3 Chain Conformations and Polymer Properties ~~~ ~ By G. ALLEN and C. PRICE Department of Chemistry University of Manchester IN this report emphasis is laid on work published in 1969 but in view of the lapse of nine years since the previous report’ on this topic reference is made to some of the major developments over this longer period. We shall deal mainly with synthetic organic polymers ; inorganic polymers biological materials and resins will be excluded. Chain Statistics.-A polymer chain has numerous rotational isomers by virtue of internal rotation about main chain 0 bonds. In the crystal the conformation adopted by the chain’ is usually the one of lowest internal energy consistent with efficient packing of chains in the lattice. In solution or in the melt the conforma-tion of the chain is continually fluctuating between all possible conformations, and a statistical analysis is required in order to specify the moments of the required physical quantities (usually end-to-end distance or radius of gyration) over the total population of conformations.The presence of an asymmetric centre in the repeat unit of a polymer molecule introduces a distinction3 otherwise not present and gives rise to stereochemical isomers. Thus whereas different stereochemical configurations of poly(methy-lene) poly(methy1ene oxide) and poly(ethy1ene oxide) do not exist poly(propene), poly(acetaldehyde) and poly(propene oxide) exhibit iso- syndio- and a-tactic stereochemical sequences. For these polymers a statistical analysis of chain configurations is required.In the literature there is confusion between the two terms ‘configuration’ and ‘conformation’ as applied to polymer chains. In this review ‘conformation’ applies specifically to the spatial distributions of the chain i.e. rotational iso-merism ; ‘configuration’ is used to denote stereochemical isomerism. Chain Conformation. Perhaps the most important event in 1969 from a reviewer’s point of view has been the publication of Flory’s This is a lucid account of developments which have occurred since the publication of Volkenstein’s treati~e.~ It describes in detail developments of the past five years. The analysis G. Allen and M. N. Jones Ann. Reports 1960 57 102. See for example ref. 4 ch. VI. P. J. Flory ‘Statistical Mechanics of Chain Molecules,’ Interscience New York, 1969.M. V. Volkenstein ‘Configuration Statistics of Polymeric Chains,’ Interscience New York 1963. ’ C. W. Bunn Discuss. Faraday SOC. 1958 25 95 20 G. Allen and C . Price of the rotational isomeric state model of a polymer chain has been extended to cope more effectively with the interdependence of rotations about neighbouring bonds in the chain and to include calculations on real chains comprising repeat units of virtually any complexity. Computer methods are required for some of the complex analyses and consequently the results are not always available as analytical solutions in a closed form. The simplest analysis of the conformations of a polymer chain treats a linear molecule made up of n links of length 1. There are no restrictions on bond angles and internal rotations and a phmtom chain is assumed so that it can pass through itself and different units can occupy the same point in space at the same time.To the approximation that the chain obeys Gaussian statistics the mean square of the end-to-end distance is found to be ( r 2 ) = nf2 This is the random-flight model and the result holds for freely jointed chains. If the bond lengths in the chain differ l2 is then the mean square bond length. This model is made more realistic by introduction of a fixed bond angle 8. A simple chain is then characterised by n 1 and 13. In the limit of large n, (r2)free = n12(1 + cos e)/(l - cos e) = nP . qe) A real chain does not have free rotation there is a symmetrical rotational function V(4i) influencing rotation about bond i and dependent on the azimuthal angle between bonds i - 1 and i + 1.In a phantom chain we can assume that V(+i) about the bond i is independent of rotations about neighbouring bonds and hence = n12. f(0)f(+i T ) where The introduction of V(+J represents a very important step since the chain dimen-sions may now be temperature dependent. Eveh so conformations of real chains depart from their phantom model in a most important respect namely that they cannot cross their own paths. Out of all the phantom conformations only a small fraction will be free from self intersec-tions and will therefore be acceptable for a real chain. Average dimensions of the real chain e.g. ( r 2 ) are thus increased. The problem for a real chain can be separated into two parts.Firstly there are the short-range interactions between atoms and groups which are neighbours or near neighbours along the chain, secondly there are long-range interactions involving pairs of units which are widely separated in the chain sequence but which come near to one another in space in certain chain conformations. By definition we take ( r 2 ) o to denote the value of ( r 2 ) which obtains in the absence of long-range effects. A factor a wa Chain Conformations and Polymer Properties 21 introduced by Flory6 to describe the increase in a linear dimension of the average conformation as a result of long-range effects (i.e. the excluded volume effects), thus ( r ’ ) = a2(r2),-, Much of Flory’s new book is devoted to the mathematical description of the equilibrium set of conformations corresponding to ( r 2 ) o available to real chains.The rotational isomeric state model is used and interdependent rotational potentials are included. The total conformational energy is expressed as a sum of energies of first-neighbour pairs of bonds. The statistical weights (u) corres-ponding to the energies (E) of pairs of bonds in given orientations are obtained from u = exp [ - E / k T ] and these can be obtained for all the states [ of a particular bond i. The statistical weight of a conformation of the chain of n links as a whole is n- 1 and the conformational partition function 2 is obtained from a summation over all conformations. The energy E has to be estimated from knowledge of barriers to internal rotation and non-bonded interactions and there are usually insufficient data available to perform a priori calculations.Furthermore this direct evalua-tion of 2 would be prohibitive for a chain having n > 15. Alternative methods requiring less computational effort are outlined in the text and a comprehensive list of references is given. In the case of the poly(methy1ene) chain it is possible to use the method to make an a priori estimate of ( r 2 ) o or C = (r2)o/nlz and dln (r2)o/d? At 140°C C becomes substantially independent of n for n > 200 at a value of 6.87 which compares with phantom chain estimates of C = 2.0 for freely rotating links with tetrahedral bond angles and C = 3.2 for independent hindered rotations. For other structures there are at present insufficient data on potential functions to allow the selection of the appropriate rotational isomeric states at or near potential minima and also the evaluation of the statistical weights of the chosen states.In these cases experimental values of ( r 2 ) o dipole moments etc. and the temperature coefficients of these values are used to calculate the statistical weights. These results can then be compared with qualitative estimates of the form of the conformational energy based on inferences from analogous molecules and approximate estimates of the principal contributions to the energy. Polymers analysed in this manner include poly(tetrafluoroethylene) (methylene oxide), (ethylene oxide) (trimethylene oxide) (tetramethylene oxide) (dimethylsiloxa,3-.e), (amides) (esters) (1,4-butadiene) (1,4-isoprene) (isobutene) and stereo-regular and stereo-irregular forms of poly(viny1) chains.In a recent paper Williams and Flory’ have shown that an analysis of the random conformations of the bisphenol P. J. Flory ‘Principles of Polymer Chemistry,’ Cornell University Press Ithaca 1953. ’ A. D. Williams and P. J . Flory J . Polymer Sci. Part A-2 Polymer Plzys. 