Pure & App!. Chem., Vol. 58, No. 12, pp. 1 553—1 560, 1986.
Printed in Great Britain.
© 1986 IUPAC
Polymer-polymer miscibility
Sonja
Krause
Department of Chemistry, Rensselaer Polytechnic Institute, Troy, IJY 12180
Abstract
The theoretical and practical aspects of polymer-polymer miscibility in the solid
amorphous state are reviewed. The polymers include homopolymers and both random and
block
copolymers. Although present theoretical treatments of polymer-polymer miscibility
all
contain the random mixing hypothesis and are thus not applicable to mixtures that
involve specific interactions between the components, most of the observed single-
phase
polymer-polymer mixtures involve hydrogen-bonding or other specific interactions
between
the components. Even in the absence of specific interactions, the composition
of a random copolymer can often be tailored to provide miscibility with a particular
homopolyner. Many polymer-polymer mixtures have lower critical solution temperatures,
and a small number of such mixtures have given indications of upper critical solution
temperatures. The special phenomena that may be observed when other polymers are
mixed with block copolymers are discussed.
INTRODUCTION
Since I have recently completed the tables on miscible polymers for the third edition
of
the Polymer Handbook (1), it seems appropriate to summarize present knowledge in this
field at this time. This study was limited to polyners that are miscible on a segmental,
submolecular scale in the solid amorphous state which may be either glassy or rubbery. A
polymer which could crystallize was considered miscible with those other polymers which were
miscible with its amorphous portions.
Unfortunately, the literature in this field is complicated by the interchangeable use
of the terms miscibility and compatibility by many workers and by the diversity of defini-
tions of polymer-polymer compatibility that are current in the polymer industry. In the
polymer industry, a compatible polymer pair is often simply one that has desirable proper-
ties after the polymers have been mixed either as solids or in solution (with subsequent
evaporation of the solvent); often, in such samples, several amorphous phases with differ-
ent compositions are present. Such polymers are not miscible, but they may be referred to
as compatible in the literature if there is good adhesion between the phases. Because of
this confusion, I shall use only the term "miscibility" in this paper, not "compatibility."
Studies of miscibility which involve polymers are also complicated by the fact that
all synthetic polymers are multicomponent systems. At the least, any sample of synthetic
polymer is polydisperse with respect to (a) molecular weight; even the so-called monodis-
perse synthetic polymers
have a measureable molecular weight distribution. any samples
are
also polydisperse with respect to (b) microstruture, that is with respect to the ways
in which the monomeric repeat units are inserted into the polymer chain. For example, a
sample of polyvinylidene fluoride has most of the -CH2CF2- repeat units in the chain added
head-to-tail, -CH2CF2CH2CF2-, but in many cases up to about 6% of the monomer additions
may have been head-to-head, -CH2CF2CF2CH2-; other examples include meAo or uuem-Lc addi-
tions of vinyl monomers such as methyl methacrylate in the polymer chain and variable mi-
crostructure such as th.s-1,4-, t'ctns-1,4- and 1,2- addition of butadiene repeat units in
polybutadiene. 1any polymers will be polydisperse with respect to (c) branching, that is,
number, length, and position of branches on the main polymer chain. For example, poly-
ethylene made by different methods varies a great deal with respect to number and length of
branches. Copolymers may, in addition, be polydisperse with respect to (d) composition of
the different polymer molecules that comprise the sample. Random copolymers prepared by
batch polymerization to high degrees of conversion of monomer to polymer may have very
broad composition distributions, so broad that some samples separate into two phases with
different average compositions (more about this later). Copolymers may also be polydis-
perse with respect to (e) sequence, that is, the sequence in which the monomers appear in
each polymer molecule. He talk about copolymers as if they are either random copolymers,
1553
1554
S. KRAUSE
in
which the different monomers are arranged randomly along the chain, or block copoly-
mers, in which the differerent monomers are arranged as two or more pure blocks attached
to each other along the chain. Not only do intermediate cases exist, but a composition
distribution in a copolymer is usually accompanied by a sequence distribution.
