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Polymer Blends Volume 1
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Polymer Blends, Volume 1 highlights the importance of polymer blends as a major new branch of macromolecular science. Topics range from polymer-polymer compatibility and the statistical thermodynamics of polymer blends to the phase separation behavior of polymer-polymer mixtures, transport phenomena in polymer blends, and mechanical properties of multiphase polymer blends. The optical behavior, solid state transition behavior, and rheology of polymer blends are also discussed.
This book is organized into 10 chapters and begins with an overview of polymer blends, with emphasis on terminology and the effect of molecular weight on the thermodynamics of polymer blends as well as phase equilibria and transitions. The discussion then turns to the miscibility of homopolymers and copolymers, in bulk and in solution, from the experimental and theoretical viewpoints. The chapters that follow explore the statistical thermodynamics of polymer blends, paying particular attention to the Flory and lattice fluid theories, along with the phase relationship in polymer mixtures. The interfacial energy, structure, and adhesion between polymers in relation to the properties of polymer blends are considered. The final chapter examines the phenomena of low molecular weight penetrant transport. Currently accepted models for unsteady-state and steady-state permeation of polymeric materials are presented. A discussion of unsteady-state absorption and desorption behavior observed in a variety of polymer blends complements the treatment of permeation behavior.
This book is intended to provide academic and industrial research scientists and technologists with a broad background in current principles and practice concerning mixed polymer systems.
Published: Academic Press an imprint of Elsevier Books Reference on
ISBN: 9780323138895
List price: $72.95
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Polymer Blends Volume 1 - Donald R Paul

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The University of Texas, Department of Chemical Engineering, Austin, Texas


Ford Motor Company, Plastics, Paint, and Vinyl Division, Detroit, Michigan

Table of Contents

Cover image

Title page



List of Contributors


Contents of Volume 2

Chapter 1: Background and Perspective

Publisher Summary








Chapter 2: Polymer–Polymer Compatibility

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Chapter 3: Statistical Thermodynamics of Polymer Blends

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Chapter 4: Phase Separation Behavior of Polymer–Polymer Mixtures

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Chapter 5: Solid State Transition Behavior of Blends

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Chapter 6: Interfacial Energy, Structure, and Adhesion between Polymers

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Chapter 7: Rheology of Polymer Blends and Dispersions

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Chapter 8: Mechanical Properties (Small Deformations) of Multiphase Polymer Blends

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Chapter 9: Optical Behavior of Polymer Blends

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Chapter 10: Transport Phenomena in Polymer Blends

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Conversion Factors to SI Units



R.A. Dickie, J.R. Fried, H.B. Hopfenberg, F.E. Karasz, Sonja Krause, T.K. Kwei, W.J. MacKnight, D.R. Paul, Isaac C. Sanchez, R.S. Stein, H. Van Oene, T.T. Wang and Souheng Wu






111 Fifth Avenue, New York, New York 10003

United Kingdom Edition published by


24/28 Oval Road, London NW1 7DX

Library of Congress Cataloging in Publication Data

Main entry under title:

Polymer blends.

Bibliography: p.

1. Polymers and polymerization. I. Paul, Donald R. II. Newman, Seymour, Date

TP1087.P64 668.4′1 77–6606

ISBN 0-12-546801-6 (v. 1)


List of Contributors

Numbers in parentheses indicate the pages on which the authors′ contributions begin.

R.A. Dickie(353),     Engineering and Research Staff, Ford Motor Company, Dearborn, Michigan 48121

J.R. Fried(185),     Corporate Research Department, Monsanto Company, St. Louis, Missouri 63166

H.B. Hopfenberg(445),     Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina

F.E. Karasz(185),     Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003

Sonja Krause(15),     Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York

T.K. Kwei(141),     Bell Laboratories, Murray Hill, New Jersey 07974

W.J. MacKnight(185),     Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003

D.R. Paul(1,     445)Department of Chemical Engineering, The University of Texas, Austin, Texas 78712

Isaac C. Sanchez*(115),     Materials Research Laboratory and Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003

R.S. Stein(393),     Polymer Research Institute and Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003

H. Van Oene(295),     Engineering and Research Staff, Ford Motor Company, Dearborn, Michigan 48121

T.T. Wang(141),     Bell Laboratories, Murray Hill, New Jersey 07974

Souheng Wu(243),     Central Research and Development Department, Experimental Station, E. I. du Pont de Nemours & Company, Wilmington, Delaware 19898

*Present address: National Bureau of Standards, Polymer Division 311.00, Washington, D.C. 20237.


At different times in the history of polymer science, specific subjects have come to center stage for intense investigation because they represented new and important intellectual challenges as well as technological opportunities. Dilute solution behavior, chain statistics, rubber elasticity, tacticity, single crystal formation, and viscoelastic behavior have all had their day of peak interest and then taken their place for continuing investigation by the community of polymer scientists. These periods of concentrated effort have served to carve out major new areas of macromolecular science to add to and build on the efforts of previous workers.

Polymer blends have now come to the fore as such a major endeavor. Their current and potential technological importance is remarkable and their ubiquitous presence in consumer products is testimony to their commercial importance.

