The Rate of Crystallization of Linear Polymers with Chain Folding

  • John D. Hoffman
  • G. Thomas Davis
  • John I. LauritzenJr.


Under a variety of circumstances commonly encountered in practice linear macromolecules crystallize into the form of thin platelets whose large upper and lower surfaces consist of an array of molecular folds. We refer to these as “chain-folded crystals” or “chain-folded lamellae,” the latter term usually being reserved for folded structures in polymers crystallized from the melt. The theory of the rate of formation of these platelets will be outlined, and the prediction and origin of the thin dimension given. The thin dimension of the crystal platelets is determined by kinetic factors, and the elucidation of the kinetics of growth is therefore of importance in polymer morphology on both a molecular and a macroscopic scale.


Surface Free Energy Linear Polymer Homogeneous Nucleation Bulk Polymer Polymer Crystal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. H. Geil, Polymer Single Crystals, Interscience Publishers, New York (1963).Google Scholar
  2. 2.
    F. Khoury and E. Passaglia, This Treatise, Vol. 3, Chapter 6.Google Scholar
  3. 3.
    P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York (1969).Google Scholar
  4. 4.
    H. D. Keith and F. J. Padden, Jr., A phenomenological theory of spherulitic crystallization, J. Appl. Phys. 34, 2409–2421 (1963).Google Scholar
  5. 5.
    F. E. Karasz, H. E. Bair, and J. M. O’Rielly, Thermal properties of atactic and isotactic polystyrene, J. Phys. Chem. 69, 2657–2667 (1965).Google Scholar
  6. 6.
    J. Boon, The effect of extreme supercooling on the number of spherulitic centers in isotactic polystyrene, J. Polymer Sci. C 16, 1739–1749 (1967).Google Scholar
  7. 7.
    T. Suzuki and A. J. Kovacs, Temperature dependence of spherulitic growth rate of isotactic polystyrene, Polymer J. 1, 82–100 (1970).Google Scholar
  8. 8.
    J. N. Hay, Crystallization kinetics of high polymers: Isotactic polystyrene, J. Polymer Sci. A 3, 433–447 (1965).Google Scholar
  9. 9.
    L. H. Bolz and R. K. Eby, Inclusion of perfluoromethyl groups in the crystals of copolymers of tetrafluoroethylene and hexafluoropropylene, J. Res. Nat. Bur. Std. (U.S.) 69A, 481–486 (1965).Google Scholar
  10. 10.
    C. W. Bunn, The crystal structure of long-chain normal paraffin hydrocarbons. The “shape” of the CH2 group, Trans. Faraday Soc. 35, 482–491 (1939).Google Scholar
  11. 11.
    J. J. Point, Enroulement hélicoïdal dans les sphérolithes de polyéthylène. Bull. Acad. Roy. Belg. 41, 982–990 (1955);Google Scholar
  12. J. J. Point and G. A. Homès, Fibre N du polyéthylène, Compt. Rend. 242, 2557–2560 (1956).Google Scholar
  13. 12.
    R. Jaccodine, Observations of spiral growth steps in ethylene polymers, Nature 176, 305–306 (1955).Google Scholar
  14. 13.
    H. D. Keith, F. J. Padden, Jr., and R. G. Vadimsky, Intercrystalline links: Critical evaluation, J. Appl. Phys. 42, 4585–4592 (1971).Google Scholar
  15. 14.
    K. H. Storks, An electron diffraction examination of some linear high polymers, J. Am. Chem. Soc. 60, 1753–1761 (1938).Google Scholar
  16. 15.
    J. D. Hoffman and J. I. Lauritzen, Jr., Crystallization of bulk polymers with chain folding: Theory of growth of lamellar spherulites, J. Res. Nat. Bur. Std. (U.S.) 65A, 297–336 (1961).Google Scholar
  17. 16.
    J. D. Hoffman, Theoretical aspects of polymer crystallization with chain folds: Bulk polymers, Soc. Plastics Eng. Trans. 4, 315–362 (1964).Google Scholar
  18. 17.
    A. Keller, A note on single crystals in polymers: Evidence for a folded chain configuration, Phil. Mag. 2, 1171–1175 (1957).Google Scholar
  19. 18.
    E. W. Fischer, Stufen-and spiralförmiges Kristallwachsturo bei Hochpolymeren, Z. Naturforsch. 12a, 753–754 (1957).Google Scholar
  20. 19.
    P. H. Till, Jr., The growth of single crystals of linear polyethylene, J. Polymer Sci. 24, 301–306 (1957).Google Scholar
  21. 20.
    W. D. Niegisch and P. R. Swan, Hollow pyramidal crystals of polyethylene and a mechanism of growth, J. Appl. Phys. 31, 1906–1910 (1960).Google Scholar
  22. 21.
    P. H. Lindenmeyer, Crystallization in polymers, J. Polymer Sci. C 1, 5–39 (1963).Google Scholar
  23. 22.
    D. C. Bassett, F. C. Frank, and A. Keller, Some new habit features in crystals of long chain compounds. Part IV. The fold surface geometry of monolayer polyethylene crystals and its relevance to fold packing and crystal growth, Phil. Mag. 8, 1753–1787 (1963).Google Scholar
  24. 23.
    M. I. Bank and S. Krimm, Mixed crystal infrared study of chain folding in crystalline polyethylene, J. Polymer Sci. A-27, 1785–1809 (1969).Google Scholar
  25. 24.
