Modelling of the inhomogeneous interior of polymer gels

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 numerous cavities distribute in the inhomogeneous interior of a gel, and probe molecules are confined within these cavities. The individual probe molecules trapped in a gel are treated as Brownian particles confined to a spherical harmonic potential. The harmonic potential is chosen to model the effective potential experienced by the probe particle in the cavity of a gel. Each field strength is corresponding to the characteristic of one type of effective cavity. Since the statistical distribution of different effective cavity sizes is unknown, several distribution functions are examined. Meanwhile, the calculated averaged MSDs are compared to the experimental data by Nisato et al (2000 Phys. Rev. E 61 2879). We find that the theoretical results of the MSD are sensitive to the shape of the distribution function. For low cross-linked gels, the best fit is obtained when the interior cavities of a gel follow a bimodal distribution. Such a result may be attributed to the presence of at least two distinct classes of cavity in gels. For high cross-linked gels, the cavities in the gel can be depicted by a single-modal uniform distribution function, suggesting that the range of cavity sizes becomes smaller. These results manifest the voids inside a gel, and the shape of distribution functions may provide the insight into the inhomogeneous interior of a gel