Furthermore, pursuit of our understanding of the physical and mechanical properties of blends has uncovered new principles, refined earlier fundamental concepts, and revealed further opportunities for research and practical problem solving. In this last respect, polymer blends or polyblends offer a strong analogy to the previously established role of copolymerization as a means of combining the useful properties of different molecular species, but blends allow this to be done through physical rather than chemical means.

Our purpose, therefore, in organizing this work has been to underscore the importance of mixed polymer systems as a major new branch of macromolecular science as well as to provide academic and industrial research scientists and technologists with a broad background in current principles and practice. A wide range of subjects must be covered to meet these objectives, and no individual could be expected to have the knowledge and experience required to write an authoritative treatment for any significant fraction of these subjects. Consequently, the book was written by a group of authors‐selected by the editors because of their particular expertise and contributions. However, a strong effort was made to have the outcome represent a cohesive treatment rather than a collection of separate contributions. The final outcome is the result of numerous decisions, and clearly different decisions could have been made. Considerable thought and consultation were devoted to a selection of topics that covered the main principles within the constraints of time and space.

Once the authors were selected, the final chapter outlines evolved through continuing consultation among the editors and authors. Each chapter has been reviewed and altered as necessary. In some cases, editorial footnotes have been added for clarification. There is extensive cross-referencing among chapters to emphasize the relations among chapters and to reduce duplication of content. A loose system of common nomenclature was developed, but exceptions were permitted to allow each subject to be developed in terms most commonly used in the literature and best understood by the reader. A mixture of unit systems appears here because various disciplines of science and technology are in different stages of conversion to the metric and SI systems at this time; hence, we have included in the Appendix selected conversion factors to help minimize the problems this creates.

We have elected to define a polymer blend as any combination of two or more polymers resulting from common processing steps. In keeping with this broad definition, we have elected to include, for example, the chapter on multilaminate films by Schrenk and Alfrey and the treatment of bicomponent fibers by Paul, both in Volume 2. However, since block and graft copolymers have been treated extensively in other recent publications, we have included only two chapters specifically devoted to these systems, i.e., Block Copolymers in Blends with Other Polymers by Kraus (Volume 2) and Interfacial Agents (Compatibilizers) for Polymer Blends by Paul (Volume 2). However, additional references to such systems are made in other chapters.

For thermodynamic reasons, most polymer pairs are immiscible. Nevertheless, the degree of compatibility may vary widely, and since this aspect of polymer blends is of such underlying importance to morphology and properties, we have set aside a considerable portion of the book for this purpose. Krause’s chapter, Polymer‐Polymer Compatibility (Volume 1), provides an authoritative, comprehensive summary and interpretation of available information on a great number of systems reported in the literature. A review of more recent statistical mechanical theories for mixtures with particular attention given to lower critical solution temperatures is presented by Sanchez in Volume 1, whereas an interpretation of experimental work on phase separation and boundaries using NMR and other techniques is found in the contribution by Kwei and Wang, also in Volume 1.

Compatible polymers represent such unique cases in the realm of blends that the editors have sought to single out some of these for special discussion. Aside from relevant discussions by Krause and Kwei and Wang, the reader is referred to the following chapters: Blends Containing Poly(ε-caprolactone) and Related Polymers, by Koleske (Volume 2); Solid State Transition Behavior of Blends, by MacKnight, Karasz, and Fried; Polymeric Plasticizers, by Hammer; and Transport Phenomena in Polymer Blends, by Hopfenberg and Paul.

A second cornerstone along with thermodynamics in the building of the often complex structure of incompatible disperse phases is the interaction of melt flow with interfacial behavior and the viscoelastic properties of multicomponent systems. We have sought to lay the groundwork for this fundamental aspect of polyblends in Wu’s chapter, Interfacial Energy, Structure, and Adhesion between Polymers (Volume 1), and Van Oene’s chapter, Rheology of Polymer Blends and Dispersions (Volume 1). More technologically oriented extensions of this subject will be found in Polyolefin Blends: Rheology, Melt Mixing and Applications, by Plochocki (Volume 2), and Rubbery Thermoplastic Blends, by Kresge (Volume 2).

Overall, mixed polymers provide an incredible range of morphological states from coarse to fine. One need only glance at Interpenetrating Networks (Thomas and Sperling, Volume 1) and Rubbery Thermoplastic Blends (Kresge) to sense the range of possibilities. However, aside from unusual possibilities of disperse phase, size, shape, and geometric arrangement such as described in Fibers from Polymer Blends (Paul, Volume 2) even more subtle complexities are possible with crystalline polymers wherein intricate arrangements of the crystalline and amorphous phases are possible as is shown by Stein in Optical Behavior of Blends (Volume 1). Here special investigatory techniques have been brought to bear on the disposition of molecules in the submicroscopic range. This chapter also presents the basic principles for understanding the optical properties of blends important in some applications.

Properties, along with composition and morphology, represent the third major area of interest. Historically, the modification of glassy polymers with a disperse rubber phase was one of the first major synthetic efforts directed to useful polymer blends. It is of particular importance because the mechanical properties of these synergistic mixtures are not related simply to the sum of the properties of the components. We have attempted to trace the growth of the concept of rubber modification in Newman’s chapter, Rubber Modification of Plastics (Volume 2). A more detailed study of toughening theory for a restricted range of systems is presented in Fracture Phenomena in Polymer Blends, by Bucknall (Volume 2). These chapters deal largely with ultimate properties. Small strain behavior is dealt with in Mechanical Properties (Small Deformations) of Multiphase Polymer Blends, by Dickie.