It is well known that the solubility of a homopolymer in a solvent or in another poly-
mer varies with the average molecular weight, the average microstructure, and with the aver-
age amount of branching of the polymer. It is also well known that the solubility of copoly-
mers varies not only with these three factors, but also with changes in average composition
and average sequence type. Experimental data that have been obtained on polymer-polymer
mixtures have often been obtained on extremely polydisperse samples whose average molecular
weights and other characteristics are as uncharacterized as their polydispersities. In
spite of this, much is now known about polymer-polymer miscibility as a result of these ex-
periments; I shall outline the results below.
THEORETICAL
TREATMENTS
The
Flory Huggins theory (2-5) of polymer solutions was the first to consider the long-
chain nature of high polymers, and, soon after it was proposed, Scott (6) and Tompa (7) ap-
plied it to polymer-polymer mixtures and obtained the following free energy of mixing of two
polymers, tGmix
1Gmix
(RTV/Vr)[(4A/xA)lnqA +
(B/xB)lnB
XABAB]
(1)
where Vr is a reference volume which is taken as close to the molar volume of the snallest
polymer repeat unit as possible, A and B are the volume fractions of the two polymers, A
and B, respectively, x and x are the degrees of polymerization of polymers A and B in
terms of the reference volume Vr, respectively, and XAB is the interaction parameter between
the two polymers. In equation 1, the first two terms on the right hand side are conbinatori-
al entropy of mixing terms, calculated for a random mixture of the two polymers. Becauseeach
of these terms has a degree of polymerization, xj or x, a number greater than 100 for any
high polymer, in the denominator, the entropy of mixing of two polymers is very small.
The third term on the right-hand-side of equation 1 is a positive enthalpy change on
mixing that was originally based on regular solution theory (8-10). Since even a snall
positive (unfavorable) enthalpy change on mixing will outweigh the very small combina-
tonal entropy change on mixing in the Flory-Huggins theory, it was generally accepted
for many years that most polymers should not be miscible with each other. Up to and in-
cluding my review article on polymer-polymer compatibility published in 1978 (11),
only about 10 percent or less of all polymer pairs investigated experimentally appeared to be
miscible, as expected from the above theoretical considerations.
Since that time, many more miscible polymer pairs have been discovered. This oc-
cured because many workers have deliberately investigated those polymers in which misci-
bility is to be expected in the amorphous state. One way to induce miscibility is to use a
polymer pair which has a negative enthalpy of mixing because of specific interactions.
These specific interactions are generally hydrogen bonds but may be ion-dipole or cation-
anion interactions. If the specific interactions are strong enough, copolymers contain-
ing only a small percentage of mutually interacting groups have been found to be mis-
ci bl e.
In the absence of specific interactions, one way to find a miscible polymer pair is
to choose an appropriate random copolymer as one of the polymers to be mixed. The reason
for this can be found in a slight amplification of Flory-Huggins theory. If the inter-
action parameter in equation 1 is written in terms of Hildebrand (8,9) solubility param-
eters, then
XAB =
(Vr/RT)(A
SB)2
(2)
where A and 6B are the Hildebrand solubility parameters for A and B, respectively.
Equation 2 shows that, when written in terms of Hildebrand solubility parameters, XAB is
always a positive number, and since the third term on the right-hand-side of equation 1 is
the enthalpy change on mixing of polymers A and B, that the enthalpy change on mixing is
also a positive number, as already mentioned. As equation 2 is written, XAB, A' and B may
refer to random copolymers as well as to homopolymers. It turns out to be relatively simple
to find out how to calculate the Hildebrand solubility parameters for random copolymers as
long as those for the homopolymers corresponding to the monomers in the random copolymers
are known. Hildebrand solubility parameters of homopolymers were discussed in reference
11.
