Abstract
A diffusion coefficient of a segment is proposed from the fact that the Mth segment from the end arrives at the place where the Nth segment is located by jumping (N–M) times. By using this and the translational diffusion coefficient derived previously, a termination-rate equation is formulated. After such an equation is applied to the diffusion-controlled model terminations, it is also applied to the polymerization rates in the polymerizations of styrene and methyl methacrylate (MMA) initiated by azo compounds, without any modification for reactions in terms of primary radicals. The mobility factor of a segment, which denotes the ratio of the segmental mobility to the mobility of a particle of the segment size, is estimated to be 0.24 for PMMA and 0.14 for polystyrene; these values would be independent of solvent properties.
Similar content being viewed by others
Article PDF
References
A. M. North and G. A. Reed, Trans. Faraday Soc., 57, 859 (1961).
A. M. North and G. A. Reed, J. Polym. Sci., A, 1, 1311 (1963).
J. P. Fisher, G. Mücke, and G. V. Schulz, Ber. Bunsenges. Phys. Chem., 73, 154 (1969).
K. Horie, I. Mita, and H. Kambe, Polym. J., 4, 341 (1973).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 10, 3159 (1972).
H. K. Mahabadi and K. F. O’Driscoll, J. Polym. Sci., Polym. Chem. Ed., 15, 283 (1977).
S. W. Benson and A. M. North, J. Am. Chem. Soc., 84, 935 (1962).
P. H. Verdier and W. H. Stockmayer, J. Chem. Phys., 35, 227 (1962).
H. J. Hilhort and J. M. Deutch, J. Chem. Phys., 63, 5153 (1975).
J. G. Kirkwood and J. Riseman, J. Chem. Phys., 16, 565 (1948).
M. Kurata and H. Yamakawa, J. Chem. Phys., 29, 311 (1958).
M. Kurata and H. Yamakawa, J. Chem. Phys., 28, 785 (1958).
P. J. Floory, “Principles of Polymer Chemistry,” Cornell University Press, Ithaca, NY, 1953.
L. Mandelkern and P. J. Flory, J. Chem. Phys., 20, 212 (1952).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 12, 2581 (1974).
H. Fujita and T. Norisuye, J. Chem. Phys., 52, 1151 (1971).
P. J. Flory, Science, 188, 1268 (1975).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 12, 1991 (1974).
U. B. Borgwardt, W. Schnabel, and A. Henglein, Makromol. Chem., 127, 176 (1969).
K. Horie and I. Mita, Macromolecules, 11, 1173 (1978).
J. Kiwi and W. Schnabel, Macromolecules, 9, 468 (1976).
G. G. Camerson and J. Cameron, Polymer, 14, 107 (1973).
W. Görlich and W. Schnabel, Makromol. Chem., 164, 225 (1973).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 15, 1759 (1977).
O. F. Olaj, Makromol. Chem., 14, 1 (1968).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 16, 2725 (1978)
G. V. Schulz and H. Baumann, Makromol. Chem., 60, 120 (1968).
F. R. Mayo, R. A. Gregg, and M. S. Matheson, J. Am. Chem. Soc., 73, 1691 (1951).
H. Utiyama, Dissertation, Kyoto University, Kyoto, Japan, November 1962.
J. Brandrup and H. Baumann, “Polymer Handbook,” John Wiley & Sons, Inc. NY, 1966.
M. G. Baldwin, J. Polym. Sci., A, 1, 3209 (1963).
C. G. Overberger and M. B. Berenbaun, J. Am. Chem. Soc., 73, 2618 (1951).
K. Ichiriki, Vinyl Polym., 8, 6 (1968).
K. Ito, J. Polym. Sci., A-1, 10, 481 (1972).
T. G Fox, Polymer, 3, 111 (1962).
W. R. Moore and R. J. Fort, J. Polym. Sci., A, 1, 929 (1963).
I. Sakurada, A. Nakashima, O. Yoshizaki, and K. Nakamae, Kolloid Z. Z. Polym., 186, 41 (1962).
T. G Fox and S. Loshaek, J. Polym. Sci., 15, 371 (1955).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., 15, 2037 (1977).
G. Bontá, B. M. Gallo, and S. Russo, J. Chem. Soc., Faraday Trans. 1, 69, 328 (1973).
G. Bontá, B. M. Gallo, and S. Russo, J. Chem. Soc., Faraday Trans. 1, 71, 1727 (1975).
J. E. Mark and P. J. Flory, J. Am. Chem. Soc., 87, 1415 (1965).
H. K. Mahabadi and K. F. O’Driscoll, J. Macromol. Sci., Chem., A11, 967 (1977).
K. Ito, J. Polym. Sci., Polym. Chem. Ed., in press.
G. C. Levy, D. E. Axelson, R. Schwartz, and J. Hochmann, J. Am. Chem. Soc., 100, 410 (1978).
H. Margenau and G. M. Murphy, “The Mathematics of Physics and Chemistry,” D. Van Nostrand Co., Inc., New Haven, Conn., 1943.
H. K. Mahabadi and K. F. O’Driscoll, Markomol. Chem., 178, 2629 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ito, K. Evaluation of Termination Rate by Segmental and Translational Diffusions in Radical Polymerizations. Polym J 11, 795–803 (1979). https://doi.org/10.1295/polymj.11.795
Issue Date:
DOI: https://doi.org/10.1295/polymj.11.795