Pressure isotherms, phase transition, instability, and structure of tethered polymers in good, Θ, and poor solvents

Abstract

The conformational and thermodynamic behavior of chain molecules tethered to a planar surface are studied for a variety of solvent qualities with a recently developed single-chain mean-field theory. The lateral pressure isotherms calculated from the theory for chains of n=50 segments show very good quantitative agreement with the recent molecular dynamics simulations of Grest, without the use of any adjustable parameter, for good and Θ solvents. The behavior of the pressure isotherms is analyzed in terms of a virial expansion and it is shown that the regimes where there is scaling of the pressure with surface coverage σ are very narrow for this chain length. Moreover, comparisons with analytical self-consistent field (SCF) theory show good agreement only when the parabolic density profile is used in the full virial equation. In the bad solvent regime the pressure isotherms for grafted chains show negative values of the pressure and also a negative compressibility for some range of surface coverages for temperatures below the Θ temperature. This indicates the possibility of microphase separation in this regime of temperature and surface coverages. For chains with translational degrees of freedom there is a first-order phase separation at temperatures below the Θ temperature into a very dilute and more concentrated polymer phase. From results of two different chain lengths it seems that there is a universal coexistence phase diagram in the scaling variables n0.5(T/Θ−1) vs nσ. In the bad solvent regime it is found that the chains are highly collapsed for very low surface coverage. As the surface coverage is increased the chains tend to stretch laterally in order to gain as much contact as possible with the other polymer chains. This is in contrast to the good solvent regime where the chains always stretch perpendicular to the surface in order to avoid as much contact as possible with the other polymer chains. In the intermediate surface coverage regime it is found that the density profiles look parabolic-like for good solvents becoming more steplike as the quality of the solvent becomes poorer, in agreement with recent neutron scattering experiments. For very high surface coverages the density profiles in the good solvent regime also look steplike.