Abstract
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.
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References
P. H. Geil, Polymer Single Crystals, Interscience Publishers, New York (1963).
F. Khoury and E. Passaglia, This Treatise, Vol. 3, Chapter 6.
P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York (1969).
H. D. Keith and F. J. Padden, Jr., A phenomenological theory of spherulitic crystallization, J. Appl. Phys. 34, 2409–2421 (1963).
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).
J. Boon, The effect of extreme supercooling on the number of spherulitic centers in isotactic polystyrene, J. Polymer Sci. C 16, 1739–1749 (1967).
T. Suzuki and A. J. Kovacs, Temperature dependence of spherulitic growth rate of isotactic polystyrene, Polymer J. 1, 82–100 (1970).
J. N. Hay, Crystallization kinetics of high polymers: Isotactic polystyrene, J. Polymer Sci. A 3, 433–447 (1965).
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).
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).
J. J. Point, Enroulement hélicoïdal dans les sphérolithes de polyéthylène. Bull. Acad. Roy. Belg. 41, 982–990 (1955);
J. J. Point and G. A. Homès, Fibre N du polyéthylène, Compt. Rend. 242, 2557–2560 (1956).
R. Jaccodine, Observations of spiral growth steps in ethylene polymers, Nature 176, 305–306 (1955).
H. D. Keith, F. J. Padden, Jr., and R. G. Vadimsky, Intercrystalline links: Critical evaluation, J. Appl. Phys. 42, 4585–4592 (1971).
K. H. Storks, An electron diffraction examination of some linear high polymers, J. Am. Chem. Soc. 60, 1753–1761 (1938).
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).
J. D. Hoffman, Theoretical aspects of polymer crystallization with chain folds: Bulk polymers, Soc. Plastics Eng. Trans. 4, 315–362 (1964).
A. Keller, A note on single crystals in polymers: Evidence for a folded chain configuration, Phil. Mag. 2, 1171–1175 (1957).
E. W. Fischer, Stufen-and spiralförmiges Kristallwachsturo bei Hochpolymeren, Z. Naturforsch. 12a, 753–754 (1957).
P. H. Till, Jr., The growth of single crystals of linear polyethylene, J. Polymer Sci. 24, 301–306 (1957).
W. D. Niegisch and P. R. Swan, Hollow pyramidal crystals of polyethylene and a mechanism of growth, J. Appl. Phys. 31, 1906–1910 (1960).
P. H. Lindenmeyer, Crystallization in polymers, J. Polymer Sci. C 1, 5–39 (1963).
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).
M. I. Bank and S. Krimm, Mixed crystal infrared study of chain folding in crystalline polyethylene, J. Polymer Sci. A-27, 1785–1809 (1969).
G. M. Martin and E. Passaglia, Density of polyethylene crystals grown from solution, J. Res. Nat. Bur. Std. (U.S.) 70A, 221–224 (1966).
A. Peterlin, The amount and location of amorphous component in polyethylene single crystals, J. Macrgmol. Sci.-Phys. B3, 19–31 (1969).
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).
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).
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).
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).
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).
E. A. DiMarzio and F. L. McCrackin, One-dimensional model of polymer adsorption, J. Chem. Phys. 43, 539–547 (1965).
E. A. DiMarzio and R. J. Rubin, Adsorption of a chain polymer between two plates, J. Chem. Phys. 55, 4318–4336 (1971).
R. R. Stromberg, D. J. Tutas, and E. Passaglia, Conformation of polystyrene adsorbed at the theta-temperature, J. Phys. Chem. 69, 3955–3963 (1965).
W. H. Grant and R. R. Stromberg, Rates of adsorption and desorption of polystyrene, ACS Polymer Preprints 11 (September), 1397–1399 (1970).
P. H. Geil, Nylon single crystals, J. Polymer Sci. 44, 449–458 (1960).
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).
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).
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).
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).
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).
W. Kern, J. Davidovits, K. J. Rauterkus, and G. F. Schmidt, Röntgenographische Untersuchungen an linearen Oligurethanen, Makrocool. Chem. 43, 106–116 (1961).