Another major area of commercial importance of blending is the rubber industry, which capitalizes on the combination of properties each component contributes to the blend. The chapter by McDonel, Baranwal, and Andries in Volume 2 illustrates the advantages and compromises in the very large area of application, Elastomer Blends in Tires. Somewhat related are the contrasting combinations of rubbery polymers and plastics treated by Hammer in Polymeric Plasticizers and Kresge in Rubbery Thermoplastic Blends.

The connections between polymer blends and the field of reinforced composites and its techniques of analysis are clearly evident in the chapters by Dickie on mechanical properties and by Hopfenberg and Paul on sorption and permeation. This is also seen in the chapters on films by Schrenk and Alfrey and fibers by Paul and to a lesser extent in the chapters by Thomas and Sperling and Newman.

A remarkable balance of diverse properties is achievable with blends as is evidenced by the chapters mentioned in the previous paragraphs. One unusual case of great commercial importance heretofore largely unnoticed in fundamental research is represented in Low Profile Behavior (Atkins, Volume 2) where polyblends of thermoplastics in cross-linked styrenated polyesters are used to control the volume of molded objects. The list of useful performance characteristics that can be controlled by polyblending is as long as the list of properties themselves.

An introductory chapter, written after all of the other chapters were completed and reviewed, has been included to fill some gaps and to provide a certain degree of perspective.

We have selected the above topics in order to achieve our goal of a comprehensive treatment of the science and technology of polymer blends. However, the growth of the field has made it necessary to publish this treatise in two volumes. We have attempted to divide the chapters equally between the two and to concentrate the fundamental and general topics in Volume 1 and the more specific and commercially oriented subjects in Volume 2.

In Volume 2, the topics dealt with are more specific and have a greater orientation toward commercial interests. It has been our purpose to make each chapter self-contained without making it necessary for the reader to be referred continually to other chapters. Nevertheless, some overlap is unavoidable in a cooperative undertaking. This does, however, permit the presentation of different points of view and thereby contributes to a balanced presentation. On the other hand, we have also sought to tie together the various chapters, and this has been accomplished in part by the addition of cross-references.

Many people have contributed to the development and completion of these two volumes through their advice and encouragement. However, we wish to mention specifically the help of F. P. Baldwin, J. W. Barlow, R. E. Bernstein, C. A. Cruz, S. Davison, P. H. Hobson, and J. H. Saunders.

Contents of Volume 2

11. Interpenetrating Polymer Networks D. A. Thomas and L. H. Sperling

12. Interfacial Agents (Compatibilizers) for Polymer Blends D. R. Paul

13. Rubber Modification of Plastics Seymour Newman

14. Fracture Phenomena in Polymer Blends C. B. Bucknall

15. Coextruded Multilayer Polymer Films and Sheets W. J. Schrenk and T. Alfrey, Jr.

16. Fibers from Polymer Blends D. R. Paul

17. Polymeric Plasticizers C. F. Hammer

18. Block Copolymers in Blends with Other Polymers Gerard Kraus

19. Elastomer Blends in Tires E. T. McDonel, K. C. Baranwal, and J. C. Andries

20. Rubbery Thermoplastic Blends E. N. Kresge

21. Polyolefin Blends: Rheology, Melt Mixing, and Applications A. P. Plochocki

22. Blends Containing Poly(ε-caprolactone) and Related Polymers J. V. Koleske

23. Low-Profile Behavior K. E. Atkins

Appendix. Conversion Factors to SI Units


Chapter 1

Background and Perspective

D.R. Paul,     Department of Chemical Engineering, University of Texas, Austin, Texas

Publisher Summary

The field of polymer science and technology has undergone an enormous expansion over the past several decades primarily through chemical diversity. First, there was the development of new polymers from a seemingly endless variety of monomers. Next, random copolymerization was used as an effective technique for tailoring or modifying polymers. Later, more controlled block-and-graft copolymerization was introduced. Though the list of new concepts in polymer synthesis has not been exhausted, it has become clear that new chemical structures or organizations are not always needed to meet new needs or to solve old problems. The successful implementation of the concept of physically blending two or more existing polymers to obtain new products or for problem solving requires different knowledge and techniques than that used to develop new polymers. This chapter provides an overview of polymer blends. The thermodynamics of polymer-polymer mixtures or composites is one of the most important fundamental elements because it plays a major role in the molecular state of dispersion, the morphology of two phase mixtures, the adhesion between phases, and consequently influences most properties and applications. The chapter also highlights the possible phase and transition behavior in polymer blends. Blends with two phases can be organized into a variety of morphologies. Many properties and uses of a blend depend critically on the nature of this arrangement of the two phases. The purpose of polymer blending is to achieve commercially viable products through either unique properties or lower cost than some other means might provide. Commercial products are based on miscible blends such as polystyrene-poly (phenylene oxide), PVF2–PMMA, PVF2–PEMA, and PVC-nitrile rubber and immiscible blends such as rubber blends in tires, impact-modified plastics, and coextruded film and fibers.

