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Polymer Blends
4
Polymer Blends WILLIAM J. MacKNIGHT and FRANK E. KARASZ University of Massachusetts, Amherst, MA, USA 4.1
INTRODUCTION
111
4.2 THERMODYNAMICS 4.2.1 Flory-Huggins 4.2.2 Equation of State 4.2.3 Lattice Fluid and Other Developments of the Flory-Huggins Approach
111 111 113 113
4.3 PHASE BEHAVIOR IN POLYMER BLENDS 4.3.1 Phase Diagrams and the Temperature Dependence ofx 4.3.2 Spinodal vs. Nucleation and Growth Decomposition Mechanisms 4.3.2.1 Spinodal decomposition 4~3.2.2 Nucleation and growth
114 114 116 116 119
4.4 FACTORS CONTROLLING MISCIBILITY IN POLYMER BLENDS 4.4.1 Specific Interactions 4.4.2 The 'Copolymer Effect' 4.4..2.1 An/( BxC 1 - x)n' 4.4.2.2 (A xB1 - x)n/(Ay B1 - y )n' 4.4.2.3 (AxBl-x)n/(CyDl-y)n' 4.4.2.4 Sequence distribution effects
119 119 121 123 124 124 126
4.5
129
REFERENCES
4.1
INTRODUCTION
The scientific understanding of the principles governing polymer miscibility or compatibility has lagged behind the technological development of the field. It may be stated that essentially all polymeric materials that are items of commerce are blends. Examples range from poly(vinyl chloride), which contains a 'polymeric plasticizer' such as poly(ethylene-co-vinyl acetate), to 'Noryl', an engineering thermoplastic based on the miscible blend of polystyrene and poly[oxy-(2,6dimethyl-1,4-phenylene)]. It is normally assumed that relatively few new polymers will attain commercial success in the coming decades, and the need for new higher performance engineering thermoplastics, composite matrix materials and elastomers will largely be met by blending known polymers in ways that will produce the desired properties. In this chapter the fundamental principles of the present understanding of the science of blending will be presented. Areas in which advances need to be made will be pointed out. Relatively little emphasis will be placed on technological or preparative aspects of blending.
4.2 THERMODYNAMICS 4.2.1
Flory-Huggins
We define a miscible polymer blend as one which satisfies the thermodynamic criteria for a singlephase system. For example, if the blend consists of two components, A and B, then, at constant 111
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Generic Polymer Systems and Applications
temperature and pressure, a single-phase mixture will be formed if (1)
where ~Gm is the Gibbs free energy of mixing and
where
It should be mentioned that if the repeat units of the polymers to be mixed are of comparable size, as is often the case, their volumes can each be taken to be equal to Vr • Equation (3) is often quoted in this form in the literature, and we shall assume it to be valid in what follows, for the sake of simplicity. For the monodisperse case, the critical conditions for miscibility are (from equation 2) (4)
and (5)
It immediately follows from equations (4) and (5) that, for polymers with appreciable degrees of polymerization, the binary interaction parameter lAB must be very small for miscibility to occur, and, for infinite degrees of polymerization, it must be zero or negative. The spinodal conditions for such a system are readily obtained from the expression (6)
and turn out to be (7)
It must be remembered that equations (4H7) are valid only for binary mixtures of monodisperse polymers having repeat units of equal size. In addition, the binary interaction parameter must be independent of concentration. The restriction to monodisperse polymers is easily removed, as shown by Koningsveld and coworkers. 5 - 7 The expression for the spinodal conditions is especially simple and has the form (8)
where XWA and XWB are the weight-average number of lattice sites occupied by A and B, respectively.
Polymer Blends
113
The critical composition is (9)
where XZA and X ZB are the z-average number of lattice sites occupied by A and B, respectively. Thus, if the appropriate moments of the distribution of chain lengths are known (identifying these with the number of lattice sites occupied by the two species), the effect of polydispersity on the thermodynamics of mixing is relatively easy to treat. It should be noted that the molecular weight distribution has a profound effect on both the location of the critical point and the composition dependence of the binodal and spinodal boundaries. The development of the mean-field lattice theory presented here differs from the original formulation of Scott only in that the binary interaction parameter is not identified with the enthalpy of mixing via the Vanlaar-Scatchard expression. For the further elaboration of the thermodynamics of polymer mixtures, it is more appropriate to consider the binary interaction parameter from the outset to be a free energy parameter in its own right. That is, lAB contains both enthalpic and noncombinatorial entropic contributions. Thus both the temperature and composition dependence can be introduced into lAB in a natural fashion (Section 4.2.3).
4.2.2
Equation of State
The original mean-field lattice theory, with lAB interpreted as an enthalpic parameter, is capable of predicting the existence of either a lower (LCST; AWABO) consolute point in polymer mixtures, or, indeed, in polymer solutions. Freeman and Rowlinson 8 observed that many hydrocarbon polymers in solvents of low polarity exhibit an LCST in addition to the more familiar VCST. The reason for this phenomenon is the proximity of the solvent's vapor/liquid critical point. As a result of these experimental findings, Flory and co-workers 9- 12 presented a new expression for AGm based on the 'equation-of-state properties' of the pure components, following earlier work of Prigogine. 13 Patterson further elaborated the new theory.14-17 Somewhat later it was recognized that phase decomposition in high molar mass polymer blends, where it could be observed, was almost always of the LCST type. In the light of these findings, McMaster 18 evaluated the Prigogene-Flory-Patterson theory and applied it to polymer-polymer mixtures. The appropriate expressions for the various thermodynamic quantities are quite complex and will not be reproduced here. Suffice it to say that the equation-of-state theory has the effect of modifying the temperature dependence of the binary interaction parameter by the addition of a 'free volume' term, B(T) (equation 10). XAB=XAB/T+B(T)
(10)
The term B(T) is always positive and has an exponential dependence on temperature. The exchange or enthalpic part of the interaction parameter, X AD' is usually positive for hydrocarbon homopolymer pairs. It can be seen from equation (10) that, in the event that X AB is negative, phase decomposition can occur only'via an LCST. If, on the other hand, X AD is positive but very small, or if the components of the mixture are of moderate molar mass, then both a VCST and an LCST may occur. Both types of behavior are rare. The former case, which usually involves specific interactions between A and B segments, is by far the more common. Table 1 lists some miscible homopolymer blends which have specific interactions (X AD negative). Naturally, LG,STs for such systems may not be experimentally observable, since they may lie above the decomposition temperatures of the polymers.
4.2.3 Lattice Fluid and Other Developments of the Flory-Huggins Approach The original Flory-Huggins formulation did not allow for volume changes upon mixing, since all the lattice sites were occupied. It is possible to modify such a mean-field approach to allow the lattice to be 'compressible'. This was done by Sanchez and Lacombe 19 and was further elaborated by other workers. 20 - 23 For the case of high molar mass polymer blends, the most important result of the lattice-fluid treatment lies in the temperature and composition dependence of the binary interaction parameter. (As with the equation-of-state theory, the lattice-fluid theory is cast in terms of the single parameter, lAB' for a binary mixture. All other parameters are known from the pure components.) PS/-E
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Generic Polymer Systems and Applications
Following Koningsveld and co-workers,24-25
lAB
may be expressed as
XAB = X o +Xt/T+ X 2 T+ X 3 1n T
(11)
where the various coefficients Xi may depend on concentration. The concentration dependence of lAB can be understood in terms of an approach suggested by Staverman 26 which leads to expressing lAB in terms of the ratios of the surface areas of the two interacting segments. In other words, the concentration dependence of lAB arises from the difference in size and shape betwe\,;n segments A and B. For many purposes, lAB can be approximated as 27 XAB=X~+X;/T+
YcPB
(12)
X ~ can be taken to refer to the entropic portion of the interaction free energy while X; refers to the enthalpic portion. Y is related to the ratio of the surface areas of the segments A and B, and must be zero for segments of the same size. It should be noted that the first two terms in equations (11) and (12) are sufficient to account for phase behavior of either the LCST-type (Xl or X; negative) or of the VCST-type (Xl or X; positive). The terms involving X 2 and X 3 allow both VCST-- and LCST-type phase decomposition to occur in the same system. Thus both the equation-of-state and the lattice-fluid theories predict a range of phase decomposition behavior in polymer blends far beyond the scope of the original Flory-Huggins formulations. The concentration dependence of lAB introduced by the difference in surface areas between the segments is often not sufficient to account for some of the complex shapes encountered in actual phase diagrams. In order to deal with this situation it is necessary to introduce the 'compressible'lattice model explicitly, which is capable of reproducing the observed phase diagrams, albeit at the expense of introducing a number of additional parameters. 25
4.3 PHASE BEHAVIOR IN POLYMER BLENDS 4.3.1
Phase Diagrams and the Temperature Dependence of l
Figure 1 presents schematic representations of various types of phase diagrams for polymer mixtures. Again, for the sake of clarity, the discussion will be restricted to monodisperse binary mixtures. Figure l(a), showing VCST behavior, is familiar from· polymer solution thermodynamics, where the critical point at infinite molar mass represents the well-known Flory (J conditions. 28 Such a phase diagram may also be expected for blends of oligomers where the enthalpic part of lAB is positive. There are a number of examples in the literature. 7,29 Such a phase diagram is very rare for high molar mass homopolymer blends, although, as will be discussed subsequently, it is not at all unusual for copolymer blends. Figure 1(b), showing LCST behavior, is the 'normal' phase diagram for high molar mass homopolymer blends where specific interactions are present (enthalpic part of lAB negative). A number of examples are cited in Table 1. Figure l(c) shows a phase diagram exhibiting a VCST and an LCST above it. This behavior is common in polymer solutions, where the LeST is usually above the boiling point of the solvent, and is predicted by the equation-of-state theory to be possible for homopolymer blends, if the enthalpic part of lAB is positive but very small (~10- 3 ). There appear to be no confirmed examples of this behavior in the literature, although it has been suggested that polystyrene and poly(2-chlorostyrene) blends might be in this category.30 There are experimental difficulties in determining such phase diagrams since the VCST may be below the glass transition temperature (Tg ) and the LCST may lie above the decomposition temperature. Once again, if copolymer blends are considered, a number of examples of· phase diagrams of the type shown in Figure l(c) have been reported. 31 - 33 It is also possible for the VeST to merge with the LCST, producing an 'hour glass' type of phase diagram, as shown in Figure l(d), or the VCST can lie above the LCST, producing a 'closed loop' phase diagram, as shown in Figure l(e). The 'hour glass' phase diagram (Figure'ld) has no temperature region for which a single phase exists over the entire composition range. This most probably represents the phase behavior of compatible blends, and, in the extreme case where the miscibility-composition limit is very small, of incompatible blends as well. There are also considerable experimental difficulties in determining phase diagrams of this type and very little quantitative information is available. Shaw 34 has developed an ingenious method based on light scattering for determining miscibility limits of components of incompatible blends.
Polymer Blends (0)
(e)
115 (b)
(d)
(e)
Figure 1 Schematic phase diagrams for polymer-polymer blends; - binodallines, --- spinodal lines: (a) a phase diagram of the UeST type; (b) a phase diagram of the LCST type; (c) a phase diagram in which both a UCST and an LCST occur; (d) an 'hourglass' phase diagram; and (e) a phase diagram in which the UCST occurs above the LCST Table 1
Miscible Homopolymer Pairs with Specific Interactions
Homopolymer pair Poly(ethylene oxide) Poly(vinyl chloride) Poly(vinylchloride) Polystyrene Polystyrene Poly(ethylene oxide) Poly(vinylidene fluoride) Polybenzimidazole Poly(ethylene oxide) Poly(vinyl chloride) Bisphenol A polycarbonate Poly(vinylidene fluoride) Poly(vinyl chloride) Polystyrene Poly(vinylidene fluoride) Poly(vinylidene fluoride)
LeST observed Poly(acrylic acid) Poly(methyl methacrylate) Poly(8-caprolactone) Poly(vinyl methyl ether) Poly[oxy(2,6-dimethyl-l,4-phenylene)] Poly(methyl methacrylate) Poly(methyl methacrylate) Polyimide Poly(ether sulfone) PolY(IX-methyl-cx-n-propyl-fJ-propiolactone) PolY(8-caprolactone) Poly(vinyl methyl ketone) Poly(butylene terephthalate) Tetramethylbisphenol A polycarbonate Poly(ethyl methacrylate) Poly(ethyl acrylate)
Yes Yes Yes
No
Yes Yes Yes Yes
No
Yes Yes
No
Yes Yes
No
There appear to be no examples at present of the 'closed loop' type of phase diagram for polymer blends. At least in the case of homopolymers, the equation-of-state theory would predict that a UCST should always occur at or below an LCST. Such restrictions may not apply to copolymer blends. Severe experimental difficulties exist in the determination of phase diagrams for polymer blends. These include, in addition to the problems noted above, the effect of polydispersity and the difficulty in attaining an equilibrium state in such highly viscous liquids. When specific interactions are present, as is the case for most miscible homopolymer blends, the presence of a low molecular weight polar impurity, such as water,- may drastically alter the segmental interactions and lead to erroneous results. Therefore, there are few examples of 'thermodynamically accurate' phase diagrams in the literature for polymer blends. Most of those that exist have been obtained by scattering methods,
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Generic Polymer Systems and Applications
usually involving either light scattering or neutron scattering. Fortunately, for many purposes, approximate phase diagrams are sufficient and these can often be obtained in much simpler ways.
