Consisting of alternating swelling and nonswelling polymeric layers (SLs and NLs), lamellar gels are 1D photonic crystals with tunable optical properties.  The lamellar structure induces a constraint between the SLs and the NLs, resulting in an anisotropic swelling behavior coupled with deformation.  The coupling gives rise to the mechano-chromatic effect, and quantitative understanding of it is the key to many applications.  This letter formulates a nonlinear continuum model for lamellar gels by considering the constrained swelling of SLs and the anisotropic deformation in both types of layers.  A finite-element method is further developed to simulate the response to non-uniform deformation.

Dear Colleagues,
I wish to bring to you my recent work with my supervisor Hui-Hui Dai on "Some  Analytical Formulas for the Equilibrium States of a Swollen Hydrogel Shell". Below is the abstract and attached is the preprint of the article. I will very much appreciate your comments and suggestions.

The Duke Soft Active Materials Laboratory directed by Prof Xuanhe Zhao is seeking a highly motivated postdoctoral fellow to study mechanics of polymers and hydrogels with applications in tissue regenerations. The work will be carried out in close collaboration with the Duke Orthopaedic Bioengineering Laboratory directed by Prof Farshid Guilak.

This paper has been accepted for publication in Soft Matter. DOI: 10.1039/c0sm00335b.

Ionic polymer-metal composite (IPMC) is a polyelectrolyte (usually Nafion or Femion swollen by simple salt solution) strip or membrane with both sides plated with metal electrodes. It is a particular design of electroactive-polymer device rather than a new class of material. When a voltage is applied between its electrodes, it will bend toward either electrode depending on the polarity (anode for a negatively charged gel), and the magnitude of deformation could be controlled by the electric signal.  Reversely, the deformation of an IPMC can generate electric signal or even energy output [1-4].  Therefore IPMC has recently becomes a hot topic in actuation, sensor and energy harvesting applications, especially when integrated with the characteristics of certain gels that are responsive to other environmental stimuli such as pH value or temperature.

A previous work suggested a critical condition to form surface creases in elastomers and gels. For elastomers, the critical condition seems to have closed a gap between experimental observations (e.g., by bending a rubber block) and the classical instability analysis by Biot. For gels, however, experiments have observed a wide range of critical swelling ratios, from around 2 to 3.7. Here we present a linear perturbation analysis for swollen hydrogels confined on a rigid substrate, which predicts critical swelling ratios in a similar range.

Many engineering devices and natural phenomena involve gels that swell under the constraint of hard materials. The constraint causes a field of stress in a gel, and often makes the swelling inhomogeneous even when the gel reaches a state of equilibrium. To analyze inhomogeneous swelling of a pH-sensitive gel, we implement a finite element method in the commercial software ABAQUS.  The program is attached here.  Contact Shenqiang Cai (shqcai@gmail.com) for a description of the program.

Inspired by recent works by Wei Hong , Xuanhe Zhao, Zhigang Suo, and their coworkers, we started a project on hydrogels, with particular interest in various instability patterns observed in experiments. The attachment is our first manuscript on this subject. Through this work we hope to achieve the following:

At the invitation of David Clarke on behalf of the UCSB/Los Alamos Institute of Multiscale Materials and Structures, I gave the following three lectures:

1. Large deformation and instability in dielectric elastomers
2. Large deformation and instability in swelling polymeric gels
3. Mechanics and electrochemistry of polyelectrolyte gels

The abstracts follow, and the slides are attached at the end of this post.

I'm attaching slides of a talk that I gave yesterday at the Schlumberger-Doll Research Center.  In preparing the talk, I made liberal use of slides prepared by Wei Hong for his own presentations.  The talk is mainly based on the following papers:

A polymer network can imbibe water from environment and swell to an equilibrium state. If the equilibrium is reached when the network is subject to external mechanical constraint, the deformation of the network is typically anisotropic, and the concentration of water inhomogeneous.  Such an equilibrium state in a network constrained by a hard core is modeled here with a nonlinear differential equation.  The presence of the hard core markedly reduces the concentration of water near the interface and causes high stresses.

Hydrogels have enormous potential for making adaptive structures in response to diverse stimuli.  In a structure demonstrated recently, for example, nanoscale rods of silicon were embedded vertically in a swollen hydrogel, and the rods tilted by a large angle in response to a drying environment (Sidorenko, et al., Science 315, 487, 2007).  Here we describe a model to show that this behavior corresponds to a bifurcation at a critical humidity, analogous to a phase transition of the second kind.

I have recently given seminars on Mechanics of Soft Active Materials (SAMs) at several universities, using this set of slides (pdf, 1.4 MB).  I also attach the slides as ppt; please feel free to use anyway you want.  Here is an abstract of the seminars, followed by a list of papers published by my group on the topic.  Each paper has initiated on iMechanica a thread of discussion, to which I'll link.  I'll give a talk at the ASME Congress in Seattle, in Session 10-12-4 Instability in Solids, 9:45 am - 11:15 am, Thursday, 15 November 2007.  

   A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel.  This paper formulates a theory of the coupled mass transport and large deformation.

These notes attempt to address the concerns raised by Weil Hong, and supplement the notes on Poroelasticity, diffusion in an elastic solid. The main purpose is to add electrical effects, so that the theory will apply to polyelectrolyte gels. I’ll adopt an approach developed by Suo, Zhao and Greene for elastic dielectric (JMPS 2007 or preprint). The theory, however, has been developed by many people in many ways. See references at the end of the notes.

Before we start this issue of J-club, I would like to recommend Prof. Langer's lecture for his MRS Von Hippel Award in the 2005 MRS Fall Meeting (Langer, 2006). His lecture not only delineated the history of the new exciting field of drug delivery and controlled release, but also told us many interesting stories happened in his career development. With Prof. Langer's pioneer work, many new materials are developed for designing new drug delivery and controlled drug release systems.