My coworkers and I showed in 1965 (12), that when random copolymers C and D were mixed,
the interaction parameter between these two random copolymers, XCD, could be calculated
from the homopolymer-homopolymer interaction parameters, XIJ, corresponding to the various
Polymer-polymer miscibility
1555
monomers,
I and J, of which the copolymers were composed:
XCD Xjdlj_
(3)
where
refers to the volume fraction of monomer I in copolymer C, with similar definitions
for the similar terms. The use of the same subscripts, I and J, for the monomers in copoly-
mers C and D is for mathematical simplicity and does not necessarily imply that the two corn-
ponents contain the same monomers. Either one or both of polymers C and D could be homopoly-
mers; if C and D are actually homopolymers A and B, then equation 3 becomes the identity
XAB XA. The interaction parameter for a homopolymer A with a copolymer C made up of
volume fraction B of monomer B and volume fraction cI
of
monomer E is then, from equation
3, equal to
XAC XAB4B + XACE
_
XBEcIBE
(4)
Equation 4 shows clearly that XAC is not simply a weighted average of XAB and XAE,
but is less than this weighted average by a factor that depends on XBE, the interaction
parameter between the two constituents of copolymer C. If each of the interaction pararne-
ters in equation 4 is written in terms of Hildebrand solubility parameters as in equation 2,
then it turns out that
C B4B E4E
(5)
where ¼
iS the Hildebrand solubility parameter of random copolymer C and 5B and E are
the Hildebrand solubility parameters of the homopolymers corresponding to monomers B and E.
Thus, the Hildebrand solublity parameter of a random copolymer is the weighted average of
those of the hornopolyrners corresponding to its constituent monomers. Thus, also, the
solubility parameter of a random copolymer is between those of the homopolyrners corres-
ponding to its constituent monomers; the exact value of aC also depends on the composi-
tion of the copolymer. Because of this, samples of random copolymer made up of the same
monomers but with different compositions may have their solubility parameters so far
apart that they will be immiscible. This may occur, as stated above, in random copolymer
samples synthesized in such a way that a drift in composition, a composition distribution,
occurred during the synthesis.
These ideas can also be used to find a random copolymer that should be miscible with
a chosen homopolymer. Thus, when considering polymers in which specific interactions
cannot occur, it is often possible to find a random copolyrner made up of monomers whose
solubility parameters straddle that of the homopolymer or other random copolymer with
which it should be miscible. If the solubility parameters of two polymers are equal or
very close to each other, then the interaction parameter between the polymers will be
zero or close to zero (equation 2) and the enthalpy change of mixing will be close to
zero, allowing even the small combinatorial entropy change on mixing of the Flory-Huggins
theory (equation 1) to induce miscibility.
Recently, equation 3 and its consequences have been rediscovered by ten Brinke et al
(13) and Paul and Barlow (14); this rediscovery has motivated some successful searches for
miscible polymers in which at least one component is a random copolymer.
Flory-Huggins theory, whether applied to homopolymers or to copolymers, predicts phase
diagrams with only upper critical solution temperatures. Both polymer-solvent and polymer-
polymer mixtures, however, are more likely to exhibit lower critical solution temperatures
than upper critical solution temperatures. Because of this, a number of authors developed
corresponding states, sometimes called equation-of-state theories of polymer solutions.
Flory's (15) corresponding states treatment of liquid mixtures was first expanded to poly-
mer-polymer mixtures by tlcMaster (16), who was able to predict both upper and lower criti-
cal solution temperatures for such mixtures. Sanchez (17) applied the corresponding states
theory of Sanchez and Lacombe (18,19) to polymer-polymer mixtures with similar results.
These
and other corresponding states theories of polymer solutions and mixtures predict
negative as well as positive enthalpies of mixing, but these are not based on specific
interactions;
the corresponding states theories are still based on the random mixing as-
sumption that does not allow for specific interactions. Therefore, no existing theoretical
treatment is applicable to those of the experimentally determined miscible polymer-poly-
mer systems which are miscible because of specific interactions.
The only polydispersity that has received
any significant theoretical or practical
attention
is that of molecular weight polydispersity. Koningsveld et al (20,21) con-
sidered the effects of molecular weight polydispersity on polymer-solvent and polymer-
polymer phase diagrams within the limitations of the Flory-Huggins theory (2-5). Among
other things, Koningsveld (21) found that a polymer with molecular weight polydispersity
1556
S. KRAUSE
has a critical point on a polymer-polymer phase diagram that is controlled by its z-aver-
age (equation 6) molecular weight
Mz (EwiM)/(wiMi)
(6)
where Mz is the z-average molecular weight of the polymer andEw is the mass
or weight of
molecules
with molecular weight M in the sample.