4.3.2
Spinodal vs. Nucleation and Growth Decomposition Mechanisms
From the foregoing discussion one may expect to find cases in which polymer blends exhibit the type of phase diagram exemplified by Figure 2, which is a somewhat more detailed version of Figure 1(b). As already noted, there will be many blends which have LCSTs below the T g or above the chemical decomposition temperature. As will be described later, it is possible to adjust the critical temperature to a certain extent by controlling molecular weight, and, more importantly, copolymer composition in copolymer blends. Assuming a blend has been identified which obeys the phase diagram given in Figure 2, annealing experiments can be carried out at various temperatures above the LCST, that is within the miscibility gap or the region in which phase decomposition will take place. If such a process is allowed to proceed to an equilibrium state, two phases will result, with compositions corresponding to those dictated by the location of the binodal boundary at that particular temperature. However, if the phase separation process is interrupted before equilibrium can be achieved, quite different morphologies will result, depending on whether the phase separation occurs in the spinodal region or the binodal region indicated in Figure 2. (Phase separation can be stopped by quenching the blend below its T g .)
Decomposition or crosslinking ....~....l~'iH+I+ - -
T decomposition- - -
~no
window
T~-----------
ToA
--
11111111111111111111.~ Glass region
o (A)
I
Volume fraction of polymer B blended ( B) with polymer A
Figure 2 A schematic phase diagram for a polymer-polymer blend of the LeST type
4.3.2.1 Spinodal decomposition The phenomenon of spinodal decomposition, in which two phases exist with a type of interconnecting network morphology, has been recognized in the metallurgical field for some time. A quantitative description of the early stages of the process has been given by Cahn and Hilliard. 35 Before citing their results, it is perhaps worthwhile to examine the thermodynamic driving forces governing phase separation in the spinodal region. Figure 3 shows the composition dependence of the free energy of mixing at a temperature, T 1 , within the miscibility gap.The spinodal boundary is defined by the condition (0 2 11Gm /04>i)=0, as indicated in the figure and previously discussed. Within the composition range bounded by the spinodal boundary, the curvature of 11Gm , a2 11Gm / o4>i, is negative, and hence any small fluctuation in composition will cause a decrease in 11Gm and therefore tend towards phase separation. Cahn and Hilliard added to this thermodynamic picture by taking into account the fact that composition gradients at interfaces between phases also contribute to 11 Gm' Based on these
117
Polymer Blends
T---~J.LA.~J.LA
1
~GM
._._._._._.-i--:7-;_._. --
_
"
: . '+-. I
I
I
: I
............
I I I
I I
I I I
I
Binodal ~J.LA ·~J.LA ~J.LB .~J.L~
Spinodal
[ ~26GM lH#JjlH#Jj
]
=0
Figure 3 Composition dependence of ~Gm at a temperature within the miscibility gap (note:
Jli=a~Gm/a
principles, Cahn and Hilliard derived a diffusion equation, which, in its linearized form, reads (13)
where m = the mobility coefficient and K = the energy gradient coefficient. m(02 ~Gmjol/Ji) may be identified with the diffusion coefficient, D, since equation (13) would reduce to Fick's diffusion equation if this were the case and K =0. However, since (0 2 ~Gmjol/Ji) is negative within the spinodal region, D must also be negative. Therefore phase separation must occur by a diffusional flux against the concentration gradient in the spinodal region. This process is sometimes referred to as 'uphill' diffusion. The elaboration of the Cahn-Hilliard approach will not be presented here; the reader is referred to the literature for details. 36,37 Suffice it to say that the solution to equation (13) predicts that phase separation in the spinodal region will produce a morphology having a characteristic repeat distance or wavelength. The magnitude of the wavelength depends on the ratio of (0 2 ~Gmjal/Ji) to K. Equation (13) is applicable only to the early stages of decomposition, and attempts have been made to extend it to the later stages by including higher order terms. 38 This can only be done at the expense of introducing much greater complexity into the original formulation and adding a number of additional parameters. A number of studies hav~ been carried out applying the Cahn-Hilliard theory to spinodal decomposition in polymer blends. The experimental techniques employed are typically light or neutron scattering 39 ,40 or assessment of morphology by microscopic methods. 41 One of the most thoroughly studied systems is the PSjPVME blend. It has already been mentioned that a specific intermolecular interaction exists in this blend, and it has a phase diagram of the type depicted schematically in Figure 2. The actual phase diagram for a PSjPVME blend, where the PS has been deuterated, is given in Figure 4. Pioneering work on the kinetics of spinodal decomposition in -PSjPVME blends was carried out by Turnbu1l42 using microscopic methods and by Kwei et al. 43 using pulsed NMR. More recently the work of Han et al. 44 using neutron scattering may be cited as of particular significance. The use of any scattering technique for the determination of polymer structure depends on the introduction of sufficient scattering contrast between the components or phases present. In neutron scattering this is usually done by deuterating one of the components. In the case of PSjPVME, PS is usually the component deuterated; the deuterated PS is denoted by PSD. This has the effect of increasing the LCST by some 60°C (Figure 5). Such differences in the thermodynamics of deuterated species compared to protonated species are not at all unusual and have been treated by several authors. 4s - 47 Phase-separation kinetics in the spinodal region were followed by Han et al. 44 using the temperature-jump light-scattering technique on the blends shown in Figure 4. The results are presented in Figure 6. The existence of peaks in the intensity, I(q), vs. q plots, their insensitivity to
Generic Polymer Systems and Applications
118
PSO/PVME
MW·435k/l88k 170
~ !
160
E ~
150
iB-
/
•
140 0
Figure 4
Phase diagram for PSD/PVME (after Han et
at., ref. 44): e, binodal;
0, spinodal
200
~ !
~ 160
e
8e
~
120
o Figure S Phase diagram for PSD/PVME andPS/PVME: e, PS, M w=233000, M w/M n =1.06;. PS, M w=l00000, Mw/Mn = 1.05; 0 PSD, M w=255000, Mw/Mn = 1.08; PSD, M w=119000, M w/Mn =1.05 (PUME, Mw=~9000, Mw/Mn =2.13) (after Han et at. ref. 44)
°
16
PSO/PVME
MW 435k/l88k 7i ·122OC Tf-151.5OC
12
4
o .2
Figure 6
I( q) vs. q for PSD/PVME blends; light-scattering profiles (after Han et at., ref. 44; numbers within lines refer to time (t) in seconds)
Polymer Blends
119
time in the early stage (t < 5000 s) and the decrease in magnitude and increase in q values at later times, are all indications of phase separation via a spinodal mechanism.
4.3.2.2 Nucleation and growth In the region between the spinodal and binodal, (0 2 AGm/ocjJi) is positive, as can be seen from Figure 3. As a result, any small composition fluctuations in this region result in unfavorable free energy changes, and phase separation will occur only when relatively large composition fluctuations are present. Such large fluctuations are normally called nuclei and the process is referred to as nucleation and growth. In this case diffusion into the new phase from the surrounding medium proceeds by the 'normal' or 'downhill' route in contrast to the 'uphill' diffusion taking place in spinodal decomposition. A schematic representation of the evolution of phase composition for both spinodal and nucleation and growth mechanisms is given in Figure 7. Modes of phase separation
Nucleation and growth
-------.]A&---- ----
cP1E ---~--cP M- ~ - -- cP2E - - - -
---
---
---
- --.
Nucleation
-
- ---
--
. ---
---
Growth
Spinodal phase separation
-----J2iE---
~
Equilibrium
cP 1E -cP M---- --- --- --- ---cP ----
/
2E
cP,E----------::---llfi·--cP
-~
,l..M _...;. 'f"2E
~----
-- -- -- -- ----- -- -- ----_
Fluctuation
Growth of fluctuation
Saturation and conti nued sepOration (phase hardening)
cPM= Composition
_
of mixture
= Equilibrium composition of phase i
Figure 7 Modes of phase separation in miscible blends
The morphology resulting from the nucleation and growth process consists of the minorcomponent phase dispersed in the continuous major-component phase. If the amounts of the two phases present are similar, lamellar morphologies may result. Normally the minor component is present in spherical form with a sharp phase boundary between the particles of the dispersed phase and-the matrix. Nucleation and growth is perhaps a more familiar mechanism for phase separation than spinodal decomposition and is usually the only mechanism observed in low viscosity solutions, where it is difficult or impossible to 'quench' the mixture sufficiently into the spinodal region for this latter mechanism to compete effectively in the phase-separation process. Unfortunately, there is no theory pertaining to rate processes operative in nucleation and growth decomposition mechanisms. A number of morphological· and scattering studies exist, but relatively few report kinetic parameters governing the process. 4.4 FACTORS CONTROLLING MISCIBILITY IN POLYMER BLENDS 4.4.1
Specific Interactions
It has already been indicated that high molar mass homopolymers are expected to be immiscible in the absence of specific interactions. By 'specific interactions' are commonly meant intermolecular
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Generic Polymer Systems and Applications
forces which are intermediate in strength between London dispersion forces and covalent chemical bonds. They include dipole-dipole, hydrogen-bonding, charge-transfer and acid-base (neutralization) interactions. All of these have been used to promote miscibility in polymer blends and the examples cited in Table 1 probably include a number of them. The difficulty in defining such interactions quantitatively in molecular terms is such that no clear understanding exists of even such well-known and well-studied interactions as those occurring in PPO/PS and PVME/PS. It is often stated that the mean-field approach cannot deal adequately with cases where specific interactions are present. This is because the specific interactions introduce locally preferred directions, i.e. all lattice sites are no longer equivalent. While this statement is formally correct, it is nevertheless true that most cases of interest in blends with specific interactions can be adequately treated if one introduces appropriate temperature and composition dependences into X. It is, of course, correct to say that methods such as the solubility parameter, based on estimates of interactions as geometric means, cannot account for specific interactions. Such methods are incapable of predicting negative values for Xij; a negative Xij is a prerequisite for the presence of a specific interaction in the context of this discussion. Although a considerable literature exists 48 on specific interactions of polymer blends, and although in some cases the magnitudes of the interactions are known in a thermodynamic sense through the experimental determination of Xij' molecular interpretations are generally lacking, as mentioned above. As examples of blends that are rendered miscible by virtue of the presence of specific interactions may be cited those based on aromatic polybenzimidazole (PBI) and aromatic polyimides (PI),49 having the generic structures shown in Figure 8. Such polymers are believed to be miscible over a comparatively wide range of composition and structural variation. All of the Pis in Figure 8 are high molecular weight fully imidized thermoplastics. These Pis and the PBI are all soluble in N,Ndimethylacetamide (DMAC), so that blends can be prepared either by precipitating a solution of the respective polymer mixture into a non-solvent, such as methanol, or by casting a film. Blend miscibility was confirmed by the presence of single composition-dependent T g values lying between those of the constituent polymers; by well-defined composition-dependent tan b dynamic mechanical relaxation peaks associated with the glass transitions; by the formation of clear films; and, in one case, by enhanced solvent resistance. An FTIR study of the PBI/PI system was undertaken using PBI/XU 218 and PBI/Ultem 1000 as representative blends. The objectives were to obtain evidence for the existence of specific interactions in this system and to elucidate the nature of these interactions. In prosecuting this study, the changes in the spectral properties of the N-H stretching bands (which arise solely from the PBI component) and of the carbonyl stretching bands (which arise solely from the PI component) were followed. FTIR has been widely used in characterizing miscible polymer sytems. Frequency shifts and band broadenings for many such blends have been ascribed to intermolecular chemical interactions and to changes in polymer-chain conformations. Many of these studies involved blends of polymers containing a carbonyl group,50 which appears to be particularly sensitive to the presence of intermolecular interactions. Figure 9(a) shows that the N-H stretching band of PBI (3400 em -1) in PBI/XU 218 blends shifts by about 55 cm - 1 with increasing PBI content. No shifts are observed in the region between 0 and 50 wt % PBI. Concomitantly, the principal phthalimide carbonyl stretching band (1725 cm -1) of XU 218 shifts by about 7 cm -1 at PBI contents in excess of 80 wt % . In attempting to analyze this behavior it is important to note that PBI is the sole source of NH groups and XU 218 is the sole source ofcarbonyl groups in the miscible blends. There are at least three possible interactions which might be responsible for the observed band shifts: (a) hydrogen bonding between carbonyl and NH groups; (b) 1t orbital interaction between imide and imidazole rings; and (c) charge-transfer interaction between the phthalimide and benzimidazole fused-ring systems. Of these three possibilities, only the first may be confidently ruled out. This decision is based on the notion that hydrogen bonding should manifest itself in the carbonyl region by the appearance of a new hydrogen-bonded carbonyl peak about 20 to 30 cm - 1 below that of the 'free' carbonyl peak of the parent XU 218. These peaks should remain at constant frequency with increasing PBI content, but the amplitude of the hydrogen-bonded carbonyl peak should increase at the expense of the free carbonyl peak, contrary to observation. Also there is a study of the blend, poly(e-caprolactone)/poly(4-vinylpnenol) (PCL/PVH), where the interaction appears to be unambiguously of the hydrogen-bonded type. 50 This blend is analogous to the PBI/XU 218 blends in that one of the components, PCL, is the sole source of carbonyl groups and the other, PVH, is the sole source of hydroxyl groups. Here the behavior of the carbonyl stretching region is 'classical' for hydrogenbonded systems. Pure PCL displays one clearly resolved carbonyl stretching band at
121
Polymer Blends
~N~N>+ N~ ~N I
H
I
H
(1) Poly[1,3-phenylene(5,5'-bibenzimidazolyl}-2,2'-diyl] [Celanese Corp.: PBI (Tg =420°C)]
+O-N
o
o
o
o
(2) Poly(1,3-phenylenephthalimido-N,4-diyloxy-l,4-phenylenedimethylmethylene-l,4-phenyleneoxyphthalimido-4,N-diyl) [General Electric Co.: Ultem lOOO(Tg = 220 °C)]
o
o (3) Condensation product of 5,5'-carbonylbis(I,3-isobenzofurandione) (3,3',4,4'-benzophenone tetracarboxylic dianhydride; BTDA) and 5-amino-3-(4'-aminophenyl)-I,I,3-trimethylindan [Ciba-Geigy Corp.: XU 218 (Tg = 320°C)]
o N
o (4) Condensation product of BTDA and a 4/1 molar mixture of 2,4-toluene diisocyanate and 4,4'-diphenylmethane diisocyanate [Dow Chemical Co.: PI 2080 (Tg = 310°C)]
(5) Condensation product ofBTDA and 3,3'-diaminobenzophenone (DABP) [Mitsui Toatsu, Inc.: LaRC TPI(Tg =267 °C)]
Figure 8 Structures of aromatic polybenzimidazoles and polyimides: the chemical name, source, common name and T g are given for each- structure
1734 cm - 1. In the blends a second carbonyl stretching band at 1708 cm - 1 appears, whose amplitude increases at the expense of the 1734 cm - 1 band as the content of PVH increases. On the basis of results to date, it is not possible to distinguish between 1[-1[ interactions or chargetranfer interactions as being the source of miscibility. Although not discussed in detail here, similar results have been obtained for PBI/2080 and PBI/Ultem blends.
