Chemistry Reference
In-Depth Information
It should be clear from this brief survey of various attempts to develop theories
for the equation of state for polymeric materials that we are still far from a fully
satisfactory solution for this difficult problem. In this situation, computer simulations
of molecular models are an attractive alternative. However, this approach is also
plagued with some problems: although a small-molecule fluid, apart from the critical
region, does not develop spatial correlations on scales larger than a few nanometers
[
57
], a single macromolecular coil exhibits a nontrivial structure from the length
of chemical bonds (0.1 nm) over the persistence length (1 nm) to the gyration radius
(10 nm) [
3
,
5
,
8
,
25
,
26
,
31
,
58
]. As a consequence, simulational modeling must
either restrict attention to relatively short polymer chains [
10
,
53
,
55
,
56
,
59 74
], or
consider coarse-grained models [
6
,
9
,
10
,
15
,
16
,
21
,
53
,
55
,
56
,
75 83
]. Even for
both small-molecule systems and for coarse-grained models it is essential that one
considers temperatures far above a possible glass transition temperature [
71
,
81 86
],
particularly if one applies molecular dynamics (MD) simulation methods [
87 91
].
We note that MC methods for polymers have been devised where moves occur that
involve bond crossing or bond breaking, etc., [
92 95
], allowing equilibration of
dense melts for very long chains. Since we are not aware that such algorithms have
been broadly used for the study of thermodynamic properties of polymer blends,
we shall not address these advanced algorithms (as well as other specialized MC
algorithms for lattice models of polymers [
96
]) in the present article.
Finally, we mention the very promising idea of mapping atomistic models to
coarse-grained ones, thus putting some information on chemical details into the
effective parameters of a coarse-grained model in a systematic way [
97 120
]. In
Sect.
2
, we shall briefly review both atomistic and coarse-grained models, as well as
mention some aspects of this systematic coarse-graining approach.
The outline of this article is as follows: after a short discussion of some of the
models (Sect.
2
) we recall the basic aspects of MD and MC methods (Sect.
3
).
Results of simulations of chemically detailed atomistic models for short alkanes,
polyethylene melts, and polybutadiene melts are mentioned. Section 4 is devoted to
a discussion of coarse-grained models for the description of the phase behavior
of alkanes in various solvents (Sects.
4.1
and
4.2
). Also, qualitative models for
semiflexible polymers that exhibit nematically ordered phases [
121 123
] and
for block copolymer solutions that exhibit micelle formation [
124
,
125
] will be
discussed. Section 5 presents our conclusions.
2 Molecular Models for Polymers and Solvents
2.1 Atomistic Models
In this article, we confine our attention to the modeling of polymeric systems in the
framework of classical statistical mechanics. Processes where electronic degrees of
freedom are involved (such as chemical reactions) are outside the scope of the