The field of polymer science and technology has undergone an enormous expansion over the last several decades primarily through chemical diversity. First, there was the development of new polymers from a seemingly endless variety of monomers. Next, random copolymerization was used as an effective technique for tailoring or modifying polymers. Later, more controlled block-and-graft copolymerization was introduced. The list of new concepts in polymer synthesis has not been exhausted. However, it has become clear that new chemical structures or organizations are not always needed to meet new needs or to solve old problems.

The concept of physically blending two or more existing polymers to obtain new products or for problem solving has not been developed as fully as the chemical approach but is now attracting widespread interest and commercial utilization. The successful implementation of this concept requires different knowledge and techniques than that used to develop new polymers. It is the purpose of this book to bring together the pertinent principles needed to implement and advance this more physical approach to polymer products. In the first part of this book, these principles are discussed in general or scientific terms; in the latter part they are illustrated by particular systems or with reference to specific applications.

The purpose of this introductory chapter is to develop some fundamental background pertinent to the early chapters and to give a perspective that to some degree will tie together the diverse subjects and viewpoints presented by the various authors throughout this book.


Polymer blends are often referred to by the contraction polyblends and sometimes as alloys to borrow a term from metallurgy. Various restricted definitions might be offered for any of these or other terms; however, the boundaries of what is intended are invariably imprecise, and the terms are not used with the same meaning by everyone. No attempt will be made here to adopt any rigid terminology, and the concept of blending will be discussed in the broadest possible manner. This book covers materials or products made by combining two or more polymers through processing steps into random or structured arrangements and includes geometries that might be regarded as polymer–polymer composites (see, e.g., Volume 2, Chapter 15 and parts of Chapter 16). We do not include, obviously, separately processed polymer items that are subsequently assembled into finished products. Block-and-graft copolymers share many common features and purposes as blends, but these materials, which generally differ from blends by only a few chemical bonds, are not included here except when they are components of blends (see Volume 2, Chapter 12 and 18).

The thermodynamics of polymer–polymer mixtures or composites is one of the most important fundamental elements since it plays a major role in the molecular state of dispersion, the morphology of two phase mixtures, the adhesion between phases, and consequently influences most properties and applications. Because of this, the early chapters including this one are devoted mainly to this subject. Like many aspects of polymer blends, an impediment to understanding the thermodynamics of blends has been a lack of suitable experimental techniques and theories; however, recent activities have made a start toward removing these deficiencies as will be seen here and in subsequent chapters. One of the first, but not the only, thermodynamic questions concerns the equilibrium miscibility or solubility of two polymeric components in a blend.

Very often the term compatibility is used synonymously with miscibility. However, in materials technology compatibility is a more general term with a wider diversity of meanings and implications, which in the extreme might result in two materials being classified as incompatible because they are miscible. In a strict technological sense, compatibility is often used to describe whether a desired or beneficial result occurs when two materials are combined together. If one is concerned with identifying polymeric plasticizers, then complete miscibility is desired, whereas, for rubbery impact modifiers of glassy plastics complete miscibility is not desirable. Generally speaking, most polymer pairs are not miscible (but more are miscible than was recognized only a few years ago) and by this terminology are incompatible. It is very likely that the use of the word incompatible as part of this general rule has been an unfortunate psychological impediment to commercial development of polymer blends because of the accompanying implication that poor results are inevitable when incompatible materials are combined. For many purposes, miscibility in polymer blends is neither a requirement nor desirable; however, adhesion between the components frequently is. In a fundamental sense, however, adhesion, interfacial energies, and miscibility are all interrelated thermodynamically in a complex way to the interaction forces between the two polymers.

Miscibility in polymer–polymer mixtures has been the subject of considerable discussion and debate in the literature. Frequently, the concern is over the size of the phases or domains implied by a particular observation; or, is mixing on a molecular or segmental scale (see e.g., [1, 2])? Interestingly, these questions are almost never raised about solutions of low molecular weight compounds, but apparently they arise naturally for macromolecules. Similar concerns existed many years ago about solutions of polymers in low molecular weight solvents and only disappeared when appropriate thermodynamic theories and experimental data appeared [3] which demonstrated that these solutions were not unusual or unique once the conformations and large size of the polymer chains were correctly considered.

Miscibility in every case is best understood, and ultimately can only be defined, in thermodynamic terms rather than through attempts that place overdue emphasis on details at the molecular or segmental level. Until recently, techniques for examining the thermodynamics of miscible polymer–polymer mixtures critically and unambiguously were extremely limited. The neutron scattering results that are now beginning to appear [4–6] seem to fill this need for conceptual clarification and quantitative results. In the experiments of interest here, one polymer is dissolved in a different polymer (the two may be regarded as solute and solvent), and the solutions are studied via neutron scattering in a manner analogous to classical light scattering of polymer in a solvent. Preferably, one of the polymers is deuterated, but this is of no fundamental concern here. Scattered intensities have been measured as a function of solute concentration and scattering angle and subsequently analyzed by the familiar Zimm plot used in treating light scattering from dilute polymer solutions. Interestingly, this analysis gives the correct molecular weight for the solute polymer, which is confirmation that these solutions are classical ones having miscibility in a true thermodynamic sense. Furthermore, the radius of gyration of the solute polymer was found to be of the size one expects in bulk or dilute solution and has a similar molecular weight dependence.

