Summary
A detailed analysis of available crystal size-crystallization temperature data for crystallization of poly (ethylene) from dilute solutions indicates that all of the data may be represented by the semi-empirical expression:\(l_{obs} = 2 \sigma _e T_{s^0 } /\Delta h_f \Delta {\rm T}_c + \bar l_c\). For good solvents,T 0 s =110.5 °C, σ e =72.0 erg cm−2, and\(\bar l_c = 59.7 {\AA}\). This semi-empirical expression differs from theoretical expressions,l *=2σ e T s 0/Δh f ΔT c +δl, only in the magnitude of δl predicted (5–15 Å) relative to the empirical value of\(\bar l_c\). One possible origin of this difference may be a temperature dependence of σ e .
Zusammenfassung
Eine detaillierte Analyse von Daten über die Abhängigkeit der Kristallgröße von der Temperatur in der Kristallisation von Polyäthylen aus verdünnten Lösungen zeigt, daß die Engebnisse wiedergegeben werden können durch die semi-empirische Gleichung:\(l_{obs} = 2 \sigma _e T_{s^0 } /\Delta h_f \Delta {\rm T}_c + \bar l_c\). Für gute Lösungsmittel:T 0 s =110,5 °C, σ e =72.0 erg cm−2 und\(\bar l_c = 59,7 {\AA}\). Diese semi-empirische Beziehung unterscheidet sich von den theoretischen Ausdrücken,l *=2σ e T s 0/Δh f ΔT c +δl, nur in der Größe des Verhältnisses des vorausgesagten δl (5–15 Å) zu dem empirisch gefundenen Wert von\(\bar l_c\). Die Temperaturabhängigkeit von σ e kann möglicherweise diesem andersartigen Verhältnis zugrunde liegen.
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References
Geil, P. H., Polymer Single Crystals (Polymer Reviews, Vol. V.) (New York 1963).
Price, F. P., J. Polymer Sci.42, 49 (1960);
, J. Chem. Phys.35, 1884 (1961).
Lauritzen, J. I. Jr. andJ. D. Hoffman, J. Res. Nat. Bur. Stand., A64, 73 (1960);
Hoffman, J. D. andJ. I. Lauritzen Jr., ibid.65, 297 (1961).
Frank, F. C. andM. Tosi, Proc. Roy. Soc. (London), Ser. A,263, 323 (1961).
Fischer, E. W., Z. Naturforschg.14a, 584 (1959).
Peterlin, A. andE. W. Fischer, Z. Physik159, 272 (1960).
Peterlin, A., E. W. Fischer andC. Reinhold, J. Chem. Phys.37, 1403 (1962);
Peterlin, A. andC. Reinhold, J. Polymer Sci., Pt. A3, 2801 (1965);
Peterlin, A., private communication.
Hoffman, J. D., SPE (Soc. Plast. Eng.) Transact.4, 315 (1964).
Baer, E. andD. R. Carter, J. Appl. Phys.35, 1895 (1964).
Carter, D. R. andE. Baer ibid.37, 4060 (1966).
Peterlin, A., Makromol. Chem.74, 107 (1964).
Mandelkern, L., F. A. Quinn Jr. andP. J. Flory, J. Appl. Phys.25, 830 (1954).
Mandelkern, L., ibid.26, 443 (1955).
Hoffman, J. D. andJ. J. Weeks, J. Res. Nat. Bur. Stand. A66, 13 (1962).
Fischer, E. W. andR. Lorenz, Kolloid-Z. u. Z. Polymere189, 97 (1963).
Holland, V. F. andP. H. Lindenmeyer, J. Polymer Sci.57, 589 (1962).
Holland, V. F., J. Appl. Phys.35, 59 (1964).
Kawai, T. andA. Keller, Phil. Mag.11, 1165 (1965).
Keller, A. andA. O'Connor, Disc. Faraday Soc.25, 114 (1958).
Keller, A. andO'Connor, Polymer1, 163 (1960).
Salovey, R. andA. Keller, Bell System Tech. J.40, 1409 (1961).
Bassett, D. C. andA. Keller, Phil. Mag.7, 1553 (1962).
Balta Calleja, F. J., D. C. Bassett andA. Keller, Polymer4, 269 (1963).
Wunderlich, B. andP. Sullivan, J. Polymer Sci.56, 19 (1962).
Wunderlich, B., P. Sullivan, T. Arakawa, A. B. Dicyan andJ. F. Flood, ibid., 3581 (1963).
Rånby, B. G., F. F. Morehead andN. M. Walter, J. Polymer Sci.44, 349 (1960).
Rånby, B. G. andH. Brumberger, Polymer1, 399 (1960).
Nagatoshi, F. andM. Takayanagi, Rep. Prog. Pol. Phys. Jap.7, 77 (1964).
Matsuo, T. andM. Takayanagi, ibid.9, 341 (1966).
Takayanagi, M., K. Imada, A. Nagai, T. Tatsumi andT. Matsuo, J. Polymer Sci. Pt. C16, 867 (1967).
Salovey, R., J. Polymer Sci.61, 463 (1962).
Hirai, N., T. Tokumori, T. Katayama, S. Fujita andY. Yamashita, Rept. Res. Lab. Surface Sci., Fac. Sci., Okayama Univ.2, 91 (1963).
Ryan, J. F., p. 86 in reference 1.
Richardson, M. J., Trans. Faraday Soc.61, 1876 (1965).
Fischer, E. W. andG. Hinrichsen, Kolloid-Z. u. Z. Polymere213, 93 (1966).
Blackadder, D. A. andH. M. Schleinitz, Polymer7, 603 (1966).
Huseby, T. W., H. E. Bair andR. Salovey, Amer. Chem. Soc. Polymer Preprints8, 125 (1967).
Jackson, J. F. andL. Mandelkern, J. Polymer Sci., Pt. B5, 557 (1967).
Flory, P. J. andA. Vrij, J. Amer. Chem. Soc.85, 3548 (1963).
Broadhurst, M. G., J. Res. Nat. Bur. Stand. A70, 481 (1966).
Cormia, R. L., F. P. Price andD. Turnbull, J. Chem. Phys.37, 1333 (1962).
Gornick, F., G. S. Ross andL. J. Frolen, J. Polymer Sci., Pt. C18, 79 (1967).
Hoffman, J. D., J. I. Lauritzen Jr., E. Passaglia, G. S. Ross, L. J. Frolen andJ. J. Weeks, Kolloid-Z. u. Z. Polymere, in press.
Wood, L. A. andN. Bekkedahl, J. Appl. Phys.17, 362 (1946).
, J. Res. Nat. Bur. Stand.36, 489 (1946).
Gornick, F. andJ. D. Hoffman, Ind. Eng. Chem.58, 41 (1966).
Hoffman, J. D., J. Chem. Phys.29, 1192 (1958).
Broadhurst, M. G., J. Res. Nat. Bur. Stand. A67, 233 (1963).
Hoffman, J. D. andJ. J. Weeks, J. Chem. Phys.37, 1723 (1962).
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Miller, R.L. 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). https://doi.org/10.1007/BF02111401
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DOI: https://doi.org/10.1007/BF02111401