Pretransitional phenomena

A characteristic property of polymer mixtures in the homogeneous phase is the increase of the concentration fluctuations accociated with an approaching of the point of unmixing. A similar behavior is found for the homogeneous phase of block copolymers, and a first example is given in Fig. 3.42. The figure shows scattering functions measured for a polystyrene-6/ocfc-polyisoprene under variation of the temperature. The temperature of the transition to the 

The general shape of the scattering curve, showing a maximum at some max and going to zero for 0 is conceivable. As explained in Sect. A.3.2 

Rq denotes the mean-squared end-to-end distance of the block copolymer, given by 

With regard to the effect of x Eq. (3.213) is equivalent to Eq. (3.165). Indeed, the physical background of both equations is similar, and they are obtained in equal manner, by an application of the random phase approximation (RPA) . The interested reader can find the derivation in Sect. A.4.1 in the Appendix. 

This is the lowest possible value and the one mentioned earlier in Eq. (3.196). 

The feature in common with the polymer mixtures is the intensity increase however, we can also see a characteristic difference The maximum of 

In polymer mixtures, one calls the curve of points in the phase diagram, where S q = 0) apparently diverges, the spinodal. One can use the same notion for block copolymers and determine this curve in an equal manner by a linear extrapolation of scattering data measured in the homogeneous phase. We again denote this spinodal by Tsp (j)). 

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V.G. Pushin and V.V. Kondrat ev, Pretransition phenomena and martensitic transformations, Phys. Met. 

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

DuPre DB (1982) Techniques for the evaluation of material constants in lyotropic systems and the study of pretransitional phenomena in polymer liquid crystals. In Ciferri A, Krigbaum WR, Meyer RB (eds) Polymer liquid crystals. Academic Press, New York... 

The investigations of solid-liquid crystal interaction by SHG are not only restricted to LG monolayers and thin films. As most of the bulk liquid crys-talhne phases are centrosymmetric, the surface SHG response can be detected also from thick liquid crystal cells , in which the material is sandwiched between two substrates. By this kind of measurements it is possible to study a relation between the bulk and the surface liquid crystalline ordering and consequently probe various pretransitional phenomena and other surface related effects. 

Here we shall give two examples of the pretransitional phenomena. Though a rigorous calculation is possible using the kinetic equation (10.39), we shall use the approximate kinetic equation (10.48) for convenience of demonstration. 

This is a chiral smectic A with symmetry Dqo. Its properties are similar to those of the achiral SmA. However, close to the transition to the smectic C phase, the chiral smectic A phase shows interesting pretransitional phenomena in the dielectric and electrooptical effects (the so-caUed soft dielectric mode and electroclinic effect). They will be discussed in Chapter 13. 

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. 

A study of the miscibility of liquid crystals is of great importance from two points of view [31]. First, mixtures manifest a variety of phases separated by phase transition lines. Varying the composition of a mixture, we can study the interaction of different structural modes (the interaction of order parameters), investigate various pretransitional phenomena [32], etc. Mixing an unknown substance with a compound having well-defined phases we can also identify the structure of the unknown substance. On the other hand, mixtures are extremely important from the technological point of view. The best liquid crystalline materials for displays are, as a rule, multicomponent mixtures with a wide temperature range of operation. Here, the problem is to compose a thermodynamically stable eutectic mixture. 

Equation (1.8) has been shown to be true for several cholesterol derivatives in the absence of pretransitional phenomena [12]. 

The isotropic phase of nematogens differs from conventional isotropic liquids in two aspects. First, the pretransitional phenomena in the vicinity of the clearing point dramatically change the bulk properties (in particular, the Kerr constant) of the isotropic phase due to the short-range nematiclike order. Second, quasi-nematic surface layers form at the interface with a solid substrate. Due to their dielectric (and optical) anisotropy they can contribute to the electrooptical properties of cells filled with the isotropic phase. For example, they can be reoriented by an external field (an analogy with the Frederiks transition). We will discuss briefly both phenomena. 

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. 

This and other mesoscopic theories assume that the molecules consist of rigid rods or ellipsoids, that a special form of the interaction potential is valid and that there are no pretransitional phenomena due to a smectic phase. As real liquid crystal molecules do not show such properties these theories only allow a very rough description of the experimental observations. A comparison between some theories has been presented by Kroger and Sellers [47]. 

Light scattering is a probe of molecular motions, and may be used effectively to study pretransitional phenomena. Stintson et al. [123] studied light scattered by order parameter fluctuations in MBBA. Their data follow the relationship ... 

T. W. Stinson, J. D. Litster, Pretransitional phenomena in the isotropic phase of a nematic liquid crystal, Phys. Rev. Lett. 1970, 25, 503. 

Cooling down from the disordered isotropic phase to the ordered blue phase an enhancement of the molecular optical rotation occurs as a result of short-range ordering. The chirality of the cholesteric liquid crystal gives rise to complex pretransitional phenomena. 

The order and dynamic behaviour of probes, revealed by suitable NMR techniques, have been used to study phase transitions and pretransitional phenomena. They are also useful for revealing segregation effects when highly ordered smectic or columnar discotic phases organize themselves, they may exclude added solutes or confine them in aliphatic or interlayer regions. 

The pretransition phenomena can also result in the appearance of a more gently sloping segment of curve t](c), as obsoved in [88, 89]. The increase w decrease in the rate of the increase in dependence tiCc) when c c is apparently determined by the morphology of the fluctuation formations when c c, which can be spherulitic in solutions of aromatic polyamides (indicated in the circles in Fig. 9.19) and fibrillar in solutions of polypeptides and polyisocyanates. 

In the vicinity of the phase transition temperature Tc, molecular correlations in liquid crystals give rise to interesting so-called pretransitional phenomena. This is manifested in the critical dependences of the laser-induced index change and the response time on the temperatiue. These critical dependences are described by... 

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