This is the first conclusive evidence that conformations in polymer–polymer solutions are substantially the same as those in other better-understood polymer states and implies that the segments of the two polymers are more or less in random contact just as solvent molecules and polymer segments mix in solution [3]. This kind of behavior was observed only for blends that showed a single glass transition temperature (Tg) (e.g., poly(methyl methacrylate)/styrene–acrylonitrile copolymer–see Stein et al. [7]). Zimm plots readily indicative of immiscibility were obtained for blends that showed two glass transitions [e.g., poly(methyl methacrylate)–poly(α-methylstyrene)]. This adds additional fundamental justification for use of the common and useful criteria of a single glass transition to indicate blend miscibility (see Chapter 5). In addition to the above important results, meaningful second virial coefficients consistent with other observations were obtained for the miscible blends. These results show that miscibility can be detected fundamentally in polymer–polymer solutions and has the same meaning as always. Furthermore, detailed knowledge about the scale of mixing is not required to decide whether miscibility exists or not; however, such information is essential when the miscibility or mixing is not complete in the thermodynamic sense. The technique of neutron scattering may be expected to be an important source of detailed, fundamental thermodynamic information on polymer–polymer systems in the future.


The unique factor affecting the thermodynamics of polymer blends compared with other systems is the large molecular weight of both components. Generally, the qualitative thermodynamic argument, which limits miscibility to a rare occurrence in polymer blends, recognizes that the entropy of mixing ΔSmix in the free energy of mixing expression


will be very small owing to the small number of moles of each polymer in the blend as a result of their large molecular weights. While the sign of the combinatorial entropy favors mixing, it is usually too small to result in the necessary negative free energy because the heat of mixing ΔHmix is generally thought to be positive, at least for relatively nonpolar systems. It will be useful background to examine this situation in more detail here.

The Flory–Huggins solution theory [3], although inadequate for some purposes, provides a useful first approximation for the terms in Eq. (1), and its applications to polymer blends is treated in detail in Chapter 2. This theory [see Eq. (1) of Chapter 2] gives for the free energy of mixing polymers A and B.


where ϕA is the volume fraction of A, Vi the molar volume of i(χTAB/Vr in the notation of Chapter 2) is an interaction parameter related to the heat of mixing, which is positive for endothermic systems. The first two terms arise from the combinatorial entropy of mixing, and each is inversely related to the size or molecular weight of that component. It will simplify this discussion to assume that both polymers have the same molecular weight M with an equivalent parameter 2ρ/Mcr, where Mcr will be a critical molecular weight. For this case, Eq. (2) can be rewritten as


Figure 1 shows various cases calculated from Eq. (3) when the factor in front has any arbitrary value. The extreme upper and lower curves are the heat of mixing (for this model, ΔHmix = ΔGmix when M →) and the entropy term in the free energy when M = Mcr, respectively. The intermediate curves are the free energy of mixing for various polymer molecular weights M, expressed relative to Mcr. Clearly, the free energy tends to more positive values as the molecular weight is increased as expected from the discussion of Eq. (1). It is, in fact, positive for some composition regions, but not all, for the case in which M is 50% larger than Mcr, but it is never positive when M is only 25% larger. For the latter case, a mixture whose composition locates it at Point A will have a negative free energy of mixing, and, therefore, simplistically one might expect the two polymers to mix since this is one of the thermodynamic requirements for processes to occur spontaneously. However, a mixture represented by Point A, if it did occur, would be unstable since it can lower its free energy even further to Point B by separating into two phases with compositions given by the end points of the dotted line. Thermodynamic stability of a one phase mixture exists only when

Fig. 1 Free energy of mixing and component terms of polymers A and B with the same molecular weight M. The curves were computed from Eq. (3).


as discussed further in Chapters 2–4 (or see [8, 9]). As it turns out, Mcr is the critical molecular weight [see Eq. (3a) of Chapter 2] where this condition is no longer satisfied for all compositions, whereas, for M < Mcr, the condition of Eq. (4) is fulfilled for all compositions. When M > Mcr, stable one-phase mixtures can exist at the extremities of the composition range, that is, partial miscibility; however, these composition zones become smaller as the ratio M/Mcr increases. For cases where MA ≠ MB, the free energy curves in Fig. 1 would be skewed toward the side of the lower molecular weight component rather than be symmetrical as shown there.

As discussed in parameter, or the heat of mixing, can be estimated from the solubility parameters δA and δB if the components are relatively nonpolar. For the above example, rearrangement of Eq. (12) from Chapter 2 permits an estimate of Mcr for the nonpolar case


When the solubility parameters differ by 1.0 (cal/cm³)¹/², Mcr is less than 1200 at 25°C; however, when the two polymers are matched more closely and this difference is 0.1 (cal/cm³)¹/², Mcr rises to about 120,000 (see Table VII of Chapter 2). Thus, polymer molecular weight has a strong influence on miscibility for systems with endothermic heats of mixing. The situation is different for exothermic systems.

