Ma. Carignano et I. Szleifer, PRESSURE ISOTHERMS, PHASE-TRANSITION, INSTABILITY, AND STRUCTURE OF TETHERED POLYMERS IN GOOD, THETA, AND POOR SOLVENTS, The Journal of chemical physics, 100(4), 1994, pp. 3210-3223
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.