J. M. Adams

Nonmonotonic models are not necessary to obtain shear banding phenomena in entangled polymer solutions

Recent experiments on entangled polymer solutions may indicate a constitutive instability, and have led some to question the validity of existing constitutive models. We use a modern constitutive model, the Rolie-Poly model plus a solvent viscosity, and show that (i) this simple class of models captures instability, (ii) shear banding phenomena is observable for weakly stable fluids in flow geometries with sufficiently inhomogeneous total stress, and (iii) transient phenomena exhibit inhomogeneities similar to shear banding, even for weakly stable fluids.

Transient shear banding in entangled polymers: A study using the Rolie-Poly model

Spatially inhomogeneous shear flow occurs in entangled polymer solutions, both as steady state shear banding and transiently after a large step strain or during startup to a steady uniform shear rate. Theoretically, steady state shear banding is a hallmark of models with a nonmonotonic constitutive relation between total shear stress and applied shear rate, but transient banding is sometimes seen in fluids that do not shear band at steady state. We model this behavior using the diffusive Rolie-Poly model in a Newtonian solvent, whose steady state constitutive behavior can be monotonic or nonmonotonic depending on the degree of convective constraint release. We study monotonic steady state constitutive behavior. Linear stability analysis of the startup to a sufficiently high shear rate shows that spatial fluctuations are unstable at early times. There is a strong correlation between this instability and the negative slope of the (time dependent) constitutive curve. If the time integral of the most unstable...

RELAXATION OF SOME TRANSVERSALLY ISOTROPIC ENERGIES AND APPLICATIONS TO SMECTIC A ELASTOMERS

We determine the relaxation of some transversally-isotropic energy densities, i.e. functions W : ℝ3×3 → [0,∞] with the property W(QFR) = W(F) for all Q ∈ SO(3) and all R ∈ SO(3) such that Rn0 = n0, where n0 is a fixed unit vector. One physically relevant example is a model for smectic A elastomers. We discuss the implications of our result for the computation of macroscopic stress–strain curves for this material and compare with experiment.

A quantitative parameter for predicting mixing behaviour in adsorbed layers: the 2D isomorphism coefficient

Abstract Mixing behaviour in adsorbed layers at the solid–liquid interface depends upon both the symmetry and the quantitative similarity of the unit cells of the two pure monolayers. Here we present data that demonstrates that this similarity can be conveniently expressed in terms of a 2D isomorphism coefficient and identify values of this coefficient that delineate regions of immiscibility, partial or complete miscibility. Here we have established the utility of this coefficient for mixtures of linear alcohols and mixtures of linear alkanes adsorbed on graphite but expect that these rules should be as general in their applicability to 2D layers as are similar rules for bulk phases.

Smectic-

Experimentally it is possible to manipulate the director in a (chiral) smectic- A elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of the layers, stretching in the plane of the layers, and compression and elongation parallel to the layer normal. We calculate, inter alia, the engineering stress and the tilt angle between director and layer normal as functions of the applied deformation. For the latter three deformations, our results predict the existence of an instability towards the development of shear accompanied by smectic- C-like order.

A

The mechanical properties of liquid crystal elastomers (LCEs) make them suitable candidates for pressure-sensitive adhesives (PSAs). Using the nematic dumbbell constitutive model, and the block model of PSAs, we study their tack energy and the debonding process as could be measured experimentally in the probe-tack test. To investigate their performance as switchable PSAs we compare the tack energy for the director aligned parallel, and perpendicular to the substrate normal, with that for the isotropic state. We find that the tack energy is larger in the parallel alignment than the isotropic case by over a factor of two. The tack energy for the perpendicular alignment can be 50% less than the isotropic case. We propose a mechanism for reversibly switchable adhesion based on the reversibility of the isotropic to nematic transition. Finally we consider the influence of several material parameters that could be used to tune the stress–strain response.

elastomers with weak director anchoring

Models of smectic-C liquid-crystal elastomers predict that they can display soft elasticity, in which the shape of the elastomer changes at no energy cost. The amplitude of the soft mode and the accompanying shears are dependent on the orientation of the layer normal and the director with respect to the stretch axis. We demonstrate that in some geometries the director is forced to rotate perpendicular to the stretch axis, causing lateral expansion of the sample-a negative Poissons ratio. Current models do not include the effect of imperfections that must be present in the physical sample. We investigate the effect of a simple model of these imperfections on the soft modes in monodomain smectic-C elastomers in a variety of geometries. When stretching parallel to the layer normal (with imposed strain) the elastomer has a negative stiffness once the director starts to rotate. We show that this is a result of the negative Poissons ratio in this geometry through a simple scalar model.

Tack energy and switchable adhesion of liquid crystal elastomers

We present a detailed analysis of the molecular packing of a strained liquid crystal elastomer composed of chiral mesogens in the smectic-A phase. X-ray diffraction patterns of the elastomer collected over a range of orientations with respect to the x-ray beam were used to reconstruct the three-dimensional scattering intensity as a function of tensile strain. We show that the smectic domain order is preserved in these strained elastomers. Changes in the intensity within a given scattering plane are due to reorientation, and not loss, of the molecular order in directions orthogonal to the applied strain. Incorporating the physical parameters of the elastomer, a nonlinear elastic model is presented to describe the rotation of the smectic-layered domains under strain, thus providing a fundamental analysis to the mechanical response of these unique materials.

Negative Poisson's ratio and semisoft elasticity of smectic-C liquid-crystal elastomers

Stenull and Lubensky [Phys. Rev. E 76, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a smectic-A elastomer subjected to a simple shear will develop smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [e-print arXiv:0708.2024; Phys. Rev. E 78, 021704 (2008)], performed shear experiments on smectic-A elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of smectic-C-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E 71, 021708 (2005)] and use it to study the magnitude of SmC-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheetlike sample, thus inducing instabilities that we discuss.

Strain analysis of a chiral smectic-A elastomer.

We present a numerical study of stretching monodomain smectic-A elastomer sheets, computed using the finite element method. When stretched parallel to their smectic layer normal the smectic layers are unstable to a transition to a buckled state. We model macroscopic deformations by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine-scale layer buckling. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson ratios postbuckling. We examine the spatial distribution of the microstructure phases for various stretching angles relative to the layer normal and for different length-to-width aspect ratios. When stretching parallel to the layer normal the majority of the sample forms a bidirectionally buckled microstructure, except at the clamps where a unidirectionally buckled microstructure is predicted. When stretching at small inclinations to the layer normal the phase of the sample is sensitive to the aspect ratio of the sample, with the bidirectionally buckled phase persistent to large angles only for small aspect ratios. We relate these theoretical results to experiments on smectic-A elastomers.