: R. St. J. Manley, Growth and morphology of single crystals of cellulose triacetate, J. Polymer Sci. A1, 1875–1892 (1963).
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).
V. F. Holland and R. L. Miller, Isotactic polybutene-1 single crystals: Morphology, J. Appl. Phys. 35, 3241–3248 (1964).
J. D. Barnes and F. A. Khoury, Formation of curved polymer crystals: Polychlorotrifluoroethylene, J. Res. Nat. Bur. Std. (U.S.), 78A, 363–373 (1974).
H. Bittiger and R. H. Marchessault, Formation of ribbonlike fibrils by crystallisation from dilute solution, Bull. Am. Phys. Soc. 15, 305 (1970).
F. J. Padden, Jr., H. D. Keith, and G. Giannoni, Single crystals of poly-Llysine, Biopolymers 7, 793–804 (1969).
H. D. Keith, G. Giannoni, and F. J. Padden, Jr., Single crystals of poly(L-glutamic acid), Biopolymers 7, 775–792 (1969).
R. G. Crystal, The polymeric nature of selenium crystallization. I. Morphology and thermodynamic considerations, J. Polymer Sci. A-2 8, 1755–1772 (1970).
Y. Yaniashita, Single crystals of poly(ethylene terephthalate), J. Polymer Sci. A 3, 81–92 (1965).
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).
F. J. Padden, Jr. and H. D. Keith, Crystalline morphology of synthetic polypeptides, J. Appl. Phys. 36, 2987–2995 (1965).
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).
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).
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).
A. C. T. North and A. Rich, X-ray diffraction studies of bacterial viruses, Nature 191, 1242–1245 (1961).
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).
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).
H. Zahn, Röntgenstruktur von Linearen Oligomeren, IUPAC Symp. on Macromolecules, paper IB 8, Wiesbaden (1959).
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).
W. D. Niegisch, Crystallography of poly-p-xylylene, J. Appl. Phys. 37, 4041–4046 (1966).
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).
G. K. Noren and J. K. Stille, Polyphenylenes, Macromolecular Rev. 5, 385–430 (1971). (Also known as J. Polymer Sci., Part D.)
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).
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.
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).
F. P. Price, The growth habit of single polymer crystals, J. Polymer Sci. 42, 49–56 (1960).
A. Keller and A. O’Connor, Study of single crystals and their associations in polymers, Disc. Faraday Soc. 25, 114–121 (1958).
C. W. Bunn and T. C. Alcock, The texture of polythene, Trans. Faraday Soc. 41, 317–325 (1945).
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).
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).
F. P. Price, On extinction patterns of polymer spherulites, J. Polymer Sci. 39, 139–150 (1959).
A. Keller, Investigations of banded spherulites, J. Polymer Sci. 39, 151–173 (1959);
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).
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).
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).
M. Herbst., Röntgenographische Untersuchung an Sphärolithen in PolyamidSpritzgussmassen, Z. Electrochemie 54, 318–320 (1950).
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).
R. P. Palmer and A. J. Cobbold, The texture of melt crystallized polythene as revealed by selective oxidation, Makromol. Chem. 74, 174–189 (1964).
A. Keller and S. Sawada, On the interior morphology of bulk polyethylene, Makromol. Chem. 74, 190–221 (1964).
C. W. Hock, Selective oxidation with nitric acid reveals the microstructure of polypropylene, J. Polymer Sci. B 3, 573–576 (1965).
J. D. Hoffman and J. J. Weeks, Rate of spherulitic crystallization with chain folds in polychlorotrifluoroethylene, J. Chem. Phys. 37, 1723–1741 (1962).
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).
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 ).
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).
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).
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).
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).
J. D. Hoffman and W. Elban, to be published.
R. K. Sharma and L. Mandelkern, The density of polyethylene crystallized in the bulk and from dilute solution, Macromolecules 2, 266–271 (1969).
L. Mandelkern, A. L. Allou, Jr., and M. Gopalan, The enthalpy of fusion of linear polyethylene, J. Phys. Chem. 72, 309–318 (1968).
