摘要:

OBNBRAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Conf3gurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Etkcts in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Fixcited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Oxidat ion Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 For current availability of Discussion volwnes, see back cover.OBNBRAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Conf3gurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Etkcts in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Fixcited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Oxidat ion Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 For current availability of Discussion volwnes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC97457FX001

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 1911 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 I918 1918 1918 1Yl8 1919 1919 1920 1920 1920 lY20 1921 1921 lY21 1921 1922 1922 1 923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 I926 1 927 1927 1 927 Subject Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotary Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures in a Laboratory Refractory Materials Training and Work of the Chemical Engineer osmotic pressura Pyrometers and Pyrometry The Setting of Cements and Plasters Hectrical Furnaces co-ordination of scientitic Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope : Its Design, Construction and Applications Basic Slags : Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer TheoricS of chemical Action Some Properties of Powders with special reference to Grading by The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physidhemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytcs Cohesion and Related Problems capillarity Hutriation Orientation Volume Trans. 3 3 6 7 8 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 16 16 16 17 17 17 17 18 18 19 19 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24GENERAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1928 1929 1 929 1929 1930 1930 1931 1932 1932 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1938 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1943 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 A950 1951 1951 1952 1952 1 952 1953 1953 1954 1954 Subject Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals.Third Repon Molecular Spoctra and Molecular Structure Optical Rotatory Power Colloid Science Applied to Biology Photochemical Proccssts The Adsorption of Gases by Solids The Colloid Aspects of Textile Materials Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerhation and Condensation Disperse System in Gases : Dust, Smoke and Fog Structure and Molecular Forces in (0) Pure Liquids, and (b) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war tho meeting The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High PolymrrS.(Joint Meeting with the Plastics Group, Society of Chemical Industty) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielearia Swelling and Shrhkhg Electrode Proastie3 The Labile Molecule Surface Chemistry.(Jointly with the sOciet6 Q Chimic Physique at Colloidal Electrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Rocea~ MeWwgy Crystal Growth Lipo-Proteins Chromatographic Analysis was abandoned, but the papers were printed in the TronsactionS) system Bordeaux.) Published by Butterworths Scientific Publications, Ltd. HeterogenioUS catalysis Physicochemical Properties and Behaviour of NucIear Acids Trans. 46 Spectroscopy and Molecular Structure and Optical Methods of In- vestigathg cell structura Disc. 9 EWtricaI Double Layer Trans. 47 Hydrocarbons Disc. 10 The Size and Shape Factor in Colloidal System Radiation Chemistry The Physical chemistry of Protains The Reactivity of Free Radicals The Equilibrium Properties of Solutions of Non-Elaolm The Physical Chemistry of Dyeing and T d g The Study of Fast Reactions Coagulation and Flocculation 11 12 13 14 15 16 17 18 Volume 24 25 25 25 26 26 27 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 35 36 37 37 38 39 40 41 42 42 A 42 B Disc.1 2 Tram. 43 Disc. 3 4 5 6 7 8OBNBRAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Conf3gurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Etkcts in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Fixcited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Oxidat ion Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 For current availability of Discussion volwnes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC974570X003

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

OBNBRAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Conf3gurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Etkcts in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Fixcited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Oxidat ion Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 For current availability of Discussion volwnes, see back cover.OBNBRAL DISCUSSIONS OF THE PARADAY SOCIETY Date 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Conf3gurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Etkcts in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Fixcited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Oxidat ion Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 For current availability of Discussion volwnes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC97457BX006

