THE KINETIC GROWTH WALK: A NEW MODEL FOR LINEAR POLYMERS

To describe the irreversible growth of linear polymers, we introduce a new type of perturbed random walk, related to the zero initiator concentration limit of the kinetic gelation model. Our model simulates real polymer growth by permitting the initiator (walker) to form the next bond with an unsaturated monomer at one of the neighbouring sites of its present location. A heuristic kinetic self-consistent field argument along the lines introduced by Pietronero suggests a fractal dimensionality, df = (d + 1)/2, in agreement with our Monte Carlo and series expansion results (including the usually expected logarithmic correction at the upper critical dimension dc = 3.