    G. M. Martin and E. Passaglia, Density of polyethylene crystals grown from solution, J. Res. Nat. Bur. Std. (U.S.) 70A, 221–224 (1966).Google Scholar
  26. 25.
    A. Peterlin, The amount and location of amorphous component in polyethylene single crystals, J. Macrgmol. Sci.-Phys. B3, 19–31 (1969).Google Scholar
  27. 26.
    E. W. Fischer, H. Goddar, and G. F. Schmidt, A remark on the surface structure of polyethylene single crystals, J. Polymer Sci. B 5, 619–624 (1969).Google Scholar
  28. 27.
    A. Keller, E. Martuscelli, D. J. Priest, and Y. Udagawa, Fold surface of polyethylene single crystals as assessed by selective degradation studies. III. Application of the improved techniques to single crystals, J. Polymer Sci. A-29, 1807–1837 (1971).Google Scholar
  29. 28.
    J. I. Lauritzen, Jr. and J. D. Hoffman, Extension of theory of growth of chain-folded polymer crystals to large undercoolings, J. Appl. Phys. 44, 4340–4352 (1973).Google Scholar
  30. 29.
    A. Silberberg, Adsorption of flexible macromolecules. III. Generalized treatment of the isolated macromolecule; the effect of self-exclusion, J. Chem. Phys. 46, 1105–1114 (1967).Google Scholar
  31. 30.
    C. A. J. Hoeve, E. A. DiMarzio, and P. Peyser, Adsorption of polymer molecules at low surface coverage, J. Chem. Phys. 42, 2558–2563 (1965).Google Scholar
  32. 31.
    E. A. DiMarzio and F. L. McCrackin, One-dimensional model of polymer adsorption, J. Chem. Phys. 43, 539–547 (1965).Google Scholar
  33. 32.
    E. A. DiMarzio and R. J. Rubin, Adsorption of a chain polymer between two plates, J. Chem. Phys. 55, 4318–4336 (1971).Google Scholar
  34. 33.
    R. R. Stromberg, D. J. Tutas, and E. Passaglia, Conformation of polystyrene adsorbed at the theta-temperature, J. Phys. Chem. 69, 3955–3963 (1965).Google Scholar
  35. 34.
    W. H. Grant and R. R. Stromberg, Rates of adsorption and desorption of polystyrene, ACS Polymer Preprints 11 (September), 1397–1399 (1970).Google Scholar
  36. 35.
    P. H. Geil, Nylon single crystals, J. Polymer Sci. 44, 449–458 (1960).Google Scholar
  37. 36.
    P. H. Geil, Jr., N. K. Symons, and R. G. Scott, Solution grown crystals of an acetal resin, J. Appl. Phys. 30, 1516–1517 (1959).Google Scholar
  38. 37.
    B. G. Ranby, F. F. Morehead, and N. M. Walter, Morphology of n-alkanes, linear polyethylene, and isotactic polypropylene crystallized from solution, J. Polymer Sci. 44, 349–367 (1960).Google Scholar
  39. 38.
    F. Khoury, The spherulitic crystallization of isotactic polypropylene from solution: On the evolution of monoclinic spherulites from dendritic chain-folded crystal precursors, J. Res. Nat. Bur. Std. (U.S.) 70A, 29–61 (1966).Google Scholar
  40. 39.
    F. C. Frank, A. Keller, and A. O’Connor, Observations on single crystals of an isotactic polyolefin: Morphology and chain packing in poly-4-methylpentene-1, Phil. Mag. 4, 200–214(1959).Google Scholar
  41. 40.
    V. F. Holland, S. B. Mitchell, W. L. Hunter, and P. H. Lindenmeyer, Crystal structure and morphology of polyacrylonitrite in dilute solution, J. Polymer Sci. 62, 145–151 (1962).Google Scholar
  42. 41.
    W. Kern, J. Davidovits, K. J. Rauterkus, and G. F. Schmidt, Röntgenographische Untersuchungen an linearen Oligurethanen, Makrocool. Chem. 43, 106–116 (1961).Google Scholar
  43. : R. St. J. Manley, Growth and morphology of single crystals of cellulose triacetate, J. Polymer Sci. A1, 1875–1892 (1963).Google Scholar
  44. 43.
    H. D. Keith, R. G. Vadimsky, and F. J. Padden, Jr., Crystallization of isotactic polystyrene from solution, J. Polymer Sci. A-28, 1687–1696 (1970).Google Scholar
  45. 44.
    V. F. Holland and R. L. Miller, Isotactic polybutene-1 single crystals: Morphology, J. Appl. Phys. 35, 3241–3248 (1964).Google Scholar
  46. 45.
    J. D. Barnes and F. A. Khoury, Formation of curved polymer crystals: Polychlorotrifluoroethylene, J. Res. Nat. Bur. Std. (U.S.), 78A, 363–373 (1974).Google Scholar
  47. 46.
    H. Bittiger and R. H. Marchessault, Formation of ribbonlike fibrils by crystallisation from dilute solution, Bull. Am. Phys. Soc. 15, 305 (1970).Google Scholar
  48. 47.
    F. J. Padden, Jr., H. D. Keith, and G. Giannoni, Single crystals of poly-Llysine, Biopolymers 7, 793–804 (1969).Google Scholar
  49. 48.
    H. D. Keith, G. Giannoni, and F. J. Padden, Jr., Single crystals of poly(L-glutamic acid), Biopolymers 7, 775–792 (1969).Google Scholar
  50. 49.