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Introductory Lecture BY P. J. FLORY Stanford University, Stanford, California, U.S.A. Received 6th March, 1974 Four types of gels are distinguished according to their structure : 1, ordered, lamellar gels (e.g., clays, soaps, and similar mesophases) ; 2, covalent polymer networks ; 3, polymer networks formed by physical aggregation of polymer chains through the agency of multistranded helices or of crystal- line domains ; 4, particulate disordered gels (e.g., fibrillar or reticular precipitates, aggregated globular proteins, etc.). Continuity of structure over macroscopic dimensions and permanency of that structure are cited as the underlying features common to gels in general. The preponderance of the gels and gelling processes brought before this Discussion are of types 2 or 3.The statistical theory of molecular distributions in randomly interlinked systems is reviewed and the theory of gelation is discussed in relation to experimental measurements and observations. The term " gel " from which this Discussion derives its title has traditionally been construed to embrace a diversity of combinations of substances. Included are such disparate systems as lamellar mesophases, inorganic clays, vanadium pentoxide gels, phospholipids, certain disordered (or partially disordered) proteins, and, of course, three-dimensional or network polymers. A more dissimilar collection, from the point of view of composition and structure, scarcely could be imagined. Yet, the connotation of the term itself is unambiguous, referring as it does to the character- istics, conspicuously apparent and patently identifiable, of gelatinous substances.It was introduced at a time when the chemical constitution of all but the simplest substances could not be perceived by the methods at hand. Physicochemical prin- ciples applicable to condensed states of matter had not been formulated. Hence, it was natural to attempt classification in terms of phenomenological characteristics manifested in properties and behaviour. Concepts concerning the structural nature of various gels were qualitative. There was, to be sure, the cherished hope that a universal principle would embody all members of the class, just as liquids are character- ized by a kind of molecular disorder that distinguishes them from crystalline solids. If earlier generations of colloid chemists should be criticized for being oblivious of the profound differences between various gels at the molecular level, then we face the risk of being blinded by these differences to the extent of failing to take cognizance of those structural features that gels may share in common, despite their manifest differences.The search for constitutive features common to different kinds of gels is surely worth the effort in any case. Moreover, in an era when subdivision of science has been carried to extremes, the organization of a Discussion that brings together workers in differentiated subdisciplines is especially to be commended. UNIVERSAL CHARACTERISTICS OF GELS Bungenberg de Jong defined a gel as a " . . . system of solid character, in which the colloidal particles somehow constitute a coherent structure, .. .". Hypothesis concerning particulate structure is joined with observational fact in this definition. With somewhat greater elaboration, P. H. Hermans presented three propositions as 78 INTRODUCTORY LECTURE follows to define a gel : “ (a) they are coherent colloid systems of at least two corn- ponents ; (b) they exhibit mechanical properties characteristic of a solid ; (c) both the dispersed component and the dispersion medium extend themselves continuously throughout the whole system.” The coiicept of coherence of structure, enunciated also by Bungenberg de Jong2 is affirmed in (a). Proposition (c) appears to be self- contradictory, for if one component is dispersed how can it extend continuously? It also blurs the significance of the coherence asserted in (a).The insistence on at least two components in (a), if taken literally, would eliminate vulcanized rubber, dry gelatin and various polymeric networks (all of these being xerogels in the terminology of Freundlich). Hermans goes on to qualify (a) above by admitting as gels those substances which, though consisting of a single component, are capable of swelling in the presence of a second component, specifically a liquid such as water, benzene, etc. To delve further into matters of definition would be at the hazard of perpetuating the practice, so prevalent in this field in the past, of obfuscating understanding by excessive preoccupation with terminology. The subject, after all, encompasses too much to admit of containment within neatly erected definitions.For, as D. Jordan- Lloyd is quoted as having said nearly a half century ago, “The colloidal condition, the gel, is one which is easier to recognize than to define.” The one feature identified almost universally as an essential characteristic of a gel is its solid-like behaviour. When deformed its response is that of an elastic body. If plastic flow occurs as well in a system deemed by accepted doctrine to have the attributes of a gel, it will so respond only above a finite yield stress ; deformation at lower stresses is held to be recoverable, and hence elastic. Further, the elastic compliance of a gel generally is large, i.e., the modulus of elasticity is low. One may infer from this universal characteristic of those systems regarded as gels that they must possess a continuous structure of some sort, the range of continuity of the structure being of macroscopic dimensions.The frequent allusion to coherence or continuity of structure in the compendious colloid literature on gels bespeaks an awareness of this implication of their solid-like behaviour. As a corollary inference, the continuity of structure must possess a degree of permanency-at least for a period of time commensurate with the duration of the experiment. Transient structures formed by bonds which dissociate or are redistributed at rates that are rapid in comparison to the time scale of observatioii of the system would not qualify. STRUCTURAL CLASSIFICATION OF GELS If it be granted that the presence of a continuous structure is the feature common to all gels, then it becomes important to differentiate the several kinds of structures occurring in various gels.The diversity of systems covered by the term gel enhances the importance of the task, and renders it more difficult as well. A scheme offered here for the purpose of classifying gels on the basis of structurai criteria subdivides them into four types as follows : 1. Well-ordered lamellar structures, including gel mesophases. 2. Covalent polymeric networks ; completely disordered. 3. Polymer networks formed through physical aggregation ; predominantly 4. Particulate, disordered structures. Soap gels and phospholipids afford familiar examples of the first type. disordered, but with regions of local order.Clays also Well-defined lamellae are arranged in parallel, giving rise to order of are included.P. J. FLORY 9 comparatively long range.4 Gels of this type are addressed by two contributions to this Discussion, one by Hayter, Mecht and White on aqueous perfluorocarboxylate systems, and the other by Callaghan and Ottewill on montmorillonite gels. The forces between the lamellae may be electrostatic, and hence of long range ; they may be mediated by polyvalent gegenions. In phospholipids, on the other hand, van der Waals forces, and dipolar interactions are dominant. Gels of the second type present the opposite extreme of complete disorder. Continuity of structure is provided by a ramified, three-dimensional network com- prising structural units covalently linked one to another.Some, at least, of the units must be polyfunctional; i.e., they must be connected to more than two other units. The network pervades the entire space occupied by the system, unless fragmented mechanically or interrupted by phase boundaries (as in an einulsion particle). Hence, the molecular weight of the network usually may be regarded as infinite, andit is appropriately referred to as a singular constituent, albeit a macroscopic one. The network ordinarily is homogeneous in the sense of being free of ordered regions, micelles or other structured aggregates. Examples are : vulcanized rubbers, the elastic structure protein elastin, condensation polymers formed from reactants some of which are polyfunctional, vinyl-divinyl copolymers, alkyd and phenolic resins, paint films and polysilicic acids. Polymeric gels of this type are well represented in this Discussion (see papers by G.Allen, Beinert, Burchard, Stepto, Wun and Covas). These include the quantitatively cross-linked polystyrene networks prepared and investigated by G. Allen, Holmes and Walsh ; networks prepared by the novel inter- linking reactions conceived and developed by Beinert, Belkibir-Mrani, Herz, Hild and Rempp ; vinyl polymer networks generated through chain transfer reactions involving a vinyl monomer unit (e.g., vinyl acetate) subject to chain transfer, these networks being treated theoretically according to cascade theory by Burchard, Ullisch and Wolf; the polyesters and polyurethanes synthesized under quantitatively controlled condi- tions and investigated by Stepto; and the gels resulting from condensation of de- camethylene glycol with benzene-l,3,5-triacetic acid discussed in the paper by Covas, Dev, Gordin, Judd and Kajiwara, and so thoroughly investigated by Gordon and his coworkers as reported in part in previous papers.Gels of this class generally undergo swelling in suitable diluents, often with mani- fold increases in volume. They are insoluble in solvents that do not attack their covalent chemical structures. If the complications of the glassy and crystalline states are circumvented by choice of conditions, they exhibit elastic behaviour that is typical of gels. The modulus of elasticity depends on the density of interlinking of the net- work. It is low for networks exemplified by vulcanized rubbers.The importance of polymer gels of type 3, and the interest they command at present, is attested by the fact that the largest group of papers (by Harrison, Beltman, Covas, Eagland, A. Allen, Morris, Reid, Derbyshire, Segeren and Smidsrrad) presented in this Discussion concerns gels of this kind. Here primary molecules, usually of linear structures but in any case of finite size, are bound together either through the formation of crystallites involving bundles of chains, or by multiple-stranded helices spanning sequences comprising a number of units in each of the chains thus joined. In the case of gelatin, triple helices like those in native collagen are formed,5* and these appear to be further aggregated to form small crystalline domains at higher concentrations (above ca.5-7 % v/v in ethylene glyc~l).~ At low concentrations the triple helices appear to be individually dispersed without aggregation as crystallites. 9 '9' Only a small fraction of the gelatin may be involved in the ordered domains, of which- ever kind. The liaisons thus established fulfill the role of the polyfunctional branches or cross linkages in gels of type 2. That is, they implement the creation of an10 INTRODUCTORY LECTURE " infinite " network that extends throughout the system as a whole. At higher con- centrations of gelatin where crystallites perform this role, the functionalities of the resulting interchain connections may be quite large, depending, of course, on the cross-sections of the crystallite bundles.The crystalline domains responsible for gelation in the copolymers of vinylidene chloride/methacrylate investigated by Harrison, Morgan and Park, and in the poly- (vinyl alcohol) gels of Beltman and Lyklema may likewise be viewed as cross linkages of large functionalities. The mucoprotein of gastric mucus may be included in the same category according to the work of Allen, Pain and Snary. Micellar junctions occurring as a result of hydrophobic interactions provide the polyfunctional con- nections required for formation of networks in these interesting and obviously im- portant gels. In the i-carrageenan and alginate gels treated in the later papers of this Discussion, the proportion of the polymer involved in helices appears to be large (see, for example, Bryce, McKinnon, Morris, Rees and Thorn), leaving only a lesser fraction of the material in the random-coil state.This is reflected in higher moduli of elasticity (see Segeren, Boskamp and van den Tempel, and Smidsrard). Gels of type 3 could be considered to partake of some of the character of those of type 1 inasmuch as the crystalline bundles, or the multistrand helices, are ordered; i.e., the participating chains are committed to a unique conformation, and in the case of crystallites they occur in a regular array as well. On the other hand, the orienta- tions of separate ordered regions in gels of type 3 are mutually uncorrelated; their locations may likewise be independent. Chains between the ordered domain are random, and generally account for the preponderance of the polymer.Hence, these gels are more closely related to those of type 2. The principal difference arises from the physical character of the interconnections responsible for the formation of the network in type 3 gels, in contrast to the covalently linked networks of those of type 2. Type 3 gels therefore are reversible ; they can be dissolved and reformed by cycling the temperature or the solvent. The fourth category of gels includes flocculent precipitates, which usually consist of particles of large geometric anisotropy, e.g., needles or fibrils in brush-heap disarray, or reticular networks of fibres as in V205 gels. Also included are gels formed by aggregation of proteins. Gelation of proteins frequently occurs under conditions promoting their partial denaturation.The protein may be fibrillar (e.g., dispersed collagen protofibrils), or globular (e.g., serum albumen; see the paper by Tombs). The interactions causing the structural protein particles to aggregate to a gel in such instances may be non-specific. On the other hand, specific interactions between well- defined sites appear to be responsible for the formation of gel-like aggregates in the early stages of clotting of fibrin and, with special note, in antibody-antigen inter- actions. Before concluding this qualitative survey of types of gel structure, a few remarks are due on the requisite of permanency of that structure. Note of this requirement is especially relevant to gels of type 3, which assume foremost prominence in this Discussion. Transitory inter-chain connections such as may be provided by hydro- gen bonds, for example, obviously would be ineffective.The resulting " structure " could be termed a network, to be sure, but the fluctuations of its connections would impair its ability to recover from deformation, except within a very short interval of time. If, however, the interchain bonds form cooperatively over domains, the permanency of the interconnections is enormously enhanced. Interchain forces much inferior to those of hydrogen bonds may then suffice. Multiple interactions over extended sequences of units or over three-dimensional domains must therefore beP. J. FLORY 11 regarded as indispensable for realization of effective physical cross-linking in gels of type 3. Gels of this class may nevertheless be vulnerable to effects of thermal fluctuations, which in the course of time may destroy the initial physically aggregated (or crystal- lized) domains and bring about formation of others in their stead.These processes will be more rapid the smaller the sizes of the domains. On a sufficiently long time scale, the existences of the domains are inevitably transitory. Under the influence of a finite stress, therefore, these gels should be susceptible, in some degree, to irre- versible deformation. Hence, rigid insistence on the rule that a true gel may not succumb to plastic flow below some finite yield stress probably would disqualify most examples of type 3. Some of the covalent networks of type 2 would have to be rejected as well owing to the susceptibility of their inter-unit linkages (e.g., esters and amides) to chemical interchange or attack, or of their cross linkages (e.g., disulphide linkages in vulcanized rubbers) to rupture or interchange.Clearly, the criterion of permanency needs to be applied with a measure of restraint. QUANTITATIVE STATEMENT OF CONDITIONS FOR GELATION THROUGH FORMATION OF INFINITE NETWORKS The critical condition for appearance of an infinite network is formulable with a minimum of ambiguity for the systems of type 2, whose structures depend exclusively on covalent linkages. Conclusions reached in the analysis set forth briefly in outline below should be applicable to those of type 3, and, in principle, even to type 4 gels. Consider a system consisting of trifunctional units in admixture with The A and B units ‘A bifunctional units B-B present in stoichiometric proportion.condense to form inter-unit linkages AB. Thus, 2A-/A i- 3B-B-+ A \A AB--B A-/ AB-BA- / \AB--B A-/ \AB-B \AB-B B--BAAB--BA--/ A AB-B \A. We assume, as an approximation, offered at this stage without justification, that condensation between an A and a B group on the same molecule is forbidden. The error committed in this approximation has been investigated and discussed on a number of occasion^.^' It does not vitiate any of the main conclusions to be drawn; the error may be looked upon as a perturbation of numerical calculations which, though small, usually is not negligible when quantitative comparison of theory with experiment is attempted. It is assumed further lo* l 2 that condensation of a given functional group does not affect the reactivities of remaining unreacted groups of the same unit, or of those located elsewhere in the same molecule.Compliance with this condition can be12 INTRODUCTORY LECTURE assured by selection of monomers in which the functional groups are sufficiently separated to assure their mutual independence. The combination of A and B groups must then take place at random (apart from the constraint imposed by the assump- tion stated in the paragraph above). It follows that the expectation that a given functional group has undergone reaction is independent of fates of other functional groups, and may be equated to the over-all extent of reaction, which we denote by p . Thus, p may also be identified as the Q priori probability that any given functional group has condensed. Passage from a given branch point in the system here considered to another branch by proceeding along a chosen path is contingent upon the prior formation of two linkages, one AB and the other BA.The probability that the necessary path has been established is specified by the branching probability a, which for the case considered is related to the extent of reactionp according to a = p 2 . This relationship requires revision and elaboration if the reactants are present in nonstoichiometric proportions, if monofunctional reactants also are present, or if functional groups differ in reactivity. A branching probability can be defined in virtually any set of circumstances, however, provided that the necessary information is at hand.If the path from one branch to the next considered above has been successfully negotiated, arrival at the next branch presents an explorer with two alternative paths. The probabilities of success and failure are a and 1 -a, respectively, along each path. It will be apparent that if a < 3, cul de sacs must eventually overcome proliferation via branches, with the result that the exploration must come to an end after a finite number of steps. Stated with reference to the problem before us, an infinite network is a statistical impossibility when a < 3, or even if a = 3. If, however, a > 3, so that the expected number of new paths to be found in the next step exceeds unity, then unlimited proliferation of paths is a possibility-unlimited, that is, apart from the bounds set by the finite amount of material in the system.We take pains to observe that unlimited proliferation starting from a given unit is a possibility, and not a certain outcome for + < a < 1. All paths leading from a given unit may be barren. Or, one of them may be productive but the branch thus reached may be fruitless; etc. But for a > a, = 3, proliferation without limit (apart from the finite size of the system) is a finite possibility. It follows that an “infinite” network must occur for a > 3, but that it will not include all of the material in the system; finite molecules must coexist with it (for a < 1). Generalization of the foregoing argument to a system containing branch units of any functionalityfleads at once to the critical condition “ 9 l2 CX, = (f-1)-1.For networks generated by random cross-linking of linear polymer chains, the cross-linkages furnish the polyfunctional units. Each cross-linked unit in a given “ primary ” chain leads to another chain. Pursuing a course analogous to that out- lined above, we focus attention on the expected number E of additional cross-linked units that may be discovered in the chain reached via the cross-linkage mentioned above. If the chain contains y units and the fraction of cross-linked units in the system as a whole is p , then lo, l2 E = p(y-l)%py. (3) in the first rendition of eqn (3) we allow for the ineligibility of the unit involved in theP. J. FLORY 13 cross-linkage by which the chain in question was reached.In general, the lengths of the primary chains will be variable. Hence, y should be replaced by its expected value yw, the weight average degree of polymerization of the primary rn01ecules.~~ Assuming j&, % 1, we have therefore that EM p j w . (4) By arguments duplicating those above, the critical condition requires E = 1. Hence 11* pc = j;? Circumstances of greater complexity than those presented by simple condensation in a system containing a single polyfunctional reactant (f> 2), or by the binary combination of chains through cross-linkages (tetrafunctional) are common. The foregoing schemes then require elaboration or replacement by alternative procedures. In general, however, it is possible to deduce, from statistical arguments, the critical condition for emergence of an " infinite '' network, i.e., a coherent, continuous structure requisite to appearance of a gel.It is essential, however, that the gel in question be one of random structure. This qualification at once excludes gels of type 1. In the most general terms, structural elements must be appropriately chosen. These may be linear polymer chains, or polyfunctional units, etc. Then, if the gel- forming process joins these elements at random, the necessary and sufficient condition for gelation (i.e., infinite network formation) requires that the expected number of elements joined to any arbitrarily chosen element must exceed two. In these general terms, the identification of gelation with the appearance of a continuous network may be applicable, in principle, also to gels of type 4.The critical conditions for gelation, as derived above from elementary statistical considerations, have been verified experimentally. 7* O -l 9 I4 The error arising from the neglect of intramolecular (cyclic) connections within finite species usually is reflected in a displacement of the gel point by a few percent in polyfunctional con- densations. It appears to be variable depending on the system. The combination of decamethylene glycol with benzene- 1,3,5-triacetic acid investigated by Covas, et Q Z . , ~ appears to be a particularly felicitous choice in this respect, the vitiation of the gel point being less than one percent. The joining together of molecules to form an infinite network calls to mind a number of interesting analogies.Games of chance provide intimate parallels-and useful mathematics as well. Analogies to demographic problems, to the Galton- Watson process whereby family names are weeded out, to chemical explosions brought about by branching chain reactions and to nuclear chain reactions l 6 , l 7 induced by neutrons, are readily apparent. Vapour-liquid condensation often is cited as an analogous process. The analogy here occurs, however, in the graph-theoretical pattern of the cluster integrals used in the mathematical formalism, rather than in the physical clustering of molecules at incipient condensation, as might at first thought be presumed. In all of the analogues mentioned above, with the exception of the last one, the matter of concern is the critical event : the gambler's realization of limitless gain ; an explosion, population, chemical or nuclear ; etc.The patterns of the branching paths by which the process proceeds are only of fleeting significance. The precise sequences of events leading to the critical state are overshadowed by the catastrophe, and hence are of little interest in themselves. In a system of non-linear polymers, " events " delineate molecules co-existing in time and sharing the same space, and the14 INTRODUCTORY LECTURE " catastrophe " is a benign network, amenable to quantitative measurement without wreaking havoc in the laboratory-or to mankind. The statistical distribution of finite molecular species as a function of their size and complexity assumes significance without parallel in the analogous examples cited.MOLECULAR DISTRIBUTIONS Deeper insight into the nature of the process of gelation through network formation is gained by examination of the distribution of molecular species according to size and complexity. Again consider a trifunctional branching system. Out of all the polyfunctional (f = 3) units in the system, the fraction that are situated in molecules containing exactly x branches is found by statistical analysis to be lo where a being the branching probability defined earlier. (The original result given in ref. (10) has been translated to present terminology and expression according to eqn (6) by re-normalization.) Since the molecular weight is approximately proportional to x, we may, with little error, regard w, as the weight fraction of all species of " size " x.The function p reaches its maximum value Pmax = BC = + at a = a, = 3. It will be apparent that w, is a rapidly decreasing function of x throughout the physically significant range 0 < a d 1. Stockmayer's generalization of this result to systems of any functionality f is * W, = [3(2x)!/(x +2)!(~ - 1) !I( 1 - a)2a-1/P (6) p = a(1-a), (7) w, = If(fx - x)/ ! ( f x - 2x + 2) !(x - 1) !I( 1 - a)2a-1 B" (8) p = a(1 -a)f-2. (9) where Again, /? reaches its maximum values Bc at a = a, = (J- l)-'. These distribution functions for non-linear polymers possess a characteristic that is both revealing and useful. lo This characteristic becomes apparent if one inspects the normalization of these functions. Let w, be the sum over all species.Then (10) The value of the summation in this equation depends only on p and not otherwise on a. Since a is a double-valued function of B for fl < /3, it follows that w, must differ for the two a's corresponding to a given value of p. Letting these roots of /3 be denoted by a' and a with a' < a, < a, we find that the distribution function is indeed normalized, i.e., w, = 1, for a' < a,, in keeping with its derivation. It follow that for a > cc, which is less than unity. 03 X w, E c w, = (1-a)2a-1 c [f(fx-x)!~(fx-2x+3)!(x-l)!]p". 1 1 w, = (1 - a)2a'/( 1 - a')2a (1 1) w, = (1 -a)3/a3 a 2 a,. (12) For f = 3 this result simplifies to This apparent violation of the condition of normalization of the distribution function w, when a exceeds its critical value seemed at first sight to suggest that these functions should be confined to the pre-critical range.Yet, re-examination of the derivation revealed no basis for such limitation. What came to light was the fact that the derivation comprehends only molecular species that are bounded, and therefore finite." Hence, the sum over w, leaves the infinite component out of account. This omission was at once turned to advantage, for it was apparent thatP. J. FLORY 15 the sum over u’, for a > a, must give precisely the amount of“ sol ” to the exclusion of gel. Thus, w, can be identified with the weight fraction of sol and wg = 1 - H’, with the weight fraction of gel. The partitioning of the polymer between sol and gel finds analogy in the ancient problem of gambler’s ruin, or of extinction in the current terminology of cascade theory. The distribution functions given above have been re-derived by the methods of cascade theory, which have proved powerful and versatile, especially for obtaining characteristics of the distribution relevant to light scattering and other measurements conducted on polymeric systems (see especially the work of Gordon and collaborators cited in their paper at this Discussion; also see Burchard, Ullisch and Wolf).It will be obvious that an infinite network cannot conform to the assumption, common to all treatments of molecular distributions, that intramolecular connections may be ignored. The term “ network” itself was deliberately chosen, in fact, to acknowledge their presence.This being the case, it has on occasion been argued that the treatment recited above is palpably invalid beyond a = a, inasmuch as intra- molecular reactions are essential to the gelation process. The objection is without force, however, for our derivation is addressed implicitly to finite species only.“ The derivation is oblivious of the network, the amount (ws) of which is determined only by its absence from the distribution function.12 As a advances beyond the gel point, fl diminishes and the distribution function retrogresses. Larger species, never present in major amount, become less abundant, as follows from the dependence on flX in eqn (6) and (8). The dwindling amount of species of degree of branching x with increase in x, even at the gel point, leads to the conclusion that the distinction between sol and gel is discrete.This distinction may be likened to that between a vapour and the liquid with which it is in equilibrium. (The critical point for gelation is not analogous to the vapour-liquid critical point, however.) It is a discontinuity-or, at least, about as close to a discontinuity as one encounters in the real physical world. Which is to say that it cannot be a discontin- uity in an absolute sense, as Gordon and his coworkers point In order to delve further into the nature of the discontinuity, it is useful to con- sider the asymptotic form for w, for large x. Forf= 3, we obtain lo from eqn (6) wxz((3/Jn)(l -~)‘a-~(fl//3~)”(~+ I)-%, x B 1. (13) The weight fraction of x-mer decreases monotonically with x at all stages.The decrease is least pronounced at the critical point where #?/Be = 1. It accelerates as the system is displaced from the gel point, in either direction, owing to the decrease of this ratio below unity. The attrition is the more severe the larger the size (x). The corresponding expression for any f > 2, which differs significantly from eqn (1 3) only in the numerical factor, is given by Covas, et aZ.,7 (this Discussion). As they show, the “ discontinuity ” can be traced continuously by use of this relation if the sample is small, say of the order of 1 mg. The demarcation between sol and gel must become much more diffuse in the case of an emulsion particle consisting of about 1 pg (10-l2 g) of polymer which, even if combined into a single molecule would have a molecular weight only of about 1 tD (10” Daltons).Molecular distributions resulting from the introduction of cross-linkages into a system of linear “ primary ” molecules are similar to those described above for syst- ems formed by polycondensation.12* For the case of long primary chains of uniform length, for example, the weight fraction of species comprising z chains connected by z - 1 cross linkages is lo w, = (zZ-l / z ! y)(/I/ey x ( J2xr)-lj~z-* (14)16 INTRODUCTORY LECTURE where y is the “ cross-linking index ” or ratio of cross-linked units to primary mole- cules in the system (equal to E of eqn (3) for the chains of uniform length here con- sidered), and Again, /I exhibits a maximum at y = yc = 1 from which it follows that for y > 1 where y‘ and y are solutions of eqn (1 5) for the given value of /I, with y‘ < 1 < y.The close correspondence between eqn (1 3) and (1 5) is apparent. The characteristics of the molecular distributions for gelling systems embodied in these relationships appear to be quite general. The molecular distribution does not lend itself readily to direct experimental determination. Gordon and coworkers ’9 have shown, however, that the species of lowest complexity in the decamethylene glycol-benzene triacetic acid system occur in amounts that agree with theory at various stages of the polycondensation. Chro- matographic analyses of the molecular species present in silicate melts investigated by Wess 2o were found to be in approximate accord with the distribution prescribed by eqn (6).Evidence for critical gelation, dependent upon the cation and its concen- tration in molten silicates, was also presented by Hess.20 Gordon and coworkers have adduced concrete evidence for retrogression of the distribution within the sol fraction as the system is carried beyond the gel point. Larger species of greater complexity are selectively converted from sol to gel, with the result that, according to theory, the molecular distribution in the residual sol reverts toward lower species as was noted above. Gordon, et aZ.,7 have obtained evidence confirming this most important aspect of the distribution functions for gelling systems, which heretofore appears not to have been examined quantitatively, although various qualitative observations could be cited in its support.Characteristics of the distri- bution, such as may be deduced from light scattering measurements, afford further confirmation of the theory in this respect (see also Burchard, et al., this Discussion). In the light of these results and those afforded by determinations of gel points, the applicability of the statistical theory is well established, at the very least in its broader aspects. Further definitive experiments are needed, however, to assess its reliability in detail. B = Y exp(1 -Y>. (15) ws = Y‘/Y (1 6) PHYSICAL PROPERTIES OF GELS It would be impracticable to attempt to summarize the properties of gels compre- hensively within the confines of this Introduction. Certain properties that reflect the structure of gels deserve mention nevertheless, especially as they assume prominence in a number of the contributions to this Discussion.Foremost, perhaps, is the elast- icity manifested by lightly cross-linked networks exemplified by vulcanized rubber, and illustrated also by the polystyrene gels prepared and investigated by Allen, Holmes and Walsh. The central issues of concern here focus on the modulus of elasticity and its relation to structure according to current theory of elasticity of polymer networks. The theory is derived for an idealized network comprising “phantom” chains in which the only operative constraints are those delivered directly through the network junctions or cross-linkages. The degree to which real networks may depart from this idealization is difficult to ascertain on theoretical grounds ; resort to experiments on networks whose structures can be quantitatively evaluated appears more promising at present, and this is the approach chosen by Allen, et al.But the difficulties do not end here. Characterization of the structure of a real network requires comideration of “ imperfections,’’ or “ defects,” on the one hand,P. J. FLORY 17 and entanglements on the other. The former arise from chain ends that relieve portions of the structure from the constraints prevailing within a perfect network, and from cyclic paths of short range within the network. These imperfections must reduce the effective degree of cross-linking ; entanglements must increase it. Cor- rection for defects arising from chain ends can be introduced in a satisfactory manner, in the opinion of this author, views to the contrary notwithstanding.Consideration of cyclic connections raises an unanswered question : How small must a cycle be for it to be ineffective as a network connection? Moreover, the concept of entangle- ments, although realistic, remains a qualitative one. Allen, et al., attempt to take account of entanglements semi-empirically-a strategy that seems rational at present, although less than satisfying from the point of view of theory. Until the vagaries of entanglements and structural defects can be overcome, quantitative correlation of elastic properties with the structure of gel networks faces severe difficulties. Nevertheless, elasticity measurements will continue to serve as an index of the degree of interconnection in such gels.The utility of such measurements is demonstrated in the contributions of Beltman and Lyklema, of Segeren, Boskamp and van den Tempe1 and of Smidsrard. It has long been recognized that equilibrium swelling measurements provide an alternative to the modulus of elasticity for the characterization of gel networks. The thermodynamic interaction of the diluent with the polymer enters the scheme, in conjunction with the elastic response of the network to the concomitant isotropic dilation of the system. Recent experiments 2 1 show that the thermodynamic inter- action, as expressed in the parameter x, is the same as for the corresponding linear polymer at the same concentration. However, quantitative characterization of the network structure on the basis of swelling measurements is fraught with the same difficulties confronting use of elasticity measurements for this purpose.DuSek, in his paper, introduces an effective functionality in order to take account of network defects in the treatment of the thermodynamics of swelling. The dynamic behaviour of gels is a subject of perpetual interest and fascination. Theories continue to be cast in terms of mathematical models which must be judged according to their compatibility with experimental measurements rather than their correspondence to the detailed chemical structure, and the architecture of the network in the case of a gel. Nevertheless, Edwards in his paper offers assurances that a gen- eral theory can be formulated to represent the essential properties of polymers, inclusive of polymer gels. Inelastic scattering methods using light (Wun, Feke and Prins) or neutrons (Hayter, Hecht and White) are amongst the newer experimental methods available for investigating molecular motions in gels. The motions of diluent molecules can be monitored also by n.m.r. techniques (Hayter, et al. ; Duff and Derbyshire). These methods hold the promise of a greatly enlarged body of information on mobility in gels at the molecular level. Thomas Graham, Phil. Trans. Roy, SOC., 1861, 151, 183 ; J. Chem. SOC., 1864, 17, 318. Amsterdam, 1949), p. 2. P. H. Hermans, as in ref. (2), pp. 483-494. see Discussions of the Faraday Society, No. 42 (1966). P. J. Flory and R. R. Garrett, J. Amer. Chem. SOC., 1958, 80, 4836. P. J. Flow and E. S. Weaver, J. Amer. Chem. SOC., 1960, 82,451. D. Eagland, G. Pilling and R. G. Wheeler, this Discussion. R. J. Goldberg, J. Amer. Chem. SOC., 1952, 74, 5715 ; 1953, 75, 3127. * H. G. Bungenberg de Jong, Colloid Science ZI, ed. H. R. Kruyt (Elsevier Publ. Co., Inc., ’ C. A. L. Peniche-Covas, S. B. Dev, M. Gordon, M. Judd and K. Kajiwara, this Discussion. lo P. J. Flory, J. Amer. Chem. Soc., 1941,63,3083,3091 and 3096; J. Phys. Chem., 1942,46,132.18 INTRODUCTORY LECTURE I ' W. H. Stockmayer and L. L. Weil, Advancing Fronts in Chemistry, ed. S . B. Twiss (Reinhold Publishing Co., New York, 1945), Chap. 6. * P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, N.Y., 1953) Chap. IX. l3 R. W. Kilb, J. Phys. Chem., 1958, 62,969. l4 R. F. T. Stepto, this Discussion. l 5 W. H. Stockmayer, J. Chem. Phys., 1944, 12, 125. l6 E. Schrodinger, Proc. Royal Irish Academy, 1945,51, 1. l8 W. H. Stockmayer, J. Chem. Phys., 1943, 11, 45. l9 N. S. Clarke, C. J. Devoy and M. Gordon, Brit. Polymer J., 1971, 3, 194. 2o P. C. Hess, Geochim. Cosmochim. Acta, 1971,35,289. 2 1 Unpublished results of H. Neidlinger and Y. Tatara, Stanford University, 1972-73. R. P. Feynmann, Los Alamos Scientific Laboratory, Ser. €3, LA-524 (1947).