4.4.2 The 'Copolymer Effect' In random copolymers, blended either with a homopolymer or a second random copolymer, a. mechanism other than specific interactions can lead to miscibility. This may occur if the mutual PS 7-E*
122
Generic Polymer Systems and Applications 3420
(a)
3400
3380 T
E 2~
.8
3360
f'f
,,1
,
t-t-~-+--r . t/
1"
E ::J
J
1728
(b)
r-t-2'--cr- ~_ .
~"
1724
1720
'1',
1"--Q.._~
Figure 9 Peak maxima as a function of blend composition for: (a) the N-H stretching band of PBI; (b) the principal phthalimide carbonyl stretching band of XU 218
repulsion between the dissimilar segments in the copolymer is sufficient to overcome the repulsion between these segments and those in the second component of the mixture. In thermodynamic terms, this can lead to the negative net interaction energy necessary to create miscibility. Such effects have been recognized on an empirical basis for some time. An example is the wellknown miscibility of poly(vinyl chloride) with random copolymers of ethylene and vinyl acetate for certain composition ranges of the latter system. 51 These and similar findings have recently been explained using a mean-field theory for miscibility in copolymer blends. 52 This theory has permitted substantial insight into the effect of chemical structure and composition, of temperature and of molecular weight on phase behavior in such systems. The theory is a development of the mean-field approaches discussed in Section 4.2.3 and can be most easily expressed by writing the X parameter, Xblend' in a blend containing copolymers, as a linear combination of individual binary interaction parameters of the form Xblend = L Cii Xii
(14)
i,i
where Xij corresponds to each possible segmental interaction in a given system. The coefficients cij are functions of the copolymer composition(s) with O
Xblend =X lAB + (l-x)XAc- x (l-x)XAB
For the general case of two random copolymers (Ax B1 corresponding to a different segmental interaction
x )..
and (Cy D 1 -
y ).."
there are six Xij' each
Xblend =xYXAc+(I-x)YXBc+ x(l- Y)xAo+(I-x)(I- Y) XBo-x(l-x) XAB- y(l- y) Xco
(16)
This first-order treatment neglects many of the corrections discussed in Section 4.2.3. These can be introduced in principle at the expense of additional complications. For example, the temperature, composition and concentration dependences of individual Xij values could be introduced at the outset using the methods described in Section 4.2~3. The present treatment has been found sufficient,
123
Polymer Blends
however, to account in a self-consistent manner for most of the phenomena experimentally observed. These include the existence of 'windows of miscibility' in homopolymer/copolymer blends and the sensitivity of many blend phenomena to small changes in chemical composition, temperature and molecular weight. 53 (Windows of miscibility are seen when miscibility behavior occurs for homopolymer/copolymer blend as a function of temperature and copolymer composition; these have been designated 'T-c plots', see Figure 10). Furthermore, in a recent test the theory was found to have predictive value. Thus values of Xij obtained from data for miscibility in poly[oxy(2,6-dimethyl1,4~phenylene)] (PPO) and poly(halostyrene) binary combinations were used to predict behavior in the polystyrene (PS)/poly(o-chlorostyrene-co.. p-chlorostyrene) systems with reasonable success. 54
280
T 240
Two phases
200
o
Flgure 10 Miscibility window for PPO/poly(o-chlorostyrene-co-p-chlorostyrene) blends
The determination of Xij values from the present theory requires the experimental observation of miscibility-immiscibility boundaries as a function of copolymer composition. The number of such boundaries at a given temperature must be equivalent to, or greater than, the number of independent Xij values which are to be determined. 55 This can be achieved, in principle, by permuting the copolymer compositions until the required number of boundaries is obtained. For example, a system An/(BxC1-x)n' may yield from zero to two boundaries at a given temperature, which can be combined with those from the system Bn,,/(AxC1-x)n'" and/or those from the third homopolymer/copolymer permutation to determine independently the desired Xij values. The same mean-field treatment may also be used to account for miscibility in blends of other copolymeric combinations of the given segments. For example, in blends of the type An/(AxB1-x)n' miscibility behavior is a function of the single interaction parameter, XAB' and by determining the miscibility-immiscibility boundary here for finite n, n' (see below) this parameter can be determined. An alternative approach would be to determine behavior in the copolymer~opolymer blend (AxBl-x)n/(AyBl-y)n" which iTS also a function of XAB alone. This simple strategy is predicated, of course, on the validity of the composition-independent Xij assumption. However, this could be investigated and, if necessary, taken into account by measuring miscibility for different ranges of x and y.
4.4.2.1
An/(BxC1-x)n'
The most extensively studied blends in terms of the mean-field theory are those consisting of a homopolymer and a copolymer. As already described, this involves three independent interaction parameters, which can be evaluated from appropriate miscibility boundary data. Blends of the homopolymer, PPO~ with copolymers containing a combination of styrene and halostyrene monomers have been studied in this context. 52 Miscibility windows are observed, since all Xij>O, and, in particular, XBC is sufficiently large to render Xblend <0 for certain ranges of x. For copolymers containing styrene homopolymer, a single boundary in the T-e plot is observed, consistent with the fact that PPO and PS are themselves miscible. More recently, mixtures of polystyrene with copolymers of 0- and p-chlorostyrenes have been studied. 54 These data have permitted a refinement of the Xij values for this system and the calculation of a self-consistent set of values for a wider range
124
Generic Polymer Systems and Applications
Two
phases
Copolymer composition
c
Figure 11 Predicted miscibility boundary for an A,.I(Bx C t - x )II' blend (XAB <0, and the two other X values are positive) displaying both upper and lower critical solution temperatures; the boundary is the locus of VCSTs and LCSTs for positive and negative slope temperature regimes, respectively
of Xij. All the systems studied to date have displayed LCST behavior; however, UCST behavior may also be found. The predicted T-c behavior for this case is shown in Figure 11. The extremum in this plot corresponds to the case in which the two consolute points just merge. Systems containing PS and copolymers of 0- and p-styrene exhibit extreme sensitivity to the degree of polymerization of either or both components. This is partly a result of the very low positive value of the Xparameter representing styrene and o-chlorostyrene interactions. A recent extension of these investigations to lower molecular weight systems has shown that the temperature maxima of the miscibility windows increase substantially as the degree of polymerization is' lowered; these maxima can readily be selected to cover the entire accessible experimental temperature range.56 The resulting data have permitted a calculation of the temperature dependence of the respective Xij values with some accuracy. 56
4.4.2.2
(AxB1-x)n/(AyB1-y)n'
Blends of random copolymers containing identical segments but different overall compositions are predicted to be immiscible when the respective polymers are of infinite molecular weight. The limiting miscibility condition, Ix - yl =0, is relaxed, however, for n, n' < 00. This behavior has been verified for chlorinated polyethylenes (which may conveniently be treated as random copolymers of -CH 2- and -CHCI.,... segments) in recent studies. 57 It may be noted that an extensive series ofUCST values has been observed for chlorinated polyethylene blends whose T g values are sufficiently low. 58
4.4.2.3
(AxB1-x)n/ (CyD1-y)n'
The first systematic study of random copolymer mixtures with four distinct repeat units of the type (AxBI_x)..!(CyDI_y)..,59,60 has recently been completed. The results are summarized in Figure 12, which shows miscibility maps for four different cases. The shaded areas represent experimental results obtained primarily from differential scanning calorimetry (DSC) measurements, while the solid lines represent theoretical fits to the data using the values of the Xparameter given in the figure. Each case is discussed individually below. (i) Figure 12 (a): Poly (styrene-eo-acrylonitrile) /poly[oxy (2 ,6-dimethyl-1,4-phenylene) -co-oxy(2,6-dimethyl-3-phenylsulJonyl-1 ,4-phenylene) (P( S-AN) /SPPO) The SPPOs were -synthesized in our laboratories 6o and the P(S-AN)s were obtained commercially. XAB was taken from the published data of Molau,61 XAC was taken as an average value from ·several sources, XAD was determined from approximate phase boundaries observed in the system polystyrene/SPPO and XCD was determined from approximate phase boundaries observed in blends of sulfonylated PPOs of different compositions. The resulting fit represented by the solid lines
Polymer Blends
125
(0 )
( b)
P(S-AN) ~
SPPO
~
1
I
0
0
I-x
XAe = 0.700
XAC =-0.043
X ec = 0.745
XeD
: 0.097
X AD = 0.200 XCD
XAe = 0.080 X ac = 0.053
: 0.150
I-x XAC : -0.043
X AD = 0.200
XeD = 0.022
XCD
X crit • blend
X~~~~ = 0.003
: 0.150
0.004
(d)
(e)
P(S-o-FS) SPPO
P(S-MA) SPPO
~
1
~
1
0
X Ae = 0.40 X ec = 0.004
0
I-x
1-
X
X AC =-0.043
XAD : 0.200
XAe = 0.150
XAC =-0.043
X AD : 0.200
Xeo = 0.113
X CD = 0.150
X ec : 0.290
XeD: 0:020
X cD =O.I50
X crit : blend
0.004-
X~=0.004
Figure 12 Miscibility maps for several (AxBt-x)n/(C,Dt-,)n' copolymer~opolymerblends. The shaded areas represent experimental regions of miscibility and the solid lines are theoretical fits using Xi) values stated in the figure. The studies from which the Xij were obtained were performed at 290°C
+-0+Me
Me
(7) B
(8) C
Me (9) D
in the figure was obtained by adjusting the two parameters XBC and XBD to give the best representation of the data. It is apparently not possible to achieve quantitative agreement with the experimental results using the approach outlined above. This may be due to factors such as .the concentration dependence of the X values, the effect of the molecular weight distribution, and the fact that the observed phase boundaries from which the X values are derived do not represent true critical points. From the discussion in the earlier sections, the composition dependence of the spinodal boundary must be known in detail in order to deduce thermodynamically correct values for the binary interaction parameters. Considering the approximation and uncertainties involved, the predictions from the simple meanfield approach for the composition diagram of P(S-AN)jSPPO are remarkably good. PPO is
126
Generic Polymer Systems and Applications
miscible with P(S-AN) copolymers at 290°C, at the molecular weights used, up to an acrylonitrile content in the copolymers of about 25 mol%. The diagram also shows a 'window of miscibility' for the homopolymer of SPPO with P(S-AN) copolymers. (ii) Figure 12 (b): poly (styrene-co-p-fluorostyrene) / SPPO
A is a styrene repeat unit, B is the styrene repeat unit substituted in the para position on the ring with fluorine, and C and D are units of the sulfonylated PPO copolymers, as for Figure 12(a). XAB was obtained from the approximate phase boundaries in the appropriate systems. XAC,XAD and XCD assume the values used for Figure 12(a) and XBC and XBD aretreated as adjustable parameters in the equation used to calculate the curves shown in Figure 12(b). Here the agreement between theory and .experiment is indeed remarkable, especially since the same remarks concerning the approximate, not to say crude, nature of the approach apply as for Figure 12(a). A 'window of miscibility' is predicted and observed for poly(p-fluorostyrene) and the SPPO copolymer. (iii) Figure 12( c): poly (styrene-co-o-fluorostyrene) / SPPO
The position of the fluorine substituent on the benzene ring has a profound effect on the miscibility behavior, as shown in Figures 12(b) and 12(c). The various X parameters listed on the figure were obtained in the same manner as before. However, XBC was taken to be equal to Xcr for the blend, since experiments with blends of poly(o-fluorostyrene) and PPO revealed the existence of a single composition-dependent T g • XAB and XBD were taken as adjustable parameters to obtain the best fit to the data. (iv) Figure 12(d): poly(styrene-co-methyl acrylate)/SPPO (P(S-MA)/SPPO)
Here, as for Figure 12(c), no miscibility windows exist, and the domain of miscibility is severely restricted. XAC' XAD and XCD assume the same values as in the other cases. XAB was obtained from the phase boundaries observed in P(SxMA1-x)/P(SyMA1-y) blends. XBC and lBD are treated as adjustable parameters. In summary, the first experimental results for blends of the type AxBl-x/CyDl-y show remarkable agreement with the simple mean-field approach. Formally, six Xij are required to describe these systems. The blends described above share the same XAC' XAD and XCD and, in each case, one of the other parameters was determined independently. Fits to the isothermal miscibility curves were then made using the remaining two Xij as adjustable parameters. The theory described above explains a range of phenomena for blends containing random copolymers. The derived interaction parameters have been shown to be of predictive value in several cases. The experimental determination of miscibility boundaries for copolymer/copolymer sys.tems provides further verification of the treatm.ent. An important aspect of the work described here is the possibility for a rational design of copolymers to yield miscible systems. For example, miscibility that occurs in the AB/AC system may be viewed as a miscibilization of homopolymers of Band C by the respective copolymerization with the common segment, A. Special requirements, such as the conditions for minimizing the total consumption of A, for example, may be readily evaluated. Extensions of the theory to take into account the composition and concentration dependences of the interaction parameters are formally possible. In addition, studying the effect of chain microstructure, where the requirement of random monomer placement in the copolymer is relaxed, is feasible and will be described in the next section.
