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Register a new userDynamic scaling in entangled mean-field gelation polymers
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We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. (PRE, 60, 5657, 1999) to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed by Lusignan et al. are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the `rheologically relevant linear segment length is smaller than that estimated by them. We use a numerical method based on tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior - which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches Rouse-like value.
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Ditopic bis-(triazole-pyridine)viologens are bidentate ligands that self-assemble into coordination polymers. In such photo-responsive materials, light irradiation initiates photo-induced electron transfer to generate pi-radicals that can self-associate to form pi-dimers. This leads to a cascade of events: processes at the supramolecular scale associated with mechanical and structural transition at the macroscopic scale. By tuning the irradiation power and duration, we evidence the formation of aggregates and gels. Using microscopy, we show that the aggregates are dense polydisperse micron size spindle shaped particles which grow in time. Using microscopy and time resolved micro-rheology, we follow the gelation kinetics which leads to a gel characterized by a correlation length of a few microns and a weak elastic modulus. The analysis of the aggregates and the gel states vouch for an arrested phase separation process.
Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statistics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.
Surface segregation of the low-molecular weight component in a polymeric mixture leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer and oligomer-gel systems following a temperature quench. We compute equilibrium and time varying migrant density profiles and wetting layer thickness using coarse grained molecular dynamics and mesoscale hydrodynamics simulations to demonstrate that surface migration in oligomer-gel systems is significantly reduced due to network elasticity. Further, phase separation processes are significantly slowed in gels, modifying the Lifshitz-Slyozov-Wagner (LSW) law $ell(tau) sim tau^{1/3}$. Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics.
In addition to the terminal flow (the region I) and the shear thinning (the region II), we discover two new flow regions in capillary flow at the wall stress higher than the plateau modulus of the polymer. The region III violates the empirical Cox-Merz rule with a significantly weaker shear thinning than the region II, and the region IV exhibits unexpected shear thickening. Moreover, the crossover shear rates between the regions II and III and between the regions III and IV scale with the number of entanglement per chain, Z=M_w/M_e, as Z^(-2.0) and Z^(-1.2) respectively. We attribute the weakening in shear thinning and the emergence of shear thickening to the deformation-induced non-Gaussian stretching of polymers. These observations offer the first experimental quantification of the deformation behaviors of polymer melts at high-stress shear.
Aqueous colloidal Laponite clay suspensions transform spontaneously to a soft solid-like arrested state as its aging or waiting time increases. This article reports the rapid transformation of aqueous Laponite suspensions into soft solids due to the application of a DC electric field. A substantial increase in the speed of solidification at higher electric field strengths is also observed. The electric field is applied across two parallel brass plates immersed in the Laponite suspension. The subsequent solidification that takes place on the surface of the positive electrode is attributed to the dominant negative surface charges on the Laponite particles and the associated electrokinetic phenomena. With increasing electric field strength, a dramatic increase is recorded in the elastic moduli of the samples. These electric field induced Laponite soft solids demonstrate all the typical rheological characteristics of soft glassy materials. They also exhibit a two-step shear melting process similar to that observed in attractive soft glasses. The microstructures of the samples, studied using cryo-scanning electron microscopy (SEM), are seen to consist of percolated network gel-like structures, with the connectivity of the gel network increasing with increasing electric field strengths. In comparison with salt induced gels, the electric field induced gels studied here are mechanically stronger and more stable over longer periods of time
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