ISSN:0301-7249    

DOI:10.1039/DC9745700007

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Model Polystyrene Networks BY G. ALLEN, P. A. HOLMES AND D. J. WALSH Chemistry Dept., University of Manchester, Manchester MI 3 9PL Received 28th December, 1973 Model networks have been prepared, at different concentrations in an inert solvent, in such a way that the number of crosslinks is accurately known, and the topology of the network can be varied in a controlled way. The contribution of various network defects to the modulus of the net- work has been examined. A theoretical estimate of their effect has been made and compared to the experimental result. Two tentative conclusions have been made ; first, that the front factor A in the equation for the free energy of deformation of the network has a value of 3 and not the alternative value 1 ; and secondly that the contribution of entanglements to the modulus of the network varies as the concentra- tion squared rather than as the concentration to the first power.The various theories of rubber elasticity lead to a general expression for the free energy change on deformation of a network of the form : where v = the number of elastically effective network chains, k = the Boltzmann constant, T = the absolute temperature, Ax, Ay, ,Iz = the deformation ratios in the directions specified by the x, y and z axes and A and B are constants. Flory and Wall predict that A = 1 and B = +,1-4 whereas James and Guth 5-8 give a value of A which is dependent on the crosslinking process and for the random crosslinking of existing polymer chains is 3, and a value of B = 0. Edwards also obtains a result which is consistent with that of James and Guth, with A = 3, without assuming any crosslinking process.The values of the constants A and B differ for the various theories. The theory results in a value of G, the shear modulus, of G = AvkT = 2AnkT (2) where rz = the effective number of crosslinks per unit volume. It should also be pointed out that these equations would have to be corrected for the change in dimensions of the network chains if the network was prepared in the presence of a solvent and the concentration of this solvent changed before the modulus was determined. But as long as the network is prepared in solution at a high enough concentration for the chains to exhibit their unperturbed dimensions, and the modulus is measured at the same concentration, this can be ignored.Thus, by measuring the modulus of a network containing a known number of elastically effective chains it is, in principle, possible to determine the value of A. Previous attempts to measure the number of elastically effective chains have met two main problems, the difficulty of knowing precisely the number of chemical cross- links, and the difficulty of assessing the effect of network defects on the modulus. 1920 MODEL POLYSTYRENE NETWORKS The three commonly considered network defects are lo : (i) unreacted functionalities and free chain ends, (ii) closed loops, and (iii) entanglements. In a previous paper l1 we described a procedure for preparing networks of poly- styrene containing a known number of crosslinks, at various concentrations in an inert solvent.The moduli of the network were measured and the results were inter- preted in terms of the above network theory and the effect of network defects. The results were consistent with a value of A = 3. In this paper we report the preparation of similar networks to those prepared in the previous paper under conditions in which we have been able to alter the number, and hence effect, of network defects in a controlled manner. The results have again been compared to a theoretical prediction. EXPERIMENTAL 1. THE PREPARATION AND CHARACTERIZATlON OF THE PARENT SUBSTITUTED POLYSTYRENE Polystyrene containing a small, accurately known number of amine groups randomly placed along the polymer chain was obtained in the same way as in previous papers.11* l2 Polystyrene (of the desired molecular weight and distribution) in solution in carbon tetra- chloride was reacted with chloromethyl methyl ether in the presence of anhydrous stannic chloride, thus introducing chloromethyl groups into the para positions. Any required degree of substitution can be obtained by stopping the reaction after a given time.The pro- duct was extracted and purified by repeated precipitations from chloroform solution into methanol and then dried. The product was reacted with a primary amine (n-butylamine or isopropylamine) thus converting the chloromethyl sites into secondary amine groups. A small part of this aminated polystyrene was reacted with 1 fluoro, 2,4 dinitrobenzene and the degree of substitution determined from the ultra-violet spectra of the product. 2.SIMPLE NETWORK FORMATION Simple polystyrene networks were prepared in the same way as described in a previous paper.l1 The amine substituted polymer was dissolved in tetralin at a concentration to give a final concentration in the range 5-25 %. To the solution was added a known quantity of hexamethylene diisocyanate (calculated to be about 5 % less than the stoichiometrically required quantity) dissolved in a little tetralin, the mixture was stirred and poured into the required mould where gelation took place. Networks were prepared from polystyrene with greatly differing degrees of substitution, thus not only producing networks with different crosslink densities, but also with different percentages of the crosslinks wasted in closed-loop network defects.3. PREPARATION OF ISOCYANATE-SUBSTITUTED POLYSTYRENE Polystyrene containing a small number of isocyanate groups along the chain was prepared from the arnine substituted polymer. " Aminated " polystyrene (20 g) was dissolved in benzene (200cm3, dried over calcium hydride) and stoppered in a flask. Hexamethylene diisocyanate (50 to 100 times the required stoichiometric quantity) was dissolved in dry benzene (200 an3) in a stoppered flask. The two flasks and all the other requirements of the preparation were placed in a large dry-bag, which was then flushed with dry air. Inside the dry-bag the solution of polymer was slowly poured with stirring into the solution of diisocyanate and the mixture was allowed to stand for 1 h. The polymer was then pmipi- tated into isooctane (41., dried over calcium hydride), filtered, redissolved in benzene, re- precipitated, filtered and washed with dry isooctane.The polymer was broken into as fine lumps as possible and placed in a flask which was then transferred to a drying line where it was exhaustively dried under vacuum at a pressure of Torr of mercury.G. ALLEN, P. A. HOLMES AND D. J . WALSH 21 4. PREPARATION OF NETWORKS CONTAiNING NO LINKS FROM ONE PRIMARY CHAIN TO ITSELF By reaction of polymer containing amine groups with polymer containing isocyanate groups networks were formed which contained no simple closed loops. The isocyanate group containing polymer was dissolved at a suitable concentration (between 5 % and 25 %) in tetralin (dried over calcium hydride).Aminated polystyrene, of the same batch from which the isocyanate containing polymer had been made, was dissolved at the same con- centration in the same volume of the same solvent. The two solutions were quickly mixed and poured into a mould. Typically the mould was a 3 i in. crystallizing dish, into which was poured a total of 150 cm3 of solution. A most suitable polymer, optimized to keep the viscosity of the solution prior to cross- linking, and the chain end corrrtion of the resultant network, both to a minimum was prepared from polystyrene of M , = 100 0o0 and M,/Mn = 1.06. The use of isopropyl- amine in the amination reaction caused the gelation to proceed slower and allowed gels of higher concentration to be prepared. 5. MEASUREMENT OF EFFICIENCY OF REACTION The number of unreacted isocyanate groups remaining in the gel after completion of the reaction was determined by reacting them with carbon-14 labelled methanol.After each sample of gel was prepared and tested, an approximately 10 g part of it was broken into small lumps and to it were added tetralin (10 cm3) and C-14 labelled methanol (2 cm3 of a suitable activity). The mixture was then left to stand for a week to ensure com- pletion of reaction. The gel was separated from the excess liquid by decanting, and then extracted by putting it into a large excess of first methanol and then tetrahydrofuran, on alternate days for ten days ; finally it was dried, swollen in benzene, and freeze dried. Samples of the gel swollen in toluene and mixed with a " scintillation cocktail " of 0.3 % diphenyl oxazole and 0.03 % bis(5 phenyl oxazol-2-yl) benzene in xylene, were counted on a Packard Model 3320 Liquid Scintillation Spectrometer, and compared with a dilute solution of the original C-14 methanol and a blank.The efficiency of counting, found from a comparison of the counts of the two channels of the spectrometer was found not to be reduced by more than 1 % by the inhomogeneity of the gel sample. From the results, the number of free isocyanate groups remaining in the gel could be calculated, and a correction to the number of crosslinks made. This method of extracting excess C-14 methanol was found to be the best of several methods tried. Measurements were taken after successivechanges of solvent until a constant value was obtained, and 10 days extraction was generally found to be sufficient. 6.MEASUREMENT OF MODULI The moduli of the networks were determined in the same way as described in a previous paper. The method is based on the identation of the gel by a rigid sphere. A modified dial gauge measures the indentation of the gel by a ball bearing produced by a series of loads. The modulus G of a gel into which a sphere of radius R is caused to indent a distance d by a load P is found to be l3 CALCULATION AND RESULTS In order to compare our results with the various theories we must calculate the number of chemical crosslinks per unit volume, which for an ideal network is equal to n. This factor is given by22 MODEL POLYSTYRENE NETWORKS where N is Avogadro's number, c is the concentration of polymer in kg dm-3, N is the mean number of monomer units between crosslinks, K is a correction for the number of crosshks required to join the chains into an infinite network, given by 1.5 h b 3 1.0- 0.5 2 x i 0 4 X ~ an K = 1- where M,, is the number average molecular weight of the original polymer.- '-, - sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 polymer A A A A C B B D C D D E D E* E* E* E' E* E* TABLE 1 nkTl Ng concn./kg dm-3 N Nm-2 X lo4 G/Nm-2 X lo4 65 0.05 76 0.695 0.265 65 0.075 76 1.05 0.56 65 0.05 71 0.765 0.345 62 0.075 71 1.14 0.64 60 0.125 68 1.64 1.18 66 0.175 75 2.28 2.03 66 0.20 75 2.59 2.68 164 0.106 191 0.245 0.225 149 0.125 180 0.40 0.45 164 0.159 185 0.42 0.56 164 0.212 189 0.54 0.86 1 50 0.250 177 0.825 1.15 164 0.265 193 0.64 0.99 150 0.05 175 0.165 0.165 150 0.095 167 0.355 0.41 140 0.150 154 0.665 0.98 140 0.170 156 0.715 1.02 150 0.200 166 0.765 1.155 140 0.250 156 1.05 1.67 A Mw = 240 O00 M w / g n 1.6 (n-butylamine) €3 a, = 70 OOO Hw/Mn 1.06 (n-butylamine) C a, = 110 000 A Z w / g n 1.06 (isopropylamine) D Ew = 85 OOO @,/M, 1.20 (isopropylamine) E M , = 90 OOO H w / E f n 1.20 (isopropylamine) * polymers produced containing no simple closed loops.2.0} 1 - 1 , I 0 0.05 0.10 0.15 Ci.2? 0.25 0.30 concentration/kg d m 3 Glnkr 0.38 0.53 0.45 0.56 0.72 0.89 1.03 0.92 1.13 1.32 1.59 1.40 1.56 1 .00 1.17 1.45 1.42 1 S O 1.58 FIG. 1.-Experimental results ; a plot of GpkTagainst concentration. A-N, = 63 ; 0--samples with Ng = 157 ; 0- samples with Ng = 145 containing no closed loops.G.ALLEN, P . A . HOLMES AND D . J . WALSH 23 N is calculated from the amount of diisocyanate added and is thus 1.05 x N,, where No is the average number of monomer units between reactive groups on the polymer, in the ideal case. A correction to N is also made for incomplete reaction of isocyanate and incomplete transfer of crosslinking agent where applicable. In table 1 the results are presented for three series of gels ; the first has values of N, = 63 +3 ; the second has values of N, = 157+8 ; the third is a series prepared by the method used to ensure that no simple closed loops are formed. The poly- styrene from which they were prepared and the amine used to inti-oduce the amine groups are indicated. For each sample the measured modulus G is given and a value of nkT calculated.A value for G/nkT is calculated, and in fig. 1 we have plotted G/nkT against the concentration of the gel for each of the three series of gels. INTERPRETATION OF RESULTS The results obtained for the three series of gels are explained in terms of network defects. The two main types of network defects are closed loops, which will result in a reduced modulus, and entanglements which will result in an increased modulus. These may be represented as simple closed loop closed loop involving two chains entanglement The probability of formation of simple closed loops can be estimated from chain statistics in the manner of Kuhn,14 and Jacobson and Stockmayer,ls and the fraction of chemical crosslinks which will take the form of a simple closed loop can be shown to be l 1 K K + c where c is the concentration at which crosslinking occurs and K is a constant for the polynier system.P This expression can be generalized for any value of No to give P+cNZ' (7) The contribution of closed loops involving two chains is calculated in a similar way but the average loop size will be twice as big and hence is P P+c(2Ng)+' Using the arguments presented in a previous paper l1 we can show P to have a value of approximately 30. Larger loops involving three or more chains can also be considered, but their effect will become progressively smaller. The larger loops could also be partially elastically effective as indeed may be the smaller ones. Just considering the first two must therefore be considered an approximation.24 MODEL POLYSTYRENE NETWORKS The calculation of the effect of entanglements can be done in two alternative ways : (a) Assuming a constant molecular weight between entanglements (Me), which for polystyrene has been calculated as 35 O0O,l6 the contribution of entanglements to the modulus of the gels will be proportional to the concentration.This gives a final expression for the modulus : G = 2AnkT 1- 1- ( P + l N t ) ( or G P nkT - = 2A[( l- P+J(' - P + c(*N,)J+ 4 (9) where Q can be shown to be 3.3 x lo4. In fig. 2 this theoretical equation has been plotted for our three types of network assuming a value A = 3. For the network containing no simple closed loops the appropriate term is eliminated. 2 0 . 0 5 0.10 0.15 0 . 2 0 0.25 (n3C I 1 I I I concentration/kg dm-3 FIG.2.-A theoretical plot of G/nkT against concentration, based on eqn (10). - is a plot for N g = 63; - - - is a plot for N, = 157 ; - - - is a plot for Ng = 145 containing no closed loops. (b) Edwards1' has suggested that entanglements should be proportional to c and experiments on the dynamic modulus of swollen uncrosslinked rubber give a similar dependence.18 This would give an expression : or G P nkT R has been given a value of lo5 in order to produce a best fit with the results. Measurements of the modulus of swollen uncrosslinked natural rubber would predict a value of R between 2 x lo5 and 3 x lo5 but polystyrene chains would not be expected to give the same value. In fig. 3 this theoretical equation has again been plotted for our three types of network.The simple closed loop correction is again eliminated from the appropriate plot.G. ALLEN, P. A. HOLMES AND D. J . WALSH 25 In each series of gels, an average value of c/nkT has been used to calculate the en- tanglement contribution. This factor which should be constant for each value of Ng shows a slight variation due to scatter in N, and differences in chain end correction I i I I I I 9 C.05 0.10 0.15 3.20 0.25 0.30 concentration/kg dm-j N, = 157 ; - - - is a plot for N, = 145 containing no closed loops. FIG. 3.-A theoretical plot of G/nkT based on eqn (12). - is a plot for Ng = 63 ; - - - is a plot for arising from the use of different molecular weight polymers. This effect is, however, small, and only at the lower degrees of substitution where the relative contribution of chain entanglements is greater, could they account for a significant amount of scatter in the results.1. K = P/N? except that K is an approximation including both types of closed loop. 2, K' = QclnkT 3. K" = Rc'InkT. Q and R are also affected by using different units. The constants P, Q, R are related to the constants K, K' and K" of a previous paper by : CONCLUSION Previously we reported that two series of simple polystyrene gels having N, of 63 and 75 respectively gave results which implied that the factor A in eqn (1) tended towards 3 rather than 1. There was also tentative evidence that the contributions of physical entanglements to the observed modulus were more consistent with a c2 dependence rather than with a constant molecular weight between entanglements.In the present work we find additional support for both of these conclusions. A series of simple gels having N, = 145 and a series in which the probability of the formation of simple loops is very small also produce results which are consistent with GlnkT + 3. We have also made a more confident analysis of the effect of physical entangle- ments on the moduli of the gels. We find clearer evidence than previously reported that the c2 concentration dependence of chain entanglements gives an equation of the right general form though it must be stressed that eqn (12) is not an exact representa- tion. Apart from uncertainties introduced by experimental errors, we have made two major assumptions in the analysis of our results : (i) that physical entanglements are independent of the degree of crosslinking, i.e., of N,, and (ii) that closed loops do not contribute at all to the observed modulus.Neither of these assumptions may be strictly true and we have not been able to assess their physical significance.26 MODEL POLYSTYRENE NETWORKS It is also worthwhile noting that eqn (12) predicts a value of G/nkT greater than 2 for networks formed at 100 % concentration, which would explain why a value of A = 1 might appear to fit experimental results better for networks formed in this way, when network defects are ignored. We wish to thank Prof. S. F. Edwards and G. Gee for many helpful discussions. P. J Flory, Princfples of Polymer Chemistry (Cornell University Press, 1953). P. J. Flory, J. Chem. Phys., 1950, 18, 108, 112. F. T. Wall and P. J. Flory, J. Chem. Phys., 1951, 19, 1435. F. T. Wall, J. Chem. Phys., 1943,11,527. H. M. James and E. Guth, J. Chem. Phys., 1947, 15, 669. H. M. James, J. Chem. Phys., 1947, 15, 651. ' H. M. James and E. Guth, J. Chem. Phys., 1953, 21, 1039. E. Guth, J. Polymer Sci. C, 1966, 12, 89. S . F. Edwards and K. F. Freed, J. Phys. C. (Solid St. Phys.), 1970, 3, 739, 750, 760. I0 P. J. Flory, Chem. Rev., 1944, 35, 51. I 1 D. J. Walsh, G. Allen and G. Ballard, Polymer, 1974, in press. I * G. AIlen, J. Burgess, S. F. Edwards and D. J. Walsh, Proc. Roy. Suc. A, 1972, 334,453. l3 N. E. Waters, Brit. J. Appl. Phys., 1965, 16, 557. l4 W. Kuhn, Kolloid 2, 1934, 68,2. l 5 H. Jacobson and W. H. Stockmayer, J. Chem. Phys., 1950, 18, 1600. l6 R. S. Porter, W. J. McKnight and J. F. Johnson, Rubber Chem. and Tech., 1968, 41, 1. l7 S. F. Edwards, Third International Conference on Non-crystalline Solids, ed. Ellis and Douglas (Wiley, New York). N. Yoshimura, Ph. D . Thesis (Victoria University of Manchester, 1969).

