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

Maximally Stiffening Composites Require Maximally Coupled Rather Than Maximally Entangled Polymer Species

Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive characterisation of material properties over a highly-dimensional parameter space, as well as a quantitative understanding of the physical principles underlying desirable features. Here we couple large-scale Molecular Dynamics simulations with optical tweezers microrheology to characterise the viscoelastic response of DNA-actin composites. We discover that the previously observed non-monotonic stress-stiffening of these composites is robust, yet tunable, in a broad range of the parameter space that spans two orders of magnitude in DNA length. Importantly, we discover that the most pronounced stiffening is achieved when the species are maximally coupled, i.e. have similar number of entanglements, and not when the number of entanglements per DNA chain is largest. We further report novel dynamical oscillations of the microstructure of the composites, alternating between mixed and bundled phases, opening the door to future investigations. The generic nature of our system renders our results applicable to the behaviour of a broad class of polymer composites.Comment: Accepted in Soft Matte

From reactor to rheology in industrial polymers

This article reviews current efforts towards quantitative prediction of rheological properties of industrial polymer resins, based upon their polydisperse branched molecular structure. This involves both an understanding of how reactor and reaction conditions influence the distribution of chain lengths and branch placement (which is the province of reactor engineering) and an understanding of how the molecular structures in turn give rise to the rheology (the province of polymer physics). Both fields are reviewed at an introductory level, focussing in particular on developments in theoretical prediction of rheology for both entangled model polymers and industrial polymers. Finally, we discuss three classes of reaction for which the fields of reactor engineering and polymer physics have been truly combined to produce predictions from reactor to rheology

Determination of both the binodal and the spinodal curves in polymer blends by shear rheology

The thermorheological complexity at low frequencies in polymer blends near macrophase separation is quantitatively accounted for. The behaviour of both storage, G', and loss, G'', moduli at low frequencies as the temperature, T, approaches phase separation is due to the critical concentration fluctuations in the one-phase region. The temperature at maximum slope of the G' vs. T dependence at low frequencies is identified with the cloud point curve, whereas a plot of $[(G'')^2/(G'T)]^{2/3}$ vs. 1/T leads to the identification of the spinodal temperature

Structure and rheology of branched polyamide 6 polymers from their reaction recipe

The structure and rheology of randomly branched polyamide melts, in particular that of branched polyamide 6, are predicted on the basis of their initial reaction recipe. To this end, a Monte Carlo approach has been developed in order to build different molecular architectures from the initial reactant monomers at the appropriate conversion level. This approach allows us to analyze the composition of these melts in terms of topological architecture and molecular weight of the various polymer species present. Subsequently, the linear rheology of each sample is predicted within the tube model framework [van Ruymbeke et al., Macromol. 2006], based on the position/seniority of the different branches in these polymer species, by averaging over a limited number of representative segments. This approach allows us to discuss the role the different polymer architectures play in the overall viscoelastic response, the importance of the different initial monomers to adequately tune the composition (and thus the rheology) of these branched systems and the necessity of reaching a high conversion level in order to obtain a large zero-shear viscosity. We also extend this approach by applying a bimodal distribution to describe the solid state polycondensation of these products. The predictions are in good agreement with experiments. This method may be applied to any branched polymer product that is synthesized via a melt condensation type reaction and can be used as a tool to test and screen in detail the flow properties of materials without prior synthesis

Monte Carlo simulation of randomly branched step-growth polymers: Generation and analysis of representative molecular ensembles

A Monte Carlo simulation procedure has been set up and applied to generate representative ensembles of randomly branched step-growth polymers based on their reaction recipe. The molecular distributions thus obtained are consistent with those from statistical/analytical approaches. However, because the current method gives access to the complete ensemble of simulated molecules, a very detailed structural analysis is possible. Our procedures are applicable to any ‘AfBg’ system with f¿+¿g = 1. We apply this approach to randomly branched polyamides in order to gain insight into their molecular structure and understand the effect of the reaction recipe on the final product

Proposal to Solve the Time-Stress Discrepancy of Tube Models

Recently, Liu et al. (Macromolecules 2006, 39, 3093) showed a systematic discrepancy of tube model predictions for describing the apparent plateau modulus of short (weakly entangled) linear chains while predicting very accurately their terminal relaxation times. In the present article, we investigate the origin of this problem, which We call "time-stress discrepancy", by confronting our time-marching algorithm (TMA) with experimental viscoelastic data of nearly monodisperse linear polymers. We show that the contour length fluctuations of the outer molecular segments are overestimated, not taking into account the fact, that I chain needs a short but essential time to be considered in equilibrium ill its tube, Indeed, tube models consider that stress relaxation by reptation or contour length fluctuations starts at time t = 0 after an imposed small deformation, whereas in reality. there is a proceeding fast Rouse relaxation, which is especially important for shorter chains. Therefore, We propose to use a new segment coordinate system for describing the contour length fluctuations process, which restores the consistency with the tube definition and ensures that the necessary time for reaching an equilibrated system is equal to the relaxation time of an entanglement segment, tau(e). Results obtained with the so-corrected TMA model show I very good agreement with experimental data. In particular, the molecular-weight dependence of the apparent plateau modulus, the zero-shear viscosity, and the terminal relaxation time are now correctly predicted