Chemistry Reference
In-Depth Information
for more detail on the (already rather elaborate!) technical aspects of the available
methods, the interested reader is directed to the available topics on simulation
methods and to the original articles describing the work that is reviewed here.
A general conclusion is that the study of phase equilibria in polymer solutions by
simulation methods is still in its infancy. Due to the large scales of length and time
that need to be bridged when one wishes to simulate macromolecules with high
molecular weight, the simulation of polymers in general is a challenge if one insists
that the simulation reaches complete thermal equilibrium. Although special tech-
niques exist to deal with this problem, both for single-chain problems and for dense
melts, the case of solutions seems to have found somewhat less attention in the
literature. We also note that in a semidilute solution of very long macromolecules,
there exists an intermediate large length scale, the concentration correlation length
(sometimes also referred to as the radius of “concentration blobs”, i.e., the size of
regions over which, in the good solvent limit, excluded-volume interactions are
not yet screened out, unlike dense melts where the screening length of excluded-
volume interactions is only on the order of a few molecular diameters). This
incomplete screening of excluded volume in polymer solution has then an interest-
ing interplay with thermal effects when the solvent quality deteriorates, and ulti-
mately the polymer solution separates into a diluted solution of collapsed globules
and a concentrated solution of strongly overlapping chains. The critical point of
this phase separation moves towards the theta temperature of the solution (and the
critical concentration tends to zero) when the polymer chain length tends to infinity.
However, the precise character of this crossover in critical behavior, which is
associated with this limit according to theoretical predictions, cannot yet be reliably
assessed even by the study of strongly coarse-grained, qualitative models that
consider the solvent only implicitly (by postulating suitable weak effective attrac-
tions between the effective monomeric units formed from groups of successive
chemical monomers along the chain) rather than explicitly. In view of the lack of
recent progress with this interesting but difficult problem, we have not reviewed it
here, but rather focused only on the phase behavior of solutions of very short chains,
considering flexible homopolymers almost exclusively. As an example of the rich
science that emerges when this restriction is relaxed, we have pointed towards the
possibility of orientational ordering in solutions of stiff polymer chains, and on
micelle formation in solutions containing diblock copolymers. Of course, many
interesting phenomena exist in solutions containing polymers with more complex
architecture (star polymers, comb polymers and bottle brushes, multiblock copoly-
mers, etc.), giving rise to many possibilities of mesophase formation that are
outside the scope of our article.
One topic we have addressed in detail is the explicit modeling of solvent
molecules, which are described in a simplified, coarse-grained fashion in view of
the fact that even the most “atomistic” models are based on united-atom-type
approximations for the description of polymer chains, or use even coarser models
so that an all-atom modeling of solvent molecules is not warranted. We have also
emphasized that in the description of solvent oligomer phase equilibria, the pres-
sure (in addition to the composition of the solution and its temperature) is an