ISSN:0301-7249    

DOI:10.1039/DC9745700019

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

New Crosslinking Processes BY GBRARD BEINERT, AHMED BELKEBIR-MRANI, JEAN HERZ, * GBRARD HILD AND PAUL REMPP Centre de Recherches sur les MacromolCcules-CNRS- 6, rue Boussingault-67083 Strasbourg Cedex (France) Received 2nd January, 1974 Synthesis of model-networks characterized by the quasi-constant length of the linear chain elements between two successive branch points has been carried out by anionic block copolymerization of two monomers, one being bifunctional. The influence of various parameters (concentration, temperature, number of molecules of bifunctional monomer added per active chain end) on the behaviour of the gels is discussed. This method can be applied to several systems. Another method was successfully used to synthesize networks : reaction of a, w-difunctional linear polymer chains with tri- or tetrafunctional molecules, in stoichiometric amount was shown to lead to gels in which both the length of the linear chain elements and the functionality of the branch points are controlled. Reactions of terminal carbon metal bonds with electrophilic groupings of various kinds were used, as well as reaction of silane end groups with allylic double bonds.The gels obtained were characterized by their swelling behaviour, in relation to the molecular weight of the chain elements and the functionality of the branch points. The numerous methods which have been developed to synthesize crosslinked polymeric networks can be classified into two groups :-(i) Methods involving random copolymerization of two monomers, one of which is bifunctional. (ii) Methods involving bridge formation between preexisting linear polymer chains, by vulcaniza- tion, peroxidation, etc.Neither of these methods yields well defined networks, since copolymerization as well as chemical transformation of polymers are random processes. The networks obtained cannot be characterized easily by their structural parameters. The length of their linear chain elements fluctuates very much around its average value, which is not experimentally accessible. In many cases the homogeneity of the gels is not satisfactory, especially when syneresis (solvent expulsion) takes place during the process. Finally the “ gel point ” has no physical significance since it usually takes place at an early stage of the reaction. The present paper gives an account of research on the synthesis of well-defined model-networks, by several methods.A model-network is a cross-linked macro- molecule which consists of v elastic chain elements connected by (2v/’) $functional branch points. The linear chain elements are in first approximation identical in length and each of them is connected by its two ends to two diflerent branch points. The model-network should be homogeneous, it should contain neither pendent chains nor loops, and no solvent expulsion should take place during its preparation. Finally the gelation process itself should not involve any major change of the segment concentration; this is a necessary condition for the gel point to have a physical significance. One can expect, therefore, to establish a relationship between the segment concentration at the gel point and the “ memory-term ” h, characterizing the relaxation state of the linear chain elements at the segment concentration at which crosslinking occurred.2728 NEW CROSSLINKfNG PROCESSES The principle of these new crosslinking processes is quite different from the above indicated classical methods. Here a linear " precursor " polymer is equipped with reactive end-groups ; in a second step branch points are formed, each connecting f chain-ends together. This method allows one to characterize adequately the linear " precursors " molecules, and to check for their polydispersity. Furthermore, their average molecular weight can often be chosen rather precisely in advance, so one can choose the porosity of the network, since the length of the elastic chains determines the average pore size of the network. Three methods will be discussed in this paper.Two of them are anionic cross- linking methods, the third one starts from a, o-difunctional polymeric chains which are reacted under proper conditions with a plurifunctional reagent. NETWORK FORMATION BY ANIONIC BLOCK COPOLYMERIZATION POLYSTYRENE MODEL-NETWORKS It was shown '* a few years ago that star-shaped polystyrene can be prepared anionically by block copolymerization of styrene and some divinylbenzene, the initiator being monofunctional : butyl-lithium or cumyl-potassium (fig. 1). The reaction is carried out at low temperature, in an aprotic solvent, under inert atmos- phere. STAR POLYMER FORMATION FIG.1. In a first step, a monofunctional " living " polystyrene is obtained by reaction of the initiator with a given amount of styrene. Such a polymer exhibits a sharp molecular weight distribution because anionic " living " polymerization with fast initiation yields macromolecules of low polydispersity. To the solution of this " living " polymer a small amount of divinyl-benzene (DVB) is added : its poly- merization is initiated solely by the living carbanionic sites. Each star-molecule is constituted by a smalf crosslinked nodule of poly@VB) connected with f identical linear polystyrene branches. These " star '' molecules can be well characterizedG . BEINERT, A. BELKEBIR-MRANI, J . HERZ, G. HILD, P. REMPP 29 by the length of the individual branch (which is the “ precursor ” polystyrene itself) and byfwhich can be determined by the ratio of the molecular weight of the “ star ” molecule to that of the “ precursor ”.such as bi-sodium a-methylstyrene ‘‘ tetramer ” or naphthalene-sodium, a bifunctional “ living ” polystyrene is formed, the chain of which is equipped at both ends with organometallic sites. Addition of a small amount of DVB to the solution of this “ living ” polymer leads to rapid gelation of the reaction medium. A crosslinked network is formed in which each linear chain element (“ precursor ”) should be con- nected with two different branch points (poly-DVB nodules). Here again, the average length of the “ precursor ” polystyrene can be chosen arbitrarily, and determined precisely. If the experimental conditions have been chosen adequately (solvent, concentration, temperature, adequate stirring etc.) the obtained gels are homogeneous and close to ideality.It should be noted that in such a process, gelation occurs without any major change of the segment concentration, since it only involves polymerization of the small amount of DVB initiated by the “living” ends of the “ precursor ”. The only drawback of this method of synthesis is that the actual average functionality fof the branch points (number of elastic chains connected with a given nodule of poly-DVB) remains unknown : f is neither determined, nor experimentally accessible. The polystyrene model-networks so obtained have nevertheless been successfully 5* used to test the validity of equilibrium swelling theories on ideal gaussian networks.We have been able to conclude that this model of the ideal gaussian network, as developed by FloryY2’ and more recently by Dusek and Prins fits satisfactorily. This result indicates that defects such as pendent chains, couplings, loops, and also entanglements are few, and that the behaviour of the elastic chains in the swollen network follows gaussian statistics. Moreover, from equilibrium swelling measure- ments in a pure diluent on a homologous series of polystyrene networks-using precursor polymers of various molecular weights-it was shown that the experimental results were consistent with a functionality of the branch points of the order of 4. If instead of a monofunctional initiator, we use a bifunctional initiator GENERALIZATION The preceding method of network formation by anionic block copolymerization has been applied to other anionically polymerizable monomer systems.In such a process, it is necessary that the carbanionic “living” ends of the “precursor” polymer initiate rapidly and quantitatively the polymerization of the bifunctional monomer. This condition involves that the electroaffinity of the bifunctional monomer be equal to or greater than that of the first monomer. In the following experiments, the crosslinking agent is either divinylbenzene (DVB) or ethylene dimethacrylate (DME) : CH2=C-C-O-CH,-CH2-O-C-C=CH, II I 0 CH3 I II CH30 Model-networks have been obtained with the following systems : styrene + DVB ; isoprene + DVB ; 2-vinylpyridine + DVB (or DME) * ; methylmethacrylate + DME * ; butylmethacrylate + DME ; isopropylidene glyceryl methacrylate -I- DME.S30 NEW CROSSLINKING PROCESSES These results call for the following comments : (a) Concerning gels of plyisoprene it would have been interesting to obtain 1,4 cis stereoregular plyisoprene chain elements between branch points in order to compare the properties of the gels obtained with vulcanized rubber.But it is well known that 1,4 cis polymerization of isoprene occurs only in non-polar solvent media. Unfortunately, none of the common bifunctional Li-initiators is soluble in non-polar solvents. Recent attempts to over- come this difficulty are rather promising, however. (b) With poly-2-vinylpyridine gels, curiously enough, DVB can be used as the second monomer, which means that the electroaffinity of DVB is definitely higher than that of styrene.(c) For metha- crylic esters, DVB cannot be used since its polymerization cannot be initiated by the polymethacrylate ester anions. In this case, DME is used as second monomer. (d) Water soluble gels cannot be prepared anionically. But it has been possible to synthesize isopropylidene glyceryl methacrylate monomer : / \ CH3 CH3 and to obtain anionic gels using ethylene dimethacrylate as bifunctional monomer. In this case, subsequent acid hydrolysis of the networks obtained destroys the acetal group and regenerates the remaining OH functions of glycerol, without touching the ester function ; this process yields polyglyceryt methacrylate networks, CH2=C-C-O-CH2-CH-CH2 I I OH OH I II CH30 glyceryl met hacrylate which swell in water.NETWORK FORMATION BY CHEMICAL REACTIONS INVOLVING " LIVING " ANIONIC POLYMERS It is well known that anionic " living '' polymers react not only with any proton donating substance, but also with many electrophilic functions, to yield a-functional polymers. Alkyl halides, acid chlorides, esters, nitriles, anhydrides, as well as carbon dioxide or ethylene oxide do react with carbanionic sites. The idea of using pluri- functional electrophilic reagents to link two or more chain-ends together has been used many times. Coupling agents as COC1, or (CH3),SiC12 are commonly used. Star polymer synthesis was attempted ClCH, CH,CI using various compounds such as : but two types of difficulties were encountered: (i) the decreasing reactivity of the sites, as the degree of substitution increases and (ii) metal halogen exchange reactions, which yield undesired side products.In most cases using monocarbatiionic precursor polymers, mixtures of star- molecules with p , p - 1, p - 2 . . . branches were obtained. Moreover, an excess ofG . BEINERT, A . BELKEBIR-MRANI, J . HERZ, G . HILD, P. RBMPP 31 fiving polymer has generally to be used to attain complete reaction. Therefore, one cannot expect to obtain adequate model-networks by using this method with bifunctional precursors. Many structural defects would be introduced in the molecular structure during the process. But it was noticed that tris(ally1oxy)triazine (TT) reacts quantitatively with “ living ” monocarbanionic polystyrene to yield star-molecules according to the reaction ’ : s with R = CH2=CH-CH2-- This shows that the three functions do react.The same reaction can be applied to synthesis of model-networks. Thus, starting from bifunctional “ living ” polystyrene and reacting it with a stoichiometric amount of TT, under efficient stirring, one obtains well-defined networks. This method enables one to synthesize networks in which both the length of the elastic chains and the functionality of the branch points are known, and are subject only to very small fluctuations within a sample. It has to be assumed, however, that no pendent chains are left over (which is a reasonable assumption if stoichiometry and stirring are adequate) and that only very few loops are formed. As a matter of fact, the probability of formation of such loops can be calculated roughly, it depends both upon the molecular weight of the precursor and upon the overall concentration at the gel point.It should also be emphasized that the gelation does not involve any variation of the segment concentration, since the crosslinking process merely consists of bond formation between chain-ends of several molecules. Attempts were made to extend this method to preparation of networks with tetra (or even hexa) functional branch points. To achieve this, a new crosslinking agent was made by reacting an excess of TT with tetraphenyl-disodiobutane. The adduct obtained, bis(diallyloxytriazy1) tetraphenylbutane, is purified and can be used as tetrafunctional deactivator for living polystyrene.All0 OAll This was first checked again with monocarbanionic polystyrene. As expected the obtained star-polymer has four branches. Next, a bifunctional living polystyrene was reacted in stoichiometric amount with this compound. Gelation occurs as expected, while the red colour of the carbanions vanishes. The model-network thus obtained is constituted of elastic chains connected by tetrafunctional branch points ;32 NEW CROSSLINKING PROCBSSBS if stoichiometry has been effective and stirring adequate, one can expect that the number of structural irregularities will remain low. NETWORK FORMATION BY CHEMICAL REACTIONS INVOLVING FUNCTIONS AT CHAIN ENDS As already mentioned, chemical reactions on a polymer chain is one effective method for the production of tridimensional networks.The most famous of these reactions is the so-called vulcanization of rubber. But, aside from the fact that such a reaction is a random process, it should be indicated that the number of pendent chains in such a process amounts to almost twice the number of primary molecules, since there is little chance that the crosslinking reaction occurs precisely at chain ends. Such networks are, therefore, far from ideal ; they cannot be considered to be well-defined. Recently, much attention has been devoted to network synthesis by reactions involving functions located at chain ends. The carbanionic sites of " living " polymers can play the role of active functions, as was shown in the preceding section. But several other systems have also been investigated, especially crosslinking of a, o-dihydroxy polymers (or oligomers) using commercial plurifunctional urethanes as crosslinking agents.We have used a similar method of making polymeric networks, but we have used a quite different reaction, namely the addition of silanes onto allylic double-bonds, according to l9 1 I I I - Si-H + CH,=CH-CH,-R-+ - Si-CH2-CH2-CH2-R CH3 CH3 We attempted to react polydimethylsiloxanes fitted at chain ends with silane functions * onto tetrallyloxyethane.20 The reaction is carried out either in bulk or in the presence of a diluent : heptane, a good solvent of the PDMS chain, or toluene, a poor solvent of the polymer. Stoichiometric amounts of the reactants are needed as well as adequate mixing to provide satisfactory homogeneity of the reaction mixture.Chloroplatinic acid catalyses the reaction, which takes place at tempera- tures ranging from 20" to 70°C. Gelation of the reaction mixture takes place readily, and the model-networks thus obtained are constructed from elastic PDMS chains connected by their ends with tetrafunctional branch-points. To obtain adequate stoichiometry, precise characterization of the PDMS- precursor molecules is necessary. Molecular weight measurements are performed by osmometry, as well as by silane end group determination. The agreement is satis- factory. The polydispersity of the samples should not be too broad, though molecular weight average measurements by light scattering are possible only for the highest molecular weight samples. Also some gel-permeation chromatography diagrams were obtained.So far as the imperfections of the networks are concerned, the same remarks can be made as in the preceding case: pendent chains may be left over, Ioops may be formed, and on the other hand chain entanglements may lead to some supplementary " physical " crosslinks. * The PDMS fitted with silane end groups were obtained from the Silicon Division of Rhone- Poulenc ; we wish to express our appreciation for its help in this work.@. BEINERT, A . BELKEBIR-MRANI, J . HERZ, G . H I L D , P. REMPP 33 The crosslinked samples were submitted to prolonged solvent extraction (Soxhlet). It was found that the gels contained only very little extractable polymer. It should be noted, in addition, that the PDMS precursor samples may well contain a small percentage of cyclic macromolecules which obviously cannot take part in the reaction.This shows that the probability for any reactive chain end to react is very close to 100 %, and from this result it follows that the percent amount of pendent chains should remain very low. We attempted to use a similar method to make PDMS networks with branch points of functionality other than 4. Triallyloxytriazine was tried as a 3-functional reagent. In that case a network is formed at first, as expected, but it is again destroyed on standing for a couple of days, because the acid which catalyses the reaction is able to hydrolyse the triazine links between chain ends : the precursor is thus reformed. A six-functional reagent was also synthesized : bis (triallyoxy methyl) ethyl ether : This compound was obtained from dipentaerythritol and ally1 bromide as starting materials.This hexa-functional reagent yields nice crosslinked model-networks with our PDMS precursor molecules. In order to relate the physical behaviour of the PDMS gels to their structural characteristics we have carried out equilibrium swelling and uniaxial compression experiments. Our results indicate that within the limit of experimental accuracy the crosslinked gels obtained show ideal behaviour according to theoretical expecta- t i ~ n . ~ Of course, this does not mean that no defects (pendent chains, loops, entanglements) are present in the gel, but their total effect on its physical behaviour is negligible. CONCLUSION Until recently, any theoretical or experimental approach to the physical and mechanical behaviour of crosslinked gels and vulcanizates required assumptions concerning their structural characteristics ; the necessity of creating well-defined model-network syntheses was evident.The purpose of our paper is to show that several methods are now available to prepare such networks, and to report results obtained recently in this field in our laboratory. Comparison between theoretical expectation and experimental results obtained with model gels yielded rather satisfactory agreement, showing the validity of the main hypothesis made in the theoretical treatment of Dusek and Prins. However, it should be emphasized once more that the limitation of the preparation methods cannot be overcome entirely, since structural defects such as pendent chains, loops, entanglements and fluctuations over M and fare still possible to some extent.Our experimental results however have shown that their influence can be neglected in first approximation. J. G. Zilliox, P. Rempp and J. Parrod, J. Polymer Sci. C, 1968,22, 145. D. J. Worsfold, J. G. Zilliox and P. Rempp, Canad. J. Chem., 1969,47, 3379. A. Kohler, J. Polacek, I. Kossler, J. G. Zilliox and P. Rempp, European Polymer J., 1972,8,627, P. Weiss, G. Hild, J. Herz and P. Rempp, Makromol. Chem., 1970, 135, 249. A. Haeringer, G. Hild, P. Rempp and H. Benoit, MakromoZ. Chem., 1973,169,249. D. Froelich, D. Crawford, T. Rozek and W. Prins, Macromolecules, 1972, 5, 100. ’ K. Dusek and W. Prins, Adu. PoZyrner Sci., 1969, 6, 1. * G. Hild and P. Rempp, Compt. Rend., 1969,269, 1622. G. Beinert, G. Hild and P. Rempp, Makromol. Chem.. 1974, 175, 2069. l o S. P. S. Yen, Makromol. Chem., 1962, 81, 152. 57-B34 NEW CROSSLINKING PROCESSES l 1 T. Altares, D. P. Wyman, V. R. Allen and K. Meyersen, J. Polymer Sci. A , 1965, 3, 4131. l2 W. A. Brice, G. M. Gibbon and I. E. Meldrum, Polymer, 1971,11,290. l3 J. C. Meunier and R. van Leemput, Makromol. Chem., 1971,142,l. l4 J. E. L. Roovers and S . Bywater, Macromolecules, 1972,5, 384. l5 M. Morton, T. H. Helminiak, S. Gadkary and F. Bueche, J. Polymer Sci., 1962,57,471. l6 J. A. Gervasi and A. B. Gosnell, J. Polymer Sci. A-1, 1966,4, 1391. l 8 M. Hert, C1. Strazielle and J. Herz, Compt. Rend. C, 1973, 276, 395. l9 G. Greber, Angew. Makromol. Chem., 1971,141,145. 2o J. Herz, A. Belkebir-Mrani and P. Rempp, Eurupean Polymer J., 1973, 9, 1165. 21 P. J. Flory, Principles of polymer chemistry (Cornell University Press, Ithaca, N.Y., 1953). J. Herz, M. Hert and C1. Strazielle, Makromol. Chern., 1972, 160,213.

