Branched polymer approach to the structure of lattice animals and percolation clusters

Characterization of polysaccharide hydrogels for modified drug delivery

Hydrogels are hydrophilic macromolecular networks that are capable of retaining a large amount of water. A precise description of these systems is actually quite complex and the practical use of hydrogels for drug delivery and biomedical applications is often not supported by a well-defined knowledge of the overall structure of the polymeric network. In this paper, we report the characterization of two different systems: a chemical network based on Guar Gum (GG) and a physical gel prepared with Xanthan (Xanth) and Locust Bean Gum (LBG). The dynamo-mechanical properties of the gels were analysed: the cohesiveness and the adhesion of the networks were strongly dependent on time, temperature, and composition. The kinetics of the chemical crosslinking was followed by means of rheological measurements, i.e. recording the mechanical spectra of the gelling system, and the power law exponent at the gel point was evaluated. Furthermore, the networks, loaded with model drugs with different steric hindrance, were used as matrices for tablets and the rate of release of such model drugs was studied. The diffusion of the guest molecules was deeply dependent on their dimensions; in the case of Xanth-LBG tablets the release profiles were almost independent from the different cohesion properties of the starting hydrogel composition.

Statistics of ideal randomly branched polymers in a semi-space

We investigate the statistical properties of a randomly branched 3-functional N-link polymer chain without excluded volume, whose one point is fixed at the distance d from the impenetrable surface in a 3-dimensional space. Exactly solving the Dyson-type equation for the partition function Z(N, d )=N(-theta)e(gamma N) in 3D, we find the "surface" critical exponent theta=[Formula: see text], as well as the density profiles of 3-functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.

Cluster diversity and entropy on the percolation model: the lattice animal identification algorithm

We present an algorithm to identify and count different lattice animals (LA's) in the site-percolation model. This algorithm allows a definition of clusters based on the distinction of cluster shapes, in contrast with the well-known Hoshen-Kopelman algorithm, in which the clusters are differentiated by their sizes. It consists in coding each unit cell of a cluster according to the nearest neighbors (NN) and ordering the codes in a proper sequence. In this manner, a LA is represented by a specific code sequence. In addition, with some modification the algorithm is capable of differentiating between fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshen, M. W. Berry, and K. S. Minser, Phys. Rev. E 56, 1455 (1997)] is used to compose the set of NN code sequences of each cluster. Using Monte Carlo simulations on planar square lattices up to 2000x2000, we apply this algorithm to the percolation model. We calculate the cluster diversity and cluster entropy of the system, which leads to the determination of probabilities associated with the maximum of these functions. We show that these critical probabilities are associated with the percolation transition and with the complexity of the system.