    R. G. Crystal, The polymeric nature of selenium crystallization. I. Morphology and thermodynamic considerations, J. Polymer Sci. A-2 8, 1755–1772 (1970).Google Scholar
  51. 50.
    Y. Yaniashita, Single crystals of poly(ethylene terephthalate), J. Polymer Sci. A 3, 81–92 (1965).Google Scholar
  52. 51.
    F. J. Balta Calleja and A. Keller, On the relation between long spacings, molecular length, and orientation in long chain compounds with reference to the possibility of chain folding. Part II. Poly(ethylene oxide)s, J. Polymer Sci. A2, 2171–2179 (1964).Google Scholar
  53. 52.
    F. J. Padden, Jr. and H. D. Keith, Crystalline morphology of synthetic polypeptides, J. Appl. Phys. 36, 2987–2995 (1965).Google Scholar
  54. 53.
    S. H. Carr, A. G. Walton, and E. Baer, Epitaxial crystallization of poly(ybenzyl L-glutamate) on alkali halide single crystals, Biopolymers 6, 469–477 (1968).Google Scholar
  55. 54.
    G. Giannoni, F. J. Padden, Jr., and H. D. Keith, Crystallization of DNA from dilute solution, Proc. Nat. Acad. Sci. (U.S.) 62, 964–971 (1969).Google Scholar
  56. 55.
    A. K. Kleinschmidt, D. Lang, D. Jackerts, and R. Zahn, Darstellung and Langenmessungen des Gesamten Desoxyribonucleinsaure-Inhaltes von T -Bakteriophagen, Biochim. Biophys. Acta 61, 857–864 (1962).Google Scholar
  57. 56.
    A. C. T. North and A. Rich, X-ray diffraction studies of bacterial viruses, Nature 191, 1242–1245 (1961).Google Scholar
  58. 57.
    A. Keller and Y. Udagawa, Crystallization of short aliphatic polymer chains. I. General chain-folding behavior, J. Polymer Sci. A-2 10, 221–238 (1972).Google Scholar
  59. 58.
    L. D’Ilario, A. Keller, and E. Martuscelli, Crystallization of short aliphatic chains. II. Example of even fold surface with adjacent fold reentry and of a transition to chain extension, J. Polymer Sci. A-2 10, 239–252 (1972).Google Scholar
  60. 59.
    H. Zahn, Röntgenstruktur von Linearen Oligomeren, IUPAC Symp. on Macromolecules, paper IB 8, Wiesbaden (1959).Google Scholar
  61. 60.
    J. P. Arlie, P. Spegt, and A. Skoulios, Etude de la cristallisation des polymères II. Structure lamellaire et repliement des chaînes du polyoxyéthylène, Makromol. Chem. 104, 212–229 (1967).Google Scholar
  62. 61.
    W. D. Niegisch, Crystallography of poly-p-xylylene, J. Appl. Phys. 37, 4041–4046 (1966).Google Scholar
  63. 62.
    A. J. Bur and D. E. Roberts, Rodlike and random-coil behavior of poly(n-butyl isocyanate) in dilute solution, J. Chem. Phys. 51, 406–420 (1969).Google Scholar
  64. 63.
    G. K. Noren and J. K. Stille, Polyphenylenes, Macromolecular Rev. 5, 385–430 (1971). (Also known as J. Polymer Sci., Part D.) Google Scholar
  65. 64.
    N. Yoda and M. Kurihara, New polymers of aromatic heterocycles by polyphosphoric acid solution methods, Macromolecular Rev. 5, 109–193 (1971) (also known as J. Polymer Sci,Part D).Google Scholar
  66. 65.
    W. Traub and K. A. Piez, in Advances in Protein Chemistry (C. B. Anfinsen, Jr., J. T. Edsall, and F. M. Richards, eds.), Academic Press, New York (1971), p. 305.Google Scholar
  67. 66.
    J. I. Lauritzen, Jr. and J. D. Hoffman, Theory of formation of polymer crystals with folded chains in dilute solution, J. Res. Nat. Bur. Std. (U.S.) 64A, 73–102 (1960).Google Scholar
  68. 67.
    F. P. Price, The growth habit of single polymer crystals, J. Polymer Sci. 42, 49–56 (1960).Google Scholar
  69. 68.
    A. Keller and A. O’Connor, Study of single crystals and their associations in polymers, Disc. Faraday Soc. 25, 114–121 (1958).Google Scholar
  70. 69.
    C. W. Bunn and T. C. Alcock, The texture of polythene, Trans. Faraday Soc. 41, 317–325 (1945).Google Scholar
  71. 70.
    H. D. Keith and F. J. Padden, Jr., The optical behavior of spherulites in crystalline polymers. Part. I. Calculation of theoretical extinction patterns in spherulites with twisting crystalline orientation, J. Polymer Sci. 39, 101–122 (1959).Google Scholar
  72. 71.
    H. D. Keith and F. J. Padden, Jr., The optical behavior of spherulites in crystalline polymers. Part II. The growth and structure of spherulites, J. Polymer Sc.i. 39, 123–138 (1959).Google Scholar
  73. 72.
    F. P. Price, On extinction patterns of polymer spherulites, J. Polymer Sci. 39, 139–150 (1959).Google Scholar
  74. 73.
    A. Keller, Investigations of banded spherulites, J. Polymer Sci. 39, 151–173 (1959);Google Scholar
  75. A. Keller, Morphology of crystalline polymers, a review, in Growth and Perfection of Crystals (R. H. Doremus, B. W. Roberts, and D. Turnbull, eds.), pp. 499–532, Wiley, New York (1958).Google Scholar
  76. 74.