ISSN:0301-7249    

DOI:10.1039/DC9745700027

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. I(. DuSek (Czechoslovakia) said: (a) The indentation method for measuring the elastic moduli of gels is very simple and could be used in cases when other methods fail. I wonder whether the dependence between the load and indentation depth has been examined in terms of the free energy change of rubberlike networks bearing in mind that the local stresses may be quite high. Is the experimental ratio P/d* inde- pendent of d and what is its dependence on the degree of swelling? (b) The relation between the concentration of elastically active network chains (EANC), v, and the concentration of elastically effective crosslinks (EEC) in eqn (2) v = 2n may lead to a confusion for real systems with free chain ends. Some EEC give rise to three and others to four EANC, contributing thus by 3 and 3, respectively, to the number of EANC (cf. e.g., Dobson and Gordon, J.Chem. Phys., 1965,43,705). The correction to v in the form of eqn (5) is then valid only in the close vicinity of the gel point where all EEC are effectively trifunctional. With regard to the paper by Beinert et al., it seems to me that the deactivation of living ends in model polystyrene-divinylbenzene networks by a monofunctional termination agent (methanol) produces dead ends in divinylbenzene units and thus lowers the effective functionality of the crosslink. If, e.g., two living ends of poly- styrene chains reacted with a divinylbenzene molecule, this branch point would become bifunctional after deactivation with methanol, i.e., elastically ineffective.Would the results be different if one used a bifunctional termination agent, capable of joining two living ends of divinylbenzene units? Dr. D. J. Walsh (University of Manchester) said: (a) A lot of work has been done on this method of measuring modulus by people at the Malayan Rubber Producers Research Association in Welwyn Garden City, who find it to give answers in good agreement with other methods. We have done relatively little but think that as very small deformations can be measured, and the stress may be spread through a large part of the sample, the local stresses need not be very high. We have found the ratio P/d3 to be independent of d, which is an important point, but as we always prepare and test samples at one concentration we have no information of the effect of swelling.(b) I agree that other authors would suggest a smaller chain end correction than that calculated by Flory. Having looked into this I agree that these may be more justified. However, an alteration in the size of this correction term would have only a small effect, certainly within the limit of other uncertainties, and would not sub- stantially alter the interpretation of the results. This alteration would also take the results slightly further away, rather than sligbtly nearer to the alternative value of A = 1. Dr. J. Herz (Strasbourg) said: The answer to Dugek is no. The addition of the terminating-agent (methanol or any other ‘‘ proton donor ”) takes place when the crosslinking reaction is completed and the gel already formed. The remaining carbanionic groups are all located within the crosslinked polydivinylbenzene nodules.Deactivation of these “ living ” groups by protons cannot change the structure of the gel nor introduce, at this stage, supplementary pendent chains. Moreover the termination reaction by bifunctional or by monofunctional proton- donor is the same. Coupling reactions by bifunctional terminating agents as C0Cl2 3536 GENERAL DISCUSSION or dichlorodiniethylsiloxane should not modify the structure of the gel, since they would merely introduce further links within each nodule, and not between them. Prof. M. Gordon (University of Essex) said: Two remarks on the statistical importance of short chain segments: first random cross-linking leads to a most- probable (Flory-) distribution of segments between cross-links, in which short segments have high probability.Secondly, the situation may be illustrated by calculating the average over all cross-links of the ratio of the longest to the shortest among the four chain-segments which issue from a cross-link. (The model adopted is merely that of lightly cross-linking long primary chains). This ratio turns out to be quite high-may I challenge the audience to estimate it? Prof. W. Prim (University of Syracuse) said : Ten. Prof. M. Gordon (University of Essex) said: Yes, it is of this order. The exact value is 8-s. Very short chains will constitute a kind of network flaw. The synthetic procedures by Beinert et al. (this Discussion) avoids these. One would expect the greatest effect of their improved networks to be felt mostly in ultimate properties, where the short chains become highly strained.Dr. D. J. Walsh (University of Manchester) said : I agree with Gordon that very short chains will act as a defect, the effect of which on the modulus is difficult to esti- mate. One could estimate for instance for a system with number average degree of polymerisation between crosslinks = 150, what fraction of the chains are below 50 units long. These could be less elastically effective but only the shortest of these would be completely ineffective. I think that the effect would not be large enough to alter the conclusions reached from my results. Also the smallest of chains would be more likely to be removed in the form of closed loop defects. I also agree that the effect on ultimate properties would be far greater but these have not been examined.Dr. R. F. T. Stepto (UMIST) said : The probabilities of ring formation, for rings of the smallest two sizes, as defined by expressions (7) and (8) of Allen’s paper, are incorporated into eqn (9) to (12) as essentially (1 - r l ) (1 - r2), where r1 and r2 represent expressions (7) and (8). It would appear that the relationship between rl and r2 is rather approximate. Although the mutual concentrations of a pair of groups able to form loops of the two sizes are proportional to iVi9 and (2N3-3, there will be pro- portionately more pairs of groups able to form rings of the larger size, and P in expression (8) should be larger than P in expression (7). Approximate calculation shows that, depending upon the degree of crosslinks, up to a 4-fold increase in P in expression (8) as compared to (7) could occur.Do the authors have any knowledge of how the relative values of rl and rz affect their interpretation of the results, in particular with regard to the comparison of the curves in fig. 2 and 3? Dr. D. J. Walsh (University of Manchester) said: To take up Stepto’s point, the relative size of r2 is not easy to estimate and will not be the same as in the case of the crosslinking of a trifunctional monomer. Using a simple approach I estimate that three times the number of sites are available for forming the second type of closed loop but that it only reduces the number of effective chains by 1 (as against 2 for the first type). One of the resultant chains is in effect 2 chains both linking two pointsGENERAL DISCUSSION 37 the effect of which is difficult to estimate. The larger closed loops are also more likely to entrap other chains thus contributing to the entanglements.The conclusion is that this part of the expression can only be approximate. Fortunately the effect of r2 is extremely small over the range considered, a fact which is verified by the experimental results on networks containing none of the first type of closed loops. Mr. H. Beltman and Prof. J. Lyklema ( Wageningen) said : There appears to be some analogy between Allen's results and ours. We have found that in the early stages of gelation the extent of wasting is proportional to the squared polymer concentration c2. From our eqn (12) a c2 dependency can also be inferred, at least if one neglects the Rc2 term due to entanglements and sets c22%N,3 P2 - - P c22%N (' - =:)(' - P + ( P + cNi)(P + cN;2+) for cN3 < P.Although Allen's derivation applies to a different stage in the gelling process we would nevertheless appreciate his comment as to whether or not the observed c2 analogy is fortuitous. Dr. D. J. Walsh (University of Manchester) said: The form of the expression would depend on the number of defects one wished to consider. If only the first order closed loop was considered, for example, a first order dependence would be obtained. The observation of Beltman and Lyklema may justify the use of the two types of closed loop. The approximation made in the expression will only be valid at con- centrations lower than those we have used.Dr. R. F. T. Stepto (UMIST) said: In addition to the many syntheses suggested in the paper of Beinert et al., it would seem that model networks, within the limits defined by the authors, could be made using conventional polycondensations, pro- vided that monomers (prepolymers) of large enough molecular weight are used. For example, poly(propy1ene oxide) triols of various molecular weights can be reacted with di-acid chlorides, or diisocyanates. The triols have well-defined chemical functionalities, and, within the limits of the Poisson distribution, equal chain lengths (of 100 bonds or more) between functional groups. The materials are commercially available, and hence appear to provide a relatively easy route to model networks. Can the authors see any disadvantages of such syntheses compared to those described in their paper? Dr. J. Herz (Strasbourg) said: The reaction of OH endgroups of well characterized star-shaped poly(propy1eneoxide) triols with the difunctional compounds mentioned by Stepto should indeed lead to interesting model-networks, provided exact stoichio- metry can be obtained, and assuming that the reaction with diisocyanates is free of side-reactions, which is not always the case.

