Diffusion of a polymer chain in random media (original) (raw)
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Monte Carlo Studies of the Brownian Motion of a Polymer Chain under Topological Constraints
Polymer Journal, 1974
Studies are made to examine the validity of the de-Gennes' theory of the stochastic motion of a polymer chain in the presence of fixed obstacles. The two-dimensional cases are treated. The topological requirement that the chain cannot intersect any of the obstacles is imposed on the stochastic motion. Observations are made on the diffusion coefficient of the center of mass, the relaxation time of the end-to-end vector and the mean-square displacement of a monomer, by varying the chain length and the concentration of the obstacles. The results are compared with those of de-Gennes' theory and Rouse's. It is found that de-Gennes' theory provides a reasonable explanation for the slow relaxation phenomena• under topological restrictions. Some minor revisions are made to obtain better agreement. It is found that, for the fast relaxation phenomena, the agreement is not good even if the concentration of the obstacles is sufficiently large. The condition for the applicability of the de-Gennes' theory is also discussed. The transition from the Rouse-type motion to the de-Gennes-type motion is observed and found to be rather diffuse.
Diffusion of a polymer chain in porous media
Physical Review E, 1997
Using an off-lattice Monte Carlo bead-spring model of a chain in a random environment, we study chain conformations and dynamic scaling of diffusivity and relaxation times with chain length N and density of the host matrix C obs. Our simulational results show that with growing C obs the mean size ͑gyration radius͒ of the polymer, R g 2 , initially slightly decreases and then rapidly increases as the macromolecule exceeds the size of the average entropic wells and stretches through bottlenecks into neighboring wells. The chain dynamics changes from a Rouse-like one into a reptational one as the permeability of the matrix decreases. Although at variance with some previous treatments ͓M. Muthukumar, J. Chem. Phys. 90, 4594 ͑1989͔͒, these findings agree well with a recent analytic approach "S. V. Panyukov, Zh. É ksp. Teor. Fiz. 103, 1287 ͑1993͒ ͓Sov. Phys. JETP 76, 631 ͑1993͔͒… to chain conformations in random media. We also suggest a simple scaling analysis, based on a ''blob'' representation of the polymer chain, whereby the blob size is governed by the size of the cavities in the host matrix and yields a faithful description of our computer experiments.
Drift of a polymer chain in a porous medium --A Monte Carlo study
The European Physical Journal E, 2002
We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C ≈ 0.75. For field intensities below a C-dependent critical field strength Bc, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B c itself is found to decrease linearly with C.
Dynamics of a polymer in a quenched random medium: A Monte Carlo investigation
Europhysics Letters (EPL), 2004
We use an off-lattice bead-spring model of a self-avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte-Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length N and on the degree of Gaussian disorder ∆. The first one from normal to anomalous diffusion regime is found at short time τ1 and observed to vanish rapidly as τ1 ∝ ∆ −11 with growing disorder. The second crossover back to normal diffusion, τ2, scales as τ2 ∝ N 2ν+1 f (N 2−3ν ∆) with f being some scaling function. The diffusion coefficient DN depends strongly on disorder and drops dramatically at a critical dispersion ∆c ∝ N −2+3ν of the disorder potential so that for ∆ > ∆c the chain center of mass is practically frozen. The time-dependent Rouse modes correlation function Cp(t) reveals a characteristic plateau at ∆ > ∆c which is the hallmark of a non-ergodic regime. These findings agree well with our recent theoretical predictions.
Polymer chain in a flow through a porous medium: A Monte Carlo simulation
Physical Review E, 1997
We study conformational and dynamic properties of dilute polymer solutions drifting through a random environment of obstacles at varying intensity of the external field B and of the host matrix density C ob using dynamic Monte Carlo simulation of an off-lattice bead-spring model. The presence of obstacles is found to influence strongly the conformational properties of the drifting chains: with growing strength of the field B and C ob ϭ0 the chain mean size ͑gyration radius͒, R g 2 , rapidly increases while the ratio between the end-to-end distance, R ee 2 , and R g 2 drops essentially below the usual value of 6, typical in the absence of drift, suggesting a hooflike shape of the chain with both ends directed along the external field vector. We confirm the finding of G. M. Foo and R. B. Pandey ͓Phys. Rev. E 51, 5738 ͑1995͔͒ of a critical strength of the external field B c above which the permeability of the host matrix sharply drops. A detailed study of this phenomenon suggests that B c may be related to a dramatic growth of a specific ''capture'' time, characterizing the interaction of the chains with the obstacles, so that a simple model describing the drift of chains among obstacles may be shown to reproduce our findings. ͓S1063-651X͑97͒10912-6͔
Diffusion-limited growth of polymer chains
Physical review. A, 1986
A new self-avoiding walk (SAW) which grows without terminating is introduced as a model of the diffusion-limited growth of linear polymers. The model is in a different universality class than the equilibirum SA% and previously considered kinetic SA%'s, with v 0.774+0.006 in two dimensions and v 0.56+ 0.02 in three dimensions. The "indefinitely gro~ing SA%" is sho~n to emerge as a particular limit of our model.
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2002
Monomer density profile of polymer chains in the good solvent condition near an impenetrable wall was examined in lattice Monte Carlo simulation. It was found that a positive penetration depth k is necessary for the density profile to follow the prediction of the scaling theory. In dilute solutions, k was 0.13-0.22 of the lattice unit from a weak confinement to a strong confinement. With an increasing concentration, k increased gradually to a value close to 0.36. These findings corroborate our hypothesis that the need of the positive k and a greater k at higher concentrations result from non-even chain transport due to a large difference in site occupancy, especially at higher concentrations.
Anomalous diffusion of ideal polymer networks
Physical Review E, 1997
Internal dynamics of swollen polymer arrays were investigated with Brownian dynamic techniques applied to regular Rouse networks. In all cases local or self-diffusion decayed as a power law with a power proportional to the given topological dimension. This behavior allows for the classification of three dynamic regimes: subcritical topologies accommodate power law anomalous diffusion; logarithmic anomalous diffusion occurs within the critical topological dimension d t ϭ2; and upper-critical topologies siege bounded anomalous diffusion. ͓S1063-651X͑97͒13206-8͔
Monte Carlo study of the translocation of a polymer chain through a hole
European Polymer Journal, 2010
The translocation of a polymer chain through a narrow hole in a rigid obstacle has been studied by the static Monte Carlo simulations. A modified self-avoiding walk on a cubic lattice has been used to model the polymer in an athermal solution. The entropy of the chain before, in the course, and after the translocation process has been estimated by the statistical counting method. The thermodynamic generalized forces governing the translocation have been calculated. The influence of the system geometry on the entropic barrier landscape is discussed.