1968 6, 1945 22 G . Allen and C. Price A polycarbonate leads to a value of (r2>o/n12f(0) = 1.0. The calculations imply that such a value close to that expected for a chain without hindered internal rotation is to be expected for other polymers containing polyphenylene units, and this has been found to be so for 2,6-disubstituted poly(pheny1ene oxide^)^^^*'^ and a poly(sulphone).’ Over the past five years important progress has also been made with the excluded volume problem.Physically it is easy to see that the effect of finite volume must be to expand and broaden the distribution of end-to-end distances. Monte Carlo calculations” based on various lattice models including a tetra-hedral one appropriate to poly(methylene) lead to the result that ( r 2 ) a n l + y where 0.22 > y > 0.18 for long chains. However Monte Carlo calculations are subject to uncertainty associated with the enrichment procedure used to combat the rapid attrition of successful non-intersecting walks as n increases. DombI3 has calculated exact values of ( r 2 ) for n-alkanes up to C1 based on geometrical analyses of all possible conformations.Extrapolation to infinite chain length gives a value for y similar to that derived from Monte Carlo methods. But again there is uncertainty since the extrapolated result is derived from calculations made on chains far too short to display excluded volume effects comparable with those experienced in a long polymer chain. More recently Edward~’~ has suc-ceeded in obtaining an asymptotic solution in a closed form for the position of the nth link in an infinite chain. In the limit n - co this leads to a mean square end-to-end distance. ( r 2 ) a n6” Thus the exponent gives y = 0.20 in agreement with the Monte Carlo result, and in fact the result anticipated many years ago by Flory. Edwards has ex-tended his analysis to the behaviour of a single polymer chain in the critical ‘0’ region,’ topological constraints experienced both by an infinitely long chain16 and by chains crosslinked into a network,’ ’ and the entropy of a confined polymer chain.’ A comprehensive review of conformational problems of polymer chains has been written by another theoretical physicist De Gennes.’ Experimental Studies of Chain Conformation.In the crystal X-ray diffraction methods still provide by far the most extensive and detailed information on chain P. J. Akers G. Allen and M. J. Bethell Polymer 1968 9 575. J. M. Barrales-Rienda and D. C. Pepper European Polymer J. 1967 3 535. G. Allen and J. McAinsh European Polymer J. 1969 5 319. F. T. Wall and J. J. Erpenbeck J . Chem. Phys. 1959 30 634. l o A. Opshoor Polymer 1968 9 599. l 3 C .Domb J . Chem. Phys. 1963,38 2957. l4 S. F. Edwards Proc. Phys. SOC. London 1965 85 613. l 5 S. F. Edwards ‘Critical Phenomena,’ N.B.S. Misc. Publication 1965 273 225. l 6 S. F. Edwards Proc. Phys. SOC. London 1967,92 9. l 7 S. F. Edwards J . Phys. (0 1969 2 1. l 8 S. F. Edwards and J. K. Freed J . Phys. ( A ) 1969,2 145. l 9 P. G. De Gennes Reports Progr. Phys. 1969 32 187 Chain Conformations and Polymer Properties 23 conformation. Neutron diffraction will no doubt have a role to play but to date no results have been published. Information based on X-ray studies has been recently reported for isotactic poly(vinylcyclopropane),” poly(tetrahydrofuran),2 and poly(viny1idene fluoride).22 The structures of polymorphs have been studied in truns-poly(butadiene),2 isotactic p~ly(propene),~~ and poly(but- 1-ene).’ 5 y 2 An extensive compilation of crystallographic data on polymers is available through the table prepared by Miller.27 Considerable advances in laser Raman spectroscopy have resulted in this technique taking its place alongside i.r.spectroscopy as a useful and complemen-tary way of observing the vibrational spectra of polymers2* in bulk. Poly(prop-ene),29 p~ly(styrene),~~ hexagonal and orthorhombic forms of poly(methy1ene ~ x i d e ) ~ 1 3 2 and poly(viny1 fluoride)33 have been investigated. In general how-ever vibrational spectroscopy is a secondary tool in the determination of chain conformation in crystals. It is difficult to obtain unambiguous evidence of a par-ticular conformation from vibrational studies and despite advances in technique and interpretation X-ray diffraction is still the primary technique yielding bond angles and lengths in addition to molecular symmetry.One recent paper34 points out that defects may complicate the interpretation of i.r. spectra of poly-mers. There are no satisfactory methods for obtaining conformational information about chains in polymeric glasses. In rubbers stress-temperature coefficients can be used to determine the temperature coefficient of unperturbed dimen-s i o n ~ ” ~ ~ and Tre10ar~~ has reported that measurements in torsion rather than in simple elongation are to be preferred because the correction to constant volume conditions involves terms which can be evaluated more precisely. Most of the conformational data on the random coil comes from dilute solution measurements under @-conditions or from extrapolations from measurements made in moderately good solvents.The techniques will be covered in the 2 o H. D. Noether C. G . Overberger and G . Halek J . Polymer Sci. Part A-1 Polymer Chem. 1969,7,201. E. F. Vainshtein M. Ya. Kushnerev A. A. Popov and S. G . Entelis Vysokomol. Socpdineniya. 1969 7 A 1606. 2 2 E. L. Gal’perin and B. P. Kosmynin Vysokomol. Soedineniya 1969 7 A 1432. 2 3 R. Nagaeo Polymer 1969 10 175. 2 4 D. R. Morrow J . Macromol. Sci. 1969 B3 53. 2 5 G. Goldbach and G . Peitscher J. Polymer Sci. Part B Polymer Letters 1968 6 783. 2 6 G. Gianotti and A. Capizzi Makromol. Chem. 1969 124 152. 2 7 R. L. Miller in ‘Polymer Handbook Section 3,’ ed. J. Brandrup and E.H. Immergut, Interscience New York 1966. T. Kajiura and S. Muraisi J . Chem. SOC. Japan 1968 89 1187. S. W. Cornell and J. L. Koenig J. Appl. Phys. 1968 39 4883. H. Sugeta T. Miyazawa and T. Kajiura J. Polymer Sci. Part B Polymer Letters, 1969 7 25 1. 2 9 G. Zerbi and P. Hendra J. Mol. Spectroscopy 1969,30 159. 3 1 G. Zerbi and P. Hendra J . Mol. Spectroscopy 1968 27 17. 30 3 2 3 3 J. L. Koenig and F. Boeno Makromol. Chem. 1969 125 302. 34 C. G. Opaskar and S. Krimm J. Polymer Sci. Part A-2 Polymer Phys. 1969 7 57. 36 L. R. G . Tre!oar Polymer 1969 10 279. 3 7 L. R. G . Treloar Polymer 1969 10 291. P. J. Flory Trans. Faraday SOC. 1961 57 829. 