    H. D. Keith and F. J. Padden, Jr., Spherulitic crystallization from the melt. I. Fractionation and impurity segregation and their influence on crystalline morphology, J. Appl. Phys. 35, 1270–1285 (1964).Google Scholar
  77. 75.
    H. D. Keith and F. J. Padden, Jr., Spherulitic crystallization from the melt. II. Influence of fractionation and impurity segregation on kinetics of crystallization, J. Appl. Phys. 35, 1286–1296 (1964).Google Scholar
  78. 76.
    M. Herbst., Röntgenographische Untersuchung an Sphärolithen in PolyamidSpritzgussmassen, Z. Electrochemie 54, 318–320 (1950).Google Scholar
  79. 77.
    A. Keller, The spherulitic structure of crystalline polymers, Part II. The problem of molecular orientation in polymer spherulites, J. Polymer Sci. 17, 351–364 (1955).Google Scholar
  80. 78.
    R. P. Palmer and A. J. Cobbold, The texture of melt crystallized polythene as revealed by selective oxidation, Makromol. Chem. 74, 174–189 (1964).Google Scholar
  81. 79.
    A. Keller and S. Sawada, On the interior morphology of bulk polyethylene, Makromol. Chem. 74, 190–221 (1964).Google Scholar
  82. 80.
    C. W. Hock, Selective oxidation with nitric acid reveals the microstructure of polypropylene, J. Polymer Sci. B 3, 573–576 (1965).Google Scholar
  83. 81.
    J. D. Hoffman and J. J. Weeks, Rate of spherulitic crystallization with chain folds in polychlorotrifluoroethylene, J. Chem. Phys. 37, 1723–1741 (1962).Google Scholar
  84. 82.
    E. Passaglia and H. K. Kevorkian, Specific heat of atactic and isotactic polypropylene and the entropy of the glass, J. Appl. Phys. 34, 90–97 (1963).Google Scholar
  85. 83.
    F. Rybnikar, Mechanism of secondary crystallization in polymers, J. Polymer Sci. A 1, 2031–2038 (1963); A. J. Kovacs, Cinétique de Cristallisation du Polyéthylène, Ric. Sci. 25A, 668–685 (1955) (IUPAC Symp. on Macromolecular Chemistry, Milan, 1954 ).Google Scholar
  86. 84.
    W. L. Holt and A. T. McPherson, Change of volume of rubber on stretching: Effects of time, elongation, and temperature, J. Res. Nat. Bur. Std. U.S.A. 117, 659–678 (1936).Google Scholar
  87. 85.
    E. Passaglia and G. M. Martin, Dependence of mechanical relaxation on morphology in isotactic polypropylene, J. Res. Nat. Bur. Std. (U.S.) 68A, 519–527 (1964).Google Scholar
  88. 86.
    J. D. Hoffman, G. Williams, and E. Passaglia, Analysis of the a, ß, and y relaxations in polychlorotrifluoroethylene and polyethylene: Dielectric and mechanical properties, J. Polymer Sci. C 14, 173–235 (1966).Google Scholar
  89. 87.
    E. Ergoz, J. G. Fatou, and L. Mandelkern, Molecular weight dependence of the crystallization kinetics of linear polyethylene. I. Experimental results, Macromolecules 5, 147–157 (1972).Google Scholar
  90. 88.
    J. D. Hoffman and W. Elban, to be published.Google Scholar
  91. 89.
    R. K. Sharma and L. Mandelkern, The density of polyethylene crystallized in the bulk and from dilute solution, Macromolecules 2, 266–271 (1969).Google Scholar
  92. 90.
    L. Mandelkern, A. L. Allou, Jr., and M. Gopalan, The enthalpy of fusion of linear polyethylene, J. Phys. Chem. 72, 309–318 (1968).Google Scholar
  93. 91.
    D. Turnbull, Kinetics of heterogeneous nucleation, J. Chem. Phys. 18, 198–203 (1950).Google Scholar
  94. 92.
    B. Vonnegut, Variation with temperature of the nucleation rate of supercooled liquid tin and water drops, J. Colloid Sci. 3, 563–569 (1948).Google Scholar
  95. 93.
    D. Turnbull and R. L. Cormia, Kinetics of crystal nucleation in some normal alkane liquids, J. Chem. phys. 34, 820–831 (1961).Google Scholar
  96. 94.
    A. J. Pennings, Hydrodynamically induced crystallization of polymers from solutions, in Crystal Growth (Proc. Int. Conf. on Crystal Growth, Boston, 1966; H. S. Peiser, ed.), Pergamon Press, New York (1967), pp. 389–393.Google Scholar
  97. 95.
    H. D. Keith, F. J. Padden, Jr., and R. G. Vadimsky, Further studies of intercrystalline links in polyethylene, J. Appl. Phys. 37, 4027–4034 (1966).Google Scholar
  98. 96.
    A. Keller and M. S. Machin, Oriented crystallization in polymers, J. Macromal. Sci. (Phys.) Bl, 41–91 (1967).Google Scholar
  99. 97.
    E. H. Andrews, Crystalline morphology in thin films of natural rubber. II. Crystallization under strain, Proc. Roy. Soc. (London) A277, 562–570 (1964).Google Scholar
  100. 98.
