What really enhances the adsorption of polymers onto chemically nonuniform surfaces: Surface randomness or its heterogeneity?

Abstract

We theoretically perform a comparative analysis of the adsorption of polymers onto the regularly and randomly nonuniform surfaces. By developing and making use of the self-consistent perturbation expansion we calculate the surface excesses of the polymers adsorbed on the random and periodically patterned surfaces. In both cases the enhancement of the polymer adsorption is indicated, as compared to the adsorption onto the homogeneous surface that has the same average affinity for polymers. Moreover, the results obtained for the randomly nonuniform and periodically patterned adsorbing surfaces show striking quantitative similarity, when compared at the same characteristic sizes of inhomogeneities of these surfaces. This finding leads to the conclusion that the adsorption ability of the nonuniform surface primarily depends on the characteristic size of the surface inhomogeneity, rather than on the spatial distribution of the inhomogeneities on this surface. In all cases, the calculated total surface excess is found to be a decaying function of the ratio of the radius of gyration of polymers to the characteristic size of the surface inhomogeneity. The effect of the excluded volume is found to reduce the polymer adsorption.

Analytic theory of the adsorption-desorption transition of Gaussian polymers interacting with a periodic lattice of adsorbing centers

“…20 that the main factor that affects the adsorption ability of the nonuniform substrate is the relation between the gyration radius R G of polymers and the size of the surface patterns d. Observing the same trends in the dependence of the excess density on d / R G for a completely different system considered in the present work by using a different theoretical method will give an additional evidence in favor of the above statement. Depending on the relation between the magnitudes of the above depletion and adsorption forces, one of the three regimes of adsorption/desorption occurs.…”

“…As is theoretically shown in our previous work, 20 the most important factor that affects the reversible adsorption of polymers onto chemically patterned surfaces is the relation between the correlation length describing polymer system ͑e.g., gyration radius R G for Gaussian polymers͒ and the size of the surface patterns. In this respect, it should be noted that the method employed in Ref.…”

“…20 that was first to demonstrate dominant role of the relation between the correlation length describing a size of the characteristic nonuniformity of the polymer system and the periodicity of the patterned substrate for the polymer adsorption. This scaling law is reasonably well described by the independently derived simple scaling arguments, which result in the less precise scaling law of the form cr sc ϳ d −1 .…”

Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: Large chain limit

“…The use of this matrix method on lattices such as those shown in Figs lattices, which are difficult, [26][27][28] if not impossible, to treat using continuum methods. As shown previously in the case of striping, i.e., non-uniform surface chemistry, a shift in the phase transition temperature (critical condition) (−ε/k B T) occurs.…”

Block Copolymer Morphology Formation on Topographically Complex Surfaces: A Self‐Consistent Field Theoretical Study

“…Note that the surface we studied here is patterned, not a randomly rough surface. However, based on the knowledge of polymer absorption on patterned and random substrates, both surfaces could be equivalent for directing the transition from parallel lamellae to perpendicular lamellae.…”