ISSN:0301-7249    

DOI:10.1039/DC9745700035

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Themoreversible Gelation in Polymer Systems Part 2. Gel/Sol Transition in Vinylidene Chloride/Methyl Acrylate Copolymer Gels BY M. A. HARRISON, P. H. MORGAN AND G. S . PARK* Chemistry Department, UWIST, King Edward VII Avenue, Cardiff, CFl 3NU Received 1 st November 1973 Those vinylidene chloride/methyl acrylate copolymers that show crystallinity in the solid state form reversible gels when dissolved in benzene, chlorobenzene, rn-dichlorobemene or o-dichloro- benzene. The temperature Tm of the gel/sol transition increases with the vinylidene chloride content of the copolymer and with decreasing dipole moment of the solvent. Polymer concentration and molecular weight have only a small effect on Tm and so the Ferry and Eldridge relationship, a In C/aT;l = AHJR, gives very large values (80-240 kJ mol-') for the junction point energy AH,.This increases with the vinylidene chloride content of the copolymer and with the dipole moment of the solvent. Equating the gel/sol transition with the crystalline melting point enables Flory's relationships between copolymer composition, solvent power and the melting point to be applied to Tm. This gives x values for poly(viny1idene chloride) increasing from 0.67 to 0.80 as the dipole moment of the solvent decreases and a heat of fusion of 2.64 kJ mol-' per vinylidene chloride unit. It is suggested that the network junction points of the copolymer are between 30 and 100 units long and this ac- counts for the absence of gelation in copolymers having less than 80 mol % of vinylidene chloride units.Many solutions of poly(viny1 chloride) form weak gels on standing or cooling and these revert to the sol state on heating. This reversible gelation has been attri- buted to network formation in which the network linking points consist of minute crystallites formed from the occasional syndiotactic runs that occur in the predom- inantly atactic polymer. Since there is some uncertainty about the syndiotactic content of these polymers it is of interest to investigate reversible gel formation in solutions of polymeric substances that contain known amounts of crystallizable and non-cry s t allizable units. The methylacrylate/vinylidene chloride copolymers are such substances. The reactivity ratios in the free radical polymerization are unity for both monomers and so random copolymers of constant composition can easily be made.This enables the stability of the resulting gels to be related to polymer composition as well as to other factors such as molecular weight and concentration. The gel melting point (the temperature at which the gel/sol transition occurs) gives a ready means of investigating gel stability and can be related to the energy changes involved in network formation. EXPERIMENTAL COPOLYMERS Vinylidene chloride/rnethylacrylate copolymers were prepared by free radical polymer- ization of well out-gassed solutions in cyclohexanone using azoisobutyronitrile as initiator at 40°C. After about a 10 % conversion the polymers were separated by precipitation in methanol and were purified by repeated solutions in tetrahydrofuran followed by precipit- 38M .A . HARRISON, P . H . MORGAN A N D G . S . PARK 39 ation in further quantities of methanol. The polymers were dried at 6040°C under vacuum and the copolymer compositions were found from C and H determinations. Molecular weights were measured in tetrahydrofuran solution using a Hewlett-Packard 502 automatic membrane osmometer. The characteristics of the copolymers are given in table 1. TABLE 1 .-VINYLIDENE CHLORIDE : METHYL ACRYLATE COPOLYMER CHARACTERISTICS mol % vinylidene chloride designation 13 18 17 19 11 22 20 21 24 23 26 25 27 28 16 29 10 14 nominal 83.3 83.3 83.3 83.3 91.2 91.2 91.2 91.2 93.8 93.8 93.8 93.8 95.2 95.2 95.2 95.2 95.5 87.5 actual b 81.1 83.1 85.2 83 .O 91.3 91.5 89.8 92.4 93.2 92.8 93.9 94.0 95.6 95.6 97.6 95.0 84.0 96.6 Id/dl g-l 0.423 0.561 0.575 0.835 0.543 0.602 0.71 3 0.877 0.489 0.584 0.663 0.675 0.540 0.603 0.683 0.748 - - G n x c 32 030 0.378 77 900 0.390 84 500 0.399 20 900 0.405 70 600 0.333 74 500 0.381 0.402 88 900 23 O00 0.377 58 700 0.369 79 400 0.349 79 600 0.408 84 700 0.383 70 100 0.3 16 71 700 0.41 5 74 700 0.408 82 300 0.404 36 560 - - - 15 88.9 88.3 - 49 280 0.354 12 90.0 88.3 - - - a Calculated from composition of monomer feed ; b calculated from C and H analysis data ; x values in tetrahydrofuran from the dependence of osmotic pressure on concentration. GEL MELTING POINTS Uniform gels of the copolymers were prepared in sealed tubes as described previously for poly(viny1 chloride) gels.' The temperature at which a pressure head caused flow through a fine capillary was used as a measure of the gel melting point, Tm.This was determined using a technique described elsewhere.2 In many of the gels, syneresis occurred on standing for a day or more and so the gel melting points were determined soon after the gels had been formed. In some experiments at high solvent concentrations, syneresis was so rapid that gel melting points could not be determined. No significant change in the observed value of Tm was found on changing the pressure head or altering the diameter of the capillary. RESULTS Benzene, chlorobenzene, m-dichlorobenzene and o-dichlorobenzene could all be used as solvents for the copolymer at high temperatures. Solutions of polymers containing less than 80 mol % of vinylidene chloride units remained mobile even on prolonged standing. Polymers containing about 83 % of vinylidene chloride units gave solutions that set to weak gels on prolonged standing for a few days.Polymers containing 90 % or more of vinylidene chloride gave gels on cooling to room temper- ature and standing for only a few minutes. Most of the gels were cloudy.40 VINYLIDENE CHLORIDE COPOLYMER GELS Fig. la gives the gel melting points T, for gels of various concentrations of co- polymer 11 having a nominal vinylidene chloride content of 91 rnol % and having a molecular weight of 70 600 in all four solvents, while fig. lb, l c and Id give data for solutions in o-dichlorobenzene for copolyniers having various compositions and molecular weights. (4 FIG. l.-Dependence of gel melting points Tm on concentration C.(a) Polymer 11 (nominal vinyl- idene chloride = 91.2 mol %, Gn = 70 600) in various solvents. 0, CsHs ; A, rn-C6H4Cl2 ; 0, C6H5Cl ; 0, o-C6H4CI2. (b) Polymers 11, 22, 20, 21 (nominal vinylidene chloride = 91.2 rnol %) in o-dichlorobenzene. Mn : 0, 70 600 ; 0, 74 500 A, 88 900 ; 0,123 OOO. - (c) Polymers 24, 23, 26, 25 (nominal vinylidene chloride = 93.8 rnol %) in o-dichlorobenzene. Mn : 0, 58 700 ; D, 79 400 ; A, 79 600 ; 0, 84 700. (d) Polymers 27, 28, 16, 29 (nominal vinylidene chloride = - 94.2 rnol %) in o-dichlorobenzene. Mn : 0, 70 100 ; 0, 71 700 ; A, 74 700 ; 0, 82 300. DISCUSSION THE FERRY AND ELDRIDGE RELATIONSHIP Ferry and Eldridge treated reversible gelation as an equilibrium between actual network junctions and potential network junction sites.At the gel melting point theM. A . HARRISON, P. H. MORGAN AND G . S. PARK 41 number of actual network junctions is the minimum required for a continuous net- work. This enabled the equilibrium constant for network formation to be related to both concentration and molecular weight. By application of the vant’ Hoff isochore to this equilibrium Ferry and Eldridge obtained the relationship Here, Tm is the gel melting point, M , is the molecular weight of the polymer, C is the concentration and, in the original theory, AH, and AH, were both equal to the heat of formation of a mole of network junctions from potential network junction points. An extention of this treatment to junctions involving n polymer chains retains the significance of the AHm but gives AH, = AH,,&- l), (3) FIG.2.-Ferry and Eldridge plots for the concentration dependence of Tm (a), (b), (c), (d) and the symbols have the same meaning as in fig. 1.42 VINYLIDENE CHLORIDE COPOLYMER GELS so that AH, is more closely related to the energy change on uniting a mole of potential network junction points to partially formed network junctions. It is interesting to see if eqn (1) and (2) can be used to give the junction point energies in vinylidene chloride/methyl acrylate copolymer gels. Since data for copolymers covering a range of molecular weights for copolymers with a sufficiently constant composition are not available (fig. l), it was not possible to obtain values of TABLE 2.-JUNCTION FORMATION ENERGIES, &.HX FOR COPOLYMER NO.11 (91 % NOMINAL VINYLIDENE CHLORIDE CONTENT M , = 70 600) IN VARIOUS SOLVENTS dipole moment/ TnZ/"C for 6 % AH=/ crystallite length* solvent debye solution k J mol- 1 C6H6 0 90.5 - 80 31 C~HSCI 1.70 74.8 134 52 m-C 6H4C12 1.72 74.8 163 63 O-C6H4C12 2.48 70.8 180 69 * no. of vinylidene chloride units AH, from eqn (1). The relative insensitivity of T, to changes in concentration in fig. 1 indicates that AH, in eqn (2) must be large. The logarithmic plots in fig. 2a enable the AH,,, values given in table 2 for various solvents to be obtained. As the dipole moment of the solvent is increased on passing from benzene to o-dichlorobenzene, the gel melting point decreases as might be expected for increasing solvent power but, surprisingly, the values of AH, increase.TABLE 3 .-JUNCTION FORMATION ENERGIES AHx FOR VARIOUS COPOLYMERS IN O-DICHLORO- BENZENE nominal vinylidene TmlOC polymer chloride content/ - for 5 % A&/ AH2/kJ mol-1 crystallite no. (mol O A Mn soln . kJ mol-1 mean value length* - 50 113 11 91.2 70 600 22 91.2 74 500 76.5 20 91.2 88 900 - 21 91.2 123 OOO - 109 130 24 93.8 58 700 - 163 23 93.8 79 400 - 172 66 26 93.8 79 600 87.2 25 93.8 84 700 - 243 27 95.2 70 100 - 28 95.2 71 700 - 243 93 16 95.2 74 700 101.3 29 95.2 82 300 - 117 ii4 * no. of vinylidene chloride units The dependence of AH, on polymer composition is given by the slopes of the plots for gels in o-dichlorobenzene in fig. lb, lc, and Id. Table 3 indicates a large amount of scatter in the data but average values for each composition show an increase in AH, with increasing vinylidene chloride content and this is accompanied by an increase in gel melting point.It is interesting to compare these results with those for poly(viny1 chloride) ge1s.l In poly(viny1 chloride) gels high T, values were obtained when more regular polymer containing larger crystallizable syndiotacticM. A . HARRISON, P . H . MORGAN A N D G . S. PARK 43 runs were used. In the present work this is paralleled by the increase in T, for larger runs of vinylidene chloride units in the copolymers but in these gels and in contrast with the poly(viny1 chloride) gels, higher AHx values accompany the higher T, values as would be expected if network junctions are small crystallites which are larger when the runs of vinylidene chloride units are larger.CRYSTALLINITY A N D GEL FORMATION The hypothesis that the copolymer gels are held together by minute crystallites is in accord with the increased difficulty of gel formation with decreasing vinylidene chloride content. X-ray examination showed no evidence of crystallinity in solid copolymers containing 80 % or less of vinylidene chloride, while crystalline reflec- tions were obtained with polymers containing 83 % vinylidene chloride units or more. This composition was also the critical one below which gel formation did not occur. Direct evidence of crystallite formation in actual gels is not as easy to obtain from X-ray examinations and so indications of crystallinity were sought from differential thermal analysis of a 10 % gel in o-dichlorobenzene of a copolymer containing 95 % of vinylidene chloride units.Fig. 3 shows the trace obtained using a DuPont model 900 instrument. The rapid endotherm at 102°C coincides with the melting temper- ature of this gel and gives good evidence that the disappearance of the gel structure on heating coincides with the end of a period of rapid crystallite dissolution. 2.c 1.5 Y iz' d 1.0 0.5 ----- b I I I I I I 8 0 120 160 temperature/'C FIG. 3.-D.T.A. plot for a 10 % gel of polymer 16 (95.2 nominal mol % vinylidene chloride Mn = 74 700 in o-dichlorobenzene: a, heating ; 6, cooling ; heating rate 20°C min-'. The zero point on the temperature difference AT scale is arbitrary. EFFECT OF METHYLACRYLATE UNITS O N THE GEL MELTING POINT If gel formation is due to a crystallite-linked network the gel melting point should be related to the crystalline melting point of the vinylidene chloride crystallites in the gel.In copolymer/solvent mixtures both copolymer composition and solvent concentration affect the melting point. These factors have been treated separately by Flory to give the relationship44 VINYLIDENE CHLORIDE COPOLYMER GELS Here TE is the melting point of pure vinylidene chloride, and T, is the melting point observed for a copolymer containing mol fraction x of non-crystallizable comonmer with volume fraction 4 of solvent. AH, is the enthalpy change on converting pure perfectly crystalline polyvinylidene chloride to unit volume of melt ; V, and V are the molar volumes of a crystallizable unit in the amorphous polymer and of the pure solvent, while x is the Flory-Huggins interaction parameter for the poly(viny1idene chloride) +solvent system.0.8 n I R' / 0 . 6 - e b4 2 W 0.4'- _1 - c - I I I 1 I j I I rnol fraction methyl acrylate, x FIG. 4.-Gel melting point Tm variation with methyl acrylate content of copolymer. Polymer concentrations : 0, 3 % ; 0, 6 % ; 0, 9 %. T," = 463 K. Actual x values for C and H deter- minations on copolymers 22, 26, 28, 16. Identifying T, with T,, eqn (4) predicts a linear relationship between l/Tm and x. The data for four of the copolymers at three concentrations in o-dichlorobenzene are plotted in fig. 4. There is some indication of curvature but taking the best straight line through the points the values for the energy of melting per mole of crystallizable units, Vv(AH,), shown in table 4 are obtained.The mean figure of about 2.64 kJ TABLE 4.-HEAT OF MELTING V"(A&) FROM THE EFFECT OF COPOLYMER COMPOSITION ON THE GEL MELTING POINTS concentration/(g l.-l) 30 60 90 mean V,(AH,)/(kJ mol-I) 2.52 2.57 2.83 2.64 mo1-1 for the heat of fusion is small. Values of about 10 W mol-l are typical for most crystalline polymers. Low values are, however, commonly obtained from the application of this sort of theory to the melting point of copolymers and a similar treatment for poly(viny1 chloride) gels led to heats of fusion that were only a quarter of the established value for large poly(viny1 chloride) crystallites. This is, at least partly, due to the large surface energy that results from the small crystallite size in the gel but errors may also arise from the persistence of crystallinity at temperatures above T,.This has been well established in the poly(viny1 chloride) system and may also occur with the present copolymers.M. A . HARRISON, P . H. MORGAN AND G. S . PARK 45 EFFECT OF SOLVENT PROPERTIES ON THE GEL MELTING POINT Eqn (4) enables the gel melting point to be correlated with solvent properties. At considerable dilution, as the volume fraction 4 approaches unity, eqn (4) approxi- mates to Values of (1 -x)/V can be obtained from this relationship by combining the AH, values with the data of fig. l(a) after extrapolating to infinite dilution. The results together with the derived x values, are shown in table 5. As expected, x increases on TABLE 5.-x VALUES FOR CO~OLYMER 11 (91 % NOMINAL VINYLIDENE CHLORIDE CONTENT M , = 70 600) IN VARIOUS SOLVENTS molar volume/ V Tm 1°C at (i-X)/vx 1031 solvent cms zero conc.cm-3 X C6H6 89 77 2.30 0.80 C6HjCl 102 67 2.76 0.72 m-C 6H4C12 115 69 2.66 0.69 0-C6H4C12 113 64 2.90 0.67 Molar volume of vinylidene chloride units V, = 58.4 cm3 mol-' ; melting point of pure poly- (vinylidene chloride), T," = 463 K. going from nz-dichlorobenzene to benzene. All of the values are greater than 0.5 which indicates that these liquids are non solvents. If these x values are correct then presumably the solution that occurs is due to the low molecular weight of the poly- (vinylidene chloride) sequences. A similar treatment for poly(viny1 chloride) gels in which l/Tm is plotted against (1 -x)/V led to T," values that were too small.This may have arisen in part because the copolymeric character of the poly(viny1 chloride) was ignored, i.e., a zero value of x was assumed; but it is also likely that the minute size of the fringed micellar crystallites linking the network structure would also lead to a low T," value. This same effect may be occurring in the vinylidene chloride copolymer gels and so the true values for poly(viny1idene chloride) could be less than those in table 5. SIZE OF NETWORK JUNCTION POINTS The AH, values from the Ferry and Eldridge theory give a measure of the size of the network junction crystallites. The number of continuous vinylidene chloride units along a polymer chain that are needed to form a network junction crystallite can be calculated from the ratio of AHx to the heat of fusion per mole of vinylidene chloride units. If the figure of 2.64 kJ mol-1 for V,(AH,) is taken from the treatment of the effect of copolymer composition on T,, crystallite lengths of between 30 and 100 vinylidene chloride units are obtained. The actual values are included in tables 2 and 3. As would be expected, the size increases with the vinylidene chloride content of the copolymer. The large number of units needed to form a crystallite presumably accounts for the absence of crystallinity or gel formation when the vinylidene chloride content is 80 mol % or less. This contrasts with the findings for poly(viny1 chloride) gels in which runs of only about 10 crystallizable units are needed to form junction points.46 VINYLIDENE CHLORIDE COPOLYMER GELS This paper reports work carried out with the support of the Procurement Execu- tive, Ministry of Defence. M. A. Harrison, P. H. Morgan and G. S. Park, European Polymer J., 1972,8, 1361. M. A. Harrison, P. H. Morgan and G. S. Park, Brit. PoZymer J., 1971, 3, 154. J. E. Eldridge and J. D. Ferry, J. phys. Chem., 1954,58,992. P. J. Flory, J. Chern. Phys., 1949, 17,223.