In a consideration of the miscibility of block copolymers with homopolymers (or with
random copolymers), the peculiarities of block copolymers must be considered. tiost block
copolymers that have been synthesized up to this time are phase-separated; blocks of each
chemical type within the molecules form separate phases. The size of these separate phases
is limited by the lengths of the blocks, thus, the phases are submolecular in dimension,
generally with dimensions in at least one direction as small as 3 to 100 nm. Therefore, one
often speaks of rnicrophase separation in block copolymers. In a microphase separated mono-
disperse block copolymer, the microphases may appear in a number of different morpholoqies
(see Figure 1).
O—25%A
25—40%A
50%A
spheres
cylinders
Iamellae
cylinders spheres
Increasing A—content
Decreasing B—content
Figure
1. Equilibrium Morphologies of Block Copolymers
Figure 1 indicates that there is little volume within most of the block copolyner
microphases to accommodate other polymer molecules; if another polymer dissolves in a
microphase, the microphase must expand in at least one direction to accommodate the con-
comitant increase in volume. It is obvious that a microphase cannot increase in dirien-
ions
indefinitely because the blocks in the block copolymer cannot expand indefinitely.
Therefore,
only a limited amount of other polymer can dissolve in a microphase. There
are other complications in a consideration of miscibility of other polymers into block
copolymers.
These will be considered briefly in terms of mixtures of binary block co-
polymers,
those composed of just two chemically different monomers, A and B, with one
of the chemically identical homopolymers, poly-A. When present at very low concentra-
tion in poly-A, the A-B block copolymer may migrate to the surface causing this surface
to have the properties of poly-B, and/or the A-B block copolymer may dissolve in the
poly-A and, in addition, it may form micelles with poly-B block cores in the bulk of
poly A. At higher concentrations of A-B block copolymer in the poly-A, the micelles of
A-B block copolymer may merge to form microphase separated regions as in Figure 1; these
microphase separated arrays are sometimes called "mesophases." The poly-A regions of the
"mesophases" may or may not contain admixed poly-A homopolymer; furthermore, several
"mesophases", containing different percentages of admixed poly-A homopolymer, may be in
equilibrium. A "mesophase" may be in equilibrium with a homogeneous phase containing
A-B block copolymer molecules dissolved in poly-A homopolymer. Two homogeneous phases
containing different percentages of block copolymer may be in equilibrium. And so on.
Whitmore and Noolandi (22) have used a mean field theory of inhomogeneous multicomponent
polymeric systems (23) to calculate some very complex phase diagrams for this type of mix-
ture. Similar complex phase diagrams were obtained experimentally for some mixtures of
butadiene-styrene block copolymers with either polystyrene or polybutadiene by Roe and
Zin (24). Three-component mixtures containing block copolymers are expected to present
additional complications.
EXPERIMENTAL
DETERMINATION OF POLYMER-POLYMER MISCIBILITY
AND PHASE DIAGRAMS
The experimental study of polymer-polymer
miscibility is complicated by the high vis-
cosity of polymers, even when they are well above their glass transition temperatures.