3 24 G . Allen and C . Price following section on dilute solutions. ( r') or ( r2),/n12 can be compared with the value of (r') calculated on the assumption of free rotation about fixed angles for the phantom chain.The conformational parameter o2 = (r2)o/(r')free is the most widely quoted parameter. For poly(2,6-dimethyl phenylene ~ x i d e ) ~ > ~ * lo poly(2,6-diphenyl phenylene oxide),' the poly(su1phone)' ' made from bisphenol A and 4,4-dichloro-diphenyl sulphone and for the polycarbonate7 of bisphenol A 0 is close to unity. For vinyl polymers CJ ranges from 1.6 to ca. 2.8 and a roughly linear relationship between the molar volume of the side group and o has been noted.38 Flory4 lists experimental results for many polymers but more recent results include values of o at 30" for poly( 1-~inylnaphthalene)~~ [1.76] poly(2-~inylnaphthalene)~~ [2-45] poly(viny1 d i b e n ~ y l ) ~ ~ [2-65] and poly(ethy1ene oxide)39 [1.55].Values of C at 30" are reported for poly(tetramethy1ene oxide)40 [60] and p0ly(l,3-diollglan)~' [4.0]. In most cases estimates of dln (r2),/dT are made but it must be noted that such estimates are subject to very large experi-mental error. Indeed over-optimistic estimates of the experimental errors pertinent to measurements of ( r 2 ) e are also characteristic of this field. Chain Configuration. The statistics of stereoregularity in homopolymer chains has been established for almost a decade4' for Bernoullian and Morkoffian chains and little development has been required on the theoretical side. High resolution n.m.r. spectroscopy on polymer solutions is still the principal method4' of studying stereochemical configuration.Improvements in instrumentation, particularly the advent of 220 MHz instruments have focused attention on the possibilities of investigating higher sequences and also of analysing spectra in which the chemical shifts were too small to measure accurately at lower resonance frequencies. Reports on poly(methy1 metha~rylate)~~ and poly(viny1 chloride)44 illustrate the usefulness of higher resonance frequencies. Now we have the prospect ofimproved ' 3C n.m.r. spectra (already used for the analysis ofcopolymer sequences)45 and the use of Fourier transform n.m.r. spectroscopy about to make their impact on this field. Useful review^^^,^^ of the determination of polymer structure by n.m.r. spectroscopy have been published recently. An interesting controversy exists over the interpretation of the methylene proton resonances in vinyl polymers with special reference to highly isotactic poly(propene).Natta and Segre,48y49 supported by Bovey and co-worker~,~~ 38 L. A. Utracki and R. Simha Makromol. Chem. 1968 117,94. 39 D. R. Beech and C. Booth J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 575. 40 S. Gorin and L. Monnerie J . Chim. phys. 1968 65 2069. 4 ' F. A. Bovey and G. V. D. Tiers Adv. Polymer Sci. 1963 3 139; R. L. Miller and L. E. Nielsen J . Polymer Sci. 1960 46 303. 4 2 F. A. Bovey Pure Appl. Chem. 1966 12 525. F. Heatley and F. A. Bovey Macromolecules 1969 2 241. R. C. Ferguson Macromolecules 1969 2 237. J. Schaefer Macromolecules 1969 2 2 10. J. L. Binder Appl. Spectroscopy 1969 23 17. 43 44 4 5 46 R.S. Sudal Analyt. Chim. Acta. 1969,46 23 1 247. 48 G. Natta M. Farina A. Zambelli and A. L. Segre Makromol. Chem. 1967 110 1. 49 A. L. Segre Macromolecules 1968 1 93. 5 0 H. L. Frisch C. L. Mallows F. Heatley and F. H. Bovey Macromolecules 1968 1, 47 5 3 3 Chain Conformations and Polymer Properties 25 claim that the n.m.r. spectra are consistent with a degree of isotactic placements of about 98 % Flory” maintains that the same spectra could be consistent with a much higher percentage of syndiotactic placements (possibly as high as 10-20%). The contention of Natta and Segre that less than 2% of syndio-tactic placements can be detected rests on the assumption that the peak com-prising the resonances for racemic dyads in predominantly isotactic chains has a breadth comparable to that observed in the predominantly syndiotactic polymer.Flory et al. argue5’ that the nature of the resonances associated with a given kind of tetrad depends considerably on the conformations of the surround-ing dyads the variation being manifests2 in broader peaks and different spectra observed for resonances associated with different tetrads. The whole argument bears on an analysiss3 of the conformational behaviour of isotactic vinyl polymers in dilute solutions and thermoelastic properties of polymers in bulk from which it was concluded that so-called isotactic forms of poly(propene) poly(but-1-ene), poly(styrene) etc. are stereo-irregular to an appreciable degree. Solution Properties-Dilute Solutions. Results on conformational parameters measured under 0-conditions in dilute solutions have been presented.The 8-temperature for a given polymer solvent system is usually established by deter-mining the temperature at which the second virial coefficient A2 is zero or by the extrapolation to infinite molecular weight of the precipitation temperatures of a series of polymer samples of different molecular weights from solution. Napper has recently discussed the determination of B-c~nditions,~~ especially with reference to the theory of the cloud-point method.” The existence of two &points for polymers dissolved in binary mixtures has been e~tablished.’~ At the lower 8-point A = 0 at the higher &point the chain obeys random-flight statistics. Only when there is no preferential absorption of one solvent component on the polymer chain do the two temperatures coincide.Second virial coefficients in binary solvent mixtures have also been discussed by C~wie.’~ When a 8-solvent is not accessible extrapolation methods for the determination of un-perturbed coil dimensions from measurements made on moderately good solvents are often used.’* A cautionary note on these procedures has been issued by H ~ d e ’ ~ though it does appear that when the extrapolation methods are used with care they produce answers in agreement with direct observation. The light scattering technique continues to provide important information, and light scattering photorneters have been discussed.60 The technique is now 5 1 P. J. Flory and Y . Fujiwara Macromolecules 1969 2 3157 327.5 2 A. Zambelli and A. L. Segre J . Polymer Sci. Part B Polymer Letters 1968 6 473. 5 3 P. J. Flory J. E. Mark and A. Abe J . Polymer Sci. Part B Polymer Letters 1965, 5 4 D. H. Napper Makromol. Chem. 1968 120 231. 5 5 D. H. Napper Polymer 1969 10 181. 5 6 A. Dondos and H. Benoit J . Pol-vmer Sci. Part 5 Polymer Letters 1969,7 335. 5 7 J . M . G. Cowie Polymer 1968 9 587. 5 8 See refs. 9 and 1 1 . 5 9 A. J. Hyde and A. G . Tanner Polymer 1968,9 585. 6 o H. Utiyama N. Sugi M. Kurata and M. Tamura Bull. Znst. Chem. Res. Kyoto Uniu., 3 973; J . Amer. Chem. SOC. 1966 88 639. 