4.4.2.4
Sequence distribution effects
In this section is described a formalism 62 that allows extension of the mean-field theory to any copolymer chain microstructure (i.e. random, block, alternating, etc.). It is necessary, however, to stipulate that the copolymer in question does not undergo microphase separation. Thus, in the case of block copolymers in particular, applicability is limited to fairly short blocks and/or blocks with very small positive or negative binary interaction parameters between the components.
127
Polymer Blends
In order to proceed further, it is necessary to introduce an order parameter () that describes the binary sequence distribution of the monomers in a copolymer chain. By varying (), block, random or alternating copolymers can be described. It is then possible to discuss the various cases already treated for the random copolymer sequence distribution in Sections 4.4.2.1-4.4.2.3 above. Here will be elaborated the An/(BxCt-x)n' and the (AxBt-x)n/(AyBt-y)n' systems. (i) A n/ (BxCt-x)n'
For the random copolymer case, Xblend is given by equation (15) for the system An/(BxCt-x)n'. In order to proceed further, the assumption is made that the interaction energy for the A-B pair is influenced by the units that are chemically bonded to B. This idea is reasonable if the Xij parameters are related to the product of the electronic polarizability (a) for each unit i and j.63 Since it is well known that a of an atom in a molecule is influenced by the neighbors to which it is chemically bonded (e.g. electron-withdrawing or -donating groups), it seems reasonable to expect that XAB will depend on the local sequence distribution. In order to consider all the possible homopolymer-eopolymer interactions, or A-B and A-C interactions, all the possible triplets with B or C occupying the central site must be enumerated. Next the probability of occurrence for each specific triplet is calculated. Then an energy value is assigned to each A-triplet interaction. Table 2 illustrates this procedure for A-B interactions. In the first column is the energy assigned to the configuration found in the second column, whose probability of occurrence is given in the third column. A similar scheme can be constructed for the A-e interactions.
Table 2 Interactions of an A Unit with a B-centered Triplet in the Blend System AII /(B x C t - x )II' with Volume Fractions
Configuration
Probability of occurrence
C XCBC,A
B+-A C
C XCBB,A
B+-A B
2XCB X BB ) ( - - 2XB
B XBBC,A
B+-A C
(
(2XCBXBB) - -
2X CB X BB ) (2XCBXBB) - - 2
B XBBB,A
B+-A B
In column 1, the interaction energies have been identified with the Flory interaction parameter, X. The probabilities in column 3 are expressed in terms of XB and Xc, the fraction of Band C molecules, respectively, in a single copolymer chain. Furthermore, XBC, XCC' and XBB are the pair probabilities of BC, CC and BB pairs in a single chain. Finally, the cPi values are the volume fractions of the various species. The variables listed above are all linearly related to each other. 63 In addition, probabilities for the occurrence of any given triplet can be expressed in terms of the appropriate pair probabilities. These triplet probabilities can be estimated for various distributions by appropriate techniques. In order to reduce the large number of X parameters required to describe the energetics in the An/(BxCt-x)n' system, the following simplifications are introduced. All B-B and C-e interactions are equivalent and equal zero; all B-C interactions are equivalent with the value lBC == lAB == XCBC, A
Generic Polymer Systems and Applications
128
= XBBC, A = XCBB, A = XBBB,A;
lCA
== XBCB, A = XBCC, A == XCCB, A = XCCC, A' We may then write for Xblend = Xcomp + Xdist
X
blend (17)
Xcomp = XBIBA + XC ICA -
xBX C lAB
(18)
Xdist = (XiB/XB)L1XB +(X~c/Xc) L1Xc
(19)
L1XB == XBBB, A- IBA
(20)
L1 Xc == XCCC, A- ICA
(21)
It is clear that Xcomp is equivalent to Xblend given by equation (15), and that the term Xdist represents a zero-order correction taking into account sequence distribution effects. A negative ~XB implies that BBB-A interactions are more favorable than any other B-A interaction and, conversely, a positive !!J.XB implies that BBB-A interactions are less favorable than all other B-A interactions. It has already been stated that an order parameter, 8, must be introduced to describe the sequence distribution of Band C monomers in the copolymer chain. 8 is defined by (22)
XAB=20XAXB
From equation (22) it can be seen that a .random copolymer corre$ponds to 8=t, a block copolymer to 8 approaching 0, and an alternating copolymer to 8 = 1. Introducing 8 into equation (19) results in (23)
With the aid of equation (23), the dependence of Xdist on the sequence distribution can be evaluated. It can be shown 63 that if the absolute value of the ratio ~XB/~Xc is less than 1, there is always an extremum in Xdist for some value of 6, i.e. for a particular sequence distribution in the copolymer. This means that a window of miscibility or immiscibility can occur due to sequencedistribution effects alone. Of course, without knowing the values of ~XB and ~Xc it is impossible to predict what values of 8 will result in a maximum or minimum in Xdisl' I~XB/~Xcl > 1. Xdist is a monotonic function of 8; the smallest value of Xdist will occur either for the alternating or block copolymer. For Xc ~ X B , if XB~XB + xc~ Xc> 0, the alternating copolymer will have the smallest value of Xdist. Conversely if XB~XB+XC~XC
A special case of the An/(BxC 1- x )n' system is the An/(AxC1-x)n' blend, where -
2
(24)
Xcomp = XAC Xc
Proceeding as before, unique X parameters differing from (AAA-eCC) and (ACA-CAC). Then Xdist becomes
XAC
are assigned only to the triplet pairs
Now from equation (24), it can be seen that at infinite chain lengths and for positive values of lAC' the blend system An/(AxC1-x)n' is immiscible for any value of XC' The inclusion of Xdist (equation 25) may modify this conclusion for some value of 8 depending on the values of ~Xc and ~Xb. In fact, windows of miscibility and immiscibility are theoretically possible in this system, even for infinite chain lengths. (ii) (AxB1-x)n/ (AyB1-y)n'
In this case
Xcomp
is given by (26)
Xcomp = (x - y)2 lAB
Again, for infinite chain lengths this system is immiscible unless can be tolerated in the. copolymer. Proceeding as before we write
X
= y, i.e. no composition difference
Xdist= 16Axa (O;ylYB-o;xlxB) (O;YAyi-O;xAxi)-16L1x b (O;y:-O;xi)(O;xl-O;yl) b (L1 ~ = lAB - XBAB, ABA; L1 X = XAAA, BBB - lAB)
(27)
where Ox and Oy refer to the sequence distribution parameters in the two copolymers AxB 1- x and A;B 1- y , respectively.
Polymer Blends
129
The consideration of sequence distribution effects once again modifies the conclusions about miscibility in copolymer blends differing only in composition. For example, it can be shown 64 that for a 50: 50 blend of an alternating copolymer (8= l).with a 50:50 random copolymer, even though Xcomp is zero, Xdist may be positive and thus it is possible for alternating and random copolymers with the same composition to be immiscible. An experimental confirmation of .this prediction is afforded by the system poly(vinyl chloride)jchlorinated polyethylene. (PVCjCPE). In this context, CPE may be considered as a random copolymer of -CH 2- and -CHCI- units, while PVC may be considered as an alternating copolymer composed of the same units. The PVC/CPE ·blend system is indeed immiscible at the same composition. 65 A second consequence of interest is the dependence of the composition difference Ix - y I at which phase separation will take place, on the copolymer composition itself. Ignoring sequence distribution effects, Ix - y I is independent of composition and has the value (28)
~ I
0.5
~
o
1.0
1 . 0 . . . . - - - - - - - - - - . . - - - - - - -...
~
0:5....-_ _- -
o
1.0
The dependence of (a) the maximum tolerable composition difference IXA -- YAI and (b) the corresponding values on X A for a 1: 1 mixture (cPt =4>2 =0.5) of random copolymers (8=0.5) with equal degree of polymerization and XAB= -0.3, AX&=0.5 and AX b =0.7 .
Figure 13 YA
However, if appropriate values of the parameters in equation (27) are chosen, this conclusion is no longer valid, even· for mixtures of two statistical copolymers. An example, (8x =8,=t), is given in . Figure (13). Once again, such behavior has been observed experimentally.66
4.5 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
;Po J. Flory, J. Chern. Phys., 1941, 9, 660; J. Chern. Phys., 1942, 10, 51. M. L. Huggins, J. Chern. Phys., 1941, 9, 440; Ann. N. Y. Acad. Sci., 1942, 43, 1. R. L. Scott, J. Chern. Phys., 1949, 17, 279. H. Tompa, Trans. Faraday Soc., 1949,45, 1142.. . M. Gordon, H. A. G. Chermin.and R.Koningsveld, Macromolecules, 1969,2, 207. R. Koningsveld, H. A. G. Cherminand M. Gordon, .Proc.R. Soc. London, Sere A, 1970,319, 331. R. Koningsveld, L. A. Kleintjens and H. M. Schoffeleers, Pure Appl. Chern., 1974,39,1. P. I. Freeman and J. S. Rowlinson, Polymer, 1960, 1, 20. P. J. Flory, R. A. Orwoll and A. Vrij, J. Am. Chern. Soc., 1964, 86, 3515. P. 1. Flory, J. Arn. Chern. Soc., 1965, 87, 1833.
