Scaling of surface roughness and polymer structure in a model for film growth and polymerization

Abstract

We study a model of growth of polymer films using numerical simulations and scaling concepts. During the deposition, each new monomer flows in a direction perpendicular to the substrate, aggregates at the first contact with the deposit and executes up to G steps along the polymers, propagating an existing chain or nucleating of a new polymer. Some qualitative results agree with those of a previous model for vapor deposition polymerization (VDP) with collective diffusion, such as the roughness increase and density decrease with G . This supports the interpretation of G as a ratio between diffusion coefficient and monomer flux. We perform a systematic study of scaling properties of the outer surface roughness and of polymer size and shape. For large G , the polymers are stretched in the direction perpendicular to the substrate and have typical size increasing as G(1/2). This is explained by the solution of the problem of random walk trapping, which illustrates the connection of surface processes and bulk properties. The distributions of polymer sizes are monotonically decreasing for all G and very broad, thus a large number of small chains and of chains much larger than the average is found in typical samples. The outer surface roughness obeys Kardar-Parisi-Zhang scaling, in contrast to the apparent anomalous scaling of previous VDP models with oblique monomer flux. However, the calculation of reliable exponents requires accounting for huge finite-size corrections. Possible applications and extensions of this model are discussed.