Fluctuations pretransitional

We may also predict pretransitional enhancement of the height fluctuation. By assuming that ( ) has the profile of the Rayleigh wave, we may calculate the excess free energy in terms of the height deviation h, Eq. (7.3), in the form,... 

Frenkel, J. A general theory of heterogenous fluctuations and pretransition phenomena. J. Chem. Phys. 7, 538—547 (1939). 

In practice there are three main difficulties in the use of this technique. The 2kF and 4kF scattering is not observed in all materials or at all temperatures. Fortunately, pretransitional effects (one-dimensional fluctuations) are often observed in a wide temperature range above Tc [114]. Second, the corresponding scattering is often very weak and requires special measurement techniques. For example, in the case of TTF-TCNQ, the intensity of 2kF satellites is 10 4 that of main reflections and the onedimensional scattering at 60 K is a further 10 2 to 10 3 weaker [133]. Third, to get p, one must decide whether the observed instability occurs at the 2kF or at the 4kF electronic wave vector. 

From a fitting to the Bonner-Fisher law, a value for /eff/fcB can be estimated to be on the order of 130 K, constant from 300 to 100 K, with enhancement below this temperature. It is interesting to notice that this temperature (100 K) corresponds to the appearance of the 2diffuse lines. The behavior of the susceptibility below 100 K could be attributed to pretransitional spin-Peierls fluctuations, with a depression on the xmiu(j ) as observed in (BCPTTF)2AsF6 (Fig. 3). 

The characteristic behavior described above is particularly well observed with the salts of the last series. For instance, for the representative salt (BCPTTF)2PF6 [46], pretransitional structural fluctuations are found by x-rays to exist on cooling from Tp = 100 K to TsP = 37 K, these fluctuations being almost one-dimensional between 100 and 50 K. The magnetic susceptibility of this salt with regular behavior fits well the Bonner-Fisher law at high T, with J = 165 K, and it starts to deviate appreciably from this law below 100 K, that is, well above Tsp-... 

In a very recent calculation by Markwick et al. targeted molecular dynamics methods were implemented in the framework of Car-Parinello molecular dynamics to study the nature of the double proton transfer [48]. They predict a concerted proton transfer reaction. In the very early stages of this reaction the system enters a vibrationally excited pretransitional state. Whereas in the global minima large amplitude fluctuations have been found in the pretransitional region, the frequency of these fluctuations is found to increase dramatically while the amplitude of the oscillation decreases when approaching the transition state. 

Our illustration of pretransitional behavior in frustrated NLC systems is restricted to fluctuations in the biaxial structure of the hybrid nematic cell with equal strengths of homeotropic and planar anchorings. The detailed analysis of the pretransitional dynamics of all five degrees of freedom around the bent-director configuration is somewhat more complicated because of the nonuniformity of the base tensors. 

In the nearest proximity around the binodal, there appear critical phenomena with their characteristically high level of correlated fluctuations of the order parameter (density for a substance or component concentration for a mixture ). By virtue of the universality principle, the properties of such fluctuations arc similar for both a one-component liquid-vapour system, a solution of low-molecular compounds, and a polymer solution. The critical phenomena in these systems aj e discussed iii this book in detail. The question as to the absence of any pretransition phenomena necir the liquidus is discussed as well. 

If the apparatus operates in a linear and repeatable manner, desmearing according to the convolution integral is an exact method capable of producing the true heat flow rate of the respective sample. Figure 6.23 illustrates this in the case of the melting curve of octadecane on the basis of a measured curve obtained by means of a DSC. The increase of the resolution in temperature is obvious and shows the pretransition more clearly, whereas the fluctuations (noise Ag) of the desmeared heat flow rate function increase accordingly . 

De Gennes explained the pretransitional orientation fluctuations in nematic systems in terms of a phenomenological treatment as far as thermodynamic and structural... 

The pretransitional fluctuation model assumed that BPIII is simply a manifestation of pretransitional fluctuations in the isotropic phase at the blue phase-isotropic boundary [3], [4], This idea was discounted [56] by the fact that the observed BPIII scattering [53] is several orders of magnitude too large for pretransitional fluctuations. In any case, the calorimetry data [26] rule out the pretransitional fluctuation model. 

These results are in line with others obtained by different - but less direct-techniques applied to unilamellar systems. For instance, ultrasound propagation and attenuation were found continuous at [12] and a critical slowing down of membrane relaxation was obseiwed [13]. Pretransitional phenomena in L, pha near are correlated to structure fluctuations in the form of gel-like domains, of finite size and lifetime, and whose existence was experimentally detected by fluorescence spectroscopy [14]. 

Collective motions are elastic deformations in liquid crystalline samples, but can also exist in their isotropic phases with a finite coherence length, giving rise to pretransitional phenomena [6.2]. These motions are perceived as hydrodynamic phenomena and are influenced by molecular properties such as elastic constants and viscosities of the liquid crystalline medium. At best, director fluctuations can only provide indirect information on the anisotropic intermolecular interactions. On the contrary, motion on a molecular level must reflect the shape of the instantaneous potential of mean torque on each molecule. Both both molecular rotation and translation are expected to be sensitive to the nature of anisotropic interactions, which determine the formation of various liquid crystalline structures. 

When a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These pretransitional fluctuations were called cybotactic clusters in the early literature (Fig. 5.21). Regardless of a physical picture of such fluctuations, it has been observed that the cluster size grows as the transition is approached. Furthermore, these clusters are anisotropic, being elongated along the director. They also grow faster along this direction as the transition is approached from above. 

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.

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