Modelling of the inhomogeneous interior of polymer gels

Abstract

A simple model has been investigated to elucidate the mean squared displacement (MSD)of probe molecules in cross-linked polymer gels. In the model, we assume that numerouscavities distribute in the inhomogeneous interior of a gel, and probe molecules are confinedwithin these cavities. The individual probe molecules trapped in a gel are treated asBrownian particles confined to a spherical harmonic potential. The harmonic potential ischosen to model the effective potential experienced by the probe particle in the cavityof a gel. Each field strength is corresponding to the characteristic of one typeof effective cavity. Since the statistical distribution of different effective cavitysizes is unknown, several distribution functions are examined. Meanwhile, thecalculated averaged MSDs are compared to the experimental data by Nisato et al (2000Phys. Rev. E 61 2879). We find that the theoretical results of the MSD are sensitive tothe shape of the distribution function. For low cross-linked gels, the best fit isobtained when the interior cavities of a gel follow a bimodal distribution. Such aresult may be attributed to the presence of at least two distinct classes of cavityin gels. For high cross-linked gels, the cavities in the gel can be depicted by asingle-modal uniform distribution function, suggesting that the range of cavity sizesbecomes smaller. These results manifest the voids inside a gel, and the shape ofdistribution functions may provide the insight into the inhomogeneous interior of a gel.