1968 46 77 26 G . Allen and C . Price being complemented by the use of small-angle X-ray diffraction studies which can be used for measurements at low degrees of polymerisation.61 The asymptotic behaviour of the reciprocal light scattering function,62 from which it is possible in principle to determine M as well as M has been investigated and the relation-ship63 between random coil conformations and light scattering has been further considered.Two particularly interesting instrumental developments are des-cribed. Bergmann and R ~ b i n ~ ~ have studied light scatteringfrom shearedpolymer solutions undergoing degradation. JenningP reports structural information ob-tained from light scattered by poiymer solutions subjected to electric fields. The Huggins and Kraemar equations generally used to analyse specific viscosity data do not always yield identical values for intrinsic viscosity and kl and k l ’ do not always add up to i. A new equation66 has been proposed to overcome these difficulties.At the same time the hopeless search for a single-point deter-mination of intrinsic goes on. Intrinsic viscosity measurements are still the most prolific source of data on unperturbed dimensions of polymers in solution.68 Variation of intrinsic viscosity with chain t ~ p o l o g y ~ ~ ~ ’ ~ is a particularly important topic since there is still no general method for assessing branching in polymer molecules. Ullman7* has discussed the statistical mechan-ics of worm-like polymers and Wolff 7 3 considers the non-Newtonian viscosity of very dilute solutions of flexible polymer chains. Among experimental studies of intrinsic viscosity rod-like molecules,74 low molecular weight polymer^,^^,^^ and polymers in mixed solvents7 have produced interesting results.Concentrated solutions. In addition to the traditional combinatorial entropy and pair interaction terms current solution theories contain ‘equation of state’ contributions which allow for changes in local structure on mixing. Parameters characterising the free volume of the pure components (e.g. density thermal expansion coefficient and thermal pressure coefficient) are thus taken into account in the analysis of the properties of mixtures. These more sophisticated treatments were initially based on (a) the cell model for liquids and/or (b) the use of the corresponding states prin~iple.~ * The most successful and practically convenient 6 1 R. G. Kirste and G. Wild Makromol. Chem. 1969 121 174. 6 2 A. R. Shultz and W. H. Stockmayer Macromolecules 1969 2 178.6 3 R. Koyama J. Phys. SOC. Japan 1969,26,493. 64 E. A. Bergmann and I. D. Rubin J. Polymer Sci. Part B Polymer Letters 1968 6, 6 5 B. R. Jennings Brit. Polymer J. 1969 1 70. 6 6 S. H. Maron and R. B. Reznik J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 309. 6 7 R. N. Schroff J. Appl. Polymer Sci. 1968 12 2741. 6 8 P. C. Deb and S. R. Chatterjee Makromol. Chem. 1968 120 49. 6 q V. A. Bloomfield and P. A. Sharp Macromolecules 1968 1 380. 7 0 K. Kurata and S. Kobayoski Chem. High Polymers (Japan) 1969 26 89. 7 1 D. Decker Makromol. Chem. 1969,125 136. 7 2 R. Ullman J . Chem. Phys. 1968,49 5486. 7 3 C. Wolff J . Chim.phys. 1968 65 1569. 7 4 A. Isihara J . Chem. Phys. 1968 49 257. l 5 U. Bianchi and A. Peterlin J. Polymer Sci.Part A-2 Polymer Phys. 1968 6 1759. l6 R. R. Buch H. M. Klimisch and 0. K. Johannson J. Polymer Sci. PartA-2 Polymer 7 7 A. Dondos and D. Patterson J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 209. 7 8 I . Prigogine ‘The Molecular Theory of Solutions,’ North-Holland Publishing Co., 789. Phys. 1969 7 563. Amsterdam 1957 Chain Conformations and Polymer Properties 27 approach however has been developed by F l ~ r y ' ~ who makes use of a partition function previously proposed by Hirschfelder and Eyring. An appraisal of the various theories has been made by Patterson" and a number of points of current interest are raised in a paper dealing with the influence of concentration and molecular weight on the heats of dilution of poly(styrene) solutions.' The use of experimental liquid-liquid coexistence curves for testing polymer solution theories is well known.Detailed studies by Koningsveld and Staver-mann82 have shown that erroneous conclusions can be drawn if the calculations are made on the assumption that a polymer solution is a binary system; even after carefully fractionating the polymer the mixture will still contain many polymer components and the solutions must be treated as quasi-binary. These assertions have been confirmed by detailed experimental studies of liquid-liquid phase separations near upper critical solution temperatures. As predicted theoretically for quasi-binary solutions there is found to be a depression in the cloud-point curve at the critical point the critical point is located on the right-hand branch of the cloud-point curve and there is a backward deflection of some of the shadow curves.In spite of the difficulties arising from the quasi-binary behaviour it has been shown82 that if the volume ratios of the two phases are measured as a function of temperature and concentration the critical conditions and the interaction parameter for the system can still be determined with con-siderable accuracy. The most recent contribution to this field deals with equations governing the spinodal and critical Prior to 1959 only a few polymer solutions were known to exhibit liquid-liquid phase separation at a lower critical solution temperature (L.C.S.T.). The solvent was invariably water and the polymers included poly(ethy1ene oxide) and poly(methy1 vinyl ether).In these solutions the L.C.S.T. phenomenon is related - to the negative partial molar enthalpies (ATl) and entropies of mixing (AS1) associated with hydrogen bond formation between polymer and solvent. At higher temperatures thermal agitation is sufficient to break down the specific interactions as a result of which al and a1 become positive and hence an U.C.S.T. is eventually observed. The necessity for strong specific interactions restricts phase behaviour of this type to polar polymers. It is now known that L.C.S.T.'s are a widespread phenomenon and occur quite generally at temper-atures close to the gas-liquid critical point of the solvent when polymer solutions are heated in sealed tubes under the partial vapour pressure of the s o l ~ e n t . ~ ~ . ~ ~ Recent studies by Patterson give L.C.S.T.'s for polyisobutene in solution in some 7 9 P.J. Flory R. A. Orwoll and A. Vrij J . Amer. Chem. Soc. 1964,86 3507; P. J. Flory, ibid. 1965 87 1833; P. J. Flory J. L. Ellenson and B. E. Eichinger Macromolecules, 1968 1 279. D. Patterson Rubber Chem. Technol. 1967,40 1. " G. Lewis and A. F. Johnson J . Chem. Soc. ( A ) 1969 18 16. 8 2 R. Koningsveld and A. J. Staverman J . Polymer Sci. Part A-2 Polymer Phys. 1968, 8 3 M. Gordon H. A. G. Chermin and R. Koningsveld Macromolecules 1969 2 207. 