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Macromolecular dimensions obtained by an efficient Monte Carlo method without sample attrition

J. Chem. Phys. 63, 4592 (1975); doi:10.1063/1.431268

Issue Date: 1 December 1975

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Frederick T. Wall and Frederic Mandel
William Marsh Rice University, Houston, Texas 77001
The statistical dimensions of macromolecular chains of fixed contour length can be rapidly calculated by Monte Carlo methods applied to a model consisting of dynamic self-avoiding random chains on a lattice. This ''slithering snake'' model involves moving the head of a chain one space in a lattice with all other elements of the chain moving forward along the old contour. Possible moves of the head are selected at random, but if such a move is precluded by double occupancy, the old configuration is retained, with head and tail interchanged, and then counted as if a move were made. This technique gives unbiased statistical results except for the effect of double cul-de-sacs. The method can also be applied to interacting chains, either free or confined to a box. Calculations have been made for 10-link chains on a square planar lattice for two different concentrations in infinite space and for two concentrations in a small box. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
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PACS

  • 05.50.+q
    Statistical physics and thermodynamics Lattice theory and statistics; Ising problems
  • 36.30.Ba
    Studies of special atoms and molecules Polymers Stochastic models of polymer structure
  • YEAR: 1975

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
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REFERENCES (9)

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  1. F. T. Wall and J. Erpenbeck, J. Chem. Phys. 30, 634 (1959).
  2. F. T. Wall, S. Windwer, and P. J. Gans, J. Chem. Phys. 38, 2220 (1963).
  3. P. Gans, J. Chem. Phys. 42, 4159 (1965).
  4. Z. Alexandrowicz, J. Chem. Phys. 51, 561 (1969).
  5. S. D. Stellman and P. J. Gans, Macromolecules 5, 516 (1962).
  6. R. Grishman, J. Chem. Phys. 58, 220 (1973);
  7. 58, 5309 (1973).
  8. J. Curro, J. Chem. Phys. 61, 1203 (1974).
  9. From results to be published later by F. T. Wall and R. A. White.
  10. The 90% confidence limits were computed by multiplying the standard deviation of the mean by 1.645. The standard deviation of the mean was estimated by dividing the standard deviation of the N data points by sqrt(N). See for example, P. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1954).

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