Interestingly, Flory’s equation of state analysis has shown that the actual entropy of mixing for some systems is less than that given by the combinatorial value employed in Eq. (2) and may even be negative when the two polymers have very large molecular weights [10].


As shown in the last section, miscibility of nonpolar polymers of substantial molecular weights occurs only when the solubility parameters are precisely matched. Attempts to find miscible polymer pairs by matching similar structures, or solubility parameters, is doomed to produce very few cases, unless the molecular weights are low, since the enthalpy of mixing at the very best can only approach zero. However, the enthalpy of mixing can be negative, or exothermic, if certain specific interactions between polar groups are involved, and consequently ΔGmix will be negative in spite of the small entropy. These interactions may arise from a variety of mechanisms, such as dipole–dipole forces, but it is often useful to think in terms of donor and acceptor groups in analogy to hydrogen bonding. As a result, it may be possible to select two polymers having chemical moieties within or attached to the chains which have the proper complementary dissimilarity to yield an exothermic heat of mixing, although, it should be recognized that there will still be an endothermic contribution from the dispersive interactions, or van der Waals forces, between the remaining parts of the structure that do not interact specifically. This is illustrated nicely by some calorimetry data on model compounds designed to understand the solvating power of cyclic ethers and ketones for poly(vinyl chloride) [11]. Heats of mixing were measured for various singly and doubly chlorinated hydrocarbons (4-6 carbons) and poly(vinyl chloride) (PVC) with tetrahydrofuran (THF) and for hexane with cyclohexane. The heats of mixing ΔHmix were all essentially parabolic with composition such that the ratio shown on the ordinate in Fig. 2 was nearly constant for a particular system. Two monomer units of PVC were used in computing the mole fractions xA and xB. These data are plotted versus the extent of chlorination in Fig. 2 where the cyclohexane–hexane system is taken as a nonpolar model for estimating the endothermic contribution of the dispersive bonding to ΔHmix for the chlorinated hydrocarbon–THF system. It is interesting that all of the data for singly chlorinated hydrocarbons with THF fall in a very narrow band, while the doubly chlorinated ones fall in another similar band. The position of the chlorines has essentially no effect including replacing the α hydrogen with a methyl group. The latter appears to rule out the hydrogen bonding argument frequently invoked for such systems [11]. Instead, there seems to be some direct interaction between the chlorines and the oxygen, and all that matters is the number of interactions. The data in Fig. 2 are nicely connected by a straight line suggesting that the contributions from specific and dispersive interactions are simply additive as one might expect, that is,

Fig. 2 Calorimetrically determined heats of mixing showing the effect of a specific interaction between chlorine atoms on hydrocarbons with the oxygen in THF.


where N is the number of such interactions (related to number of chlorines in is positive.

The specific interaction involved in Fig. 2 perhaps explains the many examples of miscibility or partial miscibility among halogenated polymers and those containing oxygen (e.g., ester groups) (see the tables in Chapter 2). However, as Eq. (6) and Fig. 2 show, there must be sufficient interactions to outweigh the dispersive contribution to make ΔHmix exothermic or a sufficiently small positive value. The striking structural example provided by the much greater miscibility with PVC of the syndiotactic compared to the isotactic isomer of poly(methyl methacrylate) [12] teaches that, in addition to having the proper type and number of interacting groups, they must also be properly articulated spatially to produce the interaction.

Quantitative knowledge about specific interactions is limited; however, such data would be very useful for understanding the miscibility in certain blend systems and to design or select components for miscibility. Such data can be obtained by a well-planned calorimetry program using model compounds.

It is evident from examining the known cases of miscibility in blends that there is a greater opportunity for discovering new miscible systems by trying to select complementing dissimilar structures rather than by matching similar structures as most general rules teach. The number of examples of polymer–polymer miscibility is expanding rapidly and may be expected to continue as this relatively new viewpoint is exploited. Careful research that quantifies the specific interaction and its origin will be most useful.


Above their melting points, metals are usually quite miscible with one another and some other elements [13]. However, mixing of different metals in the crystal lattice below the melting point is more restricted and only occurs when certain size and valency requirements, summarized in the Hume–Rothery rules [9], are met. Solid-metal alloys may consist of one or two phases and each offers certain advantages. For polymer blends, there seems to be no established cases in which the two cocrystallize into the same lattice. In fact, isomorphism of comonomers randomly or regularly distributed in the chain is not common but does occur in some instances [14]. Evidently, miscibility in polymer blends is restricted to amorphous phases.

It is well recognized that many solutions of low molecular weight compounds have limits of solubility, and the same is true for polymer blends. There are various mechanisms for these limits. The phase separation discussed in connection with Fig. 1 results in two liquid phases and is very much affected by temperature. Figure 3a shows one general pattern of liquid–liquid phase equilibrium, which includes upper (UCST) and lower (LCST) critical solution temperature behavior. These and other phase diagram forms are discussed in Chapters 2–4.

Fig. 3 Possible phase and transition behavior in polymer blends.