84 P. I. Freeman and J. S . Rowlinson Polymer 1960 1 20; G. Allen and C. H. Baker, 8 5 C. H. Baker W. B. Brown G. Gee J. S. Rowlinson D. Stubley and R. E. Yeedon, 6 305 325 349 367 383. ibid. 1965 6 181. Polymer 1962 3 21 5 28 G .Allen and C . Price thirty different alkanes.86 Strong specific interactions between polymer and solvent are not essential the effect being associated with the enhanced importance of the equation of state term in this region. Since the critical point of the solvent can always be approached provided that the polymer has sufficient thermal stability the widespread occurrence of the phenomenon in polymer solutions is readily understood. Reported studies of L.C.S.T.'s invariably include cloud-point determinations, from which it is possible to estimate the composition and temperature of the threshold point in most cases. However we must again emphasise that in view of the multi-component nature of polymer solutions the critical and threshold points can not be expected to coincide.'' For a given solution the cloud-point curves associated with the L.C.S.T.appear to be broader and flatter than those for the U.C.S.T. None of the curves reported to date for a L.C.S.T. appears to contain the characteristic depression associated with an U.C.S.T. (except perhaps some given in ref. 85) although undoubtedly many of the polymers studied had broad molecular weight distributions. This inconsistency is probably mainly due to the lack of experimental points in the regions of greatest interest a considerable number of the studies seemingly having been misdirected towards establishing threshold points. BurchardS7 has reported light-scattering studies on poly(carbani1ate) solutions in several polar organic solvents. In three cases 6-temperatures and phase separa-tion were observed on heating the solutions.Burchard argues that these solutions exhibit a third class of L.C.S.T. because the organic solvents used in the investiga-tion do not exhibit ordered structures similar to that of water yet phase separation takes place well below the boiling point and the L.C.S.T.'s are shifted to lower temperatures on decreasing the molecular weight of the polymer. Non-Crystalline States-We must distinguish here between rubbers which have molecular mobility similar to that of a liquid and glasses which have a frozen-in state of disorder. Rubber Elasticity. The Gaussian theory of rubber elasticity" predicts that the equilibrium force required to maintain a rubber at elongation ratio 1 is f = c(n - 1-2) where C is a characteristic of the network structure and that the energetic con-tribution to this force (aU/aL),, = fT.dln (r2)o/dIT The theory is based on the postulates : (a) polymer chains adopt random spatial distributions in the bulk state ; (b) the retractive force is predominantly intramolecular in origin ; (c) the network chains are subject to affine behaviour and are constrained only by the network junctures. 8 6 J. M. Bardin and D. Patterson Polymer 1969 10 247. 8 7 W. Burchard Polymer 1969 10 467. 8 8 K. Dusek and W. Prins Fortschr. HochpoIym.-Forsch. 1969 6 1 Chain Conformations and Polymer Properties 29 However in the reglon where Gaussian theory should hold a better fit of the experimental data is given by f = C1(l - A P ) + C2(l -where C1 and C2 are two empirical parameters.Earlier fears that non-Gaussian behaviour was solely a reflection of departure from thermodynamic equilibrium now seem to have been firmly ruled out and attention has been focused on deciding which aspects of the theoretical model require revision." An attempt to clarify certain aspects of the theoretical position has been made by Gordon and col-l e a g u e ~ . ~ ~ Direct determinations of (a U/C?L)v,T and (dS/C?L),, for natural rubber indicate that the C 2 term like C1 is mainly entropic in origin ;90 this result is in direct conflict with earlier suggestions that the observed deviations between experiment and theory were largely due to the neglect of certain energetic contributions. A completely fresh approach on the theoretical side seems necessary in order to interpret these findings on a molecular basis ; it is expected that the mathematical techniques currently being developed by Edwards will be helpful in this respect.'&'' Further data on (aU/aL),, have been reported recently for poly-(dimethylsiloxane) but do not cover sufficient range of A to be c~nclusive.~' The theoretical analysis of the stress-tension relations for rubber has been almost exclusively concerned to date with simple extension.T r e l ~ a r ~ ~ ~ now reports a complete analysis for rubber in torsion which should stimulate experi-mental work in this area. There have been a number of recent studies on the photoelastic properties of networks92 and a useful analysis of the factors govern-ing ~train-dichroism.~~ A method has been outlined for characterising polymer networks by means of swelling pressure and unilateral compression experi-m e n t ~ .~ ~ The accepted method of applying polymer solution theory to swollen gels usually for the purpose of testing network theories has been questioned by Mijnlieff and Jaspers.95 The theory of polymer gelation has been recon~idered~~ and experimental studies have been reported on the properties of hydrophilic gels.97 Further work has been carried out by Tobolsky and his colleagues on the properties of elastomers with labile cro~s-links.~~ 8 9 M. Gordon J. A. Love and D. Pugh J. Chem. Phys. 1968,49,4680. 90 C . Price J. C. Padget M. C. Kirkham and G. Allen British Polymer Physics Group 9 1 C. Price J. C. Padget M. C. Kirkham and G.Allen Polymer 1969 10 573. 9 2 A. N. Gent Macromolecules 1969,2,262; N. J . Mills and D . W. Saunders J . Macromol. Sci. 1968 B2 369; A. N. Gent and V. V. Vickroy jun. Rubber Chem. Technol. 1968, 41 1182. Conference April 1968. 93 P. J. Flory and Y. Abe Macromolecules 1969 2 335. y4 E. J. Van De Kraats J . J. M. Potters M. A. M. Winkeler and W. Prins Rec. Trav. y 5 P. F. Mijnlieff and W. J. M. Jaspers J . Polymer Sci. Part A-2 Polymer Phys. 1969, 96 A. Amemiya and 0. Saito J. Phys. SOC. Japan 1969 26 1264. 9 7 K. Dusek and M. Bohdanecky Coll. Czech. Chem. Comm. 1969,34,289; V. Baresova, ibid. 1969 34 545 707; M. Ilavsky and J. Hasa ibid. 1969 34 2199. P. F. Lyons T. C. P. Lee and A. V. Tobolsky J . Macromol. Sci. 1968 A2 1149; A. V. Tobolsky P. F. Lyons and N.Hata Macromolecules 1968 1 5 15. chim. 1969 88 449. 7 357 30 G. Allen and C. Price Glasses. It is well e~tablished~~ that the temperature at which glass formation is observed to occur (T,) is determined by the correlation between the rate of relaxa-tion and the time scale of the experiment. From a theoretical stand-point, therefore the fundamental problem is to predict how the relaxation process is influenced by the macroscopic variables (e.g. pressure temperature and applied stress). Whilst a rigorous treatment of the problem is not feasible at the present time there are two less exact approaches which continue to find wide acceptance ; the free volume theory,'00~101*'02 which has been the subject of extensive review,lo3 and the more recent entropy theory which was proposed by Gibbs and DiMarziolo4 in 1958 later extended by the original author^"^ to include copolymers and plasticised systems and then subsequently by DiMarzio' O6 to include cross-linked materials and the effect of stress.The entropy theory predicts the existence of a second-order transition at a temperature T2 at which the configurational entropy vanishes on cooling. The experimental glass-transition temperature (T,) is higher than T, but it is assumed that numerous predictions for T2 will also hold quantitatively for 5. Adam and Gibbs"' extended the entropy theory further to take into account the temperature dependence of the co-operative relaxation properties in glass-forming liquids and in this way obtained an expression for melt viscosity similar to that predicted by the W.L.F.free volume theory."' Attempts have been made to assess