    E. H. Andrews, P. J. Owen, and A. Singh, Microkinetics of lamellar crystallization in a long chain polymer, Rubber Chem. Tech. 45, 1315–1333 (1972); Proc. Roy. Soc. A324, 79–97 (1971).Google Scholar
  101. 99.
    P. H. Geil, F. R. Anderson, B. Wunderlich, and T. Arakawa, Morphology of polyethylene crystallized from the melt under pressure, J. Polymer Sci. A 2, 3707–3720 (1964).Google Scholar
  102. 100.
    D. V. Rees and D. C. Bassett, Crystallization of polyethylene at elevated pressures, J. Polymer Sci. A-2 9, 385–406 (1971).Google Scholar
  103. 101.
    P. D. Calvert and D. R. Uhlmann, Crystallization of polyethylene at high pressure: A kinetic view, J. Polymer Sci. A-2 10, 1811–1836 (1972).Google Scholar
  104. 102.
    D. C. Bassett and B. Turner, New high-pressure phase in chain-extended crystallization of polythene, Nature (Phys. Sci.) 240, 146–148 (1972).Google Scholar
  105. 103.
    B. Wunderlich, L. Melillo, C. M. Cormia, T. Davidson, and G. Snyder, Surface melting and crystallization of polyethylene, J. Macromol. Sci.-Phys. Bl, 485–516 (1967).Google Scholar
  106. 104.
    T. W. Huseby and H. E. Bair, Dissolution of polyethylene single crystals in xylene and octadecane, J. Appl. Phys. 39, 4969–4973 (1968).Google Scholar
  107. 105.
    H. E. Bair, T. W. Huseby, and R. Salovey, The equilibrium melting temperature and surface free energy of polyethylene single crystals, ACS Polymer Preprints 9, 795–805 (1968).Google Scholar
  108. 106.
    A. Nakajima, F. Hamada, S. Hayashi, and T. Sumida, Effect of solvent on single crystal formation from dilute polyethylene solution. I. Surface free energy of single crystals estimated from kinetic theory, Kolloid-Z. u. Z. Polymere 222, 10–16 (1968).Google Scholar
  109. 107.
    A. Nakajima, S. Hayashi, T. Korenaga, and T. Sumida, Effect of solvent on single crystal formation from dilute polyethylene solution. II. Surface free energy of single crystals estimated from dissolution temperatures, and density of those crystals, Kolloid-Z. u. Z. Polymere 222, 124–130 (1968).Google Scholar
  110. 108.
    H. E. Bair and R. Salovey, The Effect of molecular weight on the structure and thermal properties of polyethylene, J. Macromol. Sci.-Phys. B3, 3–18 (1969).Google Scholar
  111. 109.
    R. G. Brown and R. K. Eby, Effect of crystallization conditions and heat treatment on polyethylene: Lamellar thickness, melting temperature and density, J. Appl. Phys. 35, 1156–1161 (1964).Google Scholar
  112. 110.
    J. D. Hoffman, J. I. Lauritzen, Jr., E. Passaglia, G. S. Ross, L. J. Frolen, and J. J. Weeks, Kinetics of polymer crystallization from solution and the melt, Kolloid-Z. u. Z. Polymere 231, 564–592 (1969).Google Scholar
  113. 111.
    J. D. Hoffman and J. J. Weeks, X-ray study of isothermal thickening of lamellae in bulk polyethylene at the crystallization temperature, J. Chem. Phys. 42, 4301–4302 (1965).Google Scholar
  114. 112.
    J. J. Weeks, Melting temperature and change of lamellar thickness with time for bulk polyethylene, J. Res. Nat. Bur. Std. (U.S.) 67A, 441–451 (1963).Google Scholar
  115. 113.
    A. Peterlin, Thickening of polymer single crystals during annealing, J. Polymer Sci. B 1, 279–284 (1963); A. Peterlin, Molecular weight dependence of isothermal long period growth of polyethylene single crystals, Polymer 6, 25–34 (1965).Google Scholar
  116. 114.
    L. A. Wood and N. Bekkedahl, Crystallization of unvulcanized rubber at different temperatures, J. Res. Nat. Bur. Std. (U.S.) 36, 489–510 (1946); J. Appl. Phys. 17, 362–375 (1946).Google Scholar
  117. 115.
    J. D. Hoffman and J. J. Weeks, Melting process and the equilibrium melting temperature of polychlorotrifluoroethylene, J. Res. Nat. Bur. Std. (U.S.) 66A, 13–28 (1962).Google Scholar
  118. 116.
    J. H. Magill, Crystallization and morphology of d, 1- and 1-poly(propylene oxide), Makromol. Chem. 86, 283–288 (1965).Google Scholar
  119. 117.
    B. Wunderlich and L. Melillo, Morphology and growth of extended chain crystals of polyethylene, Makromol. Chem. 118, 250–264 (1968).Google Scholar
  120. 118.
    T. Arakawa and B. Wunderlich, Thermodynamic properties of extended chain polymethylene single crystals, J. Polymer Sci. C 16, 653–658 (1967).Google Scholar
  121. 119.
    P. E. McMahon, R. L. McCullough, and A. A. Schlegel, Molecular mechanics of point defects in polyethylene, J. Appl. Phys. 38, 4123–4139 (1967).Google Scholar
  122. 120.
    P. Corradini, V. Petraccone, and G. Allegra, Chain folding in polyethylene crystals. The cooperative effect of bond angle deformation and rotational strain, Macromolecules 4, 770–771 (1971).Google Scholar
  123. 121.