ISSN:0301-7249    

DOI:10.1039/DC9745700038

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

The Dynamics of Networks BY S. F. EDWARDS* Cavendish Laboratory, Cambridge Received 23rd January, 1974 A review is presented of recent work calculating the dynamic properties of polymers in solution, where an attempt is made to see how changes in frequency, density and flexibility take one through various regimes of viscosity to elastic behaviour and how the number of entanglements and cross links affect this behaviour. It is argued that a series of lengths and frequencies naturally present themselves, and most of these regimes are capable of theoretical resolution. The problem of considering the dynamics of networks is complicated by the pre- sence of many different parameters, and the fact that the macroscopic behaviour is a consequence of complex microscopic behaviour. Consider an assembly of JV chains each (for simplicity) of length L, randomly coiled in structure of effective step length 1.Suppose they are immersed in a liquid of viscosity v, at a temperature T, and that the natural period for the chain to flip from one local configuration is z (to be fixed more precisely later). External disturbances, e.g., shear waves have a frequency co. For this paper we consider 8 conditions, but the work is easily extended over most of the range. Consider the changes of circum- stance as parameters change. If V is the volume of the solution, the spacing of the chains can be described by The size of a chain by Ro = (V/N)*. R, = (L1)j and a further parameter introduced to characterize the mean freedom of a point on a chain in dense conditions, an entanglement radius Re = R$PR;*.(To see the significance of this variable, consider a heavily entangled chain which is diffusing very slowly, so that one can refer to an initial point on the chain r(;) and a subsequent position r,. One can expect r, to be found near r(:) and a reasonable representation would be ~ X P ( - Y 1 ( r n - 4°')2) n for the whole set of rn which make up the chain. Adding another chain JV 3 M+ 1 can be expected to increase y in the proportion 1 / M , i.e., y oc NL/V. One then expects the diffusion equation for the single entangled chain, which for a free chain is (;-bv")P(r, s) = 0 * at present at the Science Research Council, State House, High Holborn, London WClR 4TA. 4748 THE DYNAMICS OF NETWORKS to become where we have made the transition from the discrete set of points .. . r,, . . ., to the continuous curve ~(s). It is well known that the solution to (1.2) is exp { +(r - r(o))2} or i.e., or The significance of these parameters appears when presented in this way. When Ro % R, the solution is dilute, each chain is on average remote from the rest and the physical properties are dominated by the hydrodynamic behaviour of a single chain. The chains induce a change in viscosity proportional to M* where A4 = L/Z is a dimensionless version of the molecular weight. As the chains get closer to one another, the coherent hydrodynamical effects along any one chain are weakened by the screening effects of the (incoherent) inter- action with other chains. When Ro - R, and then R, > Ro, the hydrodynamic interaction is screened out and the viscosity correction varies like M.As the density or length of the chains further increases there comes a point where the diffusion of the chains is radically reduced and when Re - R, the viscosity jumps to M3m4 experimentally, but the subsequent discussion here will obtain M3. The material now is heavy entangled, but still creeps with a high viscosity. If it is cross linked one can introduce an analogue of the Re, which can be called R,, by R, = Z/n, n being the number of cross links per unit length. The final characteristic length associated in the gel with both entanglements and cross links we call R,, and so that in the case of no cross links R, = Re, whereas in the (phantom) case of no entanglements R, = R,.When R, is the dominant length the material is elastic and the elastic modulus varies as Rg2. Now consider time scales. The external time scale is w-l. This can be compared with the time it takes for hydrodynamic disturbance to traverse a polymer. From the Navier Stokes equation one can see that this time w - l is given by so that the hydrodynamic screening which alters the naive viscosity dependence from M to M* will disappear as o + > wh. Both this and the screening effect above will tend to return the viscosity to the simple M law, the more important effect being determined by the relative magnitudes of (v/c@ and Ro relative to R,, indeed (v/wh)* can be referred to as a hydrodynamic length Rh. In this discussion the polymer has been considered simply as a loose chain drifting in and with the fluid.In fact it will have internal barriers and these will be jumped in a manner just described for aS . F . EDWARDS 49 different problem by Kramers, and extended to polymer problems by Stockmayer and Verdier and by Edwards and Goodyear.2 There is a characteristic time associ- ated with the jumps of the molecule, (z/kT) or frequency oj. Lf o > wj the polymer appears as rigid and the viscosity does not decrease with w. But for w < w the poly- mer drifts freely. Of course the normal viscous drag and hydrodynamic effects are still present and complicate a complete analysis, but the general result is that a plateau in viscosity will appear as co > coj. Now proceed to the gel. In order to be a gel it must be sufficiently cross linked orland sufficiently entangled.The network of chains will drift through the fluid, but having some mean position, or an approximate mean position for uncross-linked gels, where the " mean position " will slowly drift. Obviously, there will be screening of the hydrodynamic effects, and one can envisage applying frequencies w > w j such that shear waves in the fluid have to force themselves past a virtually rigid network. At lower frequencies the network can sustain elastic vibrations which will be damped by the internal frictional effects within the network, but more important by the relative motion of the fluid to the gel. The elastic modulus will depend on Re and R,, but for high frequencies the effect of cross linking will weaken since the vibra- ting chain will not notice its reduction in degrees of freedom.This effect will appear as w reaches the natural period of the chain associated with R, i.e.? or the appropriate modification for mh and R,. The effects on entanglements will be two-fold; firstly the same effect as for cross links which is to weaken the effect, but also the effective number of entanglements will increase with w, for at a high fre- quency, configurations which are not true entanglements and from which a chain could extricate itself in time now appear as true entanglements, I have not yet produced a convincing criterion for this latter effect; it has been observed experi- mentally (Ferry, personal communication, 1974). Having catalogued the effects, the next section will give an outline of the mathe- matical structure which models them.In addition to well known results in the litera- ture this paper will amount to a review of work on polymer solutions by myself and K. F. Freed and on gel-liquid systems by myself and A. Miller.4 co = ~ T I V ~ R : 2. MATHEMATICAL MODELS Physical properties peculiar to polymerized systems have to do with the great length of the chain. It is therefore important to adopt a notation which clings to this essential point whilst casting all other characteristics of the molecules into various constants that appear. The study of these constants is of course important, but they do not help in getting those phenomena which are unique to polymer systems. A chain can therefore be simplified to a series of points R(,,) on an inextensible chain Such arrays appear in crystals and it is well known that the way to study long waves in a crystal is to consider fourier series of the unit cell coordinates.Likewise in polymer problems the key variable is the fourier sum R(,,- 1,1 = 1. The complex variable is more useful than the real. The finite number of units on the chain, N , implies that R, is not a perfect variable, in as much as its use implies the adequacy of a cyclic condition That this is not true does show up that the modes of motion of polymers are not perfectly separable in these fourier variables. Nevertheless, even when extensive machine calculations are made to =50 THE DYNAMICS OF NETWORKS find “ best possible ” Rouse-Zimm modes, these are extremely close to fourier variables.(It is possible to show that more accurate theories of dilute solutions than the Rouse-Zimm theory give even closer results to the fourier modes, and that for gels the fourier modes are indeed exact modes.) The probability distribution of the small q modes for Gaussian chains is well known to be with a consequent entropy in 6 conditions of 3kT 21 - - q21RqI2. Thus if we want the simplest theory of the Brownian motion of a chain, and postulate a viscous drag of [ and a random forcef, 3kT 5Rq++Rq = fq(t) for each q value. If the probability of finding the R4 is P(. . . rq . . . ; t ) then standard theory gives where (f,(t) f-q(t‘)> = 3ckT6(t - t’). (2.6) The equilibrium solution for P is (2.2). Eqn (2.5) amounts to the well known Rouse equation where only the q -+ 0 values are used.What we wish to do in this section is to put the effects of cross linking, hydro- dynamic interaction and entanglements into this kind of formalism. Before getting to gels proper, consider the effects of a surrounding liquid. The boundary condition between the polymer and the liquid can be taken to be that of no slip, i.e., &n> = u(R(n,, t ) (2.7) where U(E, t ) is the fluid velocity. (It doesn’t seem to matter what condition one takes as long as it is unambiguous, see Zwanzig 5 ) . The mathematical way to handle such a constraint is to use a Lagrange multiplier and to modify the equations of hydro- dynamics to Du = c ou,,6(r -R#) + F (2.8) 9 R P ) = -a,+ f (2.9) u,n where a labels the chain and n the monomer.where D denotes the operator of the linearized Navier Stokes equations and 9 the equation of motion of the polymer, and F, fare forces acting, random and external. The equation of the polymer could be taken to be that of a chain without rigidity or mass, i.e., 3kT BRq = ----q2R z q (2.10)S . F . EDWARDS 51 i.e., if we think of -+ R(s, t ) s an arc label (2.11) But if we think of the polymer making random jumps of its own with a characteristic time z one has (2.12) One must solve for u in terms o f 0 and eliminate 0 from the equation by the condition I? = t, on the polymer. When this is done, one finds the form ( ~ k , + ~ q ' R ~ +.X(q, p)k, = 9+f 3kT ) (2.13) where% gives the effect of the liquid and 9 is the force stemmiiig from the forces F acting on the liquid, transmitted to the polymer.For example, in the case of a little (massless) sphere embedded in a liquid, X would be the Stokes term 6na9. For a dilute solution p - 0 or more precisely R, < Ro, 3- is independent of p but varies like 43, which is a well known result expressed in the present notation. This result comes from the fact that the motion of one part of the polymer forces the liquid to move, which then affects another part of the polymer cooperatively. However, a more accurate attack again puts in the time dependence of this hydrodynamic effect and replaces X in (2.13) by s.X(q, p, t - t')R(t') dt' i.e., one can fourier transform also on t, to get (2.14) The full form of X is complicated and is given by Edwards and Freed structure varies like but the according to which is the largest.Thus the hydrodynamic interaction is screened by p or o, i.e., by the intercession of other chains, or by the time it takes for the motion to get from one point on the polymer to another. The expression is further complicated by z, for the smallest q will be - L-l and if z is larger than this it implies that the chain responds so slowly to the forces acting on it that the hydrodynamic intervention is irrelevant. The details of these calculations we do not give here; the point made is that the variables q, o give a description of the various circumstances that arise. The static viscosity increment can be developed from (2.14) (and indeed the dyna- mic viscosity also), and has a simple form, being We shall not employ z further and consider chains freely moving.(2.16) (2.17) (2.18)52 THE DYNAMICS OF NETWORKS How can one extend this to situation in a gel where the chains are not just overlapping, so that hydrodynamic effects are screened out, but heavily entangled so that they can only move cooperatively ? When an oscillating shear wave is applied, elastic effects will dominate, but one framework so far should handle weak, steady shear and yield a viscosity. One can see how this might be handled by returning to (2.4) and (2.5). The effects of the random forcef, is countered by the fact that the chain is boxed in by its neighbours. Thus if one can expect where whereas interaction), h, Note the sign; the presence of the other chains to diminish this by h,(q) say, so that (2.20) ho is independent of q (there being screening of the hydrodynamic will be dependent on q and have the form for clearly the weakening effect of h, will be diminished over small h l h ) = h1(0)-h2q2. (2.2 1) distances and be at its strongest over large distances.Note also that q takes positive and negative values, and there cannot be terms linear in q since the resulting expression must be even. It could of course be that the expansion should be IqJ', but this re- presents a higher level of sophistication than is used here. We just expand it and keep the first term. Thus h = (ho-hl)+h2q2. (2.22) Now h, will depend on the number of polymers to give rise to entanglements, so for a fixed molecular weight, as p increases ho -hl decreases and at a critical density gives zero.Thereafter h = h2q2 and since at this point only the physical quantity Re can be involved, The viscosity in this regime is then (with 5 - p-I the screened term (2.15)) 6 V - OO .M3p3; PV R, > Ro > Re. (2.23) Experimentally the power of M is greater than 3, but the expansion (2.22) represents the simplest approach to the problem. An explicit realization of the structure of h l , h2 has been given by Edwards and Grant,6 but much more needs to be done to make this approach convincing. In particular, the transition has been treated by considering the behaviour past it, by the statement that only R, can appear. In fact, one can hold p constant and vary M so that through the transition hl will behave as h,(M, p ) taking the value ho as p + coy independent of M.One would like also to keep p fixed and study the transition as a function of M, which for technical algebraic reasons seems quite difficuIt in practice though not in principle. It will be noted that if one considers a( [ R,12)>lat one finds zero for q = 0, simply because ([R,12) is the equilibrium value. But in our fourier variables q = 0 corresponds to the motion of the centre of mass, R = -R,=, 1 N (2.24)S . F. EDWARDS 53 and directly by multiplying (2.20) by R* and integrating aW2 2h(0) - = - d t N (2.25) the normal Browman motion of the polymer as a whole. However, after transition - = o aR2 a t (2.26) since h(q) = 0 at q = 0. The transition corresponds then to the chains ceasing to drift except at the very slow level implied by the motion of the free ends which do not have entanglements.Under these conditions it is not the low viscosity which will appear as the dominant physical phenomenon, but the emergence of elastic moduli at all but the lowest frequencies. In order to study this aspect, a good start is to consider the effects of cross linking on the network. The constraint is now that certain points on certain chains are the same as certain points on other chains R(@)(SP, t ) = P ( s e , t). As a model for this we can consider an average position of one chain, say R(A) and another R(g). Then and R(2) will not stray far from R(A) and R(g). The kind of equation one might expect is then (2.27) where 402 represents effects restoring R4 to its mean position. Now 402 will be the result of the various cross links and entanglements.Suppose it is known, then one can estimate the effect of one link between chains 1 and 2 by putting in a Lagrange multiplier into equations of motion which are otherwise (2.27). The total effect of such terms must then be 4:. This programme is easily carried out, and yields (2.28) 402 = n/SG(q, w) dq where i.e. (2.29) (2.30) together with a change in structure of the equation, by which the many other chains interacting with the one particular one under consideration are reasonably represented by the mean displacement of the solid (2.31) (2.32) Physically, this means that the average effect of cross links is to tie down a chain relative to a mean position plus the average distortion of the materials as a whole. One can now go ahead and solve (2.32) for R in terms of u and hence derive equations54 THE DYNAMICS OF NETWORKS for u directly, which give the elastic equations of motion and conform in structure with classical work, but also give the clamping and frequency shifts.A detailed account is given in Edwards.2 Notice however that qg is frequency dependent, i.e., the effect of a cross link depends on frequency, in the limit of a very high frequency nq, = n2 as m-+O which then modifies the wave equation, which is now C02&+kTqOV2Uk = F k . (2.33) (2.34) (2.35) (2.36) Finally, one can add entanglements into (2.32) in the static sense very easily, for the additional constraint must be proportional to the density and the qo equation modifies to 402 = nqo+Cp. (2.37) But the full theory is more difficult, and it is speculated upon in the next section.FURTHER PROBLEMS An outline has been given of how increasing density leads to chains getting less and less mobile until they reach a state of very low mobility and high viscosity. From the other end of a cross linked elastic solid, the entanglement of the chains acts as an enhancement of the cross links and increases the elastic modulus in a well defined way (provided that the material is randomly cross linked these predictions can be checked, see for example Allen et al. 9 ’). There are two obvious areas which should be explored. First, when there are cross links the formula for their effect is frequency dependent. One can expect that for entanglements to be so also, but in two ways. One is that the response of the chain to forces is frequency dependent-the same effect as for cross links, but also that the number of entanglements increases.For example at low frequency the configurations / (I, are the same from the point of view of cal- culating the effect of entanglement on the en- tropy : one can deform one into the other. However at high frequency only a small segment of the chain notices the rest of the reduced. Another problem is the precise behaviour when there are no cross links. At a high enough frequency, the number of entanglements will increase so that the presenceS. F. EDWARDS 55 of cross links is unimportant, and one can set the problem up as an elasticity problem. But as frequency or density diminishes one reaches the region where a highly viscous liquid is a more appropriate description. How can one span these regions? The principal difficulty seems to be in the fact that the formal theory of entanglements (which is not touched on in this review) though quite easy to write down in a formal way, leads to very awkward mathematics. Yet the physical picture is clear enough, so I hope to be able to find an adequate bridge. I have benefited from discussions with Prof. Ferry and Stockmayer at the 1973 Les Houches Summer School, and as ever from G. Allen and K. F. Freed. W. F. Stockmayer and P. H. Verdier, J. Chem. Phys., 1962, 36,227. S . F. Edwards and A. G. Goodyear, J. Phys. A , 1972,5,965. S . F. Edwards and K. F. Freed, J. Chem. Phys., 1974, 61, 1189, 3626. S. F. Edwards and A. Miller, to be published. R. Zwanzig, private communication. S. F. Edwards and J. W. V. Grant, J. Phys. A , 1973,6, 1169, 1186. 'S. F. Edwards, J. Phys. A , 1974, 7, 318. G. Allen et al., Proc. Roy. SOC. A, 1973, 334,453,465, 477. G. Allen, Farday Disc. Chem. Soc., 1974,57, 19.