the relative merits of the free volume and entropy theories by accurate measurement of viscosity over wide temperature lo However, Goldstein," in reviewing the situation has made the point that since the two theories are only semi-quantitative meaningful conclusions can only be drawn by comparing a wide variety of physical phenomena ; judged by this criterion he feels the entropy theory is the more successful. On the experimental side recent studies have been made of the problems which arise when differential scanning calorimetry is used for the determination of T . l I 2 Glass transition studies have been reported for some aromatic poly-acrylates,' l 3 for poly(viny1 chloride) in the presence of solvents,' l 4 and for 99 T.A. Litovitz in 'Nan-crystalline solids' ed. V. D . Frechette Wiley 1960. l o o T. G. Fox and P. J. Flory J. Appl. Phys. 1950 21 5 8 1 . l o ' M. L. Williams R. F. Landel and J. D. Ferry J. Amer. Chem. SOC. 1955 77 3701. I o 2 D . Turnbull and M. H. Cohen J. Chem. Phys. 1961 34 120. I o 3 R. F. Boyer Rubber Rev. 1963 36 1303. I o 4 J . H . Gibbs and E. A. DiMarzio J. Chem. Phys. 1958,28 373. l o 5 E. A. DiMarzio and J. H. Gibbs J. Polymer Sci. 1959,40 121 J . Polymer Sci. Part A , General Papers 1963 1 1417. E. A. DiMarzio J. Res. Nat. Bur. Stand. Sect A 1964 68 1 1 . l o ' G. Adam and J. H. Gibbs J. Chem. Phys. 1965,43 139. l o g R. J. Greet J. Chem. Phys. 1966 45 2479. l o 9 A. A. Miller J. Polymer Sci.Part A-2 Polymer Phys. 1966 4 415. l o M. R. Carpenter D. B. Davies and A. J. Matheston J. Chem. Phys. 1967 46 2451. 1 1 1 M. Goldstein J. Chem. Phys. 1969 51 3728. ' 1 2 J. M. Barton Polymer 1969 10 1 5 1 ; A. Lambert ibid. 1969 10 319; S. Strella and P. F. Erhardt J. Appl. Polymer Sci. 1969 13 1373. G. Pizzirani and P. L. Magagnini Chimica e Industria 1968 50 121 8. A. Packter and M. S. Nerurkar Kolloid-Z. 1969 229 7 Chain Conformations und Polymer Properlies 31 poly(a-methylstyrene) as a function of molecular weight." The thermal expan-sion of vitreous selenium has been studied over a wide range of temperature1l6 and a general investigation has been made of the thermal behaviour of heat-treated amorphous polymers. '' At stresses well below the fracture stress glassy polymers are known to develop crazes which are thin plate-like regions from one of which fracture is eventually initiated.' l8 Crazes are not cracks however but contain an optically continuous polymer filling.' Crazes reflect light strongly because oftheir low refractive index (compared with the normal polymer) which can be determined from measure-ments of the critical angle for total reflection at the craze-normal polymer inter-face. From craze indices and the Lorentz-Lorenz equation densities of crazes have been shown to be approximately half those for normal polymer.12' It has been concluded that craze formation is a process of plastic orientation in the tensile stress direction and can be viewed as an alternative mode of plastic deformation to cold drawing.Application of the Griffith fracture theory to glassy polymers leads to values of the surface free energy which are 1000 times greater than those calculated from a single layer breakage of chemical bonds. In attempting to explain such results Berry related interference colours which he observed at the crack tip in poly-(methyl methacrylate) to thin polymer layers produced by an energy-dissipating ductile process.' ' Kambour developed these ideas further and tentatively related the Griffith energy of crack formation to the energy required to transform normal density polymer to craze regions which can sustain large viscous deforma-tions.12' Thus the study of the structure and properties of crazes has become a matter of considerable importance. The concept of crazes has now been success-fully applied to explain (a) the effect of orientation on the deformation behaviour of poly(styrene),12' (b) the role of organic solvents in the mechanism of so-called environmental crazing and cracking,' 2 2 and (c) the mechanism of ductile deforma-tion in rubber-modified glassy polymers.' Crystalline State.-An excellent article dealing with the general concept of crystal-linity in polymers has been written by Miller.'24 A number of reviews are available which attempt to stress the controversial and unsettled aspects of the J .M. G. Cowie and P. M. Toporowski European Polymer J . 1968 4 621. R. K. Kirby and B. D. Rothrock J . Amer. Ceram. Soc. 1968 51 535. J . P. Berry J . Polymer Sci. 1961 50 107 3 13. R. P. Kambour J . Polymer Sci.Part A General Papers 1964 2 41 59; J . Polymer Sci., Part A-2 Polymer Phys. 1966 4 17 349. E. F. T. White B. M. Murphy and R. N. Haward J . Polymer Sci. Part B Polymer Letters 1969 7 156. I ' T. Hatakeyama and H. Kanetsuna. Chem. High Polymers (Japan) 1969,26 68. l 9 0. K. Spurr and W. D. Niegisch J. Appl. Polymer Sci. 1962 6 585. ''' G. A. Bernier and R. P. Kambour Macromolecules 1968 I 393. 1 2 3 C. B. Bucknall and R. R. Smith Polymer 1965 6 437. R. L. Miller 'Encyclopedia of Polymer Science and Technology,' vol. 4 section 3, John Wiley & Sons 1966 32 G . Allen and C. Price s ~ b j e c t ' ~ ~ ' ~ ~ ' ~ ~ and fairly wide coverage is provided by a series of papers presented at the Symposium on Crystallisation Phenomena held at Garmisch-Partenkirchen in 1967.12* Crystallisation Kinetics.A general kinetic formulation for polymer crystallisation in which nucleation processes assume a controlling role is well established.' 29 In spite of this there is still a lack of detailed information concerning crystallisa-tion mechanisms partly due to the notorious inconsistency of the available data. Recent kinetic studies deal with the isothermal crystallisation of isotactic poly-(styrene),13' poly(ethy1ene oxide),'31 and Nyl0n-6'~' in the bulk state and with poly(ethy1ene terephthalate) in the swollen state.'33 Single Crystals. The properties and morphology of single crystals grown from dilute solution remain one of the major regions of i n t e r e ~ t . ' ~ ~ . ' ~ ~ For this mode of crystallisation the well-known lamella crystals are formed whose thickness is - 100 A (the exact value depending on the crystallisation temperature) and whose transverse dimensions can be of the order of several microns.Since selected-area electron diffraction has established that the chain axes are oriented perpendicular to the wide faces of the lamella there arises the requirement that a high molecular weight polymer must return to and transverse a given lamella many times. However the detailed nature of the fold interface remains a matter of controversy in spite of the wide variety of methods currently being used in its investigation including density i.r. spectroscopy enthalpy of fusion broad line n.m.r. spectroscopy and selective 0~idation.I~ 7*135 The observed increase of lamella thickness on annealing is intimately connected with the general problem of folding.Fischer and Schmidt'36 studied the long-spacing (I) increase of poly-(ethylene) single crystals as a function of time for different temperatures. They found that 1 = lo + B(T) In (t/to + 1) where lo is the spacing at time to and B(T) is the proportionality constant at temperature T. It is now r e a l i ~ e d ' ~ ~ that B(T) is not solely dependent on T as was sometimes considered but depends on other factors such as the crystallisation 1 2 5 J. D. Hoffman Trans. SOC. Plast. Engineers 1964,4 315. l Z 6 L. Mandelkern Polymer Engineering and Science 1967 232. 