A Spatially Nonlocal Model for Polymer Desorption (original) (raw)
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Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results
SIAM Journal on Applied Mathematics, 2002
Many practically relevant polymers undergoing desorption change from the rubbery (saturated) to the glassy (nearly dry) state. The dynamics of such systems cannot be described by the simple Fickian diffusion equation due to viscoelastic effects. The mathematical model solved numerically is a set of two coupled PDEs for concentration and stress. Asymptotic solutions are presented for a moving boundary-value problem for the two states in the short-time limit. The solutions exhibit desorption overshoot, where the penetrant concentration in the interior is less than that on the surface. In addition, it is shown that if the underlying time scale of the equations is ignored when postulating boundary conditions, nonphysical solutions can result.
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In certain polymer-penetrant ,systems, nonlinear viscoelastic effects dominate those of Fickian diffusion. This behavior is often embodied in a memory integral incorporating nonlocal time effects into the dynamics; this integral can be derived from an augmented chemical potential. The mathematical framework presented is a moving boundary-value problem. The boundary separates the polymer into two distinct states: glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. Asymptotic solutions are obtained where sharp fronts move with constant speed. The resultant profiles are quite similar to experimental results in a dissolving polymer. It is then demonstrated that such a model has a limit on the allowable front speed and a self-regulating mass uptake.
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Dynamic light scattering has been used to follow the tracer diffusion of polystyrene spheres (R % 200 nm) in dilute, semidilute, and entangled solutions of poly(viny1 methyl ether) (M , = 1.3 x lo6). Over this range of matrix concentrations, 0 5 c[r]] 5 36, the diffusivity drops by almost 5 orders of magnitude. Near c* (=[r]]-') for the matrix, the diffusivity exceeds that estimated from the bulk solution viscosity via the Stokes-Einstein relation by a factor of about 3. Such "positive deviations" from Stokes-Einstein behavior have been reported previously in several systems. However, once the matrix concentration is sufficiently high for entanglements to be effective, Stokes-Einstein behavior is recovered. This new result was confirmed via forced Rayleigh scattering. In addition, these data can reconcile measurements of sphere diffusion with reptation-based models for chain mobility in well-entangled systems. The behavior near c* is discussed in terms of the matrix correlation length, E, which has a maximum at 6 = R, for c x c*. It is noted that the fluid layer within a distance 5 of the sphere surface will, in general, differ in composition from the bulk solution, and consequently the sphere mobility may well not sense the macroscopic solution viscosity, particularly near c*. As a corollary, for large matrix chains, dynamic light scattering may not monitor the long-time diffusion of the spheres near c*, because q t % qR, % 1, rather than q t << 1.
Topological influences on polymer adsorption and desorption dynamics
Physical Review Letters, 1993
The desorption of polymer chains through an overlayer of strongly adsorbed chains was studied to determine the influence of topological constraints on the polymer desorption process. The desorption time of linear chains fits a power law, M a , where M is molecular weight and a =2.3 ± 0.2. A comparison of linear and star-branched chains shows that desorption of star-branched chains was greatly suppressed. These findings are reminiscent of entanglement effects in bulk systems. They suggest a unifying perspective from which to analyze polymer mobility at surfaces.
Dynamics of Semiflexible Polymer Solutions in the Highly Entangled Regime
Physical Review Letters, 2008
We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E 63, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus G 0 ∝ ρ 4/3 L −1/3 p (where ρ is the contour length per unit volume and Lp is the persistence length) of semi-flexible polymer solutions, in the highly entangled concentration regime. Competing theories, including a self-consistent binary collision approximation (BCA), have instead predicted G 0 ∝ ρ 7/5 L −1/5 p
Journal of Chemical Physics, 2017
Coarse grained simulation approaches provide powerful tools for prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.