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Configuration and Free Energy of a Polymer Molecule with Solvent Interaction
1.P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953), Chap. 14.
2.R. J. Rubin, J. Chem. Phys. 20, 1940 (1952);
2.B. H. Zimm, W. H. Stockmayer, and M. Fixman, J. Chem. Phys. 21, 1716 (1953). These papers and that cited in footnote 9 contain many other references to the literature., J. Chem. Phys.
3.E. W. Montroll, J. Chem. Phys. 18, 734 (1950).
4.G. W. King, National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C.), No. 12, June 1951;
4.M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 20, 1360 (1952);
4.R. S. Lehman and G. H. Weiss, J. Soc. Ind. Appl. Math. 6, 257 (1958).
5.J. M. Hammersley and K. W. Morton, J. Roy. Statist. Soc. B16, 23 (1954).
6.F. T. Wall, L. A. Hiller, and D. J. Wheeler, J. Chem. Phys. 22, 1036 (1954);
6.F. T. Wall, L. A. Hiller, and W. F. Atchison, J. Chem. Phys. 23, 913 (1955); , J. Chem. Phys.
6.F. T. Wall, L. A. Hiller, and W. F. Atchison, 23, 2314 (1955); , J. Chem. Phys.
6.F. T. Wall, L. A. Hiller, and W. F. Atchison, 26, 1742 (1957); , J. Chem. Phys.
6.F. T. Wall, R. J. Rubin, and L. M. Isaacson, J. Chem. Phys. 27, 186 (1957)., J. Chem. Phys.
7.F. T. Wall and J. J. Erpenbeck, J. Chem. Phys. 30, 634 (1959).
8.W. J. C. Orr, Trans. Faraday Soc. 42, 12 (1946).
9.M. E. Fisher and M. F. Sykes, Phys. Rev. 114, 45 (1959).
10.C. Domb, Advances in Phys. 9, 149 (1960).
11.C. Domb and M. F. Sykes, J. Math. Phys. (to be published).
12.E. Teramoto, M. Kurata, R. Chujo, C. Suzuki, K. Tani, and T. Kajikawa, J. Phys. Soc. Japan 10, 953 (1955).
13.T. M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642 (1957).
14.H. L. Frisch, F. C. Collins, and B. Friedman, J. Chem. Phys. 19, 1402 (1951).
14.Note that the upper bounds quoted in this paper are incorrect. The lower bounds, however, are quite valid and the method used to derive them forms the starting point for the later developments of Fisher [M. E. Fisher, Discussions Faraday Soc. 25, 200 (1958)].
15.B. J. Hiley and M. F. Sykes, J. Chem. Phys. (to be published).
16.As explained in Sec. V a slight error has been discovered in this data for chains of eight links.
17.M. F. Sykes, J. Math. Phys. (to be published).
18.J. M. Hammersley, Phys. Rev. 118, 656 (1960).
19.The limits on the estimates of α quoted by Fisher and Sykes for these lattices did not take full account of the uncertainties in μ.
20.C. Domb and M. E. Fisher, Proc. Cambridge Phil. Soc. 54, 48 (1958); see also Appendix A herein.
21.Rosenbluth and Rosenbluth (work cited in footnote 4) quote some direct estimates for Their value for differs from the exact result by more than 1% which supports our conclusion regarding probable accuracy. W. H. Stockmayer [Makrmol. Chemie 35, 54 (1960)] considers that wall and Erpenbeck’s data could be fitted equally well with the rather than 1.18.
22.F. T. Wall and J. J. Erpenbeck, J. Chem. Phys. 30, 637 (1959).
23.Statistical calculations for a walk of this type on the three‐dimensional tetrahedral lattice have been performed by F. T. Wall, L. A. Hiller, and W. F. Atchison [J. Chem. Phys. 26, 1742 (1957)].
24.Orr did not discuss the implications of this data for the mean size. His intention to do this appears to have been thwarted by his untimely death.
25.It should be noted, however, that Wall found evidence of a lower value of γ for walks of 50 steps or more although it seems possible that this was just a reflection of the statistical uncertainties.
26.P. J. Flory, see work cited in footnote 1, p. 414.
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