12' A. Keller Reports Progr. Phys. 1968 31 623. 128 High Polymer Physics Symposium Kolloid-Z. 1969 231 385. 29 L. Mandelkern 'Crystallization of Polymers,' McGraw-Hill New York 1964.30 J. Boon G. Challa and D. W. Van Krevelen J. Polymer Sci. Part A-2 Polymer Phys., 1 3 1 J. N. Hay M. Sabir and R. L. T. Steven Polymer 1969 10 187; J. N. Hay and M. 132 T. Ishibashi and Y. Tani Chem. High Polymers (Japan) 1969 26 199. 1 3 3 H. G. Zachmann and G. Konrad Makromol. Chem. 1968 118 189. ' 3 4 H. K. Livingston Macromolecules 1969 2 98. lJ5 R. K. Sharma and L. Mandelkern Macromolecules 1969 2 266; D. A. Blackadder and T. L. Roberts Makromol. Chem. 1969 126 116; A. Peterlin J. Macromol. Sci., 1969 B3 19. 1968 6 1791. Sabir ibid. 1969 10 203. 1 3 6 E. W. Fischer and G. F. Schmidt Angew Chem. 1962 74 551 Chain Conformations and Polymer Properties 33 conditions and the environment in which annealing occurs.Thus the lower the temperature at which crystal formation occurred (i.e. the lower the initial fold length) the faster the crystals anneal at a given temperature. Also the rate is faster in single crystal mats surrounded by an inert liquid than in mats lying on a solid surface. Whilst single crystal studies on poly(ethy1ene) still attract a dis-proportionate amount of attention,' 3 5 7 1 3 8 some work continues on other systems and current reports include poly(viny1 alcohol)' 39 and poly(4-methylpent-l-ene). 140 Morphology and Properties of the Bulk State. For homopolymers in the bulk state a wide range of experimental data is available from such sources as low-angle X-ray diffraction electron microscopy of surface replicas and the study of selectivity oxidised poly(ethylene) which suggests that under normal conditions the lamella crystallite is a characteristic product of thermal crystallisation.The evidence which is usually assembled to support the contention that there is regular folding at the lamella interfaces has been subjected to much criticism.'26 Extensive use is now being made of dynamic ~alorimetry'~' to study time dependent properties ; the two common techniques are differential scanning calorimetry (DSC) and differential thermal analysis (DTA). The development of simple-to-operate intermediate-precision instruments has been a major factor in encouraging such studies. The accuracy of heats of fusion and specific heats measured by DSC is of the order of fI 1 to 2 % but by DTA unless extreme care is taken the accuracy is much less (%lo%).However DTA permits ex-tremely fast heating rates (far in excess of what could be achieved by for example, dilatometry) and is proving extremely useful in the location of transition tem-peratures. A good example of the use of dynamic calorimetry is provided by the recent studies of Roberts. '42 Crystallisation at high pressure leads to the formation of much thicker cry-stalhtes. 143 Since materials containing 'extended chain crystals' should be closer to thermodynamic equilibrium than those made up of lamellae considerable attention is being paid to their physical ~ r 0 p e r t i e s . l ~ ~ The reason for the forma-tion of extended chain crystals on application of high pressure is believed to be connected with an increased rate of isothermal thickening (i.e.lamellae are first formed due to the kinetic controls but these are then able to transform fairly rapidly into the extended-chain form.) 141 142 143 1 4 4 138 C. M. L. Atkinson and M. J. Richardson Trans. Faraday SOC. 1969 65 1774; T. Kawai K . Ebara and H. Maeda Kolloid-Z 1969 229 168; J. F. Jackson and L. Mandelkern Macromolecules 1968 1 546. 139 K . Tsuboi J . Macromol. Sci. 1968 B2 603. I4O A. Nakajima S. Hayashi and T. Taka Kolloid-Z. 1969 233 869. B. Wunderlich Kolloid-Z. 1967,231,606; B. Wunderlich and L. D. Jones J . Macromol. Sci. 1969 B3 67. R. C. Roberts Polymer 1969 10 113 117. B. Wunderlich and T. Arakawa J . Polymer Sci. Part A General Papers 1964 2, 3697. T. Davidson and B. Wunderlich J .Polymer Sci. Part A-2 Polymer Phys. 1969 7 , 377; D. V. Rees and D. C. Bassett J . Polymer Sci. Part B Polymer Letters 1969 7 , 273 34 G . Allen and C. Price Application of stress during crystallisation from the melt leads to row-nucleated morphologies. Recent studies support earlier suggestions that crystallisation in drawn polymers occurs first by a bundle-like mechanism which may then be followed by folded-chain type cry~tallisation.'~~ It is argued that the relative proportion of the two types of crystallites depends upon the degree of orientation of the melt prior to crystallisation ; if this orientation is sufficiently great it is speculated that extended-chain type crystals may form excl~sively.'~~ Pen-n i n g ~ ' ~ ' has shown that a kind of row-nucleated morphology is also formed when crystals are grown from agitated solution.Studies of this nature clearly promise to reconcile many ideas concerning the existence of lamellae and fibrils which hitherto were thought to be incompatible. A large body of work currently in progress is directed towards developing techniques for the investigation of structural orientation. These include applica-tion of low-angle X-ray ~cattering,'~~ light ~cattering,'~~ and optical dichroism. 150 The similarity between metals and crystalline polymers with regard to certain gross mechanical properties such as yield curves and dynamic loss peaks is now fully realised. Dislocation theories which have been used to interpret the deformation and fracture characteristics of metals are now being applied with some success to crystalline polymers.' 51 In addition high pressure studies which played a critical role in elucidating the deformation mechanism of metals are proving extremely useful in the study of poly(ethylene) poly-(propene) and poly(tetrafluoroethylene).'52 Block Copolymers.-There has been considerable interest in the morphology and properties of block copolymers.The recently published proceedings of the Pasadena symposium on block copolymers cover many of the important issues.' There is now much experimental evidence for the existence of microphase separation in block copolymers. Especially interesting are the electron micro-graphs of osmium tetroxide treated thin films of styrene-butadiene block copoly-merS ; 1 54.15 5 the osmium tetroxide reacts with residual double bonds in the butadiene blocks and provides contrast between the microphases in transmission 1 4 5 M.J. Hill and A. Keller J . Macromol. Sci. 1969 B3 153. 146 W. R. Krigbaum J. V. Dawkins and G. H. Via J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 257; W. R. Krigbaum T. Adachi and J. V. Dawkins J . Chem. Phys., 1968 49 1532. 4 ' A. J . Pennings J . PoIymer Sci. Part C Polymer Symposia 1967,16 1799; A. G. Wikjord and R. St. John Manley Canad. J . Chem. 1969,47 703. 1 4 8 E. W. Fischer H. Goddar and G. F. Schmidt Makromol. Chem. 1968,118 144; ibid., 1968 119 170; Kolloid-Z. 1968 226 30. 