Until recently, there was little mention of such phase boundaries in the literature on polymer blends. Lower critical solution temperature behavior, however, is apparently common. The few systems in which this behavior has been reported are reviewed in Chapters 2–4; however, since the time when these chapters were written, LCST behavior has also been found in the following systems [15]: poly(vinylidene fluoride) (PVF2)–poly(ethylmethacrylate) (PEMA); PVF2–poly(methyl methacrylate) (PMMA); PVF2–poly(methyl acrylate); PVF2–poly(ethyl acrylate); and poly(ε-caprolactone)–polycarbonate.

The literature on polymer blends has been more concerned in the past with solid–liquid-type transitions (Tg or Tm, as discussed in Chapter 5) than the liquid–liquid type. Figure 3b shows the expected behavior of these transitions for a mixture of two miscible polymers free of any phase boundaries of the type on the left in the region of interest. If both polymers are amorphous, the glass transition Tg varies monotonically with composition as shown. If one polymer is crystallizable, its melting point Tm will be depressed slightly [16] as it is diluted with the other polymer. Presumably, it crystallizes by itself, and the remaining amorphous phase is a homogeneous mixture whose composition is somewhat altered by the removal of some but not all of the crystallizable component. This amorphous phase will be rubbery above Tg and glassy below. While the crystallization does represent a phase separation, it is of a different origin than the liquid–liquid type in Fig. 3a. Crystallization of one component offers the system another way to lower its free energy below that of a single phase in analogy to the change from A to B in Fig. 1. However, the system may be quite stable to any liquid–liquid separation, and thus it possesses the basic thermodynamic attributes for complete miscibility in the sense of Fig. 1. The propensity to crystallize might be removed by some slight structural alteration of this component or it may be avoided kinetically. The latter case does not represent an equilibrium state with respect to crystallization; however, the one phase system may still be in equilibrium with respect to liquid–liquid phase separation. Until recently [16, 17], there was relatively little information in the literature on potential miscibility for blend systems with crystallizable components apparently because it was felt that the crystallization itself indicated immiscibility and thus such systems were of no interest. However, it seems more pertinent to focus on the state of miscibility in the remaining amorphous phase since the crystallization per se should not rule out interest in potential usefulness—many important polymers crystallize.

For some systems, the two types of phase behavior shown in Fig. 3 no doubt have regions of overlap (see, e.g., Bernstein et al. [15] and Kwei et al. [18]). This may result in a rather complex situation with regard to a detailed fundamental study; however, it may not alter practical interest.

A central point here is that historically polymer blends have often been regarded as miscible or compatible only when they have one phase for all component proportions and are stable with respect to all types of phase changes (see Chapter 2); however, there is a growing recognition that the many types of partial miscibility [17], largely ignored in the past, offer interesting areas for fundamental study and opportunities for commercial utilization.


Blends with two phases can be organized into a variety of morphologies as the subsequent chapters demonstrate. Many properties, and subsequently uses, of a blend depend critically on the nature of this arrangement of the two phases. One phase may be dispersed in a matrix of the other, and in this case the matrix phase dominates the properties. A parallel arrangement allows both phases to contribute to many properties in direct proportion to their composition in the blend, but this is a nonisotropic structure since perpendicular to this direction the system may represent a series arrangement with properties that disproportionately favor one phase. For mechanical properties, adhesion between phases is an issue that is more critical for some morphologies than others.

An intriguing morphological concept, which avoids some of the dilemmas pointed out above, is one in which both polymers are continuous simultaneously and thereby form interpenetrating networks (IPN) of phases. A related but different concept is the idealized interpenetration of two molecular networks (see Volume 2, Chapter 11). The IPN structure can (a) be spatially isotropic, (b) allow each phase to contribute to properties more nearly in proportion to their concentration in the blend, and (c) remove somewhat the stringent necessity for adhesion inherent to other morphologies. There are at least two routes to forming IPN type morphologies that might be used: one is by judicious control of rheological factors during processing as described in Volume 2, Chapter 20, and the other is phase separation from a homogeneous phase via the spinodal decomposition mechanism described in Chapter 4. The latter has resulted in practical applications in other materials technology [19] but apparently not for polymer blends.

It would be of interest to examine more closely how such properties as modulus (Chapter 8) or permeability (Chapter 10) depend on composition and component properties for an IPN type structure. This is a very complex geometry for exact analysis; however, an approximate treatment for the modulus is shown in Fig. 4. Kraus and Rollman [20] proposed an isotropic extension of a Takayanagi type model (see Chapter 8) that in one limit (their parameter b → 1) reduces to a very special IPN. This IPN is a regular lattice of cubes, like that shown in Fig. 4, each containing a regular arrangement of Phases 1 and 2 (light and shaded respectively). The volume fraction of Phase 2 is related to the linear fraction a it contributes to the cube edge: ϕ2 = a² (3–2a). Via the Takayanagi approach, approximate upper and lower bounds for the IPN modulus can be deduced and these have been used to define the shaded zone in Fig. 4. Within this zone should lie a reasonable estimate for actual IPN structures. Also shown for comparison in Fig. 4 are the upper and lower bounds for all phase arrangements, viz., parallel and series respectively, plus a dispersion of Component 2 in a matrix of 1. It is interesting to note that the IPN structure gives a modulus in all directions only slightly below the parallel arrangement, that is, just below perfect additivity—note that on arithmetic coordinates the parallel arrangement would yield a straight line.

