Excluded volume effects on the structure of a linear polymer under shear flow

Determining Gyration Tensor of Orienting Macromolecules through Their Scattering Signature

A method is presented for quantitatively evaluating the shape and size of deformed particles in dispersion from their two-dimensional anisotropic spectra by small-angle scattering. By means of real spherical harmonic expansion, we derive analytical expressions of the gyration tensor R in terms of experimentally measured anisotropic scattering functions, yielding a tensorial extension of the Guinier law. We demonstrate the usefulness of this approach by a model study of an affinely deformed Gaussian chain. We further show that radius of gyration R_g is the source term of intraparticle structure factor at the mean-field limit, and from this perspective, we address the connection between R and conformation asphericity. The developed method not only facilitates quantitative scattering studies of deforming materials, but also provides insightful information regarding their deformation behavior at the molecular level based on the symmetric properties of real spherical harmonics.

Structure and dynamics of cylindrical micelles at equilibrium and under shear flow

The dynamics and rheology of semidilute unentangled micellar solutions are investigated by Langevin dynamics mesoscopic simulations coupled to a microreversible kinetic model for scissions and recombinations. Two equilibrium state points, differing by the scission energy and therefore by the corresponding average micelle length, have been examined. The kinetic rates are tuned by an independent parameter of the model, whose range is chosen in such a way that the kinetics always strongly couple to the chain dynamics. Our results confirm, as predicted by Faivre and Gardissat, that the stress relaxation, as well as the monomer diffusion, is characterized by a time tauLambda, defined by the lifetime of a segment Lambda, whose Rouse relaxation time is equal to its lifetime. Moreover, the power-law dependence of the zero-shear viscosity versus tauLambda was evidenced. Under stationary shear, the chains are deformed and their average bond length is increased, which enhances the overall scission frequency. In turn, this induces an overall shortening of the chains in order to increase the overall corresponding chain-end recombination frequency, as required by the stationary conditions. Nonequilibrium simulations show that the chain deformation and orientation, as well as the rheology of the system, can be expressed as universal functions of a single reduced shear rate betaLambda=gammatauLambda (with gamma the bare shear rate). Furthermore, local analysis of the kinetics under stationary shear gives insights on the variation of the average length with shear rate.

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pairwise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a delta-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate beta, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.

Dynamics and configurational fluctuations of single DNA molecules in linear mixed flows

We examine the dynamics of DNA molecules in mixed flows where the ratio of vorticity to strain rate may be slightly above or below unity via Brownian dynamics simulation. We find that the chain dynamics in these flows are dramatically different than those found for simple shear flow. When the strain rate exceeds vorticity, the dynamics are found to be driven by the extra amount of straining. For vorticity-dominated flows, a periodicity in chain extension is observed with considerable chain deformation.