  In this thesis the formation and properties of a polymer gel on and at a
surface are investigated. The gel under investigation is defined as a
three-dimensional network of "phantom" macromolecules that form permanent links
with one another and also with confining planar surfaces. The precise location
of the crosslinks on the wall or on another macromolecule is not known prior to
linking, and will differ from sample to sample. However, once the crosslinks
are formed, they are assumed to be permanent. This random linking is the source
of the disorder in the system, over which a quenched average has to be taken.
An existing Deam & Edwards model of network formation, with polymer-polymer
crosslinks, is extended to incorporate a surface and polymer-surface
crosslinks. Within the framework of replica theory, statistical averages and
physical properties of the system are calculated by means of a variational
approach. Macroscopic information, in terms of the free energy of deformation,
is obtained by using two different potentials to simulate the crosslinks
mathematically.