D. Turnbull, Kinetics of heterogeneous nucleation, J. Chem. Phys. 18, 198–203 (1950).
B. Vonnegut, Variation with temperature of the nucleation rate of supercooled liquid tin and water drops, J. Colloid Sci. 3, 563–569 (1948).
D. Turnbull and R. L. Cormia, Kinetics of crystal nucleation in some normal alkane liquids, J. Chem. phys. 34, 820–831 (1961).
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.
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).
A. Keller and M. S. Machin, Oriented crystallization in polymers, J. Macromal. Sci. (Phys.) Bl, 41–91 (1967).
E. H. Andrews, Crystalline morphology in thin films of natural rubber. II. Crystallization under strain, Proc. Roy. Soc. (London) A277, 562–570 (1964).
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).
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).
D. V. Rees and D. C. Bassett, Crystallization of polyethylene at elevated pressures, J. Polymer Sci. A-2 9, 385–406 (1971).
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).
D. C. Bassett and B. Turner, New high-pressure phase in chain-extended crystallization of polythene, Nature (Phys. Sci.) 240, 146–148 (1972).
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).
T. W. Huseby and H. E. Bair, Dissolution of polyethylene single crystals in xylene and octadecane, J. Appl. Phys. 39, 4969–4973 (1968).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
J. H. Magill, Crystallization and morphology of d, 1- and 1-poly(propylene oxide), Makromol. Chem. 86, 283–288 (1965).
B. Wunderlich and L. Melillo, Morphology and growth of extended chain crystals of polyethylene, Makromol. Chem. 118, 250–264 (1968).
T. Arakawa and B. Wunderlich, Thermodynamic properties of extended chain polymethylene single crystals, J. Polymer Sci. C 16, 653–658 (1967).
P. E. McMahon, R. L. McCullough, and A. A. Schlegel, Molecular mechanics of point defects in polyethylene, J. Appl. Phys. 38, 4123–4139 (1967).
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).
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.
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).
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).
F. Gornick, G. S. Ross, and L. J. Frolen, Crystal nucleation in polyethylene: The droplet experiment, J. Polymer Sci. C 18, 79–91 (1967).
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).
F. C. Frank and M. Tosi, On the theory of polymer crystallization, Proc. Roy. Soc. (London) A263, 323–339 (1961).
F. Gornick and J. D. Hoffman, Nucleation in polymers, Ind. Eng. Chem. 58, 41–53 (1966).
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).
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).
F. P. Price, Markoff chain model for growth of polymer single crystals, J. Chem. Phys. 35, 1884–1892 (1961).
D. Turnbull and J. C. Fisher, Rate of nucleation in condensed systems, J. Chem. Phys. 17, 71–73 (1949).
P. H. Geil, Folded molecules in lamellas crystallized from molten polymers, J. Appl. Phys. 33, 642–643 (1962).
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).
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).
R. L. Cormia, F. P. Price, and D. Turnbull. Kinetics of crystal nucleation in polyethylene, J. Chem. Phys. 37, 1333–1340 (1962).
J. D. Ferry, Viscoelastic Properties of Polymers, 2nd ed., John Wiley and Sons, New York (1970).
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).
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).
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).
W. B. Hillig, A derivation of classical two-dimensional nucleation kinetics and the associated crystal growth laws, Acta Met. 14, 1868–1869 (1966).
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).
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).
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).
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.
J. I.Lauritzen, Jr., unpublished.
R. Chiang and P. J. Flory, Equilibrium between crystalline and amorphous phases in polyethylene, J. Am. Chem. Soc. 83, 2857–2862 (1961).
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).
P. J. Flory and A. Vrij, Melting points of linear-chain homologs. The normal paraffin hydrocarbons, J. Am. Chem. Soc. 85, 3548–3553 (1963).
A. M. Rijke and L. Mandelkern, Melting behavior of linear polyethylene crystallized by solution stirring, J. Polymer Sci. A-2 8, 225–242 (1970).
J. H. Magill, Crystallization kinetics of nylon 6, Polymer 3, 655–664 (1962).
J. H. Magill, Spherulitic crystillization studies of poly(tetramethyl-psilphenylene)-siloxane (TMPS). Part III, J. Polymer Sci. A-2 7, 1187–1195 (1969).