This means that two-phase systems, even when no block copolymers are involved, usually
have one of the phases present as a dispersion in a matrix of the other; it is generally
impossible to collect the separate phases and determine their compositions by simple anal-
ysis as is usually done in solutions of low molecular weight substances. Worse yet, if
the polymer mixture, or even one phase of the polymer mixture, is below its glass transi-
Polymer-polymer miscibility
1557
tion
temperature, the mobility of the polymer chains is so hindered that equilibrium is
often not achieved. Therefore, the literature on polymer-polymer miscibility contains a
number of ambiguous results, some of which have only recently been understood. For ex-
ample, in my 1978 review (11), I cited the case of polystyrene-poly(vinyl methyl ether)
mixtures, ,hich had all the characteristics of a miscible polymer pair when cast as films
from toluene solution but appeared completely immiscible when cast as films from tn-
chloroethylene solution. It has since become clear that these two polymers are miscible
at room temperature and that the appearance of incompatibility when cast fron tnichlono-
ethylene solution arises from the phase diagram of the three-component system of the two
polymers
with the solvent. An investigation of this polymer mixture in chloroform solu-
tion
(25) showed that when the solvent concentration was high, the mixture was single-
phase; as the solvent evaporated, the mixture entered a two-phase region on the phase
diagram, and, on further evaporation of the solvent, the mixture probably underwent the
glass transition in at least one of the phases before the mixture left this two-phase
region to reenter a single-phase region. Thus, the mixture remains a two-phase system
after all the solvent evaporates even though it should be a single-phase system at equi-
libnium. This is an example of a three-component phase diagram in which any set of two
components is miscible at all concentrations, but, when all three components are mixed,
phase
separation may occur at some
concentration
Polymer
miscibility is usually studied by direct observation, either visual or micro-
scopic.,
of the polymer sample, usually in the form of a thin film, or by observation of
glass transitions and crystalNne melting points in the samples. Miscible polymers that
contain no crystalline phases form transparent films and exhibit no heterogeneity in a
phase
contrast microscope or in an electron microscope. Semicrystalline polymers cannot
be studied by this method. Furthermore, immiscible fully amorphous polymers form trans-
parent films when both polymers have the same refractive index or, when the refractive
indices are different, they occasionally form two-layered films that appear transparent
when a solution of the polymers is evaporated (26). The danger of using turbidity alone
as a criterion of polymer miscibility is illustrated by the behavior of a mixture of
chlorinated polyethylene, 27% Cl, with poly(methyl methacrylate). The sample appeared
turbid below 70°C, clear up to 80°C, and then turbid again at higher temperatures (27).
It was first assumed (27) that this mixture had an upper critical solution temperature
around 70°C, followed by a lower critical solution temperature around 80°C, but later
work (28) showed that the refractive indices of the two coexisting phases had different
temperature coefficients and were coincidentally equal to each other in the 70 to 80°C
interval.
A second way, often used, of studying polymer-polymer miscibility involves the ob-
servation of the glass transition temperatures of the amorphous phases in the mixtures.
Iliscible polymers should have only a single glass transition temperature; in the case of
a
mixture of block copolymer with honopolyner, if the homopolymer is miscible with only
one
of the microphases, then two glass transition temperatures should be observed: one
for the unmixed microphase, and one for the mixed microphase. The single glass transition
temperature criterion of polymer miscibility fails when the glass transition temperatures
of the two polyme, are very close to each other, too close to be resolved by the measur-
ing techniques available. Glass transition temperatures of polymer mixtures have been
measured by a variety of methods such as dilatometry, various dynamic mechanical methods,
dielectric measurements, refractive-index versus temperature measurements, differential
scanning calorimetry, differential thermal analysis, thermo-optical analysis, and radio-
thermoluminescence. In all these methods, the sample is observed over a large tempera-
ture range; problems may occur if the miscibility of the sample changes over this tem-
perature range, especially at temperatures higher than the glass transition temperatures
of all the phases in the sample. As a matter of fact, one way of observing the exis-
tence of a lower critical solution temperature at elevated temperatures in polymer mix-
tures has been the following. A sample that has exhibited a single glass transition
temperature is heated to various temperatures above the highest glass transition tem-
perature of any phase in the sample and is then quenched to well below room temperature from
each elevated temperature in turn. After quenching from a temperature above the lower
critical solution temperature, two glass transition temperatures are observed in the
sample. Lower critical solution temperatures in polymer-polymer mixtures are often ob-
served in this way, as well as by the appearance of turbidity as the sample is heated.
Other methods for studying polymer-polymer miscibility exist, but they are either
ambiguous or very recently developed and have not yet been used to test for the presence
of one or more phases in previously untested systems. These methods will not be dis-
cussed here.
Upper critical solution
temperatures in polymer-polymer mixtures are harder to ob-
serve than
lower critical solution temperatures because the polymer mixture generally
goes through the glass transition as the temperature is lowered. Thus, a polymer mixture
that is miscible at some temperature above its glass transition temperature will have
that single phase frozen-in as the sample is cooled below its glass transition tempera-
