Shengqiang Cai

A theory of constrained swelling of a pH-sensitive 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. This paper develops a theory of constrained swelling of a pH-sensitive hydrogel, a network of polymers bearing acidic groups, in equilibrium with an aqueous solution and mechanical forces. The condition of equilibrium is expressed as a variational statement of the inhomogeneous field. A free-energy function accounts for the stretching of the network, mixing of the network with the solution, and dissociation of the acidic groups. Within a Legendre transformation, the condition of equilibrium for the pH-sensitive hydrogel is equivalent to that for a hyperelastic solid. The theory is first used to compare several cases of homogenous swelling: a free gel, a gel attached to a rigid substrate, and a gel confined in three directions. To analyze inhomogeneous swelling, we implement a finite element method in the commercial software ABAQUS, and illustrate the method with a layer of the gel coated on a spherical rigid particle, and a pH-sensitive valve in microfluidics.

Model of dissipative dielectric elastomers

The dynamic performance of dielectric elastomer transducers and their capability of electromechanical energy conversion are affected by dissipative processes, such as viscoelasticity, dielectric relaxation, and current leakage. This paper describes a method to construct a model of dissipative dielectric elastomers on the basis of nonequilibrium thermodynamics. We characterize the state of the dielectric elastomer with kinematic variables through which external loads do work, and internal variables that measure the progress of the dissipative processes. The method is illustrated with examples motivated by existing experiments of polyacrylate very-high-bond dielectric elastomers. This model predicts the dynamic response of the dielectric elastomer and the leakage current behavior. We show that current leakage can be significant under large deformation and for long durations. Furthermore, current leakage can result in significant hysteresis for dielectric elastomers under cyclic voltage.

Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment

Thin poly(N-isopropylacrylamide) (PNIPAM) hydrogels were allowed to swell under two conditions: as freestanding layers and as substrate-attached layers. Through a combination of particle tracking and defocusing methods, the positions of beads embedded within the gels were monitored over time via fluorescence microscopy, providing a convenient method to track the kinetics of swelling for layers with thicknesses of the order 100 µm. These data are compared with the predictions of linear poroelastic theory, as specialized for polymer gels. This theory, along with a single set of material properties, accurately describes the observed swelling kinetics for both the freestanding and substrate-attached hydrogels. With the additional measurement of the substrate curvature induced by the swelling of the substrate-attached hydrogels, these experiments provide a simple route to completely characterize the material properties of the gel within the framework of linear poroelasticity, using only an optical microscope.

Low flicker-noise GaN/AlGaN heterostructure field-effect transistors for microwave communications

We report a detailed investigation of flicker noise in novel GaN/AlGaN heterostructure field-effect transistors (GaN HFET). Low values of 1/f noise found in these devices (i.e., the Hooge parameter is on the order of 10/sup -1/) open up the possibility for applications in communication systems. We have examined the scaling of the noise spectral density with the device dimensions in order to optimize their performance. It was also found that the slope /spl gamma/ of the 1/f/sup /spl gamma// noise density spectrum is in the 1.0-1.3 range for all devices and decreases with the decreasing (i.e., more negative) gate bias. The results are important for low-noise electronic technologies requiring a low phase-noise level.

Creasing instability of elastomer films

The creasing instability of elastomer films under compression is studied by a combination of experiment and numerical simulation. Experimentally, we attach a stress-free film on a much thicker and stiffer pre-stretched substrate. When the substrate is partially released, the film is uniaxially compressed, leading to formation of an array of creases beyond a critical strain. The profile of the folded surface is extracted using confocal fluorescence microscopy, yielding the depths, spacings, and shapes of creases. Numerically, the onset and development of creases are simulated by introducing appropriately sized defects into a finite-element mesh and allowing the surface of the film to self-contact. The measurements and simulations are found to be in excellent agreement.

An Al/sub 0.3/Ga/sub 0.7/N/GaN undoped channel heterostructure field effect transistor with F/sub max/ of 107 GHz

An Al/sub 0.3/Ga/sub 0.7/N/GaN heterostructure field effect transistor (HFET) grown on semi-insulating SiC with an 0.2-/spl mu/m gate length is reported. A source-drain ohmic contact resistance of 0.15-/spl Omega/-mm was achieved through the use of high Al content and high n-type doping (1E19 cm/sup -3/) in the AlGaN donor layer and optimized metallization procedures. We obtained a maximum transconductance of 260 mS/mm, a saturated current density of 1.2 A/mm, and a maximum oscillation frequency in excess of 107 GHz in the devices. The results are one of the best achieved up to now, and they will open up the potential for the applications of AlGaN/GaN HFETs in high-power microwave radar, remote sensing, and communications.

Creases in soft tissues generated by growth

Soft tissues growing under constraint often form creases. We adopt the model of growth that factors the deformation gradient into a growth tensor and an elastic deformation tensor, and show that the critical conditions for the onset of creases take a remarkably simple form. The critical conditions are illustrated with tubes of tissues growing either inside a rigid shell or outside a rigid core. By comparing the critical conditions for the onset of wrinkles, we show that the creases are the preferred type of instability. Furthermore, deep creases in a tube are simulated by using the finite-element method, and the number of creases in the tube is estimated by minimizing the free energy.

Force generated by a swelling elastomer subject to constraint

When an elastomer imbibes a solvent and swells, a force is generated if the elastomer is constrained by a hard material. The magnitude of the force depends on the geometry of the constraint, as well as on the chemistry of the elastomer and solvent. This paper models an elastomer crosslinked on the exterior surface of a metallic tubing. The elastomer then imbibes a solvent and swells. After the swollen elastomer touches the wall of the borehole, a significant amount of time is needed for the solvent in the elastomer to redistribute, building up the sealing pressure to the state of equilibrium. The sealing pressure and the sealing time are calculated in terms of the geometric parameters (i.e., the thickness of the elastomer and the radii of the tubing and borehole), the number of monomers along each polymer chain of the elastomer, and the affinity between the elastomer and the solvent.

Osmotic collapse of a void in an elastomer: breathing, buckling and creasing†‡

This paper studies the collapse of a void in an elastomer caused by osmosis. The void is filled with liquid water, while the elastomer is surrounded by unsaturated air. The difference in humidity motivates water molecules to permeate through the elastomer, from inside the void to outside the elastomer, leaving the liquid water inside the void in tension. When the tension is low, the void reduces size but retains the shape, a mode of deformation which we call breathing. When the tension is high, the void changes shape, possibly by two types of instability: buckling and creasing. The critical conditions for both types of instability are calculated. A tubular elastomer collapses by buckling if the wall is thin, but by creasing if the wall is thick. As the tension increases, a thin-walled tube undergoes a buckle-to-crease transition.

Equations of state for ideal elastomeric gels

Submerged in a solvent-containing environment and subject to applied forces, a covalent polymer network absorbs the solvent and deforms, forming an elastomeric gel. The equations of state are derived under two assumptions. First, the amount of the solvent in the gel varies when the gel changes volume, but remains constant when the gel changes shape. Second, the Helmholtz free energy of the gel is separable into the contribution due to stretching the network and that due to mixing the polymer and the solvent. We demonstrate that these equations of state fit several sets of experimental data in the literature remarkably well.