We develop a method of poroelastic relaxation indentation (PRI) to characterize thin layers of gels.  The solution to the time-dependent boundary-value problem is obtained in a remarkably simple form, so that the force-relaxation curve obtained by indenting a gel readily determines all the poroelastic constants of the gel—the shear modulus, Poisson’s ratio, and the effective diffusivity.  The method is demonstrated with a layer of polydimethylsiloxane immersed in heptane.

The paper is accepted for publication by J. Appl. Phys, and can be downloaded from: http://www.seas.harvard.edu/suo/papers/254.pdf

We use instrumented indentation to characterize the mechanical and transport behavior of a pH-sensitive hydrogel in various aqueous buffer solutions. In the measurement an indenter is pressed to a fixed depth into a hydrogel disk and the load on the indenter is recorded as a function of time. By analyzing the load-relaxation curve using the theory of poroelasticity, the elastic constants of the hydrogel and the diffusivity of water in the gel can be evaluated. We investigate how the pH and ionic strength of the buffer solution, the hydrogel cross-link density, and the density of functional groups on the polymer backbone affect the properties of the hydrogel. This work demonstrates the utility of indentation techniques in the characterization of pH-sensitive hydrogels.

Ionic polymer conductor network composite (IPCNC) is a mixed conductor consisting of a network of loaded ionomer and another network of metallic particles. It is known that the microstructure of the composite, especially that of the electrodes, plays a dominating role in the performance of an IPCNC. However the microstructures of IPCNC have seldom been addressed in theoretical models. This letter formulates a continuum field theory for IPCNC by considering a supercapacitor-like microstructure with a large distributed interface area. The theory is then applied to the study of the equilibrium deformation and electrochemistry in a thin-sheet IPCNC actuator.

This paper studies the poroelastic behavior of an alginate hydrogel by a combination of theory and experiment. The gel—covalently crosslinked, submerged in water and fully swollen—is suddenly compressed between two parallel plates. The gap between the plates is held constant subsequently, and the force on the plate relaxes while water in the gel migrates. This experiment is analyzed by using the theory of linear poroelasticity. A comparison of the relaxation curve recorded in the experiment and that derived from the theory determines the elastic constants and the permeability of the gel. The material constants so determined agree well with those determined by using a recently developed indentation method.

This paper uses a method based on indentation to characterize a polydimethylsiloxane (PDMS) elastomer submerged in an organic solvent (decane, heptane, pentane, or cyclohexane).  An indenter is pressed into a disk of a swollen elastomer to a fixed depth, and the force on the indenter is recorded as a function of time.  By examining how the relaxation time scales with the radius of contact, one can differentiate the poroelastic behavior from the viscoelastic behavior.  By matching the relaxation curve measured experimentally to that derived from the theory of poroelasticity, one can identify elastic constants and permeability.  The measured elastic constants are interpreted within the Flory-Huggins theory.  The measured permeability indicate that the solvent migrate

When an indenter is pressed into a gel to a fixed depth, the solvent in the gel migrates, and the force on the indenter relaxes. Within the theory of poroelasticity, the force relaxation curves for indenters of several types are obtained in a simple form, enabling indentation to be used with ease as a method for determining the elastic constants and permeability of the gel. The method is demonstrated with a conical indenter on an alginate hydrogel.

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.

When a block of an elastomer is bent, the compressed surface may form a crease. This paper analyzes the critical condition for creasing by comparing the elastic energy in a creased body and that in a smooth body. This difference in energy is expressed by a scaling relation. Critical conditions for creasing are determined for elastomers subject to general loads and gels swelling under constraint. The theoretical results are compared with existing experimental observations.

Immersed in an ionic solution, a network of polyelectrolyte polymers imbibes the solution and swells, resulting in a polyelectrolyte gel. The swelling is reversible, and is regulated by ionic concentrations, mechanical forces, and electric potentials. This paper develops a field theory to couple large deformation and electrochemistry. A specific material model is described, including the effects of stretching the network, mixing the polymers with the solvent and ions, and polarizing the gel. We show that the notion of osmotic pressure in a gel has no experimental significance in general, but acquires a physical interpretation within the specific material model.

A network of polymers can imbibe a large quantity of a solvent and swell, resulting in a gel.  The swelling process can be markedly influenced by a mechanical load and geometric constraint.  When the network, solvent, and mechanical load equilibrate, the gel usually swells by a field of inhomogeneous and anisotropic deformation.  We show that this field in the swollen gel is equivalent to that in a hyperelastic solid.  We implement this theory in the finite-element package, ABAQUS, and analyze examples of swelling-induced deformation, contact, and bifurcation.  Because commercial software like ABAQUS is widely available, this work may provide a powerful tool to study complex phenomena in gels.

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.

      This paper studies a gel formed by a network of cross-linked polymers and a species of mobile molecules. The gel is taken to be a dielectric, in which both the polymers and the mobile molecules are nonionic. We formulate a theory of the gel in contact with a solvent made of the mobile molecules, and subject to electromechanical loads. A free-energy function is constructed for an ideal dielectric gel, including contributions from stretching the network, mixing the polymers and the small molecules, and polarizing the gel. We show that the free-energy function is non-convex, leading to instabilities. We also show that mechanical constraint markedly affects the behavior of the gel.