Nematic phase attractive forces

An exception to the mle that lowering the temperature causes transitions to phases with iacreased order sometimes occurs for polar compounds which form the smectic phase. Decreasiag the temperature causes a transition from nematic to smectic but a further lowering of the temperature produces a transition back to the nematic phase (called the reentrant nematic phase) (22). The reason for this is the unfavorable packing of the molecules ia the smectic phase due to overlap of the molecules ia the center of the layers. As the temperature is lowered, the steric iateractions overpower the attractive forces, causiag the molecules to pack much more favorably ia the nematic phase. The reentrant nematic phase can also be produced from the smectic phase by iacreasiag the pressure (23). 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

The virial expansion has enjoyed greater appeal, especially as applied to lyotropic systems. Onsager s classic theory rests on analysis of the second virial coefficient for very long rodlike particles. It was the first to show that a solution of hard, asymmetric particles such as long rods should separate into two phases above a threshold concentration that depends on the axial ratio of the particles. One of these phases should be anisotropic (nematic), the other completely isotropic. The former is predicted to be somewhat more concentrated than the latter, but it is the alignment (albeit imperfect) of the solute molecules that is the predominent distinction. The phase separation is a consequence of shape asymmetry alone intervention of intermolecular attractive forces is not required. 

The theory predicts that the handedness of cellulosic liquid crystalline solutions, designated by the sign of the pitch, depends not only on temperature (T) and on steric repulsion of the chain X), but also on an attractive interaction parameter, %, which depends on the nature of the solvent. The chiral forces are balanced when (x XkT) = 0. In this compensated condition, the pitch of the mesophase should become infinite, and the mesophase resembles a normal nematic phase. 

There are basically two possible scenarios for the behavioxir of this prenematic mean field force when the separation between surfaces is reduced, and both depend on the degree of the surface-induced nematic order. For low surface-induced order, the magnitude of the attractive force just increases when approaching the isotropic-nematic phase transition from above. On the other hand, if a surface induces a high degree of LC orientation, the prenematic phase can spontaneously transform into the nematic phase, when the separation is decreased below a certain value. This is the nematic capillary condensation, that is discussed further on in this Chapter. 

A typical force measurement that indicates the presence of the electrostatic force, is presented in Fig. 7.13. Here, the force between a silanated 10 /rm glass sphere and a flat surface of a silanated glass plate is measured in the isotropic phase of 8CB at a temperature 7.1 K above the phase transition temperature into the nematic phase (Tni). A very strong repulsive force can be observed. As one can see from the inset, this force decreases exponentially with increasing separation and can be detected even at a separation of 300 nm. At smaller separations of 20 nm, we have observed an attractive force, which is a result of the capillary condensation of the partially ordered isotropic Uquid crystal into the developed nematic phase, as already reported [58]. The exponentially decaying repulsive force showed no temperature dependence in a wide range of temperatures above the nematic to isotropic phase transition temperature. 

Fig. 8.11. (a) Structural force per unit area in a heterophase paranematic (thick lines) and nematic system with molten boundary layers (thin lines). Solid lines correspond to the force in the nematic phase and dashed lines to the force in the isotropic phase. For the thicknesses above the corresponding verticals the isotropic (paranematic) or nematic phase is stable, respectively. The force is short-range and attractive, (b) Structural presure in the hybrid nematic system in a biaxial structure (solid line) and bent-director structure (dashed line). In both cases the interaction is long-range and repulsive. 

Recently it has been shown that surface-induced molecular orientation can be determined by atomic force microscopy (AFM), both in the isotropic and nematic phase of thermotropic liquid crystals [6-10]. At separations of several nanometers between the homeotropically modified glass surface and the AFM tip or homeotropically modified glass microsphere, respectively, a temperature-dependent short-range attractive (prenematic) or on average repulsive, but oscillatory, (presmectic) force was observed [6,7,9]. 

Luckhurst and Simmonds" employed a new parametrization of the Gay-Berne potential that allowed more details of the liquid crystal behavior to be revealed. The main result was that the isotropic and nematic phases are dominated by short-range anisotropic forces, whereas the stability of the smectic A phase depends critically on the anisotropy of the attractive forces. The use of the Gay-Berne potential was criticized by others because it is too simple to find out how the particular molecular... 

For a numerical calculation, we introduce the temperature parameter t defined by t = llxi=k TfUo). We then have four parameters characterizing our systems itp, the number of segments on a flexible polymer n, the number of segments on a liquid crystal Xa. the attractive interaction (Maier-Saupe) parameter between liquid crystals x = lA, the polymer-liquid crystal interaction (Flory-Huggins) parameter whose the origin is the dispersion forces. We here define the nematic interaction parameter a = Xa/X-From Eq. (3), we can obtain the values of the order parameter S(t, < ) related to a certain temperature r and concentration (p. The nematic phase appears at fo(l- ) = 4.55 in Eq.(3) [15]. We then obtain the nematic-isotropic transition (NIT) temperature (tni) as a function of the polymer concentration 0 ... 

Theoretical treatments of liquid crystals such as nematics have proved a great challenge since the early models by Onsager and the influential theory of Maier and Saupe [34] mentioned before. Many people have worked on the problems involved and on the development of the continuum theory, the statistical mechanical approaches of the mean field theory and the role of repulsive, as well as attractive forces. The contributions of many theoreticians, physical scientists, and mathematicians over the years has been great - notably of de Gennes (for example, the Landau-de Gennes theory of phase transitions), McMillan (the nematic-smectic A transition), Leslie (viscosity coefficients, flow, and elasticity). Cotter (hard rod models), Luckhurst (extensions of the Maier-Saupe theory and the role of flexibility in real molecules), and Chandrasekhar, Madhusudana, and Shashidhar (pre-transitional effects and near-neighbor correlations), to mention but some. The devel-... 

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