ISSN:0301-7249    

DOI:10.1039/DC9745700047

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Conformational Study of Branched Vinylpolymers. Cascade Theory Applied to Chain Transfer BY W. BURCHARD,* B. ULLISCH AND CH. WOLF Institute of Macromolecular Chemistry, University of Freiburg, West Germany Received 7th December, I973 Highly branched materials, obtained by chain transfer between polymers in free radical poIymer- ization, are treated by means of cascade theory which is based on the use of probability generating functions. The necessary link probability generating functions, composed of various probabilities of reaction, have been calculated from the kinetic scheme of the polymerization process. Applica- tion of the cascade theory allows prediction of the critical point of conversion where gelation should occur. Analytical expressions are given for the number and the weight average degree of polymer- ization, the z-average mean square radius of gyration and the particle scattering factor of the mole- cules in the pre- and post-gel state of the system.Furthermore, the mass fraction of linear chains and the sol fraction in the gel are calculated, and finally, the density of branching and the number of elastically effective chains in the gel are evaluated. Evidence of branching may not be apparent from the <S2>, and P,(O) measurements of the unfractionated samples due to the presence of large amount of linear chains, but can be detected when the linear fractions are removed from the sample. No noticeable differences are observed in the properties of molecules in the pre- and post-gelation period. The increase in the number of elastically effective chains after gelation with increasing monomer conversion is compared with the case of a randomly branched trifunctional polycondensate. A much lower elastic modulus is found for the present system than for the trifunctional polycondensate.The theoretical expression for DPw, derived in this paper, shows good agreement with the experimental data of Stein on poly-vinyl acetate. While Stein did not take into consideration gel formation, the present theory now predicts gelation at a monomer conversion of about 67 %. The close agreement between experiment and theory lends not only strong support to the present calculations, but also vindicates the use of cascade theory for the study of chain transfer reactions. Chain transfer in free radical polymerization has aroused much interest in the past because of its abilities to alter properties of polymers.In particular, regulators which are mostly of low molecular weight and bear only one functional group have been widely studied. This paper, however, deals with chain transfer with poly- functional transfer reagents and the aim is to show how such transfer reactions, which necessarily lead to branched material and possibly gel formation at the end, can be given a rigid mathematical framework based on cascade theory. Two main cases can be considered. In the first case, low molecular weight polyfunctional transfer reagent with a well-defined number of active groups is added to the monomer -a process analogous to copolymerization. In the second case, to be considered here, a polymer consisting of repeat units with a functional side group acts as a poly- functional, high molecular weight transfer compound.Branched material is ob- tained in this case by homopolymerization. This type of reaction has been treated theoretically in the past by several authors, 1-5 and the method of Bamford and T ~ m p a , ~ who use a Laplace transform for calculating various moments of a given molecular weight distribution, has proved to be very efficient. Recently, Small et aL6* have applied the technique of probability generating functions to derive similar results. This, however, is only a discrete version of the Laplace transform method. In spite of their undeniable merits, these methods are restricted to the evaluation of the various molecular weight averages and molecular 56W.BURCHARD, B . ULLISCH AND CH. WOLF 57 weight distributions. The interest of the present study is focused in calculating conformational averages, by which it is hoped to get information about the structure of the polymer before and after gel formation. For deriving equations of these con- formational averages, a more powerful mathematical framework is required. Cascade theory, known in demography for a long time, has been recently applied to problems of branching in polymer s ~ i e n c e . ~ ' ' ~ The advantage of this theory is twofold: first, the desired averages, e.g., the number and weight averages of the molecular weight and the z-averages of the mean square radius of gyration and the particle scattering factor, are obtained as special cases of a general path-weighting generating function.Secondly, the branching process can be clearly represented by graphs of rooted trees.l OUTLINE OF THE THEORY In the system concerned, branching can be caused in two ways, i.e., (i) by transfer with an active side group of the polymer, and (ii) by transfer with the same side group of a free monomer ; in the latter case polymers are formed with a terminal double bond whose addition to growing radicals form branches. Statistically, any monomer unit of a polymer has to be selected at random to be planted as a root of a tree. These rooted trees appear organized into various genera- tions with the root as zeroth generation, the units linked to the root being in the first generation etc.(see fig. 1). As the polymers are synthesized by a chain reaction, and propagation always progresses from a point of initiation to a point of termination, the two functionalities to the left and to the right in fig. 1 are not statistically equiva- lent. ' \@/ r Im 1 \@h I r 2 1 0 5 4 3 2 I 0 gene r at i on FIG. 1.-Tree representation of a branched molecule ; 1, r, m denote the type of functionality. The arrows indicate the direction of propagation; -0- denotes a point of chain coupling. The graphs above show the three types of links for units in the first and all further generation. For the sake of brevity, the branch bearing the initiator will be called the left branch and the other one the right branch. The third functionality initiates a branch when the side group is converted to a radical.This branch leads to a termination point (right branch) ; but the side group radical can be also terminated by recombina- tion with a growing chain radical. In this case the branch leads to an initiation point (left branch).58 CONFORMATIONAL S T U D Y OF BRANCHED VINYLPOLYMERS Before use can be made of the cascade theory, it is necessary to set up generating functions for the link probabilities. These link probabilities are related to prob- abilities of reaction, a, t, q, w, y defined below, referred to a specific monomer conversion say p. These reaction probabilities are accessible from the kinetic scheme of polymerization 2-details of these calculations will be published separately. a is the total number of propagation steps with monomer and terminal double bonds divided by all reaction steps which a growing chain radical can take part in. t is the fraction of propagation steps with monomers only.q is the total number of initiation rezctions caused by a macromolecular initiator (a side group of a polymer) divided by the total number of initiations. p is the total number of radical recombinations divided by the sum of recombination and transfer steps. w is the total number of side chain radicals formed during the polymerization divided by the number of monomer units built in the polymers. y is the total number of reactions with monomer of all side group radicals divided by all reaction steps of these radicals. The six possible link probabilities are defined as follows : at, probability of a link between two monomer units ; a(1- t ) , probability of a link between a monomer unit and a terminal double bond ; (1 -a)q, probability of a link between a macromolecular initiator and a monomer ; (1 -alp, probability of coupling of two growing radicals ; WY, probability of a link formed by a side group radical with a monomer ; w(1 -y), probability of coupling of a side group radical with a chain radical.The probability generating functions for the three functionalities of a monomer unit are now readily set up (see, for instance, Feller 16) : where s = (SM, s1, sr). Three auxiliary variables are used in these equations : sM denotes reaction of the functionality with a macromolecular initiator or with a chain terminal double bond, s1 denotes reaction of a functionality with a repeat unit from the left branch, s, denotes reaction with a repeat unit from the right branch.three functionality generating functions of eqn. (1) The link probability generating function (zeroth generation) is the product of the &(s) = F,(s)m)~m(s). (2) In the first and all further generations, three types of generating functions have to be distinguished depending on whether the left, the right or the middle functionality is used for a link to the preceding generation (see fig. 1). In all three cases, two functionalities are available for further reactions with units in the next higher genera- tion. ThusW. BURCHARD, B . ULLISCH AND C H . WOLF 59 or, in a more compact vector, All properties of interest of a branched and eventually gelled material can now be expressed in terms of these generating functions.Analytic expressions are given below for the number average degree of polymerization, DP,, and for the three quantities obtainable by means of light scattering, viz., the weight average degree of polymer- ization DP,, the z-average of the mean square radius of gyration (S2)>, and of the particle scattering factor Pz(8). Furthermore, a condition for gel formation is derived. Finally, the mass fraction of the non-branched material and the sol fraction of the gelled sample are calculated. NUMBER AVERAGE DEGREE OF POLYMERISATION DP,, Applying general stoichiometric considerations of Stockmayer,' Malcolm and Gordon found l 2 where differentiation with respect to s means differentiation with respect to the com- ponents s,, sl, s,.AVERAGES OBTAINABLE FROM LIGHT SCATTERING MEASUREMENTS The three averages DP,, (S2)>, and P,(O) follow as special cases from the path- weighting generating function which is obtained by a cascade substitution : The exponent #,, is a general function of the distance of a unit in the 12-th generation from the root. Differentiation for a given $,, (see table 1) at s = 1 yields various averages of physical significance, such as DP, = l+r(l-P)-'e, ( 6 ) b2 2DPw 1 D P W (S2>, = -r(I-P)-2e, Pz(0) = -[I+~Z(~-PZ)-'~], (7) where e is a unit vector and r = ((I -a)q+2a(1 - t ) , at+(l -cc)p+w(l -y), cct+wy). (9) (10) (1 -a)q+2a(l -t) cct+(l -a)p P = ( (1 -cc)g+cc(l-t) cct+w(l-y) cc(1 - t ) (1 -a)p+w(l - y ) at+wy60 CONFORMATIONAL STUDY OF BRANCHED VINYLPOLYMERS with Z = exp (- b2h2/6), h = (4n/;l)sin(8/2), R being the wavelength in the medium and 8 the scattering angle. TABLE 1.4 n = 1, Ub(1) = DP,, 4 n = (r,,') = b2n, 4 H = rexp (-h2b2/6)1, Ub(1) = 2DP,(S2),, Ub(1) = DP,P,(@). CONDITION FOR GEL FORMATION Gelation occurs when DP, increases beyond all limits. This happens if II-PI = 0. (14) MASS FRACTION OF THE LINEAR CHAINS Because of the mechanism of a chain transfer reaction, there is always a certain amount of linear material present in the system, and it is of interest to know how large this amount is and how it changes with the monomer consumption. The principle for deriving this mass fraction may be demonstrated with the definition of the weight- generating function.The sum over the weight distribution of molecules can be written as b ( x ) = kljn(X)+CWb(x) = m l i n + m b = 1, (1 5 ) where the indices lin and b refer to the linear and branched fractions respectively. Passing to generating functions one finds where and wb(sb) = c O b ( x > s ~ / ~ wb(x) are the normalized weight generating functions for the linear and the branched mole- cules in the system. Hence, subtracting all terms involving &, from the weight generating function W(s) one finds W(slin), and by setting slin = 1 the mass fraction is obtained : m l i n = W(Slinlsll,== 1- (18) It is now necessary to express sl, s,, S, of eqn (1) in terms of slin and sb defined in eqn (15)-(18). In the two functionality generating functions Fl(s) and Ii,(s) of eqn (l), the variable S, denotes the formation of a branch and is identical to s,, whereas w[(l -y)sl +ysr] in the expression for F&) represents branching of probability w and is therefore equal to wsb.Subtracting now the terms of Sb in each generation of the cascade in eqn (5), one obtains W(slln) and hence the mass fraction mlin (from 18). Normalizing the residual generating functions F1(slin) and Fr(slin) for the two functionalities in (la) and (lb), the probability generating functions for the various generations of the linear molecules and a path-weighting generating function can beW. BURCHARD, B . ULLISCH AND CH. WOLF 61 constructed. Following the prescriptions developed in the previous section, calcula- tion leads to the various measurable parameters, viz., where 1 al+P DPwlin = - + -, 1-a, 1-a1 (S2)z1in = at at a, = a, = (1-a)(l-q)+at' l-a+atg is used as an abbreviation.averages for the branched fraction can be calculated as follows : Having derived mlin and the other averages of the linear fraction, the corresponding DENSITY OF BRANCHING The branching density p, defined as the number of branches per reacted monomer, is easily found from the link probability generating function of eqn (2) by collecting all the coefficients of s b . Multiplying this value by DP,, one finds the average number of branches per macro- p = (1 -a)q+2~(1 - t ) + w . (28) molecule The corresponding number of the branched fraction is N = DP,p. where nb is the number fraction of branched molecules, n b = (1 -??Zlin)DPn/DPn,.SOL FRACTION Beyond the gel point only a part of the material is insoluble and the remaining sol fraction can be extracted from the gel. All properties of the molecules in the sol62 CONFORMATIONAL STUDY OF BRANCHED VINYLPOLYMERS fraction are charzcterized by the extinction probability. This probability indicates whether a branch attached to a repeat unit of the polymer is finite in size. Cascade theory shows that the extinction probability is given by ** 11* 12* l9 where v = (uM, ul, vr). Eqn (31) is not easily tractable analytically but has been solved numerically. v = FlW, (31) The sol fraction is sol = F,(v). (32) Also for the sol fraction, the molecular and conformational averages can be calculated. Again, one has to start with the generating functions for the three functionalities of a repeat unit, eqn (1).Multiplying the components of s with the corresponding com- ponents of v, one selects those monomer units which belong to the sol fraction. Normalizing leads to the following : where and vs = (uMsM, ~ 1 ~ 1 , cryr), F,<s> = P,(s)Pr(s)Ern(s>, (34) @1(s) = (P,(s)pr(s), P ~ ( s ) P ~ ( s > , Fr(s)prn(s))- (35) These and other generating functions to be calculated by cascade substitution as outlined earlier, can be used to determine the required averages. The equations for DP,,, <S2)>, and Pz(8) are almost identical to eqn (6)-(8) with the exception that P has to be replaced by PV and r by rV, where V is a diagonal matrix whose elements are theextinction probabilities. The symbol * indicates properties of the sol fraction.A A A ELASTICALLY EFFECTIVE CHAINS The elastic modulus of rubber-like network is given by 20* 21 E = kTNeldlVA/Mo = kTv,l (36) where Nel is the number of elastically effective chains per monomer unit, d is the density of the polymer, Mo the molecular weight of the monomer unit and NA Arogaolrd's number; vel is the number of elastically effective chains per volume. As was shown by Malcolm and Gordon,12 this number can again be evaluated from the probability generating function. By multiplying each link probability by the components of the probability (1 -v), where v is the set of extinction probabilities as defined in eqn (31), one obtains the probability generating function for an infinitely extended branch. where T~(Y,s) = (1 -YI +YA)(~ -Yr +VrSr)(l -yrn+YmSm), (37) yI = [(I - a)q + a( 1 - t)]( 1 - om) +at( I - P ~ ) , yr = a(l -t)(l - u , ) + ( l -a)p(l -co,)+at(l -L$, Y , = w(l -y)( 1 - UJ + wy(1 - ur).W.BURCHARD, B. ULLISCH AND CH. WOLF The number Nel of the active network chains is then given by NeI = O.S[Tb(s),= 1 - Tb(s),=o- T3S)s=0]- 63 (39) RESULTS AND DISCUSSION Stein experimentally investigated branching of poly(viny1 acetate) due to chain transfer and gave a corresponding theoretical treatment for the derivation if DP, and DP, based on the Bamford-Tompa Using the data of Stein for the transfer constant Ct, = 1.8 x loe4 and the reduced reactivity of 0.8 for the terminal double bond, we checked our theory against Stein's experimental results. The agreement is satisfactory.3 2 I 2 2 n X 1 I \ 0 0.5 1.0 B FIG. 2.-DPw as function of monomer conversion for polyvinylacetate. 0 measurements of Stein," curve (a) calculated from eqn (6) with p =+ 0, (1 - t ) =+= 0 and Ct, = 1.8 x and reduced reactivity for terminal double bonds ; curve (b) calculated with p = 0, (1 - t ) =+= 0 ; curve (c) with p =k 0, A (1 - t ) = 0 ; curve (d) with p = (1 - t ) = 0. Dotted line shows DPw of the sol fraction. Fig. 2 shows DP, versus p, calculated from our probability theory. The full circles represent the measurements of Stein, who carried out his experiments up to a monomer conversion of about 60 %. However, our theory now predicts gel forma- tion at about 67 % monomer conversion. The gel point is essentially determined by three parameters : the chain transfer constant, the amount of incorporated chains with a terminal double bond and by the chain coupling.The influence of these factors is clearly expressed in the link probability generating function by the three probabilities w, a(1- t ) andp. Fig. 2 shows also curves of DP, versus for the special cases where64 CONFORMATLONAL STUDY OP BRANCHED VINYLPOLYMERS (i) no recombination of radicals occurs, p = 0, 1 - t # 0 (curve b) ; (ii) no polymer with terminal double bond is incorporated, 1 - t = 0,p # 0, (curve c) ; (iii) 1 - t = 0, p = 0 simultaneously (curve d). One realizes that recombination has only little influence in this system. This results from the fact that p is small, evidently because of the high amount of transfer reactions. On the contrary, the gel point is drastically shifted to higher conversion, if no chains with terminal double bond are incorporated in the polymer.Finally, gelation does not occur at any conversion, if there is no termination due to radical recombination and if no chains with terminal double bonds are added to the growing chain. In the latter case, only branching and no crosslinking takes place. The broken line in fig. 2 exhibits the decrease of DP, of the sol fraction as gelation pro- gresses. A 3 \ \ \ \ 0 0.5 I. 0 B FIG. 3.-<S2>, as function of /?, for symbols see fig. 2. Fig. 3 shows corresponding behaviour for (S2>, versus conversion. The mass fraction of the sol and that of the linear chains in the system are plotted against monomer consumption in fig. 4. This fraction of linear chains remains appreciable throughout the reaction and amounts still more than 20 % at the gel point.Information on the structure of the material in the pre-gel and post-gel state is obtained from the mean square radius of gyration, from the particle scattering factor and from the number of elastically effective chains. The dependence of (S'), on DP, is shown in fig. 5 for unfractionated samples (curve a) and for the branchedW. BURCHARD, B . ULLISCH AND CH. WOLF 1.0 C 0.5 0 0 I LO I Q5 '2 0 65 FIG. 4.-Variation of the mass fractions of linear molecules and of the sol fraction with monomer conversion. ~ ~ ~ 1 1 0 5 FIG. 5.-Dependence of the mean square radius of gyration on the degree of polymerization ; (a) for unfractionated samples, and (b) for the branched fraction.The dotted line represents behaviour of linear chains with most probable distribution. 57--c66 CONFORMATIONAL STUDY OF BRANCHED VINYLPOLYMERS fraction (curve b). The dotted line represents behaviour of linear chains with most probable distribution in length. The striking feature of the small difference in ( S 2 ) , between the linear and the unfractionated samples can be explained by the presence of 15 - to z s m 5 0 I 0 I0 20 30 40 51 h2<s2>z FIG. &-Plots of Pz(8)-1 versus hz<S2>, for (a) linear chains, and (a’) the branched fraction of the present system. Curves (b’) and (6) show behaviour of star molecules with five homodisperse and polydisperse branches respectively. large amount of linear chains in the system.Comparison of (S2), of the branched fraction with that of the linear chains of same molecular weight shows the familiar decrease, frequently expressed as the g-factor, The g-factor varies slightly between 0.89 at the beginning of the reaction and 0.766 near the gel point. The g-factors for star-molecules with branches of most probable distribution are g = 0.75 for a 3-star molecule, and g = 0.53 for a star with 5.3 branches on the average.24* 2 5 These functionalities correspond respectively to the mean number of branches per molecule in the branched fraction at the beginning and near the gel point. The g-values show similar dependence on branching, although the effect is less marked for the chain transfer system. It appears therefore a little unexpected at the first sight that the particle scattering factors show such vastly different behaviour (see fig.6). However, this can be explained as follows. The regular star-molecules are characterized by a pronounced up-turn of the I/P,(O) against h2(S2>, plot, which is considered to be typical for branching. Recently, one of us showed that the up-turn is flattened out by a molecular weight distribution sample.25* 13* l4 Since our system has a much broader molecular weight distribution (Mw/Mn z 50) compared to the star-molecules, this flattening effect is much more pronounced, although a slight up-turn still exists. Concerning the properties of gel, the change in the number of elastically effective chains with conversion is also of great interest. This behaviour for our system is compared with that of a trifunctional randomly branched polycondensate l1 and fig.7 shows a much slower increase in Nel for the present system. This is the consequenceW. BURCHARD, B . ULLISCH AND CH. WOLF 67 of the lower reactivity of the transfer functionality, compared to the other two. A much softer gel results from this effect. We are aware of the limitation of the present theory. Certainly, some complica- tions will occur at large monomer conversion. Some reactions may become diffusion controlled like the recombination of two chain radicals (Trommsdorf effect), or the 0.1 5 8.1 I 2 0.05 0 I. Q 1.25 1.5 BlBc FIG. 7.-Increase of the number of elastically effective chains with reduced conversion fl/& (a) for present system, and (a') for trifunctional randomly branched polycondensates." addition of chain terminal double bonds to growing chain radicals.It will be interesting to study the deviation from this idealized behaviour in an actual system, and this treatment may help to get more insight into the various processes at high conversions. P. J. Flory, J. Amer. Chern. SOC., 1937, 59, 241 ; 1947, 69, 2593. T. G. Fox and S. Gratch, Ann. N. Y. Acad. Sci., 1953, 57, 367. C. H. Bamford and H. Tompa, Trans. Faraday SOC., 1954,50, 1097. D. J. Stein, Makromol. Chem., 1964, 76, 157 ; 1964, 76, 169. W. W. Graessley, H. Mittelhauser and R. Maramba, Makromol. Chem., 1965, 86, 129. P. A. Small, Polynzet-, 1972, 13, 536. R. A. Jackson, P. A. Small and K. S. Whiteley, J. Polymer Sci. (Polymer Chern.), 1973,11,1781. see for instance (a) R. A. Fisher, Proc. Roy. SQC. (Edin.), 1922, 42, 321 ; The Genetical Theory of Natural Selection (Dover Publ., N.Y., 1958) ; (b) Ch. J. Mode, Mirltigle Branching Processes (Amer. Elsevier Publ., New York, 1971) ; (c) S. K. Srinivasan, Stochastic Theory and Cascade Processes (Amer. Elsevier Pub., New York, 1969), chap. 9 ; ( d ) Th. E. Harris, The Theory of Branchiqq Processes (Springer Verlag, Berlin, 1963). M. Gordon, Proc. Roy. Soc. A, 1962, 268, 240. l o I. J . Good, Pt-oc. Roy. SOC. A, 1963, 272, 54 ; Proc. Canib. Phil. SOC., 1949, 45, 360. " G. R. Dobson and M. Gordon, J . Chern. Phys. 1964, 41, 2389; 1965, 43, 705.68 CONFORMATIONAL STUDY OF BRANCHED VINYLPOLYMERS l2 D. S. Butler, M. Gordon and G. N. Malcolm, Proc. Roy. SOC. A, 1966, 295, 29. l 3 K. Kajiwara, W. Burchard and M. Gordon, Brit. Polymer J., 1970, 2, 110. l4 W. Burchard, Macromolecules, 1972,5, 604. lS B. Ullisch, Ch. Wolf and W. Burchard, in preparation. l6 W. Feller, An Introduction toProbability Theory (Wiley Int. Ed., London, 1968), vol. 1, chap. 11. l7 W. H. Stockmayer, J. Chem. Phys., 1944,12,125. l 8 P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, l9 M. Gordon, S. Kucharik and T. C. Ward, Coll. Czech. Chem. Comm., 1970, 35, 3252. 2o P. J. Flory and J. Rehner, J. Chem. Phys., 1943, 11, 521. 21 H. M. James and E. Guth, J. Chem. Phys., 1943, 11,455. 22 B. H. Zimm and MI. H. Stockmayer, J. Chem. Phys., 1949, 17, 1301. 23 W. H. Stockmayer and M. Fixman, Ann. N.Y. Acad. Sci., 1953, 57, 334. 24T. A. Orofino, Polymer, 1961, 2, 305. 2 5 W. Burchard, to be published. l6 H. Benoit, J. Polymer Sci., 1953, 11, 507. 1953), p. 384.

ISSN:0301-7249    

DOI:10.1039/DC9745700056

出版商:RSC    

年代:1974

数据来源: RSC