Fig. 4 Mechanical modulus of various polymer–polymer phase arrangements. The cube shows unit cell of an idealized interpenetrating network (IPN) structure. The shaded area is determined by upper-and lower-bound estimates for this model.

The IPN structure is a way to achieve the maximum contribution from each component simultaneously and offers opportunities for combining unique properties into a blend.


The ultimate goal of polymer blending is a practical one of achieving commercially viable products through either unique properties or lower cost than some other means might provide. Commercial products have been based on miscible blends, for example, polystyrene–poly(phenylene oxide), PVF2–PMMA, PVF2–PEMA, and PVC–nitrile rubber, and immiscible blends, for example, rubber blends in tires (Volume 2, Chapter 19 and 20), impact-modified plastics (Volume 2, Chapters 12–14), and coextruded film and fibers (Volume 2, Chapter 15 and 16). What one can accomplish with miscible versus immiscible blends is fundamentally different and in some respects resembles the differences between random versus block copolymers.

The latter chapters in this book deal with a wide spectrum of examples of present and future applications of blends, and point out their advantages and disadvantages. A careful study of these should result in a general understanding of what is required of the components thermodynamically to achieve the desired objective. This book does not include, obviously, all present examples of blend usage or future possibilities as illustrated by the following. Frequently, a small amount of a second polymer may be blended with PVC to serve as a processing aid or as a lubricant. Similar advantages have been observed recently for a wider range of polymers (see, e.g., Kraus and Rollmann [21]). These effects are complex and poorly understood at the present but offer potentially significant benefits that apparently derive from rheological processes dependent on the immiscibility, or at most partial miscibility, of the two polymers. Another attractive possibility is to use polymeric stabilizers for polymers, for example, antioxidants and UV absorbers, since they would offer the advantage of very low migration [22] similar to the permanence of polymeric plasticizers (Volume 2, Chapter 17). At least some miscibility is needed in this application.


The author gratefully acknowledges the helpful criticism and suggestions of S. Newman in preparing this chapter.


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Chapter 2

Polymer–Polymer Compatibility

Sonja Krause,     Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York

Publisher Summary

This chapter provides an overview of polymer-polymer compatibility. The term polymer compatibility refers to the total miscibility, on a molecular scale, of homo-polymers and of random copolymers with each other in various combinations. In the chapter, no distinction is made between polymers in the rubbery or glassy state. The chapter discusses the crystallizable polymers in which the polymer remains at least partially amorphous and in which the miscibility with other polymers are investigated in the amorphous state. The chapter briefly reviews methods for predicting compatibility and presents a method for predicting compatibility along with its limitations. It explains the prediction schemes for polymer-polymer compatibility. The experimental methods for determining solubility parameters of polymers involve studies of the polymers in solution or swollen by solvent, that is, the thermodynamics of the situation involves the entropy contribution to the polymer-solvent interaction parameter and it complicates the theoretical treatment. It often turns out that experimental solubility parameters for the same polymer vary a great deal, depending both on the method used and on the experimenter. The two methods used are (1) swelling of a cross-linked polymer, where it is assumed that the solubility parameter of the polymer is equal to that of the solvent which swells it most highly and (2) intrinsic viscosity of a soluble polymer sample, where the solubility parameter of the polymer is equal to that of the solvent in which its intrinsic viscosity is greatest. For the same polymer, these methods often give different results depending on the nature of the solvents, which may be non-polar, polar, or hydrogen bonding.

I Introduction

A Scope

B Literature Search and Referencing

C Definitions of Compatibility

D Experimental Determination of Compatibility

II Theoretical Aspects

A Types of Phase Diagrams

B Flory–Huggins Theory of Polymer Solutions

C Equation of State Theories of Polymer Solutions

III Experimental Data

A Arrangement of Data

B Tables of Polymers That May Be Compatible at Room Temperature

IV Prediction Schemes for Polymer–Polymer Compatibility

A Review of the Literature

B A Simple Scheme Based on Flory–Huggins Theory

C A Critique of the Simple Scheme and Comparison with Data

Appendix: Review of Data on Polymer Mixtures in the Literature

A Cellulose Derivatives and Other Cellulose Derivatives

B Cellulose Derivatives and Other Polymers

C Polyisoprene and Other Polymers

D Poly(vinyl chloride) (PVC) and Other Polymers

E Polyethylene (PE) and Other Polymers

F Polybutadiene (PBD) and Other Polymers

G Poly(vinyl acetate) (PVA) and Other Polymers

H Polystyrene (PS) and Other Polymers

I Acrylic Polymers and Other Acrylic Polymers

J Acrylic Polymers and Other Polymers

K Miscellaneous Homopolymers

L Miscellaneous Homopolymers and Miscellaneous Copolymers

M Copolymers and Other Copolymers

N Mixtures of Three Polymers

O Same Copolymer but Different Compositions




A Scope

In this chapter, the words polymer compatibility refer to the total miscibility, on a molecular scale, of homopolymers and of random copolymers with each other in various combinations. In this connection, it is understood that miscibility on a molecular scale is not necessarily random; interactions between similar or different molecules may lead to a small amount of clustering or other nonrandom arrangements