130 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Generic Polymer Systems and Applications
B. E. Eichinger and P. J. Flory, Trans. Faraday Soc., 1968,64, 2035. P. J. Flory, Discuss. Faraday Soc., 1970, 49, 7. I. Prigogine, 'The Molecular Theory of Solutions', North-Holland, Amsterdam, 1957, chap. XVI. D. Patterson, J. Polym. Sci., Part C, 1968, 16, 3379. D. Patterson,Macromolecules, 1969, 2, 672. D. Patterson and G. Delmas, Discuss. Faraday Soc., 1970,49, 98. J. Biros, L. Zeman and D. Patterson, Macromolecules, 1971,4, 30. L. P. MacMaster, Macromolecules, 1973,6,760. R. H. Lacombe and I. C. Sanchez, J. Phys. Chem., 1976, 80, 2568. J. A. Schouten, C. A. ten Seldan and N. J. Trappeniers, Physica, 1974, 73, 556. G. Kanig, Kolloid-Z. Z. Polym., 1963, 190, 1. L. A. Kleintjens, Fluid Phase Equilib., 1983, 10, 183. A. M. Lablans-Vinck, R. Koningsveld, L. A. Kleintjens and G. A. M. Diepen, Fluid Phase Equilib., 1985, 20, 347. R. Koningsveld, L. A. Kleintjens, and A. M. Lablans-Vinck, Ber. Bunsenges Phys. Chem., 1985,89, 1234. L. A. Kleintjens and P. G. Lemstra (eds.), 'Integration of Fundamental Polymer Science and Technology', Elsevier, New York, 1986. 26. A. J. Staverman, Reel. Trav. Chim. Pays-Bas, 1937, 56, 885. 27. L. A. Kleintjens and P. G. Lemstra (eds.), 'Integration of Fundamental Polymer Science and Technology', Elsevier, New York, 1986, p. 56. 28. P. J. Flory, 'Principles of Polymer Chemistry', Cornell University Press, Ithaca, NY, 1953, chap. III. 29. J. S. Higgins, private communications. 30. C. L. Ryan, Ph. D. Thesis, University of Massachusetts, 1980. 31. B. J. Schmitt, R. G. Kirste and R. G. Jelenec, Makromol. Chem., 1980, 181, 1655. 32. Y. Inoue, 'Abstracts of International Seminar on Elastomers', Pegasus House, Itoh, Japan, 1983, p. 154. 33. F. E. Karasz, W. J. MacKnight, H. Huang and C. Cong, Macromolecules, 1986,19, 2765. 34. M. T. Shaw, Polym. Eng. Sci., 1984, 25, 373. 35. J. W. Cahn and J. E. Hilliard, J. Chem. Phys., 1958, 28, 258. 36. J. W. Cahn, Acta. Metall., 1961,9, 795. 37. J. W. Cahn, J. Chem. Phys., 1968, 42, 93. 38. K. Binder, ColioidPolym. Sci., in press. 39. J. J. van Artsen and C. P. Smolders, Eur. Polym. J., 1970, 6, 1105. 40. R. G. Kirste and B. R. Lehnen, Makromol. Chem., 1976, 174, 1139. 41. L. P. McMaster, Adv. Chem. Ser., 1975, 142, 43. 42. D. Turnbull, Solid State Phys., 1956, 3, 226. 43. T. K. Kwei and T. T. Wang, in 'Polymer Blends', ed. D. R. Paul and S. Newman, Academic Press, New York, 1978, vol. I, chap. IV. 44. C. C. Han, M. Okada, Y. Muroga, B. J. Bauer and Q. Tran Cong, Polym. Eng. Sci., 1986, 26, 1208. 45. M. Warner, J. S. Higgins and A. J. Carter, Macromolecules, 1983, 16, 1931. 46. B. J. Schmitt, R. G. Kirste and J. Jelenic, Makromol.Chem., 1980, 181, 1655. 47. H. S. Yang and R. S. Stein, Macromolecules, 1986,28,7632. 48. O. Olabisi, L. M. Robeson and M. T. Shaw, 'Polymer-Polymer Miscibility', Academic Press, New York, 1979. 49. L. Leung, D. J. Williams, F. E. Karasz and W. J. MacKnight, Polym. Bull. (Berlin), 1986, 16, 457. 50. M. M. Coleman and P. Painter, Appl. Spectrosc., 1984, 20, 255. 51. C. F. Hammer, Macromolecules, 1971,4,69. 52. G. ten Bt'inke, F. E. Karasz and W. J. MacKnight, M~.cromolecules, 1983,16,1827. 53. P. Alexandrovich, F. E. Karasz and W. J. MacKnight, Polymer, 1977, 17, 1023. 54. G. ten Brinke, E. Rubinstein, F. E. Karasz, W. J.. MacKnight and R. Vukovic, J. Appl. Phys., 1984, 56, 2440. 55. F. E. Karasz and W. J. MacKnight, Polym. Mater. Sci. Eng. Prepr., 1984, SI, 280. 56. S. Cimmino, F. E. Karasz and W. J. MacKnight, Macromolecules, in press. 57. Z. Chai and R. Sun, Polymer, 1983, 24, 1279. 58. H. Ueda and F. E. Karasz, Macromolecules, 1985, 18, 2719. 59. H. S. Kang, F. E. Karasz and W. J. MacKnight, Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem., 1986, 27(2), 65. 60. H. S. Kang, F. E. Karasz and W. J. MacKnight, Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem., 1987, 28(2), 134. 61. G. E. Molau, J. Polym. Sci., Polym. Lett. Ed., 1965, 3, 1007. 62. A. C. Balazs, I. C. Sanchez, I. R. Epstein, F. E. Karasz and W. J. MacKnight, Macromolecules, 1985,18,2188. 63. P. G. de Gennes, 'Scaling Concepts in Polymer Physics', Cornell University Press, Ithaca, NY, 1979, p. 72. 64. P. C. Balazs, F. E. Karasz, W. J. MacKnight, H. Ueda and I. C. Sanchez, Macromolecules, 1985, 18, 2784. 65. H. Ueda and F. E. Karasz, in press. . 66. F. Kollinsky and G. Markert, Makromol. Chem., 1969,121,117.
Polymer Blends WILLIAM J. MacKNIGHT and FRANK E. KARASZ University of Massachusetts, Amherst, MA, USA 4.1
INTRODUCTION
111
4.2 THERMODYNAMICS 4.2.1 Flory-Huggins 4.2.2 Equation of State 4.2.3 Lattice Fluid and Other Developments of the Flory-Huggins Approach
111 111 113 113
4.3 PHASE BEHAVIOR IN POLYMER BLENDS 4.3.1 Phase Diagrams and the Temperature Dependence ofx 4.3.2 Spinodal vs. Nucleation and Growth Decomposition Mechanisms 4.3.2.1 Spinodal decomposition 4~3.2.2 Nucleation and growth
114 114 116 116 119
4.4 FACTORS CONTROLLING MISCIBILITY IN POLYMER BLENDS 4.4.1 Specific Interactions 4.4.2 The 'Copolymer Effect' 4.4..2.1 An/( BxC 1 - x)n' 4.4.2.2 (A xB1 - x)n/(Ay B1 - y )n' 4.4.2.3 (AxBl-x)n/(CyDl-y)n' 4.4.2.4 Sequence distribution effects
119 119 121 123 124 124 126
4.5
129
REFERENCES
4.1
INTRODUCTION
The scientific understanding of the principles governing polymer miscibility or compatibility has lagged behind the technological development of the field. It may be stated that essentially all polymeric materials that are items of commerce are blends. Examples range from poly(vinyl chloride), which contains a 'polymeric plasticizer' such as poly(ethylene-co-vinyl acetate), to 'Noryl', an engineering thermoplastic based on the miscible blend of polystyrene and poly[oxy-(2,6dimethyl-1,4-phenylene)]. It is normally assumed that relatively few new polymers will attain commercial success in the coming decades, and the need for new higher performance engineering thermoplastics, composite matrix materials and elastomers will largely be met by blending known polymers in ways that will produce the desired properties. In this chapter the fundamental principles of the present understanding of the science of blending will be presented. Areas in which advances need to be made will be pointed out. Relatively little emphasis will be placed on technological or preparative aspects of blending.
4.2 THERMODYNAMICS 4.2.1
Flory-Huggins
We define a miscible polymer blend as one which satisfies the thermodynamic criteria for a singlephase system. For example, if the blend consists of two components, A and B, then, at constant 111
112
Generic Polymer Systems and Applications
temperature and pressure, a single-phase mixture will be formed if (1)
where ~Gm is the Gibbs free energy of mixing and
where
It should be mentioned that if the repeat units of the polymers to be mixed are of comparable size, as is often the case, their volumes can each be taken to be equal to Vr • Equation (3) is often quoted in this form in the literature, and we shall assume it to be valid in what follows, for the sake of simplicity. For the monodisperse case, the critical conditions for miscibility are (from equation 2) (4)
and (5)
It immediately follows from equations (4) and (5) that, for polymers with appreciable degrees of polymerization, the binary interaction parameter lAB must be very small for miscibility to occur, and, for infinite degrees of polymerization, it must be zero or negative. The spinodal conditions for such a system are readily obtained from the expression (6)
and turn out to be (7)
It must be remembered that equations (4H7) are valid only for binary mixtures of monodisperse polymers having repeat units of equal size. In addition, the binary interaction parameter must be independent of concentration. The restriction to monodisperse polymers is easily removed, as shown by Koningsveld and coworkers. 5 - 7 The expression for the spinodal conditions is especially simple and has the form (8)
where XWA and XWB are the weight-average number of lattice sites occupied by A and B, respectively.
Polymer Blends
113
The critical composition is (9)
where XZA and X ZB are the z-average number of lattice sites occupied by A and B, respectively. Thus, if the appropriate moments of the distribution of chain lengths are known (identifying these with the number of lattice sites occupied by the two species), the effect of polydispersity on the thermodynamics of mixing is relatively easy to treat. It should be noted that the molecular weight distribution has a profound effect on both the location of the critical point and the composition dependence of the binodal and spinodal boundaries. The development of the mean-field lattice theory presented here differs from the original formulation of Scott only in that the binary interaction parameter is not identified with the enthalpy of mixing via the Vanlaar-Scatchard expression. For the further elaboration of the thermodynamics of polymer mixtures, it is more appropriate to consider the binary interaction parameter from the outset to be a free energy parameter in its own right. That is, lAB contains both enthalpic and noncombinatorial entropic contributions. Thus both the temperature and composition dependence can be introduced into lAB in a natural fashion (Section 4.2.3).
4.2.2
Equation of State
The original mean-field lattice theory, with lAB interpreted as an enthalpic parameter, is capable of predicting the existence of either a lower (LCST; AWAB
(10)
The term B(T) is always positive and has an exponential dependence on temperature. The exchange or enthalpic part of the interaction parameter, X AD' is usually positive for hydrocarbon homopolymer pairs. It can be seen from equation (10) that, in the event that X AB is negative, phase decomposition can occur only'via an LCST. If, on the other hand, X AD is positive but very small, or if the components of the mixture are of moderate molar mass, then both a VCST and an LCST may occur. Both types of behavior are rare. The former case, which usually involves specific interactions between A and B segments, is by far the more common. Table 1 lists some miscible homopolymer blends which have specific interactions (X AD negative). Naturally, LG,STs for such systems may not be experimentally observable, since they may lie above the decomposition temperatures of the polymers.
4.2.3 Lattice Fluid and Other Developments of the Flory-Huggins Approach The original Flory-Huggins formulation did not allow for volume changes upon mixing, since all the lattice sites were occupied. It is possible to modify such a mean-field approach to allow the lattice to be 'compressible'. This was done by Sanchez and Lacombe 19 and was further elaborated by other workers. 20 - 23 For the case of high molar mass polymer blends, the most important result of the lattice-fluid treatment lies in the temperature and composition dependence of the binary interaction parameter. (As with the equation-of-state theory, the lattice-fluid theory is cast in terms of the single parameter, lAB' for a binary mixture. All other parameters are known from the pure components.) PS/-E
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Generic Polymer Systems and Applications
Following Koningsveld and co-workers,24-25
lAB
may be expressed as
XAB = X o +Xt/T+ X 2 T+ X 3 1n T
(11)
where the various coefficients Xi may depend on concentration. The concentration dependence of lAB can be understood in terms of an approach suggested by Staverman 26 which leads to expressing lAB in terms of the ratios of the surface areas of the two interacting segments. In other words, the concentration dependence of lAB arises from the difference in size and shape betwe\,;n segments A and B. For many purposes, lAB can be approximated as 27 XAB=X~+X;/T+
YcPB
(12)
X ~ can be taken to refer to the entropic portion of the interaction free energy while X; refers to the enthalpic portion. Y is related to the ratio of the surface areas of the segments A and B, and must be zero for segments of the same size. It should be noted that the first two terms in equations (11) and (12) are sufficient to account for phase behavior of either the LCST-type (Xl or X; negative) or of the VCST-type (Xl or X; positive). The terms involving X 2 and X 3 allow both VCST-- and LCST-type phase decomposition to occur in the same system. Thus both the equation-of-state and the lattice-fluid theories predict a range of phase decomposition behavior in polymer blends far beyond the scope of the original Flory-Huggins formulations. The concentration dependence of lAB introduced by the difference in surface areas between the segments is often not sufficient to account for some of the complex shapes encountered in actual phase diagrams. In order to deal with this situation it is necessary to introduce the 'compressible'lattice model explicitly, which is capable of reproducing the observed phase diagrams, albeit at the expense of introducing a number of additional parameters. 25
4.3 PHASE BEHAVIOR IN POLYMER BLENDS 4.3.1
Phase Diagrams and the Temperature Dependence of l
Figure 1 presents schematic representations of various types of phase diagrams for polymer mixtures. Again, for the sake of clarity, the discussion will be restricted to monodisperse binary mixtures. Figure l(a), showing VCST behavior, is familiar from· polymer solution thermodynamics, where the critical point at infinite molar mass represents the well-known Flory (J conditions. 28 Such a phase diagram may also be expected for blends of oligomers where the enthalpic part of lAB is positive. There are a number of examples in the literature. 7,29 Such a phase diagram is very rare for high molar mass homopolymer blends, although, as will be discussed subsequently, it is not at all unusual for copolymer blends. Figure 1(b), showing LCST behavior, is the 'normal' phase diagram for high molar mass homopolymer blends where specific interactions are present (enthalpic part of lAB negative). A number of examples are cited in Table 1. Figure l(c) shows a phase diagram exhibiting a VCST and an LCST above it. This behavior is common in polymer solutions, where the LeST is usually above the boiling point of the solvent, and is predicted by the equation-of-state theory to be possible for homopolymer blends, if the enthalpic part of lAB is positive but very small (~10- 3 ). There appear to be no confirmed examples of this behavior in the literature, although it has been suggested that polystyrene and poly(2-chlorostyrene) blends might be in this category.30 There are experimental difficulties in determining such phase diagrams since the VCST may be below the glass transition temperature (Tg ) and the LCST may lie above the decomposition temperature. Once again, if copolymer blends are considered, a number of examples of· phase diagrams of the type shown in Figure l(c) have been reported. 31 - 33 It is also possible for the VeST to merge with the LCST, producing an 'hour glass' type of phase diagram, as shown in Figure l(d), or the VCST can lie above the LCST, producing a 'closed loop' phase diagram, as shown in Figure l(e). The 'hour glass' phase diagram (Figure'ld) has no temperature region for which a single phase exists over the entire composition range. This most probably represents the phase behavior of compatible blends, and, in the extreme case where the miscibility-composition limit is very small, of incompatible blends as well. There are also considerable experimental difficulties in determining phase diagrams of this type and very little quantitative information is available. Shaw 34 has developed an ingenious method based on light scattering for determining miscibility limits of components of incompatible blends.
