PRESSURE ISOTHERMS, PHASE-TRANSITION, INSTABILITY, AND STRUCTURE OF TETHERED POLYMERS IN GOOD, THETA, AND POOR SOLVENTS

The conformational and thermodynamic behavior of chain molecules tethe red 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 segm ents show very good quantitative agreement with the recent molecular d ynamics simulations of Grest, without the use of any adjustable parame ter, for good and Theta solvents. The behavior of the pressure isother ms 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 a are very narrow for this chain length. Moreover, comparisons with an alytical self-consistent field (SCF) theory show good agreement only w hen the parabolic density profile is used in the full virial equation. In the bad solvent regime the pressure isotherms for grafted chains s how negative values of the pressure and also a negative compressibilit y for some range of surface coverages for temperatures below the Theta temperature. This indicates the possibility of microphase separation in this regime of temperature and surface coverages. For chains with t ranslational degrees of freedom there is a first-order phase separatio n at temperatures below the Theta temperature into a very dilute and m ore concentrated polymer phase. From results of two different chain le ngths it seems that there is a universal coexistence phase diagram in the scaling variables n(0.5)(T/Theta-1) vs n sigma. 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 wit h the other polymer chains. This is in contrast to the good solvent re gime where the chains always stretch perpendicular to the surface in o rder to avoid as much contact as possible with the other polymer chain s. In the intermediate surface coverage regime it is found that the de nsity profiles look parabolic-like for good solvents becoming more ste plike 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.