    T. Oyama, K. Shiokawa, and T. Ishimaru, Chain conformations on the surface of polyethylene single crystals, in The Solid State of Polymers ( P. H. Geil, E. Baer, and Y. Wada, eds.), Marcel Dekker, New York (1974), pp. 229–239.Google Scholar
  124. 122.
    S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, R. Shaw, and R. Walsh, Additivity rules for the estimation of thermochemical properties, Chem. Rev. 69, 279–324 (1969).Google Scholar
  125. 123.
    D. G. Thomas and L. A. K. Stavely, A study of the supercooling of drops of some molecular liquids, J. Chem. Soc. 1952, 4569–4577 (1952).Google Scholar
  126. 124.
    F. Gornick, G. S. Ross, and L. J. Frolen, Crystal nucleation in polyethylene: The droplet experiment, J. Polymer Sci. C 18, 79–91 (1967).Google Scholar
  127. 125.
    I. C. Sanchez and E. A. DiMarzio, Dilute-solution theory of polymer crystal growth. Some thermodynamic and predictive aspects for polyethylene, Macromolecules 4, 677–687 (1971).Google Scholar
  128. 126.
    F. C. Frank and M. Tosi, On the theory of polymer crystallization, Proc. Roy. Soc. (London) A263, 323–339 (1961).Google Scholar
  129. 127.
    F. Gornick and J. D. Hoffman, Nucleation in polymers, Ind. Eng. Chem. 58, 41–53 (1966).Google Scholar
  130. 128.
    J. I. Lauritzen, Jr. and E. Passaglia, Kinetics of crystallization in multicomponent systems: II. Chain folded polymer crystals, J. Res. Nat. Bur. Std. (U.S.) 71A, 261–275 (1967).Google Scholar
  131. 129.
    J. I. Lauritzen, Jr. and J. D. Hoffman, Formation of polymer crystals with folded chains from dilute solution, J. Chem. Phys. 31, 1680–1681 (1959).Google Scholar
  132. 130.
    F. P. Price, Markoff chain model for growth of polymer single crystals, J. Chem. Phys. 35, 1884–1892 (1961).Google Scholar
  133. 131.
    D. Turnbull and J. C. Fisher, Rate of nucleation in condensed systems, J. Chem. Phys. 17, 71–73 (1949).Google Scholar
  134. 132.
    P. H. Geil, Folded molecules in lamellas crystallized from molten polymers, J. Appl. Phys. 33, 642–643 (1962).Google Scholar
  135. 133.
    A. J. Kovacs and A. Gonthier, Crystallization and fusion of self-seeded polymers. II. Growth rate, morphology and isothermal thickening of single crystals of low molecular weight poly(ethylene oxide) fractions, Kolloid-Z. u. Z. Polymere 250, 530–551 (1972).Google Scholar
  136. 134.
    H. G. Zachman, Der Einfluss der Konfigurationsentropie auf des Kristallasations-and Schmelzverhalten von hochpolymeren Stoffen, Kolloid-Z. u. Z. polymere 216–217, 180–191 (1967).Google Scholar
  137. 135.
    R. L. Cormia, F. P. Price, and D. Turnbull. Kinetics of crystal nucleation in polyethylene, J. Chem. Phys. 37, 1333–1340 (1962).Google Scholar
  138. 136.
    J. D. Ferry, Viscoelastic Properties of Polymers, 2nd ed., John Wiley and Sons, New York (1970).Google Scholar
  139. 137.
    G. Adam and J. F. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids, J. Chem. Phys. 43, 139–146 (1965).Google Scholar
  140. 138.
    D. J. Blundell and A. Keller, The concentration dependence of the linear growth rate of polyethylene crystals from solution, J. Polymer Sci. B 6, 433–440 (1968).Google Scholar
  141. 139.
    I. C. Sanchez and E. A. DiMarzio, Dilute solution theory of polymer crystal growth: Fractionation effects, J. Res. Nat. Bur. Std. (U.S.) 76A, 213–223 (1972).Google Scholar
  142. 140.
    W. B. Hillig, A derivation of classical two-dimensional nucleation kinetics and the associated crystal growth laws, Acta Met. 14, 1868–1869 (1966).Google Scholar
  143. 141.
    J. I. Lauritzen, Jr., The effect of a finite substrate length upon the polymer crystal lamellar growth rate, J. Appl. Phys. 44, 4353–4359 (1973).Google Scholar
  144. 142.
    I. C. Sanchez and E. A. DiMarzio, Dilute solution theory of polymer crystal growth: A kinetic theory of chain folding, J. Chem. Phys. 55, 893–908 (1971).Google Scholar
  145. 143.
    W. K. Burton, N. Cabrera, and F. C. Frank, The growth of crystals and the equilibrium structure of their surfaces, Trans. Roy. Soc. A243, 299–358 (1951).Google Scholar
  146. 144.
    R. L. Parker, in Solid State Physics ( H. Ehrenreich, F. Seitz, and D. Turnbull, eds.), Academic Press, New York (1970), Vol. 25, pp. 151–299.Google Scholar
  147. 145.
    J. I.Lauritzen, Jr., unpublished.Google Scholar
  148. 146.
    R. Chiang and P. J. Flory, Equilibrium between crystalline and amorphous phases in polyethylene, J. Am. Chem. Soc. 83, 2857–2862 (1961).Google Scholar
  149. 147.