Polymer Blends (0)
(e)
115 (b)
(d)
(e)
Figure 1 Schematic phase diagrams for polymer-polymer blends; - binodallines, --- spinodal lines: (a) a phase diagram of the UeST type; (b) a phase diagram of the LCST type; (c) a phase diagram in which both a UCST and an LCST occur; (d) an 'hourglass' phase diagram; and (e) a phase diagram in which the UCST occurs above the LCST Table 1
Miscible Homopolymer Pairs with Specific Interactions
Homopolymer pair Poly(ethylene oxide) Poly(vinyl chloride) Poly(vinylchloride) Polystyrene Polystyrene Poly(ethylene oxide) Poly(vinylidene fluoride) Polybenzimidazole Poly(ethylene oxide) Poly(vinyl chloride) Bisphenol A polycarbonate Poly(vinylidene fluoride) Poly(vinyl chloride) Polystyrene Poly(vinylidene fluoride) Poly(vinylidene fluoride)
LeST observed Poly(acrylic acid) Poly(methyl methacrylate) Poly(8-caprolactone) Poly(vinyl methyl ether) Poly[oxy(2,6-dimethyl-l,4-phenylene)] Poly(methyl methacrylate) Poly(methyl methacrylate) Polyimide Poly(ether sulfone) PolY(IX-methyl-cx-n-propyl-fJ-propiolactone) PolY(8-caprolactone) Poly(vinyl methyl ketone) Poly(butylene terephthalate) Tetramethylbisphenol A polycarbonate Poly(ethyl methacrylate) Poly(ethyl acrylate)
Yes Yes Yes
No
Yes Yes Yes Yes
No
Yes Yes
No
Yes Yes
No
There appear to be no examples at present of the 'closed loop' type of phase diagram for polymer blends. At least in the case of homopolymers, the equation-of-state theory would predict that a UCST should always occur at or below an LCST. Such restrictions may not apply to copolymer blends. Severe experimental difficulties exist in the determination of phase diagrams for polymer blends. These include, in addition to the problems noted above, the effect of polydispersity and the difficulty in attaining an equilibrium state in such highly viscous liquids. When specific interactions are present, as is the case for most miscible homopolymer blends, the presence of a low molecular weight polar impurity, such as water,- may drastically alter the segmental interactions and lead to erroneous results. Therefore, there are few examples of 'thermodynamically accurate' phase diagrams in the literature for polymer blends. Most of those that exist have been obtained by scattering methods,
116
Generic Polymer Systems and Applications
usually involving either light scattering or neutron scattering. Fortunately, for many purposes, approximate phase diagrams are sufficient and these can often be obtained in much simpler ways.
4.3.2
Spinodal vs. Nucleation and Growth Decomposition Mechanisms
From the foregoing discussion one may expect to find cases in which polymer blends exhibit the type of phase diagram exemplified by Figure 2, which is a somewhat more detailed version of Figure 1(b). As already noted, there will be many blends which have LCSTs below the T g or above the chemical decomposition temperature. As will be described later, it is possible to adjust the critical temperature to a certain extent by controlling molecular weight, and, more importantly, copolymer composition in copolymer blends. Assuming a blend has been identified which obeys the phase diagram given in Figure 2, annealing experiments can be carried out at various temperatures above the LCST, that is within the miscibility gap or the region in which phase decomposition will take place. If such a process is allowed to proceed to an equilibrium state, two phases will result, with compositions corresponding to those dictated by the location of the binodal boundary at that particular temperature. However, if the phase separation process is interrupted before equilibrium can be achieved, quite different morphologies will result, depending on whether the phase separation occurs in the spinodal region or the binodal region indicated in Figure 2. (Phase separation can be stopped by quenching the blend below its T g .)
Decomposition or crosslinking ....~....l~'iH+I+ - -
T decomposition- - -
~no
window
T~-----------
ToA
--
11111111111111111111.~ Glass region
o (A)
I
Volume fraction of polymer B blended ( B) with polymer A
Figure 2 A schematic phase diagram for a polymer-polymer blend of the LeST type
4.3.2.1 Spinodal decomposition The phenomenon of spinodal decomposition, in which two phases exist with a type of interconnecting network morphology, has been recognized in the metallurgical field for some time. A quantitative description of the early stages of the process has been given by Cahn and Hilliard. 35 Before citing their results, it is perhaps worthwhile to examine the thermodynamic driving forces governing phase separation in the spinodal region. Figure 3 shows the composition dependence of the free energy of mixing at a temperature, T 1 , within the miscibility gap.The spinodal boundary is defined by the condition (0 2 11Gm /04>i)=0, as indicated in the figure and previously discussed. Within the composition range bounded by the spinodal boundary, the curvature of 11Gm , a2 11Gm / o4>i, is negative, and hence any small fluctuation in composition will cause a decrease in 11Gm and therefore tend towards phase separation. Cahn and Hilliard added to this thermodynamic picture by taking into account the fact that composition gradients at interfaces between phases also contribute to 11 Gm' Based on these
117
Polymer Blends
T---~J.LA.~J.LA
1
~GM
._._._._._.-i--:7-;_._. --
_
"
: . '+-. I
I
I
: I
............
I I I
I I
I I I
I
Binodal ~J.LA ·~J.LA ~J.LB .~J.L~
Spinodal
[ ~26GM lH#JjlH#Jj
]
=0
Figure 3 Composition dependence of ~Gm at a temperature within the miscibility gap (note:
Jli=a~Gm/a
principles, Cahn and Hilliard derived a diffusion equation, which, in its linearized form, reads (13)
where m = the mobility coefficient and K = the energy gradient coefficient. m(02 ~Gmjol/Ji) may be identified with the diffusion coefficient, D, since equation (13) would reduce to Fick's diffusion equation if this were the case and K =0. However, since (0 2 ~Gmjol/Ji) is negative within the spinodal region, D must also be negative. Therefore phase separation must occur by a diffusional flux against the concentration gradient in the spinodal region. This process is sometimes referred to as 'uphill' diffusion. The elaboration of the Cahn-Hilliard approach will not be presented here; the reader is referred to the literature for details. 36,37 Suffice it to say that the solution to equation (13) predicts that phase separation in the spinodal region will produce a morphology having a characteristic repeat distance or wavelength. The magnitude of the wavelength depends on the ratio of (0 2 ~Gmjal/Ji) to K. Equation (13) is applicable only to the early stages of decomposition, and attempts have been made to extend it to the later stages by including higher order terms. 38 This can only be done at the expense of introducing much greater complexity into the original formulation and adding a number of additional parameters. A number of studies hav~ been carried out applying the Cahn-Hilliard theory to spinodal decomposition in polymer blends. The experimental techniques employed are typically light or neutron scattering 39 ,40 or assessment of morphology by microscopic methods. 41 One of the most thoroughly studied systems is the PSjPVME blend. It has already been mentioned that a specific intermolecular interaction exists in this blend, and it has a phase diagram of the type depicted schematically in Figure 2. The actual phase diagram for a PSjPVME blend, where the PS has been deuterated, is given in Figure 4. Pioneering work on the kinetics of spinodal decomposition in -PSjPVME blends was carried out by Turnbu1l42 using microscopic methods and by Kwei et al. 43 using pulsed NMR. More recently the work of Han et al. 44 using neutron scattering may be cited as of particular significance. The use of any scattering technique for the determination of polymer structure depends on the introduction of sufficient scattering contrast between the components or phases present. In neutron scattering this is usually done by deuterating one of the components. In the case of PSjPVME, PS is usually the component deuterated; the deuterated PS is denoted by PSD. This has the effect of increasing the LCST by some 60°C (Figure 5). Such differences in the thermodynamics of deuterated species compared to protonated species are not at all unusual and have been treated by several authors. 4s - 47 Phase-separation kinetics in the spinodal region were followed by Han et al. 44 using the temperature-jump light-scattering technique on the blends shown in Figure 4. The results are presented in Figure 6. The existence of peaks in the intensity, I(q), vs. q plots, their insensitivity to
Generic Polymer Systems and Applications
118
PSO/PVME
MW·435k/l88k 170
~ !
160
E ~
150
iB-
/
•
140 0
Figure 4
Phase diagram for PSD/PVME (after Han et
at., ref. 44): e, binodal;
0, spinodal
200
~ !
~ 160
e
8e
~
120
o Figure S Phase diagram for PSD/PVME andPS/PVME: e, PS, M w=233000, M w/M n =1.06;. PS, M w=l00000, Mw/Mn = 1.05; 0 PSD, M w=255000, Mw/Mn = 1.08; PSD, M w=119000, M w/Mn =1.05 (PUME, Mw=~9000, Mw/Mn =2.13) (after Han et at. ref. 44)
°
16
PSO/PVME
MW 435k/l88k 7i ·122OC Tf-151.5OC
12
4
o .2
Figure 6
I( q) vs. q for PSD/PVME blends; light-scattering profiles (after Han et at., ref. 44; numbers within lines refer to time (t) in seconds)
Polymer Blends
119
time in the early stage (t < 5000 s) and the decrease in magnitude and increase in q values at later times, are all indications of phase separation via a spinodal mechanism.
4.3.2.2 Nucleation and growth In the region between the spinodal and binodal, (0 2 AGm/ocjJi) is positive, as can be seen from Figure 3. As a result, any small composition fluctuations in this region result in unfavorable free energy changes, and phase separation will occur only when relatively large composition fluctuations are present. Such large fluctuations are normally called nuclei and the process is referred to as nucleation and growth. In this case diffusion into the new phase from the surrounding medium proceeds by the 'normal' or 'downhill' route in contrast to the 'uphill' diffusion taking place in spinodal decomposition. A schematic representation of the evolution of phase composition for both spinodal and nucleation and growth mechanisms is given in Figure 7. Modes of phase separation
Nucleation and growth
-------.]A&---- ----
cP1E ---~--cP M- ~ - -- cP2E - - - -
---
---
---
- --.
