Static and dynamic properties of the backbone network for the irreversible kinetic gelation model

We study by Monte Carlo simulations the fractal nature of the backbone network for the irreversible kinetic gelation model in both two and three dimensions. The fractal dimension of the backbone network generated at the gel point is measured by various methods, and results are found to be consistent with that of the standard percolation backbone. Our observation is different from the previous work in three dimensions, where a distinctly larger value was observed. We also measure the spectral dimension d(B)(s) and the fractal dimension d(B)(w) of random walks on a backbone, defined by, respectively, the probability of random walks returning to the starting point and the rms displacements after t time steps. Results are also found to be consistent with the corresponding percolation values. We therefore conclude that the backbone network of the kinetic gelation model exhibits the same static and dynamic properties as those of the standard percolation backbone.