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

Mechanical Properties of End-crosslinked Entangled Polymer Networks using Sliplink Brownian Dynamics Simulations

The mechanical properties of a polymeric network containing both crosslinks and sliplinks (entanglements) are studied using a multi-chain Brownian dynamics simulation. We coarse-grain at the level of chain segments connecting consecutive nodes (cross- or sliplinks), with particular attention to the Gaussian statistics of the network. Affine displacement of nodes is not imposed: their displacement as well as sliding of monomers through sliplinks is governed by force balances. The simulation results of stress in uniaxial extension and the full stress tensor in simple shear including the (non-zero) second normal stress difference are presented for monodisperse chains with up to 18 entanglements between two crosslinks. The cases of two different force laws of the subchains (Gaussian chains and chains with finite extensibility) for two different numbers of monomers in a subchain (no = 50 and no = 100) are examined. It is shown that the additivity assumption of slip- and crosslink contribution holds for sufficiently long chains with two or more entanglements, and that it can be used to construct the strain response of a network of infinitely long chains. An important consequence is that the contribution of sliplinks to the small-strain shear modulus is about ⅔ of the contribution of a crosslink

Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intra-chain entanglement is modulated by varying both solution density (from infinite dilution up to \approx 40 % volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected by the degree of inter-chain entanglement: for both unknots and trefoils the characteristic times of ring size relaxation, reorientation and diffusion change by one order of magnitude across the considered range of concentrations. Yet, significant topology-dependent differences in kinetics are observed only for very dilute solutions (much below the ring overlap threshold). For knotted rings, the slowest kinetic process is found to correspond to the diffusion of the knotted region along the ring backbone.Comment: 17 pages, 11 figure

i-Rheo: Measuring the materials' linear viscoelastic properties “in a step”!

A new analytical technique for determining a materials' linear viscoelastic properties from a simple step-strain measurement is reported. The technique avoids the need for idealisation of real measurements. The technique involves evaluating the Fourier transforms of raw experimental data describing both the time-dependent stress and strain functions. A comparison with conventional linear oscillatory measurements for a diverse range of complex materials is made and the technique is shown to be superior to existing linear oscillatory measurements in all cases

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