Direct conversion of rheological compliance measurements into storage and loss moduli

We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli ($G'(\omega)$ and $G"(\omega)$ respectively), from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.Comment: 4 page

Microphase separation in cross-linked polymer blends: Efficient replica RPA post-processing of simulation data for homopolymer networks

We investigate the behaviour of randomly cross-linked (co)polymer blends using a combination of replica theory and large-scale molecular dynamics simulations. In particular, we derive the analogue of the random phase approximation for systems with quenched disorder and show how the required correlation functions can be calculated efficiently. By post-processing simulation data for homopolymer networks we are able to describe neutron scattering measurements in heterogeneous systems without resorting to microscopic detail and otherwise unphysical assumptions. We obtain structure function data which illustrate the expected microphase separation and contain system-specific information relating to the intrinsic length scales of our networks.Comment: 8 pages, 5 figure

Arrested spinodal decomposition in polymer brush collapsing in poor solvent

We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state. The collapse process of such a polymer brush differs from individual chains, both in its kinetics and its structural morphology. We find that the resulting collapsed brush does not form a homogeneous dense layer, in spite of all chain monomers equally attracting each other via a model Lennard-Jones potential. Instead, a very distinct inhomogeneous density distribution in the plane forms, with a characteristic length scale dependent on the quenching depth (or equivalently, the strength of monomer attraction) and the geometric parameters of the brush. This structure is identical to the spinodal-decomposition structure, however, due to the grafting constraint we find no subsequent coarsening: the established random bundling with characteristic periodicity remains as the apparently equilibrium structure. We compare this finding with a recent field-theoretical model of bundling in a semiflexible polymer brush.This work was funded by the Osk. Huttunen Foundation (Finland) and the Cambridge Theory of Condensed Matter Grant from EPSRC. Simulations were performed using the Darwin supercomputer of the University of Cambridge High Performance Computing Service provided by Dell Inc. using Strategic Research Infrastructure funding from the Higher Education Funding Council for England.This is the accepted manuscript. The final version is available at http://pubs.acs.org/doi/abs/10.1021/ma501985r

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Effect of Shear Rate on the Orientation and Relaxation of a Vanillic Acid Based Liquid Crystalline Polymer

In this study, we report on the visco-elastic response during start-up and cessation of shear of a novel bio-based liquid crystal polymer. The ensuing morphological changes are analyzed at different length scales by in-situ polarized optical microscopy and wide-angle X-ray diffraction. Upon inception of shear, the polydomain texture is initially stretched, at larger strain break up processes become increasingly important, and eventually a steady state texture is obtained. The shear stress response showed good coherence between optical and rheo-X-ray data. The evolution of the orientation parameter coincides with the evolution of the texture: the order parameter increases as the texture stretches, drops slightly in the break up regime, and reaches a constant value in the plateau regime. The relaxation of the shear stress and the polydomain texture showed two distinct processes with different timescales: The first is fast contraction of the stretched domain texture; the second is the slow coalescence of the polydomain texture. The timescale of the orientation parameter’s relaxation matched with that of the slow coalescence process. All processes were found to scale with shear rate in the tested regime. These observations can have far reaching implications for the processing of liquid crystal polymers as they indicate that increased shear rates during processing can correspond to an increased relaxation rate of the orientation parameter and, therefore, a decrease in anisotropy and material properties after cooling