    M. G. Broadhurst, The melting temperatures of the n-paraffins and the convergence temperature for polyethylene, J. Res. Nat. Bur. Std. (U.S.) 70A, 481–486 (1966).Google Scholar
  150. 148.
    P. J. Flory and A. Vrij, Melting points of linear-chain homologs. The normal paraffin hydrocarbons, J. Am. Chem. Soc. 85, 3548–3553 (1963).Google Scholar
  151. 149.
    A. M. Rijke and L. Mandelkern, Melting behavior of linear polyethylene crystallized by solution stirring, J. Polymer Sci. A-2 8, 225–242 (1970).Google Scholar
  152. 150.
    J. H. Magill, Crystallization kinetics of nylon 6, Polymer 3, 655–664 (1962).Google Scholar
  153. 151a.
    J. H. Magill, Spherulitic crystillization studies of poly(tetramethyl-psilphenylene)-siloxane (TMPS). Part III, J. Polymer Sci. A-2 7, 1187–1195 (1969).Google Scholar
  154. 151b.
    J. H. Magill, Crystallization of TMPS polymers, Part II, J. Polymer Sci. A-25, 89–99 (1967).Google Scholar
  155. 151c.
    J. H. Magill, Crystallization of TMPS polymers, J. Appl. Phys. 35, 3249–3259 (1964).Google Scholar
  156. d. J. H. Magill, private communication.Google Scholar
  157. 151e.
    S. S. Pollack and J. H. Magill, Small-angle X-ray scattering from poly(tetramethyl-p-silphenylene)siloxane (TMPS) fractions, J. Polymer Sci. A-27, 551–561 (1969).Google Scholar
  158. 152.
    L. Mandelkern, N. L. Jain, and H. Kim, Temperature dependence of the growth rate of spherulites, J. Polymer Sci. A-26, 165–180 (1968).Google Scholar
  159. 153.
    E. G. Lovering and D. C. Wooden, Equilibrium melting points of the low-melting and high-melting crystalline forms of trans-1,4-polyisoprene, J. Polymer Sci. A-2 9, 175–179 (1971).Google Scholar
  160. 154.
    M. L. Dannis, Thermal expansion measurements and transition temperatures, first and second order, J. Appl. Polymer Sci. 1, 121–126 (1959).Google Scholar
  161. 155.
    E. G. Lovering, The relationship between molecular weight and spherulitic growth rates in trans-1,4-polyisoprene, J. Polymer Sci. C30, 329–338 (1970).Google Scholar
  162. 156.
    D. R. Carter and E. Baer, Lamellar crystallization and melting of polyoxymethylene, J. Appl. Phys. 37, 4060–4065 (1966).Google Scholar
  163. 157.
    W. H. Linton and H. H. Goodman, Physical properties of high molecular weight acetal resins, J. Appl. Polymer Sci. 1, 179–184 (1959).Google Scholar
  164. 158.
    E. Baer and D. R. Carter, Rate of spherulitic crystallization with chain folds in polyoxymethylene, J. Appl. Phys. 35, 1895–1897 (1964).Google Scholar
  165. 159.
    G. T. Davis and R. K. Eby, The glass transition of polyethylene: Volume relaxation, J. Appl. Phys. 44, 4274–4281 (1973).Google Scholar
  166. 160.
    J. D. Hoffman, G. S. Ross, L. Frolen, and J. I. Lauritzen, Jr., On the growth rate of spherulites and axialites from the melt in poly(ethylene) fractions: Regime I and Regime II crystallization, J. Res. Nat. Bur. Std. (U.S.) 79A (1975), in press.Google Scholar
  167. 161.
    J. Brandrup and E. H. Immergut (eds.), Polymer Handbook, Interscience Publishers, New York (1966).Google Scholar
  168. 162.
    J. Powers, J. D. Hoffman, J. J. Weeks, and F. A. Quinn, Jr., Crystallization kinetics and polymorphic transformations in polybutene-1, J. Res. Nat. Bur. Std. (U.S.) 69A, 335–345 (1965).Google Scholar
  169. 163.
    R. G. Crystal, Polymeric nature of selenium crystallization. II. Crystallization kinetics and secondary crystallization J. Polymer Sci. A-2 8, 2153–2161 (1970).Google Scholar
  170. 164.
    F. J. Padden, Jr. and H. D. Keith, Spherulitic crystallization in polypropylene, J. Appl. Phys. 30, 1479–1484 (1959).Google Scholar
  171. 165.
    L. Mandelkern, F. A. Quinn, Jr., and D. E. Roberts, Thermodynamics of crystallization in high polymers: gutta percha, J. Am. Chem. Soc. 78, 926–932 (1956).Google Scholar
  172. 166.
    V. F. Holland and P. H. Lindenmeyer, Morphology and crystal growth rate of polyethylene crystalline complexes, J. Polymer Sci. 57, 589–608 (1962).Google Scholar
  173. 167.
    M. Cooper and R. St. John Manley, Growth kinetics of polyethylene crystals from dilute xylene solution, J. Polymer Sci., Polymer Letters Ed. 11, 363–367 (1973).Google Scholar
  174. 168.
    R. L. Miller, Polymer crystal formation: On an analysis of the dilute solution lamellar thickness—crystallization temperature data for poly(ethylene), Kolloid-Z. u. Z. Polymere 225, 62–69 (1968).Google Scholar
  175. 169.
    D. H. Jones, A. J. Latham, A. Keller, and M. Girolamo, Fold length of single crystals of polystyrene: A conflict with crystallization theories at high supercoolings, J. Polymer Sci., Polymer Phys. Ed. 11, 1759–1767 (1973).Google Scholar
  176. 170a.
