Divergence pretransitional

As a rule, the phase transition from the isotropic phase into the nematic phase is a weak first-order transition [6] with a small jump in the order parameter 5 (Fig. 1.3 [7]) and other thermodynamic properties. The so-called clearing point corresponds to this first-order transition temperature Tni. At the same time, in the pretransitional region of the isotropic phase we can observe the temperature divergence in some physical parameters, such as heat capacity, dielectric permittivity, etc., according to the power law (T — T i) where T j is the other, virtual, second-order phase transition point, (Tni — T 0.1 K) and t) is an exponent, depending on the physical property under consideration. 

Figure 1. Schematic variation of the enthalpy H and specific heat capacity Cp with temperature T for transitions (at T ) that are (a) strongly first-order, (b) weakly first-order with pretransitional fluctuation behavior, (c) mean-field second-order (CP indicates the critical point on the enthalpy curve for the Landau second-order transition temperature Tc=T ), (d) and (e) are critical fluctuation dominated second-order transitions with a diverging (d) or large but finite (e) specific heat capacity at the critical temperature T =T . For the first-order transitions the latent heats AWl correspond with the steps in H(T) at T=T . 5W represent the fluctuation induced enthalpy change associated with the phase transition.

The variety of data on this homologuous series allows for a comparison of the reliability of different methods. Moreover, the octyl homologue (8-CB) [165-180] exhibits a nematic phase followed by a SmA phase and is therefore particularly interesting for the study of the critical divergence of the Kjj and K22 elastic coefficients on approaching the transition from the nematic to the SmA phase. Elastic coefficient measurements show that short-range pretransitional smectic-Uke order is found more or less in all n-CB homologues [98]. In Fig. 2a-c the elastic constants of the cyanobiphenyl series, as determined by Karat and Madhusu-... 

If there is a phase transition from a nematic to a smectic phase, pretransitional effects are observed in the neighbourhood of the transition [9, 44, 49-51]. Figure 10 [9] shows this behaviour for 4-/7-octyloxy-4 -cyanobiphenyl (80CBP) with a nematic-smectic phase transition at 340.3 K. Pretransitional effects cause a divergence of the shear viscosity coefficient 772 and the rotational viscosity /j. 

The curve for 4-n-pentyloxybenzylidene-4 - -butylaniline (50-4) shows some remarkable deviations from this course [56]. These are caused by pretransitional effects from a smectic phase at low temperatures. Due to these effects the range of flow alignment is limited to a small region below the clearing point. At lower temperatures the director begins to tumble and a viscosity between and % is observed. This leads to the pronounced minimum in the T curve for 50-4. A further deviation is caused by the divergence of rj at the transition to the smeetic phase. 

A divergence of the rotational viscosity is observed in the neighbourhood of transitions to smectic phases as the molecular rotation will be hindered by the pretransition-al formation of the smectic layer structure. Figure 10 shows this effect for 80CBP [9]. The divergence can be described by an equation similar to Eq. (35) [52-54] ... 

Pretransitional behavior of twist and splay elastic constants was also measured in CBOOA by Chu and McMillan [193]. The splay is not renormalized, whereas the twist elastic constant shows a mean-field like divergence. They also report slowing down of the twist mode near Tg, which is in apparent disagreement with both mean-field and helium-like models. A similar slowing down of the twist mode was observed by Delaye [118]. Pretransitional bend mode behavior is reported by Birecki and Litster... 

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