The static properties of a homopolymer melt between energetically
neutral walls are studied
as a function of the degree of confinement (plate spacing) and polymer
molecular weight. The cooperative
motion lattice model is used and allows all calculations to be
performed at full occupancy (i.e., at a volume
fraction of 1); chain lengths varying from 384 to 24 are examined.
Properties investigated include the
magnitude of the end-to-end vector, the radius of gyration, and
components of the end-to-end vector. In
addition, orientation effects and the distribution of chain ends are
also calculated. As the chains are
confined, the end-to-end vectors align parallel to the walls beginning
at a value of about twice the
unconstrained value of the radius of gyration, regardless of the
molecular weight. For values less than
this, chain conformations are distorted and the magnitude of the
average end-to-end vector and radius
of gyration increase. The components of the end-to-end vector
parallel and perpendicular to the walls
are considered; in the cases of confinement, it is seen that there is a
universal scaling relationship between
the parallel component of the end-to-end vector and the plate spacing.
The parallel component increases
with the decreasing plate spacing according to approximately a
one-sixth power
(〈r
2〉∥
1/2 ∼
L
-1/6). Chain
ends are most likely to be in the vicinity of one of the walls due to
entropic constraints.