Advertisement

Il Nuovo Cimento D

, 7:717 | Cite as

Computer simulation study of a simple cubic dipolar lattice

  • S. Romano
Article

Summary

The present work reports Monte Carlo calculations on a classical simple cubic lattice, consisting of point dipoles with identical dipole moments. Dipolar interactions are known not to be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can thus be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with mean-field and spherical-model treatments of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics.

PACS. 05.50

Lattice theory and statistics Ising problems 

Riassunto

Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico cubico semplice, costituito da dipoli puntiformi con identico momento dipolare. È noto che le interazioni dipolari non sono essenziali per l’ordinamento nematico, ma esse possono avere un ruolo significantivo in alcuni casi specifici; lungo le linee dell’approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto essere considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelectrico ed, a temperature piú elevata, transisce ad una fase orientazionalmente disordinata; sono riportati per confronto i risultati delle trattazioni a campo medio, ed a modello sferico per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici.

Резюме

В работе предлагается моделирование по методу Монте-Карло классической простой кубической решетки, образованной точечными диполями с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематическояо упорядочения, но они игроют существенную роль в некоторых специфических случаях. Рассматриваемая система обладает антиферроэлектрическим основным состоянием и, при высокой темлературе, претерпевает переход в ориентационно упорядоченную фазу. Проводится сравнение с приближ=yeнием среднего поля и рассмотрением в рамках сферической модели этого перехода. Псследуутся структурные свойства, посредством вычисления ориентационных корреляционных функций. Обнаружены нектторые ксчественные различия по сравнению с другими потенциалыми моделями, ранее рассмотренными для описания нематики.

