Lattice Models for Thermotropic Liquid Crystals

References

• Maier , W. and Saupe , A. 1959 . Z. Naturforsch. , 14a : 882 15a, 287 (1960)
   Google Scholar
• Deloche , B. , Cabane , B. and Jerome , D. 1971 . Mol. Cryst., Liquid Cryst. , 15 : 197
   Web of Science ®Google Scholar
• McColl , J. R. and Shih , C. S. 1972 . Phys. Rev. Letters , 29 : 85
   Web of Science ®Google Scholar
• Humphries , R. L. , James , P. G. and Luckhurst , G. R. 1972 . Faraday Soc. Transactions II , 68 : 1031
   Web of Science ®Google Scholar
• Chandrasekhar , S. and Madhusudana , N. V. 1971 . Acata Cryst. , A27 : 303
   Google Scholar
• McMillan , W. L. 1971 . Phys. Rev. A. , 4 : 1238
   Web of Science ®Google Scholar
• Lee , F. T. , Tan , H. T. , Shih , Y. M. and Woo , C. 1973 . Phys. Rev. Letters , 31 : 1117
   Web of Science ®Google Scholar
• Miyakawa , K. , Hijikuro , N. and Mori , H. 1974 . J. Phys. Soc. Japan , 36 : 944
   Google Scholar
• Meyer , R. J. and McMillan , W. L. 1974 . Phys. Rev. A. , 9 : 899
   Web of Science ®Google Scholar
• Marčelja , S. 1974 . J. Chem. Phys. , 60 : 3599
   Web of Science ®Google Scholar
• Flory , P. J. 1969 . Statistical Mechanics of Chain Molecules , New York : Interscience . Chapter III
   Google Scholar
• Zwanzig , R. 1963 . J. Chem. Phys. , 39 : 1714
   Web of Science ®Google Scholar
• Runnels , L. K. and Colvin , C. 1970 . J. Chem. Phys. , 53 : 4219
   Web of Science ®Google Scholar
• Cotter , M. A. and Martire , D. E. 1970 . J. Chem. Phys. , 53 : 4500
   Web of Science ®Google Scholar
• Lasher , G. 1970 . J. Chem. Phys. , 53 : 4141
   Web of Science ®Google Scholar
• Cotter , M. A. 1974 . Phys. Rev. A. , 10 : 625
   Web of Science ®Google Scholar
• Timling , K. M. 1974 . J. Chem. Phys. , 61 : 465
   Web of Science ®Google Scholar
• Flory , P. J. 1956 . Proc. Roy. Soc. (London) , A234 : 73
   Web of Science ®Google Scholar
• DiMarzio , E. A. 1961 . J. Chem. Phys. , 35 : 658
   Web of Science ®Google Scholar
• Cotter , M. A. and Martire , D. E. 1969 . Mol. Cryst., Liquid Cryst. , 7 : 295
   Web of Science ®Google Scholar
• Alben , R. 1971 . Mol. Cryst., Liquid Cryst. , 13 : 193
   Web of Science ®Google Scholar
• Wulf , A. and DeRocco , A. G. 1971 . J. Chem. Phys. , 55 : 12
   Web of Science ®Google Scholar
• Ågren , G. and Martire , D. E. 1974 . J. Chem. Phys. , 61 : 3959
   Web of Science ®Google Scholar
• Flory , P. J. 1942 . J. Chem. Phys. , 10 : 51 When determining the Vn + 1 's one assumes that all the rods are distinguishable, then accounts for the indistinguishability of rods pointing in the same direction by dividing by . DiMarzio19 evaluated the product by adding first the N1 rods in orientation 1, then the N2 rods in orientation 2, then the N3 rods in orientation 3. It can be shown, however, that the result does not depend on the order in which the rods are added.
   Google Scholar
• Hill , T. L. 1956 . Statistical Mechanics , New York : McGraw-Hill . Section 46
   Google Scholar
• Flory , P. J. 1953 . Principles of Polymer Chemistry , Ithaca, New York : Cornell University Press . Chapter XII
   Google Scholar
• Fowler , R. H. and Guggenheim , E. A. 1940 . Proc. Roy. Soc. (London) , A174 : 189
   Google Scholar
• The very large density discontinuities at the N → I transition can be decreased somewhat by increasing the pressure on the system. The “price” one pays, however, is that T trans rises considerably more rapidly with increasing lenght-to-breadth ratio x
   Google Scholar
• Saupe , A. 1968 . Angew. Chem. Intern. Ed. (English) , 7 : 97 The order parameter n is most commonly measured by means of proton magnetic resonance, since uniformly oriented nematic samples can be produced by modest magnetic fields and the direct proton-proton couplings obtained are proportional to n. Saupe. has summarized and discussed experimentally determined order parameters for common nematic liquids.
   Web of Science ®Google Scholar
• Gray , G. W. 1962 . Molecular Structure and the Properties of Liquid Crystals , New York : Academic Press . Chapter VIII
   Google Scholar
• Luz , Z. and Meiboom , S. 1973 . J. Chem. Phys. , 59 : 275 Z. Luz, R. C. Hewitt, and S. Meiboom, J. Chem. Phys., 61, 1758 (1974). In the quasi-chemical as well as the Bragg-Williams approximation, the system boils from an ordered state (the nematic state when wa = wi) when atmospheric pressure and reasonable segmental attractive energies are used.
   Web of Science ®Google Scholar
• Cotter , M. A. (unpublished). The same qualitative results are also obtained when an anisotropic free energy term - Wa(VoP)n2/k T is added to the isotropic Van der Waals term, both when Wa and Wi are assumed to be independent of x and when they are taken to be proportional to x
   Google Scholar
• Peterson , H. T. , Martire , D. E. and Cotter , M. A. 1974 . J. Chem. Phys. , 61 : 3547
   Web of Science ®Google Scholar
• Ågren , G. and Martire , D. E. 1975 . J. Phys. , 36 : Cl – 141 .
   Google Scholar
• Peterson , H. T. and Martire , D. E. 1974 . Mol. Cryst., Liquid Cryst. , 25 : 89
   Web of Science ®Google Scholar
• Prigogine , I. 1957 . The Molecular Theory of Solutions , Amsterdam : North Holland . (with the collaboration of V. Mathot and A. Bellemans)
   Google Scholar
• In this vein, Miyakawa, Hijikuro, and Mori8 studied a model system of rods of length-to-breadth ratio two (with anisotropic intermolecular attractions and repulsions) on a simple cubic lattice and observed four different phases corresponding to the gas, isotropic liquid, nematic and smectic phases. Becuase of their use of interleaved sublattices to define a smectic translational order parameter, however, their approach would be quite difficult to extend to longer rods.
   Google Scholar
• Lin , G. C. 1975 . Doctroral Dissertation Georgetown University .
   Google Scholar