Basu Soumendra K, McCormick Alon V, Scriven L E
Coating Process Fundamentals Program, Department of Chemical Engineering & Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA.
Langmuir. 2006 Jun 20;22(13):5916-24. doi: 10.1021/la060551o.
An in-plane constrained cross-linked gel layer absorbs an equilibrium amount of solvent and experiences in-plane compressive stress. A stability analysis of such an elastic gel layer that is attached to either a viscous or an elastic bottom layer atop a rigid substrate is considered. The effects of the top and bottom layer moduli (E(t) and E(b)), the bottom-to-top layer thickness ratio (H/h), and the polymer solvent interaction parameter (chi) on the critical condition of wrinkling, wrinkle wavelength, and amplitude are examined. When the bottom layer is viscous, the compressed top layer is always unstable, and wrinkling is rate-controlled. The viscous flow of the bottom layer governs the rate and determines the fastest growing wavelength. As E(t) rises, the bending stiffness of the elastic layer does as well, and so the fastest growing wavelength (lambda(m)) rises and the equilibrium amplitude (A(e)) falls. As H/h rises, the constraint of the rigid substrate diminishes, and so lambda(m) and A(e) rise. As chi falls or as the solvent has higher affinity for the polymeric gel, lambda(m) falls and A(e) rises because better solvents create higher compressive strain that promote low-wavelength, high-amplitude wrinkles. When the bottom layer is elastic, a critical compressive stress exists. If the generated compressive stress by solvent absorption is greater than the critical stress, the top layer wrinkles. It was found that wrinkling is most likely at intermediate E(t), low E(b), high H/h, and low chi. Further, lower chi, higher H/h, and lower E(b) were found to promote higher equilibrium amplitude and higher wavelength wrinkles.
面内约束交联凝胶层吸收平衡量的溶剂并承受面内压缩应力。考虑对附着在刚性基底上的粘性或弹性底层之上的这种弹性凝胶层进行稳定性分析。研究了顶层和底层模量（E(t) 和 E(b)）、底层与顶层厚度比（H/h）以及聚合物 - 溶剂相互作用参数（χ）对起皱临界条件、皱纹波长和幅度的影响。当底层是粘性时，压缩的顶层总是不稳定的，起皱受速率控制。底层的粘性流动控制速率并确定最快增长波长。随着 E(t) 升高，弹性层的弯曲刚度也升高，因此最快增长波长（λ(m)）升高而平衡幅度（A(e)）降低。随着 H/h 升高，刚性基底的约束减小，因此 λ(m) 和 A(e) 升高。随着 χ 降低或溶剂对聚合物凝胶具有更高亲和力，λ(m) 降低而 A(e) 升高，因为更好的溶剂产生更高的压缩应变，促进低波长、高幅度的皱纹。当底层是弹性时，存在临界压缩应力。如果溶剂吸收产生的压缩应力大于临界应力，顶层就会起皱。研究发现，在中等 E(t)、低 E(b)、高 H/h 和低 χ 时最容易起皱。此外，发现较低的 χ、较高的 H/h 和较低的 E(b) 会促进更高的平衡幅度和更长波长的皱纹。