J. H. Magill, Crystallization of TMPS polymers, Part II, J. Polymer Sci. A-25, 89–99 (1967).
J. H. Magill, Crystallization of TMPS polymers, J. Appl. Phys. 35, 3249–3259 (1964).
d. J. H. Magill, private communication.
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).
L. Mandelkern, N. L. Jain, and H. Kim, Temperature dependence of the growth rate of spherulites, J. Polymer Sci. A-26, 165–180 (1968).
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).
M. L. Dannis, Thermal expansion measurements and transition temperatures, first and second order, J. Appl. Polymer Sci. 1, 121–126 (1959).
E. G. Lovering, The relationship between molecular weight and spherulitic growth rates in trans-1,4-polyisoprene, J. Polymer Sci. C30, 329–338 (1970).
D. R. Carter and E. Baer, Lamellar crystallization and melting of polyoxymethylene, J. Appl. Phys. 37, 4060–4065 (1966).
W. H. Linton and H. H. Goodman, Physical properties of high molecular weight acetal resins, J. Appl. Polymer Sci. 1, 179–184 (1959).
E. Baer and D. R. Carter, Rate of spherulitic crystallization with chain folds in polyoxymethylene, J. Appl. Phys. 35, 1895–1897 (1964).
G. T. Davis and R. K. Eby, The glass transition of polyethylene: Volume relaxation, J. Appl. Phys. 44, 4274–4281 (1973).
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.
J. Brandrup and E. H. Immergut (eds.), Polymer Handbook, Interscience Publishers, New York (1966).
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).
R. G. Crystal, Polymeric nature of selenium crystallization. II. Crystallization kinetics and secondary crystallization J. Polymer Sci. A-2 8, 2153–2161 (1970).
F. J. Padden, Jr. and H. D. Keith, Spherulitic crystallization in polypropylene, J. Appl. Phys. 30, 1479–1484 (1959).
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).
V. F. Holland and P. H. Lindenmeyer, Morphology and crystal growth rate of polyethylene crystalline complexes, J. Polymer Sci. 57, 589–608 (1962).
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).
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).
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).
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).
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.
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).
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).
G. Lieser and E. W. Fischer, private communication; G. Lieser, Master’s Thesis, Univ. Mainz, Mainz, Germany, 1966.
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).
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).
P. R. Swan, Polyethylene unit cell variations with temperature, J. Polymer Sci. 56, 403–407 (1962).
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).
D. R. Holmes, C. W. Bunn, and D. J. Smith, Crystal structure of polycaproamide: nylon 6, J. Polymer Sci. 17, 159–177 (1955).
D. Fisher, Crystal structures of gutta percha, Proc. Phys. Soc. B66, 7–16 (1953).
G. Natta, P. Corradini, and I. W. Bassi, Crystal structure of isotactic polystyrene, Nouvo Cimento (Suppl. 1) 15, 68–82 (1960).
E. Sauter, Ein Modell der Hauptvalenzkette im Makromolekülgitter der Polyoxymethylene, Z. Physik. Chem. 21B, 186–197 (1933).
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).
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).
A. J. Bradley, The crystal structures of the rhombohedral forms of selenium and tellurium, Phil. Mag. 48, 477–496 (1924).
J. P. Colson and R. K. Eby, Melting temperatures of copolymers, J. Appl. Phys. 37, 3511–3514 (1966);
I. C. Sanchez and R. K. Eby, Crystallization of random copolymers, J. Res. Nat. Bur. Std. (U.S.) 77A. 353–358 (1973).
D. C. Bassett and R. Davitt, private communication.
J. Hine, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York (1962), p. 35.
J. I. Lauritzen, Jr., E. A. DiMarzio, and E. Passaglia, Kinetics of growth of multicomponent chains, J. Chem. Phys. 45, 4444–4454 (1966).
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).
G. S. Ross and L. J. Frolen, unpublished.
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).
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Hoffman, J.D., Davis, G.T., Lauritzen, J.I. (1976). The Rate of Crystallization of Linear Polymers with Chain Folding. In: Hannay, N.B. (eds) Treatise on Solid State Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2664-9_7
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