  We consider the diffusion and spreading of chainlike molecules on solid
surfaces. We first show that the steep spherical cap shape density profiles,
observed in some submonolayer experiments on spreading polymer films, imply
that the collective diffusion coefficient $D_C(\theta)$ must be an increasing
function of the surface coverage $\theta$ for small and intermediate coverages.
Through simulations of a discrete model of interacting chainlike molecules, we
demonstrate that this is caused by an entropy-induced repulsive interaction.
Excellent agreement is found between experimental and numerically obtained
density profiles in this case, demonstrating that steep submonolayer film edges
naturally arise due to the diffusive properties of chainlike molecules. When
the entropic repulsion dominates over interchain attractions, $D_C(\theta)$
first increases as a function of $\theta$ but then eventually approaches zero
for $\theta \to 1$. The maximum value of $D_C(\theta)$ decreases for increasing
attractive interactions, leading to density profiles that are in between
spherical cap and Gaussian shapes. We also develop an analytic mean field
approach to explain the diffusive behavior of chainlike molecules. The
thermodynamic factor in $D_C(\theta)$ is evaluated using effective free energy
arguments, and the chain mobility is calculated numerically using the recently
developed dynamic mean field theory. Good agreement is obtained between theory
and simulations.
