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Scanning Simulation Procedures for Calculation of the Entropy, the Pressure, and the Chemical Potential of Many-Chain Systems

Published online by Cambridge University Press:  26 February 2011

Hagai Meirovitch
Hagai Meirovitch*
Affiliation:
Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL 32306-4052, USA
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Abstract

Using two simulation techniques, the scanning and the hypothetical scanning methods we study a system of many chains with excluded volume contained in a “box” on a square lattice. With these methods the value of the sampling probability P of a configuration is known and therefore the entropy S can be calculated (S ∼ In P) without the need to resort to thermodynamic integration. Thus, the pressure and the chemical potential can be obtained with high accuracy directly from the entropy using standard thermodynamic relations. Our simulation results are compared to the approximate theories of Flory, Huggins, Miller and Guggenheim and to the recent improved theories of Freed and coworkers.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 278: Symposium W – Computational Methods in Materials Science , 1992 , 67
Copyright
Copyright © Materials Research Society 1992

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References

(1) Flory, P.J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, 1953.Google Scholar
(2) Gennes, P.G. de, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, 1985.Google Scholar
(3) Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics, Clarendon Press, Oxford, 1988.Google Scholar
(4) Schweizer, K.S. and Curro, J.G., J.Chem.Phys. 91, 5059 (1989).Google Scholar
(5) Baumgärtner, A., in: The Monte Carlo Method in Condensed Matter Physics, ed. Binder, K., Springer Verlag, New York, to appear.Google Scholar
(6) Computer Simulation of Polymers, ed. Roe, R.J., Prentice Hall, New Jersey, 1990.Google Scholar
(7) Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E., J.Chem.Phys. 21, 1087 (1953).Google Scholar
(8) Alder, B.J. and Wainwright, T.E., J. Chem.Phys. 31, 459 (1959).CrossRefGoogle Scholar
(9) Meirovitch, H.,J.Phys. A15, L735 (1982).Google Scholar
(10) Meirovitch, H., J.Chem.Phys. 89, 2514 (1988).Google Scholar
(11) Meirovitch, H., Int.J.Mod.Phys. Cl, 119 (1990).CrossRefGoogle Scholar
(12) Meirovitch, H., Macromolecules 16, 249 (1983); 18, 569 (1985).CrossRefGoogle Scholar
(13) Meirovitch, H., Phys.Rev. A32, 3709 (1985).CrossRefGoogle Scholar
(14) Ottinger, C., Macromolecules 18, 93, 1348 (1985).CrossRefGoogle Scholar
(15) Schmidt, K.E., Phys.Rev.Lett. 51, 2175 (1983).CrossRefGoogle Scholar
(16) Kahn, H., In: Symposium on Monte-Carlo Methods, ed. Meyer, H.A., Wiley, New York, 146 (1956).Google Scholar
(17) Hammersley, J.M. and Handscomb, D.C., Monte-Carlo Methods, Mathuen, London, 1964.Google Scholar
(18) Huggins, M.L., J.Phvs.Chem. 46, 151 (1942).CrossRefGoogle Scholar
(19) Miller, A.R., Proc.CambridgePhilos.Soc. 38, 109 (1942).Google Scholar
(20) Guggenheim, E.A., Proc.R.Soc.London Ser. A183, 203 (1944).Google Scholar
(21) Bawendi, M.G. and Freed, K.F., J.Chem.Phys. 88, 2741 (1988).CrossRefGoogle Scholar
(22) Bawendi, M.G. and Freed, K.F., J.Chem.Phys. 84, 7036 (1986).Google Scholar
(23) Dickman, R. and Hall, C.K., J.Chem.Phys. 85, 3023 (1986).CrossRefGoogle Scholar
(24) Dickman, R., J.Chem.Phys. 87, 2246 (1987).Google Scholar
(25) Dickman, R., J.Chem.Phys. 91, 454 (1989).CrossRefGoogle Scholar