Diffusion and interaction in gels and solutions. 4. Hard sphere Brownian dynamics simulations

Abstract

Results from Brownian dynamics simulations of hard sphere diffusion in polymer networks of wormlike chains are presented. The influence of the size of the diffusing particles, the polymer concentration, the polymer radius, and the persistence length of the chains were investigated. The diffusion coefficients obtained in systems of stiff chains were compared to a theory [Macromolecules 24, 6024 (1991)]. The agreement between the simulation data and the theory was satisfactory, except for dense systems where the theory predicted somewhat too high diffusion coefficients. To account for the diffusion in systems of more flexible polymers, we derived a semiphenomenological theory based on ideas from the concept of fractals. By this approach we could show how the available volume fraction for particles in polymer networks scales with the particle radii. The scaling is not a power law, but instead is a stretched exponential, and is related to the local structure of the polymer chains. Finally, the inherent assumptions in the theoretical descriptions, e.g., the negligence of the hydrodynamic interactions, and the applicability of the theory to real polymer systems, are thoroughly discussed.

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

“…They reported the radius of the polyacrylamide fiber as 9 Å in comparison to 1.5 Å found by fitting Eq. [42] to the results of the present study. A proposed radius size of 0.15 nm for the acrylamide fibers is rather small and may not reflect realistic features of the gel.…”

“…This value of r f is much less than the values previously reported by Ogston et al (64), who used the sedimentation data of different size solutes in polyacrylamide solutions and Eq. [42] to obtain the fiber radii. They reported the radius of the polyacrylamide fiber as 9 Å in comparison to 1.5 Å found by fitting Eq.…”

“…Also shown are the theoretical models developed by Maxwell (69), Perrins et al (70) (this is numerically equivalent to the volume averaging result of Ryan (71) As a result, no fitting of these models to the data is required. The Johansson-Lofroth cell model (42), based upon the Ogston (18) expression for the probability distribution of straight polymer chains, requires knowledge of the fiber radius of the polymer. The Johansson-Lofroth model (42) was evaluated with a fiber radius of 5 Å (28).…”

“…Other approaches, including hindered transport theory (40,41), have also been used to describe the effects of solute size on diffusion. Experimental data typically has been interpreted on the basis of a stretched exponential equation (36,(42)(43)(44) which can be justified theoretically through comparison with Monte Carlo simulations or derived using a specific arrangement of a unit cell. Despite these studies, a full range of experimental measurements on probe diffusion in polyacrylamide gels as functions of gel composition, including crosslinker density, has not been reported; in addition, the effects of media geometry and solute-gel interactions have not been incorporated within one comprehensive approach.…”

Modeling of the fibrin agarose plate assay and its application for thrombolytic analysis

“…Second, if the value of C min is measured, the diffusion coefficient D can be calculated more conveniently using eq. (6), circumventing complicated calculations using formulae involved in molecular diffusion models such as the steric effect model [13][14][15] and more comprehensive models [16][17][18].…”