of the formation of a crease from an initial defect. (a) The equilibrium contact length at the creased region is plotted as a function of . ( = 0.1 and = 1.55) The red dashed line denotes the critical value of obtained from the energy method in Fig. 6 . (b) Contour plot of the solvent concentration around the crease.
Comparison of the critical conditions for the onset of wrinkles and creases. (a) A gel is attached to a rigid substrate in a state of isotropic prestretch , and swells in the thickness direction to a stretch of . (b) The critical prestretch varies with and . (c) The critical swelling ratio, , varies with and . The red solid lines are the critical conditions for the onset of creases, and the blue dashed lines are the critical conditions for the onset of wrinkles.
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