Miscibility MAPS. software modeling tool for the prediction of the miscibility
of polymer blends containing statistical copolymers.

The problem of the compatibility in polymer blends has long been a subject
of interest for both theorists and experimentalists. Unlike homopolymers the
blends comprising random copolymers often show "windows" of miscibility on
their phase diagram even in the absence of specific interactions between
polymer units. Such "windows" were observed in systems where mutual repulsion
between dissimilar units in the copolymer macromolecule would suffice to
overcome the repulsion between them and units involved in other components of
the blend in hand. This "repulsion effect" is conveniently elucidated in terms
of a simple Flory-Huggins type theory enabling one to predict the location of
the boundaries of miscibility regions for an arbitrary polymer blend with
known values of the degree of polymerization of the components and the matrix
of the Flory-Huggins parameters characterizing interaction between all pairs
of their monomeric units. Such attractive theoretical approach, in view of its
simplicity, proves to be particularly advantageous when treating experimental
data on the investigation of the phase states of polymer blends and especially
for the search of new advanced materials on their basis.
Typical problem arising for thermodynamic examination of blends involving
copolymers consists in determining under given temperature those regions of
values of their composition at which the system remains homophase. The size
and shape of such miscibility regions of particular polymer specimen have been
suggested to term "miscibility map" (MM). An exhaustive classification was put
forward of all topologically conceivable kinds of such MMs depending on the
Flory-Huggins parameters for a mixture of two binary statistical copolymers
having a common monomer unit. Later the principles were formulated of such a
classification for arbitrary blends consisting of any number of components,
each comprising any kinds of units. In the mathematical model underlying this
version of the "Miscibility Maps" software the consideration was restricted
for simplicity sake to the case of rather high-molecular polymers where the
dependence of the MM shape on their molecular weight may be neglected. Such an
approximation is widely used to estimate the compatibility regions of real
polymer blends. It corresponds to ignoring the combinatorial entropy
contribution to the free energy of mixing, that for such blends is normally
small as compared to the enthalpy contribution. This simple approach has an
indisputable advantage when establishing the correlation between the topology
of the boundary which separates the regions of compatibility and
incompatibility of a blend. Within the framework of such an approximation it
is sufficient to have an information only on the values of the Flory-Huggins
parameters for all pairs of monomeric units of polymer blend under
examination. To each given set of these parameters there corresponds the
particular MM in the space of compositions of blend components. Once the MM
has been obtained, one can predict theoretically the limits of the variation
of these compositions where the appearance of "miscibility windows" can be
expected in the blends comprising statistical copolymers. In paper
"Miscibility Maps of Blends Containing Statistical Copolymers" (Polym.
Networks Blends, v. 5 N 4, 191-198 (1995)) general principles have been
formulated of classification of such polymer blends by topological types of
their MM.
Our software product permits a user to construct the MM of systems of all
these types proceeding from given values of the Flory-Huggins parameters.
Hence this product offers a possibility not only to reveal the topology of the
MM of a polymer blend containing copolymers prepared by a polymerization of
given monomers but also to determine quantitatively the boundaries of
compatibility regions of any blend depending on composition of the copolymers
involved.