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On the kinetics of multitype polymer reactions

Published online by Cambridge University Press:  14 July 2016

B. Mellein*
Affiliation:
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
J. L. Vicente*
Affiliation:
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
*
Postal address: INIFTA, Division Química Teórica, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Provincia de Buenos Aires, República Argentina.
Postal address: INIFTA, Division Química Teórica, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Provincia de Buenos Aires, República Argentina.

Abstract

A multitype polymer reaction process is considered. Its dynamics is described by means of the evolution in time of the average number of reactions (of any kind) and the mean number of unreacted chain segments (of any length), assuming that the initial chain molecule consists of n unreacted units. The asymptotic behaviour (n →∞) of the variance of the extent of reaction is also studied.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1986 

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References

Bankövi, G. (1962) On gaps generated by a random space filling procedure. Publ. Math. Inst. Hung. Acad. Sci. 7, 395407.Google Scholar
Blaisdell, B. E. and Solomon, H. (1970) On random sequential packing in the plane and a conjecture of Palásti. J. Appl. Prob. 7, 667698.Google Scholar
Boucher, E. A. (1972a) Reaction kinetics of polymer substituents: Neighbouring-substituent effects in pairing reactions. J.C.S. Faraday I 68, 22812294.CrossRefGoogle Scholar
Boucher, E. A. (1972b) On the statistics of n-fold occupation of a linear array of m sites. Chem. Phys. Letters 17, 221222.Google Scholar
Boucher, E. A. (1973) Kinetics and statistics of random cooperative and anti-cooperative occupation of linear arrays. J.C.S. Faraday II 69, 18391850.Google Scholar
Boucher, E.A. (1976) Reaction kinetics of polymer substituents: Neighbouring-group effects for ideal molecules with unique ends and related model schemes. J.C.S. Faraday II 72, 16971705.Google Scholar
Boucher, E. A. and Nisbet, R. M. (1976) Application of the transfer-matrix method to equilibria of polymer reactions and adsorption from solution. Chem. Phys. Letters 40, 6165.CrossRefGoogle Scholar
Cohen, E. R. and Reiss, H. (1963) Kinetics of reactant isolation. I. One-dimensional problems. J. Chem. Phys. 38, 680691.CrossRefGoogle Scholar
Dvoretzky, A. and Robbins, H. (1964) On the “parking” problem. Publ. Math. Inst. Hung. Acad. Sci. 9, 209224.Google Scholar
Feder, J. (1980) Random sequential adsorption. J. Theoret. Biol. 87, 237254.Google Scholar
Gonzalez, J. J., Hemmer, P. C. and Høye, J. S. (1974) Cooperative effects in random sequential polymer reactions. J. Chem. Phys. 3, 228238.Google Scholar
Gornick, F. and Jackson, J. L. (1963) Sequence selection problem in the crystallization of polymers. J. Chem. Phys. 39, 11501154.Google Scholar
Mackenzie, J. K. (1962) Sequential filling of a line by intervals placed at random and its application to linear adsorption. J. Chem. Phys. 37, 723728.Google Scholar
Mannion, D. (1964) Random space-filling in one-dimension. Publ. Math. Inst. Hung. Acad. Sci. 9, 143154.Google Scholar
Mannion, D. (1976) Random packing of an interval. Adv. Appl. Prob. 8, 477501.CrossRefGoogle Scholar
Mcquarrie, D. A. (1967) Stochastic approach to chemical kinetics. J. Appl. Prob. 4, 413478.Google Scholar
Mcquistan, R. B. and Lichtman, D. (1968) Exact occupation kinetics for one-dimensional arrays of dumbbells. J. Math. Phys. 9, 16801684.Google Scholar
Mellein, B. and Mola, E. E. (1985) A multi-type random sequential process. J. Math. Phys. 26, 514521.Google Scholar
Mullooly, J. P. (1968) A one dimensional random space-filling problem. J. Appl. Prob. 5, 427435.Google Scholar
Ney, P. (1962) A random interval filling problem. Ann. Math. Statist. 33, 702718.Google Scholar
Olson, W. H. (1978) A Markov chain model for the kinetics of reactant isolation. J. Appl. Prob. 15, 835841.Google Scholar
Page, E. S. (1959) The distribution of vacancies on a line. J. R. Statist. Soc. B 21, 364374.Google Scholar
Pomeau, Y. (1980) Some asymptotic estimates in the random parking problem. J. Phys. A. Math. Gen. 13, L193L196.Google Scholar
Renyi, A. (1958) On a one-dimensional problem concerning space-filling. Publ. Math. Inst. Hung. Acad. Sci. 3, 109127.Google Scholar
Swendsen, R. H. (1981) Dynamics of random sequential adsorption. Phys. Rev. A 24, 504508.Google Scholar
Titchmarsh, E. C. (1939) The Theory of Functions. Clarendon Press, Oxford.Google Scholar
Weiner, H. J. (1980) An alternative argument (letter to the editor). J. Appl. Prob. 17, 878880.CrossRefGoogle Scholar