1 4 9 R. S. Stein P. F. Erhardt and W. Chu. J . Polymer Sci. Part A-2 Polymer Phys., 1969 7 271 ; M. B. Rhodes and R. S. Stein J. AppI. Phys.1968 39 4903. I . Kimura M. Kagiyama S. Nomura and H. Kawai J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 709. M. L. Williams Ann. New York Acad. Sci. (Polymer Science) 1969 155 539. I s 2 K. D. Pae D. R. Mears and J. Sauer J . Polymer Sci. Part B Polymer Letters 1968, 6 773 ; D. R. Mears and K. D. Pae ibid. 1969 7 349. 'Symposium on Block Copolymers,' J . Polymer Sci. Part C Polymer Symposia, 1969 26 1 . E. Fischer J . Macromol. Sci. 1968 A2 1285. P. R. Lewis and C. Price Nature 1969 223 494 Chain Conformations and Polymer Properties 35 electron microscopy. For block copolymer samples in general evidence has been accumulated from low-angle X-ray scattering and from electron micrographs of shadowed replicas of fracture surfaces. The general problem of polymer incompatibility has aroused considerable interest for many years and there continue to be numerous publications on the subject.' 56 That microphase separation will occur in many block copolymers is readily predictable on theoretical grounds.Perhaps what is surprising however, is the high degree of structural regularity' 5 5 exhibited by some of these two-phase systems (even when both phases are non-crystalline). These observations have encouraged a number of theoretical studies on the s ~ b j e c t . ' ~ ~ " ~ ~ - ' ~ ~ It is clear, however that great care will be necessary in testing these essentially equilibrium theories since experimental studies show that the type of morphology adopted by a block copolymer is extremely dependent on kinetic factors'55 as well as chain structure.A given sample of polymer can be obtained with a microstructure based on spheres cylinders or platelets depending on the physical method of processing. Particular interest has been shown recently in polymers of the ABA type in which the polymer forming the A block is a glass at room temperature and that forming the B block is a rubber. If the A blocks are much shorter than the B blocks a microstructure can be obtained containing glassy spheres (each contain-ing many end blocks) embedded in a rubbery matrix. The glassy domains can act both as network junctures and as a reinforcing filler.16' Such materials are usually termed thermoplastic rubbers since their physical cross-links are thermally reversible. These special properties are not shared by either AB or BAB type systems.Relaxation Behaviour and Molecular Mobility.-In 1967 a comprehensive review16 of mechanical and dielectric techniques results and their molecular interpretation was published. The field is still however faced with the problems associated with a priori calculations of relaxation time distributions and the unambiguous determination of these distributions from experimental data. One note'62 has discussed the relation between relaxation mechanisms and relaxa-tion time distributions and an attempt163 has been made to treat relaxation phenomena in polymers in terms of irreversible thermodynamics. The principal techniques of study continue to be mechanical dielectric n.m.r. spectroscopic, and acoustic relaxation in the solid state.Neutron inelastic scattering promises to be a very important tool in the study of molecular motions but so far most 1 5 6 0. Fuchs Angew. Makromol. Chem. 1969 6 79; C. Hugelin and A. Dondos Mak-rornol. Chem. 1969 126 206; R. Kuhn and H. J. Cantow Makromol. Chem. 1969, 122 65. 15' D. J. Meier ref. 153 p. 81. 15' S. Krause J. Polymer Sci. Part A-2 Polymer Phys. 1969 7 249. 15' U. Bianchi E. Pedemonte and A. Turturro J. Polymer Sci. Part B Polymer Letters, 1969 7 785. G. Holden E. T. Bishop and N. R. Legge ref. 153 p. 37. Polymeric Solids' J. Wiley & Sons 1967. 1 6 ' N. G . McGrum B. E. Read and G . Williams 'Anelastic and dielectric effects in 16' A. Eisenberg and L. A. Teter J. Polymer Sci. Part B Polymer Letters 1969 7 471. l h 3 Yu. V. Zelenev and 1.P. Borodin Vysokomol. Soedineniya 1968 10 B 800 36 G. Allen and C. Price reports are confined to low-frequency motions of the lattice and the observation of optical Mechanical relaxation in poly(propene) has been studiedI6' as a function of polymorphism and the degree of lamellar orientation. Starkweather ' has reviewed mechanical relaxations and melting in semi-crystalline polymers and a method involving the integration of the loss compliance has been used'69 to estimate entanglement spacings in polymer melts. Recent reports on dielectric relaxation have been more prolific including anisotropy of relaxation in oxidised poly(ethy1ene) ;' 70 poly(propenes) of different morphologies ;' ' poly(viny1 fluoride) ;' 72 poly(viny1idene fluoride) ;' 3 3 ' 74 stereoregular poly(methy1 metha-crylate),' 7 5 poly(ethy1 methacrylate),' 7 6 poly(isobuty1 methacrylate) ;' 76 poly-(methylene oxide),177 poly(ethy1ene oxide),' 7 7 and poly(tetramethy1ene oxide)' 7 7 in the microwave and i.r.regions and poly(propene poly(epich1oro-hydrin),' 79 poly(epibromohydrin),' 79 and poly(amides)'80 at low frequencies. The introduction of the rotating frame technique for measurement of spin lattice relaxation times has effectively extended the frequency range of pulsed n.m.r. relaxation measurements down to the kHz region. Poly(propene oxide)' '' has been studied by this method and a review of current results has been pub-lished.' 8 2 In general there is a great deal of documentation and assignment of relaxation processes going on with very little advance in theoretical concepts.The power of analysis available through the application of several relaxation techniques to a given polymer system is demonstrated in a recent study of the structure and properties of ethylene-methacrylic acid copolymers and their sodium salts. ' 83 164 A. W. Henry and G. J. Safford J. Polymer Sci. Part A-2 Polymer Phys. 1969,7 433. 1 6 5 H. Matsura and T. Miyazawa J . Chem. Phys. 1969 50 915. 1 6 6 Y. I. Chiang and G. C. Summerfield J . Polymer Sci. Part A-2 Polymer Phys. 1969,7, 1 6 ' J. M. Crissman J . Polymer Sci. Part A-2 Polymer Phys. 1969 7 389. 1 6 8 H. W. Starkweather J. Mucromol. Sci. 1968 B2 781. 1 6 9 J. F. Sanders and J. D. Ferry Macromolecules 1969 2 440. 1 7 0 G. R. Davies and I. M. Ward J . Polymer Sci. Part B Polymer Letters 1969 7 353.1 7 1 V. A. Kargin G . M. Bartenev A. Ya. Berestheva Yu. V. Zelinev V. G. Kalashnikova, and L. A. Osintseva Vysokomol. Soedineniya 1969 11 A 759. 172 E. Sacher J . Polymer Sci. Part A-2 Polymer Phys. 1968 6 1813. N. Koizumi S. Yano and K. Tsunashima J . Polymer Sci. Purr B Polymer Letters, 1969 7 59. H. Sindo I. Murakami and H. Yamamura J . Polymer Sci. Part A - I Polymer Chem., 1969 7 297. 1 7 6 H. Sindo I. Murakami and H. Yamamura Chem. High Polymers (Japan) 1969 26, 358. 1 7 7 E. Amrhein and F. H. Miiller Kolloid-Z. 1968 226 97. 1 7 8 P. Lue C. P. Smyth and A. V. Tobolsky Macromolecules 1969 2 446. 1 7 9 A. R. Blythe and G. M. Jeffs J . Macromol. Sci. 1969 B3 141. I8O M. E. Baird C. T. Goldsworthy and C. J. Creasey J . Polymer Sci. Part B Polymer 405. '14 H. Kakutani Chem. High Polymers (Japan) 1969 26 83. Letters 1968 6 737. T. M. Connor and A. Hartland Polymer 1968,9 591. l S 2 T. M. Connor Brit. Polymer J. 1969 1 116. 183 B. E. Read E. A. Carter T. M. Connor and W. J. MacKnight Brit. Polymer J. 1969, 1 123