Principes en rhéologie des polymères fondus

URL: http://www-spht.cea.fr/articles/T93/082En théorie des polymères, pour des temps suffisamment longs, on peut s'attendre à observer un comportement universel qui intègre le concept de reptation valide pour des temps très longs et la relaxation de Rouse qui s'applique aux temps moins longs. Nous discutons ici l'agencement de ces principes

Self-Organization of Vortex Length Distribution in Quantum Turbulence: An Approach from the Barabasi-Albert Model

The energy spectrum of quantum turbulence obeys Kolmogorov's law. The vortex length distribution (VLD), meaning the size distribution of the vortices, in Kolmogorov quantum turbulence also obeys a power law. We propose here an innovative idea to study the origin of the power law of the VLD. The nature of quantized vortices allows one to describe the decay of quantum turbulence with a simple model that is similar to the Barabasi-Albert model of large networks. We show here that such a model can reproduce the power law of the VLD well.Comment: 4 pages including 5 figure

Scattering functions of knotted ring polymers

We discuss the scattering function of a Gaussian random polygon with N nodes under a given topological constraint through simulation. We obtain the Kratky plot of a Gaussian polygon of N=200 having a fixed knot for some different knots such as the trivial, trefoil and figure-eight knots. We find that some characteristic properties of the different Kratky plots are consistent with the distinct values of the mean square radius of gyration for Gaussian polygons with the different knots.Comment: 4pages, 3figures, 3table

Individual Entanglements in a Simulated Polymer Melt

We examine entanglements using monomer contacts between pairs of chains in a Brownian-dynamics simulation of a polymer melt. A map of contact positions with respect to the contacting monomer numbers (i,j) shows clustering in small regions of (i,j) which persists in time, as expected for entanglements. Using the ``space''-time correlation function of the aforementioned contacts, we show that a pair of entangled chains exhibits a qualitatively different behavior than a pair of distant chains when brought together. Quantitatively, about 50% of the contacts between entangled chains are persistent contacts not present in independently moving chains. In addition, we account for several observed scaling properties of the contact correlation function.Comment: latex, 12 pages, 7 figures, postscript file available at http://arnold.uchicago.edu/~ebn

Polymers as compressible soft spheres

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al., Soft Matter 6, 2282 (2010), and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radiiindependent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.Comment: 21 pages, 7 figure

Elastic Lattice Polymers

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $\rho_m = 1 - /m$ scales asymptotically for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of $\rho_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $\rho_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.Comment: 10 page

Polymer desorption under pulling: a novel dichotomic phase transition

We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $\phi$ is found to depend essentially on the interaction between different loops. The chain detachment transition turns out to be of the first order, albeit dichotomic, i.e., no coexistence of different phase states exists. These novel theoretical predictions and the suggested phase diagram of the adsorption-desorption transformation under external pulling force are verified by means of extensive Monte Carlo simulations.Comment: 10 pages, 4 figure

A multi-blob representation of semi-dilute polymer solutions

A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed their overlap threshold, allowing polymer concentrations to be explored deep into the semi-dilute regime. This quantitative multi-blob description is shown to preserve known scaling laws of polymer solutions and provides accurate estimates of amplitudes, while leading to orders of magnitude increase of simulation efficiency and allowing analytic calculations of structural and thermodynamic properties.Comment: 4 pages, 4 figure

Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to θ\theta solvent

We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the $\theta$ point and the good-solvent regime. We use the generalized free-volume theory (GFVT), which turns out to be quite accurate as long as $q = R_g/R_c\lesssim 1$ ($R_g$ is the radius of gyration of the polymer and $R_c$ is the colloid radius). Close to the $\theta$ point the phase diagram is not very sensitive to solvent quality, while, close to the good-solvent region, changes of the solvent quality modify significantly the position of the critical point and of the binodals. We also analyze the phase behavior of aqueous solutions of charged colloids and polymers, using the extension of GFVT proposed by Fortini et al., J. Chem. Phys. 128, 024904 (2008)

Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts

Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, {\it i.e.}, by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor $S^{-1}(k)$ predicted by a `one-loop' approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of a UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to $S^{-1}(k)$ are shown to be the sum of: (i) a $k$-independent contribution that arises from a renormalization of the effective $\chi$ parameter, (ii) a $k$-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to $k^{2}$ that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a $k$-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.Comment: 35 pages, 2 figure