References

  1. (1).
    M. Lax:J. Chem. Phys.,20, 1351 (1952).MathSciNetCrossRefADSGoogle Scholar
  2. (2).
    J. Frenkel:Acta Phys.-Chim. USSR,3, 23 (1935).MATHGoogle Scholar
  3. (3).
    D. E. Sullivan, J. M. Deutch andG. Stell:Mol. Phys.,28, 1359 (1974).CrossRefADSGoogle Scholar
  4. (4).
    D. J. Adams andI. R. McDonald:Mol. Phys.,32, 931 (1976).CrossRefADSGoogle Scholar
  5. (5).
    T. Niemeyer:Physica (Utrecht),57, 281 (1972).CrossRefADSGoogle Scholar
  6. (6).
    G. Lasher:Phys. Rev. A,5, 1350 (1972).CrossRefADSGoogle Scholar
  7. (7).
    P. A. Lebwohl andG. Lasher:Phys. Rev. A,6, 426 (1972);7, 2222 (1973).CrossRefADSGoogle Scholar
  8. (8).
    G. R. Luckhurst andS. Romano:Mol. Phys.,42, 129 (1980).CrossRefADSGoogle Scholar
  9. (9).
    G. R. Luckhurst andS. Romano:Proc. R. Soc. London, Ser. A,373, 111 (1980).ADSCrossRefGoogle Scholar
  10. (10).
    R. L. Humphries, G. R. Luckhurst andS. Romano:Mol. Phys.,42, 1205 (1981).CrossRefADSGoogle Scholar
  11. (11).
    G. R. Luckhurst, S. Romano andP. Simpson:Chem. Phys.,73, 337 (1982).CrossRefGoogle Scholar
  12. (12).
    R. Eppenga andD. Frenkel:Mol. Phys.,52, 1519 (1984).CrossRefGoogle Scholar
  13. (13).
    H. J. F. Jansen, G. Vertogen andJ. G. J. Ypma:Mol. Cryst. Liq. Cryst.,38, 87 (1977).Google Scholar
  14. (14).
    C. Zannoni andM. Guerra:Mol. Phys.,44, 849 (1981).CrossRefADSGoogle Scholar
  15. (15)a).
    M. Born Sitzungsber. Phys.-Math.,25, 614 (1916),b)M. Born andE. Stumpf:Sitzungsber. Phys.-Math.,27, 1043 (1916).Google Scholar
  16. (16).
    A. J. Leadbetter:Structural studies of nematic, smectic A and smectic C phases, inThe Molecular Physics of Liquid Crystals, edited byG. R. Luckhurst andG. W. Gray (Academic Press, New York, N. Y., London, 1979), Chapt. 13.Google Scholar
  17. (17).
    F. Dowell:Phys. Rev. A,31, 3214 (1985).CrossRefADSGoogle Scholar
  18. (18).
    Ferroelectrics,58, 59 (1984).Google Scholar
  19. (19).
    R. B. Griffiths:Phys. Rev.,176, 655 (1968).CrossRefADSGoogle Scholar
  20. (20).
    E. R. Smith andJ. W. Perram:Phys. Lett. A,50, 294 (1974);b)E. R. Smith:Phys. Lett. A,53, 121 (1975);c)E. R. Smith andJ. W. Perram:J. Phys. A,8, 1130 (1975);d)E. R. Smith andJ. W. Perram:Mol. Phys.,30, 31 (1975).CrossRefADSGoogle Scholar
  21. (21)a).
    J. A. Sauer:Phys. Rev.,57, 142 (1940);b)J. M. Luttinger andL. Tisza:Phys. Rev.,70, 954 (1946).CrossRefADSGoogle Scholar
  22. (22).
    M. H. Cohen andF. Keffer:Phys. Rev.,99, 1118, 1135 (1955).MATHCrossRefADSGoogle Scholar
  23. (23).
    P. H. E. Meijer andD. J. O’Keeffee:Phys. Rev. B,1, 3786 (1970).CrossRefADSGoogle Scholar
  24. (24)a).
    T. Niemeyer andH. W. J. Blöte:Physica (Utrecht),67, 125 (1973);b)T. Niemeyer andP. H. E. Meyer:Phys. Rev. B,10, 2962 (1974).CrossRefADSGoogle Scholar
  25. (25).
    T. H. Berlin andM. Kac:Phys. Rev.,86, 821 (1952).MATHMathSciNetCrossRefADSGoogle Scholar
  26. (26).
    T. H. Berlin andJ. L. Thompsen:J. Chem. Phys.,20, 1368 (1952).MathSciNetCrossRefADSGoogle Scholar
  27. (27).
    R. Rosenberg andM. Lax:J. Chem. Phys.,21, 424 (1953).CrossRefADSGoogle Scholar
  28. (28).
    M. Lax:Phys. Rev.,97, 629 (1955).MATHMathSciNetCrossRefADSGoogle Scholar
  29. (29).
    R. A. Toupin andM. Lax:J. Chem. Phys.,27, 458 (1957).CrossRefADSGoogle Scholar
  30. (30).
    A. Aharony andM. E. Fisher:Phys. Rev. B,8, 3323 (1973).CrossRefADSGoogle Scholar
  31. (31).
    A. Aharony:Phys. Rev. B,8, 3342, 3349, 3358, 3363 (1973).CrossRefADSGoogle Scholar
  32. (32).
    I. A. Favorskii, P. N. Vorontsov-Vel’yaminov, G. V. Matvienko, E. M. Ushakova andN. B. Gromova:Ferroelectrics,21, 489 (1978).Google Scholar
  33. (33).
    R. Kretschmer andK. Binder:Z. Phys. B,34, 375 (1979).CrossRefADSGoogle Scholar
  34. (34).
    P. P. Ewald:Ann. Phys. (Paris),64, 253 (1921).MATHADSGoogle Scholar
  35. (35).
    H. Kornfeld:Z. Phys.,22, 27 (1924).CrossRefADSGoogle Scholar
  36. (36).
    M. P. Tosi:Solid State Phys.,16, 1 (1964).Google Scholar
  37. (37).
    C. S. Hoskins andE. R. Smith:Chem. Phys.,13, 33 (1976).CrossRefADSGoogle Scholar
  38. (38).
    S. W. de Leeuw, J. W. Perram andE. R. Smith:Proc. R. Soc. London, Ser. A,373, 27, 57 (1980).ADSGoogle Scholar
  39. (39).
    J. A. Barker andR. O. Watts:Chem. Phys. Lett.,3, 144 (1969).CrossRefADSGoogle Scholar
  40. (40).
    C. Zannoni:Computer simulations, inThe Molecular Physics of Liquids Crystals, edited byG. R. Luckhurst andG. W. Gray (Academic Press, New York, N. Y., London, 1979), Chapt. 9.Google Scholar
  41. (41).
    G. R. Luckhurst:Molecular field theories of nematics, inThe Molecular Physics of Liquids Crystals, edited byG. R. Luckhurst andG. W. Gray (Academic Press, New York, N. Y., London, 1979), Chapt. 4.Google Scholar
  42. (42).
    P. Weiss:J. Phys. (Paris),6, 667 (1907).Google Scholar
  43. (43).
    J. G. Kirkwood:J. Chem. Phys.,8, 205 (1940).CrossRefADSGoogle Scholar
  44. (44).
    J. H. van Vleck:J. Chem. Phys.,9, 85 (1941).CrossRefADSGoogle Scholar
  45. (45).
    T. J. Krieger andH. M. James:J. Chem. Phys.,22, 796 (1969).ADSCrossRefGoogle Scholar
  46. (46).
    R. L. Humphries, P. G. James andG. R. Luckhurst:J. Chem. Soc. Faraday, Trans. 2,68, 1031 (1972).CrossRefGoogle Scholar
  47. (47).
    C. Domb andR. Brout inMagnetism: a Treatise on Modern Theory and Materials, edited byG. T. Rado andH. Suhl (Academic Press, New York, N. Y., London, 1985).Google Scholar
  48. (48).
    A. J. Stone:Intermolecular forces, inThe Molecular Physics of Liquid Crystals, edited byG. R. Luckhurst andG. W. Gray (Academic Press, New York, N. Y., London, 1979), Chapt. 2.Google Scholar
  49. (49).
    P. Simpson: Ph.D. Thesis (University of Southampton, 1982).Google Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • S. Romano
    • 1
    • 2
  1. 1.Dipartimento di Fisica dell’Università «A. Volta»PaviaItalia
  2. 2.Unità G.N.S.M.C.N.R./C.I.S.M., M.P.I.PaviaItalia

Personalised recommendations