To describe the irreversible growth of linear polymers, we introduce a new type of correlated walk, related to the zero—initiator-concentration limit of the kinetic gelation model. Our model simulates real polymer growth by permitting the walker to form the next bond from the unsaturated monomers at the neighboring sites of its present location. A heuristic kinetic argument of the Flory type suggests a fractal dimension $d_f=\frac{\mathrm{}(d+1\mathrm{})\mathrm{}}{2}$, in agreement with our Monte Carlo and series expansion results (including a logarithmic correction at the upper critical dimension $d_c=3\mathrm{}$).

• Received 30 January 1984

DOI:https://doi.org/10.1103/PhysRevLett.52.1257