    N. Overbergh, H. Berghmans, and G. Smets, Influence of thermal history on the melting behavior of isotactic polystyrene, J. Polymer Sci. C 38, 237–250 (1972).Google Scholar
  177. 170b.
    N. Overbergh, H. Berghmans, G. Groenickx, and H. Reynaers, Reorganization of semicrystalline isotactic polystyrene studied by electron microscopy and small-angle X-ray diffraction, Paper A-5 IUPAC Int. Sym. on Macromolecules, Aberdeen, Scotland, September 1973.Google Scholar
  178. 171.
    T. Kawai and A. Keller, On the effect of the crystallization temperature on the habit and fold length of polyethylene single crystals, Phil. Mag. 11, 1165–1177 (1965).Google Scholar
  179. 172.
    N. Hirai, T. Tokumori, T. Katayama, S. Fujita, and Y. Yamashita, Thickness of high polymer single crystals precipitated from solution, Rep. Res. Lab. for Surface Science, Okayama Univ. 2, 91–99 (1963).Google Scholar
  180. 173.
    G. Lieser and E. W. Fischer, private communication; G. Lieser, Master’s Thesis, Univ. Mainz, Mainz, Germany, 1966.Google Scholar
  181. 174.
    T. Korenaga, F. Hamada, and A. Nakajima, Surface free energy of poly(oxymethylene) single crystals grown in various solvents, Polymer J. 3, 21–27 (1972).Google Scholar
  182. 175.
    E. Ergoz and L. Mandelkern, Solvent influence on the dilute solution crystallization of polyethylene and polyoxymethylene, J. Polymer Sci., Polymer Letters Ed. 11, 73–79 (1973).Google Scholar
  183. 176.
    P. R. Swan, Polyethylene unit cell variations with temperature, J. Polymer Sci. 56, 403–407 (1962).Google Scholar
  184. 177.
    G. T. Davis, R. K. Eby, and J. P. Colson, Thermal expansion of polyethylene unit cell: Effect of lamella thickness, J. Appl. Phys. 41, 4316–4326 (1970).Google Scholar
  185. 178.
    D. R. Holmes, C. W. Bunn, and D. J. Smith, Crystal structure of polycaproamide: nylon 6, J. Polymer Sci. 17, 159–177 (1955).Google Scholar
  186. 179.
    D. Fisher, Crystal structures of gutta percha, Proc. Phys. Soc. B66, 7–16 (1953).Google Scholar
  187. 180.
    G. Natta, P. Corradini, and I. W. Bassi, Crystal structure of isotactic polystyrene, Nouvo Cimento (Suppl. 1) 15, 68–82 (1960).Google Scholar
  188. 181.
    E. Sauter, Ein Modell der Hauptvalenzkette im Makromolekülgitter der Polyoxymethylene, Z. Physik. Chem. 21B, 186–197 (1933).Google Scholar
  189. 182.
    G. Vidotto, D. Lévy, and A. J. Kovacs, Cristallisation et fusion des polymères autoensemencés. I. Polybutène-1, Polyéthylène et Polyoxyéthylène de haute masse moléculaire, Kolloid-Z. u. Z. Polymere 230, 289–305 (1969).Google Scholar
  190. 183.
    H. Tadokoro, Y. Chatani, T. Yoshihara, S. Tahara, and S. Murahashi, Structural studies on polyethers [-(CH2)m O-jnH, molecular structure of polyethylene oxide, Makromol. Chem. 73, 109–127 (1964).Google Scholar
  191. 184.
    A. J. Bradley, The crystal structures of the rhombohedral forms of selenium and tellurium, Phil. Mag. 48, 477–496 (1924).Google Scholar
  192. 185.
    J. P. Colson and R. K. Eby, Melting temperatures of copolymers, J. Appl. Phys. 37, 3511–3514 (1966);Google Scholar
  193. I. C. Sanchez and R. K. Eby, Crystallization of random copolymers, J. Res. Nat. Bur. Std. (U.S.) 77A. 353–358 (1973).Google Scholar
  194. 186.
    D. C. Bassett and R. Davitt, private communication.Google Scholar
  195. 187.
    J. Hine, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York (1962), p. 35.Google Scholar
  196. 188.
    J. I. Lauritzen, Jr., E. A. DiMarzio, and E. Passaglia, Kinetics of growth of multicomponent chains, J. Chem. Phys. 45, 4444–4454 (1966).Google Scholar
  197. 189.
    J. I. Lauritzen, Jr., E. Passaglia, and E. A. DiMarzio, Kinetics of crystallization in multicomponent systems: I. Binary mixtures of n-paraffins, J. Res. Nat. Bur. Std. (U.S.) 71A, 245–259 (1967).Google Scholar
  198. 190.
    G. S. Ross and L. J. Frolen, unpublished.Google Scholar
  199. 191.
    Private communication from Prof. P. H. Geil; see also J. E. Breedon, M.S. Thesis, Crack formation in polymer single crystals, Case-Western Reserve Univ., Cleveland, Ohio (1975).Google Scholar

Copyright information

© Bell Telephone Laboratories, Incorporated 1976

Authors and Affiliations

  • John D. Hoffman
    • 1
  • G. Thomas Davis
    • 1
  • John I. LauritzenJr.
    • 1
  1. 1.Institute for Materials ResearchNational Bureau of StandardsUSA

Personalised recommendations