Abstract
This paper is concerned with the application of percolation theory, and related ideas such as the statistics of lattice animals, to model the behavior of branched polymer molecules and the sol-gel phase transition in polymer systems.
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References
M.N. Barber and B.W. Ninham, Random and Restricted Walks, Gordon and Breach, New York, 1970; see also the article by Hughes and Prager in this volume.
S.G. Whittington, Adv. Chem. Physics 51, 1 (1982).
T.C. Lubensky and J. Isaacson, Phys. Rev. A. 20, 2130 (1979).
D.A. Klarner, Can. J. Math., 19, 851 (1967).
S.G. Whittington and D.S. Gaunt, J. Phys. A: Math. Gen. 11, 1449 (1978).
D.S. Gaunt, J. Phys. A: Math. Gen. 13, L97 (1980).
G. Parisi and N. Sourlas, Phys. Rev. Lett. 46, 871 (1981).
M. Daoud and J.F. Joanny, J. Physique 42, 1359 (1981).
D. Stauffer, Phys. Rev. Lett. 41, 1333 (1978).
H.J. Herrmann, Z. Phys. B. 32, 335 (1979).
F. Family, J. Phys. A: Math. Gen. 13, L325 (1980).
D.J. Klein, J. Chem. Phys. 75, 5186 (1981).
W.A. Seitz and D.J. Klein, J. Chem. Phys. 75, 5190 (1981).
S. Redner, J. Phys. A: Math. Gen. 12, L239 (1979).
J.A.M.S. Duarte and H.J. Ruskin, J. Physique 42, 1585 (1981).
D.S. Gaunt, M.F. Sykes, G.M. Torrie and S.G. Whittington, J. Phys. A: Math. Gen. 15, 3209 (1982).
H.J. Ruskin and J.A.M.S. Duarte, Phys. Rev. A. 26, 1791 (1982)1
S.G. Whittington, G.M. Torrie and D.S. Gaunt, J. Phys. A: Math. Gen. 16, in press (1983).
J.M. Hammersley and K.W. Morton, J.R. Stat. Soc. B 16, 23 (1954).
J.E.G. Lipson and S.G. Whittington, J. Phys. A: Math. Gen. submitted.
D.S. Gaunt, A.J. Guttmann and S.G. Whittington, J. Phys. A: Math. Gen. 12, 75, (1979).
D.S. Gaunt, J.L. Martin, G. Ord, G.M. Torrie and S.G. Whittington, J. Phys. A.: Math. Gen. 13, 1791 (1980).
D. Stauffer, A. Coniglio and M. Adam, Adv. Polymer Sci. 44, 103 (1982).
D. Stauffer, Physica 106A, 177 (1981).
Z. Ahmad and R.F.T. Steptoe, Colloid and Polymer Sci. 258, 663 (1980).
G. Ord and S.G. Whittington, J. Phys. A: Math. Gen. 13, L307 (1980).
G. Ord, Ph.D. Thesis, University of Toronto (1983).
R.S. Whitney and W. Burchard, Makromol. Chem. 181, 869 (1980).
G. Ord and S.G. Whittington, J. Phys. A: Math. Gen. 15, L29 (1982).
P.G. de Gennes, J. de Physique Lettres 40, L355 (1979).
M. Daoud, J. de Physique Lettres 40, L201 (1979).
A. Coniglio and M. Daoud, J. Phys. A: Math. Gen 12, L259 (1979).
D.A. Rees, Chemistry and Industry 630 (1972).
E.T. Gawlinski and H.E. Stanley, J. Phys. A 14, L291 (1981).
C. Domb, Biometrika 59, 209 (1972).
E.N. Gilbert, J. Soc. Ind. Appl. Math. 9, 533 (1961).
M.F. Sykes and J.W. Essam, J. Math. Phys. 5, 117 (1964).
A. Coniglio, H.E. Stanley and W. Klein, Phys. Rev. Lett. 42, 518 (1979).
A.J. Guttmann and S.G. Whittington, J. Phys. A: Math. Gen. 15, 2267 (1982).
H.J. Herrmann, D.P. Landau and D. Stauffer, Phys. Rev. Lett. 49, 412 (1982).
R.M. Ziff, J. Stat. Phys. 23, 241 (1980).
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Whittington, S.G. (1983). Branched polymers, polymer gels and percolation theory. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073264
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DOI: https://doi.org/10.1007/BFb0073264
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