Nucleation
-
- ---
--
. ---
---
Growth
Spinodal phase separation
-----J2iE---
~
Equilibrium
cP 1E -cP M---- --- --- --- ---cP ----
/
2E
cP,E----------::---llfi·--cP
-~
,l..M _...;. 'f"2E
~----
-- -- -- -- ----- -- -- ----_
Fluctuation
Growth of fluctuation
Saturation and conti nued sepOration (phase hardening)
cPM= Composition
_
of mixture
= Equilibrium composition of phase i
Figure 7 Modes of phase separation in miscible blends
The morphology resulting from the nucleation and growth process consists of the minorcomponent phase dispersed in the continuous major-component phase. If the amounts of the two phases present are similar, lamellar morphologies may result. Normally the minor component is present in spherical form with a sharp phase boundary between the particles of the dispersed phase and-the matrix. Nucleation and growth is perhaps a more familiar mechanism for phase separation than spinodal decomposition and is usually the only mechanism observed in low viscosity solutions, where it is difficult or impossible to 'quench' the mixture sufficiently into the spinodal region for this latter mechanism to compete effectively in the phase-separation process. Unfortunately, there is no theory pertaining to rate processes operative in nucleation and growth decomposition mechanisms. A number of morphological· and scattering studies exist, but relatively few report kinetic parameters governing the process. 4.4 FACTORS CONTROLLING MISCIBILITY IN POLYMER BLENDS 4.4.1
Specific Interactions
It has already been indicated that high molar mass homopolymers are expected to be immiscible in the absence of specific interactions. By 'specific interactions' are commonly meant intermolecular
120
Generic Polymer Systems and Applications
forces which are intermediate in strength between London dispersion forces and covalent chemical bonds. They include dipole-dipole, hydrogen-bonding, charge-transfer and acid-base (neutralization) interactions. All of these have been used to promote miscibility in polymer blends and the examples cited in Table 1 probably include a number of them. The difficulty in defining such interactions quantitatively in molecular terms is such that no clear understanding exists of even such well-known and well-studied interactions as those occurring in PPO/PS and PVME/PS. It is often stated that the mean-field approach cannot deal adequately with cases where specific interactions are present. This is because the specific interactions introduce locally preferred directions, i.e. all lattice sites are no longer equivalent. While this statement is formally correct, it is nevertheless true that most cases of interest in blends with specific interactions can be adequately treated if one introduces appropriate temperature and composition dependences into X. It is, of course, correct to say that methods such as the solubility parameter, based on estimates of interactions as geometric means, cannot account for specific interactions. Such methods are incapable of predicting negative values for Xij; a negative Xij is a prerequisite for the presence of a specific interaction in the context of this discussion. Although a considerable literature exists 48 on specific interactions of polymer blends, and although in some cases the magnitudes of the interactions are known in a thermodynamic sense through the experimental determination of Xij' molecular interpretations are generally lacking, as mentioned above. As examples of blends that are rendered miscible by virtue of the presence of specific interactions may be cited those based on aromatic polybenzimidazole (PBI) and aromatic polyimides (PI),49 having the generic structures shown in Figure 8. Such polymers are believed to be miscible over a comparatively wide range of composition and structural variation. All of the Pis in Figure 8 are high molecular weight fully imidized thermoplastics. These Pis and the PBI are all soluble in N,Ndimethylacetamide (DMAC), so that blends can be prepared either by precipitating a solution of the respective polymer mixture into a non-solvent, such as methanol, or by casting a film. Blend miscibility was confirmed by the presence of single composition-dependent T g values lying between those of the constituent polymers; by well-defined composition-dependent tan b dynamic mechanical relaxation peaks associated with the glass transitions; by the formation of clear films; and, in one case, by enhanced solvent resistance. An FTIR study of the PBI/PI system was undertaken using PBI/XU 218 and PBI/Ultem 1000 as representative blends. The objectives were to obtain evidence for the existence of specific interactions in this system and to elucidate the nature of these interactions. In prosecuting this study, the changes in the spectral properties of the N-H stretching bands (which arise solely from the PBI component) and of the carbonyl stretching bands (which arise solely from the PI component) were followed. FTIR has been widely used in characterizing miscible polymer sytems. Frequency shifts and band broadenings for many such blends have been ascribed to intermolecular chemical interactions and to changes in polymer-chain conformations. Many of these studies involved blends of polymers containing a carbonyl group,50 which appears to be particularly sensitive to the presence of intermolecular interactions. Figure 9(a) shows that the N-H stretching band of PBI (3400 em -1) in PBI/XU 218 blends shifts by about 55 cm - 1 with increasing PBI content. No shifts are observed in the region between 0 and 50 wt % PBI. Concomitantly, the principal phthalimide carbonyl stretching band (1725 cm -1) of XU 218 shifts by about 7 cm -1 at PBI contents in excess of 80 wt % . In attempting to analyze this behavior it is important to note that PBI is the sole source of NH groups and XU 218 is the sole source ofcarbonyl groups in the miscible blends. There are at least three possible interactions which might be responsible for the observed band shifts: (a) hydrogen bonding between carbonyl and NH groups; (b) 1t orbital interaction between imide and imidazole rings; and (c) charge-transfer interaction between the phthalimide and benzimidazole fused-ring systems. Of these three possibilities, only the first may be confidently ruled out. This decision is based on the notion that hydrogen bonding should manifest itself in the carbonyl region by the appearance of a new hydrogen-bonded carbonyl peak about 20 to 30 cm - 1 below that of the 'free' carbonyl peak of the parent XU 218. These peaks should remain at constant frequency with increasing PBI content, but the amplitude of the hydrogen-bonded carbonyl peak should increase at the expense of the free carbonyl peak, contrary to observation. Also there is a study of the blend, poly(e-caprolactone)/poly(4-vinylpnenol) (PCL/PVH), where the interaction appears to be unambiguously of the hydrogen-bonded type. 50 This blend is analogous to the PBI/XU 218 blends in that one of the components, PCL, is the sole source of carbonyl groups and the other, PVH, is the sole source of hydroxyl groups. Here the behavior of the carbonyl stretching region is 'classical' for hydrogenbonded systems. Pure PCL displays one clearly resolved carbonyl stretching band at
121
Polymer Blends
~N~N>+ N~ ~N I
H
I
H
(1) Poly[1,3-phenylene(5,5'-bibenzimidazolyl}-2,2'-diyl] [Celanese Corp.: PBI (Tg =420°C)]
+O-N
o
o
o
o
(2) Poly(1,3-phenylenephthalimido-N,4-diyloxy-l,4-phenylenedimethylmethylene-l,4-phenyleneoxyphthalimido-4,N-diyl) [General Electric Co.: Ultem lOOO(Tg = 220 °C)]
o
o (3) Condensation product of 5,5'-carbonylbis(I,3-isobenzofurandione) (3,3',4,4'-benzophenone tetracarboxylic dianhydride; BTDA) and 5-amino-3-(4'-aminophenyl)-I,I,3-trimethylindan [Ciba-Geigy Corp.: XU 218 (Tg = 320°C)]
o N
o (4) Condensation product of BTDA and a 4/1 molar mixture of 2,4-toluene diisocyanate and 4,4'-diphenylmethane diisocyanate [Dow Chemical Co.: PI 2080 (Tg = 310°C)]
(5) Condensation product ofBTDA and 3,3'-diaminobenzophenone (DABP) [Mitsui Toatsu, Inc.: LaRC TPI(Tg =267 °C)]
Figure 8 Structures of aromatic polybenzimidazoles and polyimides: the chemical name, source, common name and T g are given for each- structure
1734 cm - 1. In the blends a second carbonyl stretching band at 1708 cm - 1 appears, whose amplitude increases at the expense of the 1734 cm - 1 band as the content of PVH increases. On the basis of results to date, it is not possible to distinguish between 1[-1[ interactions or chargetranfer interactions as being the source of miscibility. Although not discussed in detail here, similar results have been obtained for PBI/2080 and PBI/Ultem blends.
4.4.2 The 'Copolymer Effect' In random copolymers, blended either with a homopolymer or a second random copolymer, a. mechanism other than specific interactions can lead to miscibility. This may occur if the mutual PS 7-E*
122
Generic Polymer Systems and Applications 3420
(a)
3400
3380 T
E 2~
.8
3360
f'f
,,1
,
t-t-~-+--r . t/
1"
E ::J
J
1728
(b)
r-t-2'--cr- ~_ .
~"
1724
1720
'1',
1"--Q.._~
Figure 9 Peak maxima as a function of blend composition for: (a) the N-H stretching band of PBI; (b) the principal phthalimide carbonyl stretching band of XU 218
repulsion between the dissimilar segments in the copolymer is sufficient to overcome the repulsion between these segments and those in the second component of the mixture. In thermodynamic terms, this can lead to the negative net interaction energy necessary to create miscibility. Such effects have been recognized on an empirical basis for some time. An example is the wellknown miscibility of poly(vinyl chloride) with random copolymers of ethylene and vinyl acetate for certain composition ranges of the latter system. 51 These and similar findings have recently been explained using a mean-field theory for miscibility in copolymer blends. 52 This theory has permitted substantial insight into the effect of chemical structure and composition, of temperature and of molecular weight on phase behavior in such systems. The theory is a development of the mean-field approaches discussed in Section 4.2.3 and can be most easily expressed by writing the X parameter, Xblend' in a blend containing copolymers, as a linear combination of individual binary interaction parameters of the form Xblend = L Cii Xii
(14)
i,i
where Xij corresponds to each possible segmental interaction in a given system. The coefficients cij are functions of the copolymer composition(s) with O
Xblend =X lAB + (l-x)XAc- x (l-x)XAB
For the general case of two random copolymers (Ax B1 corresponding to a different segmental interaction
x )..
and (Cy D 1 -
y ).."
there are six Xij' each
Xblend =xYXAc+(I-x)YXBc+ x(l- Y)xAo+(I-x)(I- Y) XBo-x(l-x) XAB- y(l- y) Xco
(16)
This first-order treatment neglects many of the corrections discussed in Section 4.2.3. These can be introduced in principle at the expense of additional complications. For example, the temperature, composition and concentration dependences of individual Xij values could be introduced at the outset using the methods described in Section 4.2~3. The present treatment has been found sufficient,
123
Polymer Blends
however, to account in a self-consistent manner for most of the phenomena experimentally observed. These include the existence of 'windows of miscibility' in homopolymer/copolymer blends and the sensitivity of many blend phenomena to small changes in chemical composition, temperature and molecular weight. 53 (Windows of miscibility are seen when miscibility behavior occurs for homopolymer/copolymer blend as a function of temperature and copolymer composition; these have been designated 'T-c plots', see Figure 10). Furthermore, in a recent test the theory was found to have predictive value. Thus values of Xij obtained from data for miscibility in poly[oxy(2,6-dimethyl1,4~phenylene)] (PPO) and poly(halostyrene) binary combinations were used to predict behavior in the polystyrene (PS)/poly(o-chlorostyrene-co.. p-chlorostyrene) systems with reasonable success. 54
280
T 240
Two phases
200
o
Flgure 10 Miscibility window for PPO/poly(o-chlorostyrene-co-p-chlorostyrene) blends
The determination of Xij values from the present theory requires the experimental observation of miscibility-immiscibility boundaries as a function of copolymer composition. The number of such boundaries at a given temperature must be equivalent to, or greater than, the number of independent Xij values which are to be determined. 55 This can be achieved, in principle, by permuting the copolymer compositions until the required number of boundaries is obtained. For example, a system An/(BxC1-x)n' may yield from zero to two boundaries at a given temperature, which can be combined with those from the system Bn,,/(AxC1-x)n'" and/or those from the third homopolymer/copolymer permutation to determine independently the desired Xij values. The same mean-field treatment may also be used to account for miscibility in blends of other copolymeric combinations of the given segments. For example, in blends of the type An/(AxB1-x)n' miscibility behavior is a function of the single interaction parameter, XAB' and by determining the miscibility-immiscibility boundary here for finite n, n' (see below) this parameter can be determined. An alternative approach would be to determine behavior in the copolymer~opolymer blend (AxBl-x)n/(AyBl-y)n" which iTS also a function of XAB alone. This simple strategy is predicated, of course, on the validity of the composition-independent Xij assumption. However, this could be investigated and, if necessary, taken into account by measuring miscibility for different ranges of x and y.
