Abstract
Using the isothermal-isobaric ensemble, exact equations of state are derived for three classical models of one-dimensional chain fluids. Each chain molecule is modeled by a series of linked sites which interact through nearest-neighbor bond potentials. In two of the models, the intramolecular bonds are modeled by infinitely deep square-well potentials, while in the third, the bonds are modeled by a harmonic potential. Intermolecular interactions are modeled by a hard-rod potential. Numerical results are presented for dimer and 8-mer fluids which illustrate the influence of chain length, well width and spring constant on the compressibility factor. The effect of adding an infinitely weak, infinitely long-ranged attractive interaction between the sites is also considered. The attractive tail induces a first-order phase transition of the gas-liquid type in all of the chain models. For certain values of the model parameters, however, two of the models show evidence of a second gas-liquid type transition, which appears to be associated with chain collapse.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lord Rayleigh,Nature 45:80 (1891).
L. Tonks,Phys. Rev. 50:955 (1936).
H. Takahashi,Proc. Phys.-Math. Soc. Japan (Nippon Suugaku-Buturigakkausi Kizi, Tokyo)24:60 (1942) [reprinted in ref. 5].
F. Gürsey,Proc. Camb. Phil. Soc. 46:182 (1950).
E. H. Lieb and D. C. Mattis,Mathematical Physics in One Dimension (Academic, New York, 1966), pp. 3–24.
P. Kasperkovitz and J. Reisenberger,Phys. Rev. A 31:2639 (1985).
A. Robledo and J. S. Rowlinson,Mol. Phys. 58:711 (1986).
A. Münster,Statistical Thermodynamics (Springer-Verlag, Berlin, 1969), Vol. I, pp. 292–316.
D. Koppel,Phys. Fluids 6:609 (1963).
R. S. Northcote and R. B. Potts,Phys. Fluids 7:475 (1964).
R. H. Walmsley,J. Chem. Phys. 88:4473 (1988).
M. Kac,Phys. Fluids 2:8 (1959).
G. Baker,Phys. Rev. 122:1477 (1961).
M. Kac, G. Uhlenbeck, and P. Hemmer,J. Math. Phys. 4:216 (1963) [reprinted in ref. 5].
L. Van Hove,Physica 16:137 (1950) [reprinted in ref. 5].
J. M. Kincaid, G. Stell, and C. K. Hall,J. Chem. Phys. 65:2161 (1976).
M. Bishop and M. A. Boonstra,Am. J. Phys. 51:564 (1983).
J. A. Barker,Aust. J. Phys. 15:127 (1962).
C. N. Satterfield,Heterogeneous Catalysis in Practice (McGraw-Hill, New York, 1980), pp. 164–177, 244–247, 258–259.
T. A. Weber,J. Chem. Phys. 69:2347 (1978);70:4277 (1979).
E. Helfand, Z. R. Wasserman, and T. A. Weber,J. Chem. Phys. 70:2016 (1979); E. Helfand, Z. R. Wasserman, and T. A. Weber,Macromolecules 13:526 (1980).
A. Warshel and S. Lifson,J. Chem. Phys. 53:582 (1970).
J.-P. Ryckaert and A. Bellemans,Chem. Phys. Lett. 30:123 (1975); J.-P. Ryckaert and A. Bellemans,Faraday Disc. Chem. Soc. 66:95 (1978); D. W. Rebertus, B. J. Berne, and D. Chandler,J. Chem. Phys. 70:3395 (1979); J. H. R. Clarke and D. Brown,Mol. Phys. 58:815 (1986); P. A. Wielopolski and E. R. Smith,J. Chem. Phys. 84:6940 (1986); R. Edberg, G. P. Morriss, and D. J. Evans,J. Chem. Phys. 86:4555 (1987); G. Maréchal, J.-P. Ryckaert, and A. Bellemans,Mol. Phys. 61:333 (1987).
G. Ciccotti and J.-P. Ryckaert,Comp. Phys. Rep. 4:345 (1986).
J.-P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen,J. Comp. Phys. 23:327 (1977); W. F. van Gunsteren and H. J. C. Berendsen,Mol. Phys. 34:1311 (1977); R. Edberg, D. J. Evans, and G. P. Morriss,J. Chem. Phys. 84:6933 (1986).
D. C. Rapaport,J. Phys. A 11:L213 (1978).
D. C. Rapaport,J. Chem. Phys. 71:3299 (1979).
G. A. Chapela, S. E. Martinez-Casas, and J. Alejandre,Kinam (Mexico)A 6:143 (1984); G. A. Chapela, S. E. Martinez-Casas, and J. Alejandre,Mol. Phys. 53:139 (1984); J. Alejandre and G. A. Chapela,Mol. Phys. 61:1119 (1987).
G. A. Chapela and S. E. Martinez-Casas,Mol. Phys. 59:1113 (1986).
B. J. Alder and T. E. Wainwright,J. Chem. Phys. 31:459 (1959).
D. J. Tildesley and W. B. Streett,Mol. Phys. 41:85 (1980).
A. Bellemans, J. Orban, and D. Van Belle,Mol. Phys. 39:781 (1980).
W. W. Wood,J. Chem. Phys. 48:415 (1968).
T. L. Hill,Statistical Mechanics (Dover, New York, 1987), pp. 59–80.
R. A. Sack,Mol. Phys. 2:8 (1959).
W. B. Brown,Mol. Phys. 1:68 (1958).
M. Abramowitz and I. A. Segun,Handbook of Mathematical Functions (Dover, New York, 1968), p. 298.
D. A. McQuarrie,Statistical Mechanics (Harper & Row, New York, 1976), p. 95.
L. Pauling,The Nature of the Chemical Bond, 3rd ed. (Cornell, Ithaca, New York, 1960), pp. 225–228.
J. L. Lebowitz and O. Penrose,J. Math. Phys. 7:98 (1966).
K. Huang,Statistical Mechanics, 2nd ed. (Wiley, New York, 1987), pp. 41–43.
C. K. Hall and G. Stell,Phys. Rev. A 7:1679 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Honnell, K.G., Hall, C.K. Exact equations of state for one-dimensional chain fluids. J Stat Phys 61, 803–842 (1990). https://doi.org/10.1007/BF01027302
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01027302