4.4.2.1
An/(BxC1-x)n'
The most extensively studied blends in terms of the mean-field theory are those consisting of a homopolymer and a copolymer. As already described, this involves three independent interaction parameters, which can be evaluated from appropriate miscibility boundary data. Blends of the homopolymer, PPO~ with copolymers containing a combination of styrene and halostyrene monomers have been studied in this context. 52 Miscibility windows are observed, since all Xij>O, and, in particular, XBC is sufficiently large to render Xblend <0 for certain ranges of x. For copolymers containing styrene homopolymer, a single boundary in the T-e plot is observed, consistent with the fact that PPO and PS are themselves miscible. More recently, mixtures of polystyrene with copolymers of 0- and p-chlorostyrenes have been studied. 54 These data have permitted a refinement of the Xij values for this system and the calculation of a self-consistent set of values for a wider range
124
Generic Polymer Systems and Applications
Two
phases
Copolymer composition
c
Figure 11 Predicted miscibility boundary for an A,.I(Bx C t - x )II' blend (XAB <0, and the two other X values are positive) displaying both upper and lower critical solution temperatures; the boundary is the locus of VCSTs and LCSTs for positive and negative slope temperature regimes, respectively
of Xij. All the systems studied to date have displayed LCST behavior; however, UCST behavior may also be found. The predicted T-c behavior for this case is shown in Figure 11. The extremum in this plot corresponds to the case in which the two consolute points just merge. Systems containing PS and copolymers of 0- and p-styrene exhibit extreme sensitivity to the degree of polymerization of either or both components. This is partly a result of the very low positive value of the Xparameter representing styrene and o-chlorostyrene interactions. A recent extension of these investigations to lower molecular weight systems has shown that the temperature maxima of the miscibility windows increase substantially as the degree of polymerization is' lowered; these maxima can readily be selected to cover the entire accessible experimental temperature range.56 The resulting data have permitted a calculation of the temperature dependence of the respective Xij values with some accuracy. 56
4.4.2.2
(AxB1-x)n/(AyB1-y)n'
Blends of random copolymers containing identical segments but different overall compositions are predicted to be immiscible when the respective polymers are of infinite molecular weight. The limiting miscibility condition, Ix - yl =0, is relaxed, however, for n, n' < 00. This behavior has been verified for chlorinated polyethylenes (which may conveniently be treated as random copolymers of -CH 2- and -CHCI.,... segments) in recent studies. 57 It may be noted that an extensive series ofUCST values has been observed for chlorinated polyethylene blends whose T g values are sufficiently low. 58
4.4.2.3
(AxB1-x)n/ (CyD1-y)n'
The first systematic study of random copolymer mixtures with four distinct repeat units of the type (AxBI_x)..!(CyDI_y)..,59,60 has recently been completed. The results are summarized in Figure 12, which shows miscibility maps for four different cases. The shaded areas represent experimental results obtained primarily from differential scanning calorimetry (DSC) measurements, while the solid lines represent theoretical fits to the data using the values of the Xparameter given in the figure. Each case is discussed individually below. (i) Figure 12 (a): Poly (styrene-eo-acrylonitrile) /poly[oxy (2 ,6-dimethyl-1,4-phenylene) -co-oxy(2,6-dimethyl-3-phenylsulJonyl-1 ,4-phenylene) (P( S-AN) /SPPO) The SPPOs were -synthesized in our laboratories 6o and the P(S-AN)s were obtained commercially. XAB was taken from the published data of Molau,61 XAC was taken as an average value from ·several sources, XAD was determined from approximate phase boundaries observed in the system polystyrene/SPPO and XCD was determined from approximate phase boundaries observed in blends of sulfonylated PPOs of different compositions. The resulting fit represented by the solid lines
Polymer Blends
125
(0 )
( b)
P(S-AN) ~
SPPO
~
1
I
0
0
I-x
XAe = 0.700
XAC =-0.043
X ec = 0.745
XeD
: 0.097
X AD = 0.200 XCD
XAe = 0.080 X ac = 0.053
: 0.150
I-x XAC : -0.043
X AD = 0.200
XeD = 0.022
XCD
X crit • blend
X~~~~ = 0.003
: 0.150
0.004
(d)
(e)
P(S-o-FS) SPPO
P(S-MA) SPPO
~
1
~
1
0
X Ae = 0.40 X ec = 0.004
0
I-x
1-
X
X AC =-0.043
XAD : 0.200
XAe = 0.150
XAC =-0.043
X AD : 0.200
Xeo = 0.113
X CD = 0.150
X ec : 0.290
XeD: 0:020
X cD =O.I50
X crit : blend
0.004-
X~=0.004
Figure 12 Miscibility maps for several (AxBt-x)n/(C,Dt-,)n' copolymer~opolymerblends. The shaded areas represent experimental regions of miscibility and the solid lines are theoretical fits using Xi) values stated in the figure. The studies from which the Xij were obtained were performed at 290°C
+-0+Me
Me
(7) B
(8) C
Me (9) D
in the figure was obtained by adjusting the two parameters XBC and XBD to give the best representation of the data. It is apparently not possible to achieve quantitative agreement with the experimental results using the approach outlined above. This may be due to factors such as .the concentration dependence of the X values, the effect of the molecular weight distribution, and the fact that the observed phase boundaries from which the X values are derived do not represent true critical points. From the discussion in the earlier sections, the composition dependence of the spinodal boundary must be known in detail in order to deduce thermodynamically correct values for the binary interaction parameters. Considering the approximation and uncertainties involved, the predictions from the simple meanfield approach for the composition diagram of P(S-AN)jSPPO are remarkably good. PPO is
126
Generic Polymer Systems and Applications
miscible with P(S-AN) copolymers at 290°C, at the molecular weights used, up to an acrylonitrile content in the copolymers of about 25 mol%. The diagram also shows a 'window of miscibility' for the homopolymer of SPPO with P(S-AN) copolymers. (ii) Figure 12 (b): poly (styrene-co-p-fluorostyrene) / SPPO
A is a styrene repeat unit, B is the styrene repeat unit substituted in the para position on the ring with fluorine, and C and D are units of the sulfonylated PPO copolymers, as for Figure 12(a). XAB was obtained from the approximate phase boundaries in the appropriate systems. XAC,XAD and XCD assume the values used for Figure 12(a) and XBC and XBD aretreated as adjustable parameters in the equation used to calculate the curves shown in Figure 12(b). Here the agreement between theory and .experiment is indeed remarkable, especially since the same remarks concerning the approximate, not to say crude, nature of the approach apply as for Figure 12(a). A 'window of miscibility' is predicted and observed for poly(p-fluorostyrene) and the SPPO copolymer. (iii) Figure 12( c): poly (styrene-co-o-fluorostyrene) / SPPO
The position of the fluorine substituent on the benzene ring has a profound effect on the miscibility behavior, as shown in Figures 12(b) and 12(c). The various X parameters listed on the figure were obtained in the same manner as before. However, XBC was taken to be equal to Xcr for the blend, since experiments with blends of poly(o-fluorostyrene) and PPO revealed the existence of a single composition-dependent T g • XAB and XBD were taken as adjustable parameters to obtain the best fit to the data. (iv) Figure 12(d): poly(styrene-co-methyl acrylate)/SPPO (P(S-MA)/SPPO)
Here, as for Figure 12(c), no miscibility windows exist, and the domain of miscibility is severely restricted. XAC' XAD and XCD assume the same values as in the other cases. XAB was obtained from the phase boundaries observed in P(SxMA1-x)/P(SyMA1-y) blends. XBC and lBD are treated as adjustable parameters. In summary, the first experimental results for blends of the type AxBl-x/CyDl-y show remarkable agreement with the simple mean-field approach. Formally, six Xij are required to describe these systems. The blends described above share the same XAC' XAD and XCD and, in each case, one of the other parameters was determined independently. Fits to the isothermal miscibility curves were then made using the remaining two Xij as adjustable parameters. The theory described above explains a range of phenomena for blends containing random copolymers. The derived interaction parameters have been shown to be of predictive value in several cases. The experimental determination of miscibility boundaries for copolymer/copolymer sys.tems provides further verification of the treatm.ent. An important aspect of the work described here is the possibility for a rational design of copolymers to yield miscible systems. For example, miscibility that occurs in the AB/AC system may be viewed as a miscibilization of homopolymers of Band C by the respective copolymerization with the common segment, A. Special requirements, such as the conditions for minimizing the total consumption of A, for example, may be readily evaluated. Extensions of the theory to take into account the composition and concentration dependences of the interaction parameters are formally possible. In addition, studying the effect of chain microstructure, where the requirement of random monomer placement in the copolymer is relaxed, is feasible and will be described in the next section.
4.4.2.4
Sequence distribution effects
In this section is described a formalism 62 that allows extension of the mean-field theory to any copolymer chain microstructure (i.e. random, block, alternating, etc.). It is necessary, however, to stipulate that the copolymer in question does not undergo microphase separation. Thus, in the case of block copolymers in particular, applicability is limited to fairly short blocks and/or blocks with very small positive or negative binary interaction parameters between the components.
127
Polymer Blends
In order to proceed further, it is necessary to introduce an order parameter () that describes the binary sequence distribution of the monomers in a copolymer chain. By varying (), block, random or alternating copolymers can be described. It is then possible to discuss the various cases already treated for the random copolymer sequence distribution in Sections 4.4.2.1-4.4.2.3 above. Here will be elaborated the An/(BxCt-x)n' and the (AxBt-x)n/(AyBt-y)n' systems. (i) A n/ (BxCt-x)n'
For the random copolymer case, Xblend is given by equation (15) for the system An/(BxCt-x)n'. In order to proceed further, the assumption is made that the interaction energy for the A-B pair is influenced by the units that are chemically bonded to B. This idea is reasonable if the Xij parameters are related to the product of the electronic polarizability (a) for each unit i and j.63 Since it is well known that a of an atom in a molecule is influenced by the neighbors to which it is chemically bonded (e.g. electron-withdrawing or -donating groups), it seems reasonable to expect that XAB will depend on the local sequence distribution. In order to consider all the possible homopolymer-eopolymer interactions, or A-B and A-C interactions, all the possible triplets with B or C occupying the central site must be enumerated. Next the probability of occurrence for each specific triplet is calculated. Then an energy value is assigned to each A-triplet interaction. Table 2 illustrates this procedure for A-B interactions. In the first column is the energy assigned to the configuration found in the second column, whose probability of occurrence is given in the third column. A similar scheme can be constructed for the A-e interactions.
Table 2 Interactions of an A Unit with a B-centered Triplet in the Blend System AII /(B x C t - x )II' with Volume Fractions
Configuration
Probability of occurrence
C XCBC,A
B+-A C
C XCBB,A
B+-A B
2XCB X BB ) ( - - 2XB
B XBBC,A
B+-A C
(
(2XCBXBB) - -
2X CB X BB ) (2XCBXBB) - - 2
B XBBB,A
B+-A B
In column 1, the interaction energies have been identified with the Flory interaction parameter, X. The probabilities in column 3 are expressed in terms of XB and Xc, the fraction of Band C molecules, respectively, in a single copolymer chain. Furthermore, XBC, XCC' and XBB are the pair probabilities of BC, CC and BB pairs in a single chain. Finally, the cPi values are the volume fractions of the various species. The variables listed above are all linearly related to each other. 63 In addition, probabilities for the occurrence of any given triplet can be expressed in terms of the appropriate pair probabilities. These triplet probabilities can be estimated for various distributions by appropriate techniques. In order to reduce the large number of X parameters required to describe the energetics in the An/(BxCt-x)n' system, the following simplifications are introduced. All B-B and C-e interactions are equivalent and equal zero; all B-C interactions are equivalent with the value lBC == lAB == XCBC, A
Generic Polymer Systems and Applications
128
= XBBC, A = XCBB, A = XBBB,A;
lCA
== XBCB, A = XBCC, A == XCCB, A = XCCC, A' We may then write for Xblend = Xcomp + Xdist
X
blend (17)
Xcomp = XBIBA + XC ICA -
xBX C lAB
(18)
Xdist = (XiB/XB)L1XB +(X~c/Xc) L1Xc
(19)
L1XB == XBBB, A- IBA
(20)
L1 Xc == XCCC, A- ICA
(21)
It is clear that Xcomp is equivalent to Xblend given by equation (15), and that the term Xdist represents a zero-order correction taking into account sequence distribution effects. A negative ~XB implies that BBB-A interactions are more favorable than any other B-A interaction and, conversely, a positive !!J.XB implies that BBB-A interactions are less favorable than all other B-A interactions. It has already been stated that an order parameter, 8, must be introduced to describe the sequence distribution of Band C monomers in the copolymer chain. 8 is defined by (22)
XAB=20XAXB
From equation (22) it can be seen that a .random copolymer corre$ponds to 8=t, a block copolymer to 8 approaching 0, and an alternating copolymer to 8 = 1. Introducing 8 into equation (19) results in (23)
With the aid of equation (23), the dependence of Xdist on the sequence distribution can be evaluated. It can be shown 63 that if the absolute value of the ratio ~XB/~Xc is less than 1, there is always an extremum in Xdist for some value of 6, i.e. for a particular sequence distribution in the copolymer. This means that a window of miscibility or immiscibility can occur due to sequencedistribution effects alone. Of course, without knowing the values of ~XB and ~Xc it is impossible to predict what values of 8 will result in a maximum or minimum in Xdisl' I~XB/~Xcl > 1. Xdist is a monotonic function of 8; the smallest value of Xdist will occur either for the alternating or block copolymer. For Xc ~ X B , if XB~XB + xc~ Xc> 0, the alternating copolymer will have the smallest value of Xdist. Conversely if XB~XB+XC~XC
A special case of the An/(BxC 1- x )n' system is the An/(AxC1-x)n' blend, where -
2
(24)
Xcomp = XAC Xc
Proceeding as before, unique X parameters differing from (AAA-eCC) and (ACA-CAC). Then Xdist becomes
XAC
are assigned only to the triplet pairs
Now from equation (24), it can be seen that at infinite chain lengths and for positive values of lAC' the blend system An/(AxC1-x)n' is immiscible for any value of XC' The inclusion of Xdist (equation 25) may modify this conclusion for some value of 8 depending on the values of ~Xc and ~Xb. In fact, windows of miscibility and immiscibility are theoretically possible in this system, even for infinite chain lengths. (ii) (AxB1-x)n/ (AyB1-y)n'
In this case
Xcomp
is given by (26)
Xcomp = (x - y)2 lAB
Again, for infinite chain lengths this system is immiscible unless can be tolerated in the. copolymer. Proceeding as before we write
X
= y, i.e. no composition difference
Xdist= 16Axa (O;ylYB-o;xlxB) (O;YAyi-O;xAxi)-16L1x b (O;y:-O;xi)(O;xl-O;yl) b (L1 ~ = lAB - XBAB, ABA; L1 X = XAAA, BBB - lAB)
(27)
where Ox and Oy refer to the sequence distribution parameters in the two copolymers AxB 1- x and A;B 1- y , respectively.
Polymer Blends
129
The consideration of sequence distribution effects once again modifies the conclusions about miscibility in copolymer blends differing only in composition. For example, it can be shown 64 that for a 50: 50 blend of an alternating copolymer (8= l).with a 50:50 random copolymer, even though Xcomp is zero, Xdist may be positive and thus it is possible for alternating and random copolymers with the same composition to be immiscible. An experimental confirmation of .this prediction is afforded by the system poly(vinyl chloride)jchlorinated polyethylene. (PVCjCPE). In this context, CPE may be considered as a random copolymer of -CH 2- and -CHCI- units, while PVC may be considered as an alternating copolymer composed of the same units. The PVC/CPE ·blend system is indeed immiscible at the same composition. 65 A second consequence of interest is the dependence of the composition difference Ix - y I at which phase separation will take place, on the copolymer composition itself. Ignoring sequence distribution effects, Ix - y I is independent of composition and has the value (28)
~ I
0.5
~
o
1.0
1 . 0 . . . . - - - - - - - - - - . . - - - - - - -...
~
0:5....-_ _- -
o
1.0
The dependence of (a) the maximum tolerable composition difference IXA -- YAI and (b) the corresponding values on X A for a 1: 1 mixture (cPt =4>2 =0.5) of random copolymers (8=0.5) with equal degree of polymerization and XAB= -0.3, AX&=0.5 and AX b =0.7 .
Figure 13 YA
However, if appropriate values of the parameters in equation (27) are chosen, this conclusion is no longer valid, even· for mixtures of two statistical copolymers. An example, (8x =8,=t), is given in . Figure (13). Once again, such behavior has been observed experimentally.66
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Generic Polymer Systems and Applications
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