Isotropic instabilities

As this class of electrohydrodynamic phenomena is observed in the isotropic phase as well, the mechanism of its excitation is also called isotropic. Roughly speaking, a liquid crystal optically develops and makes visible isotropic instabilities, and the corresponding optical patterns reflect specific properties of the liquid crystal. 

Isotropic instabilities in homeotropic nematic with large positive Ae (Sec. 5.2.10)... 

The first model of membrane electroporation was suggested by Crowley [1]. In Crowley s model the membrane is viewed as the isotropic elastic material. The necessary background for understanding its voltage-induced instability was discussed in Section II. Crowley s approximation for the elasticity energy term in Eq. (7) is... 

Let us examine the instability oi strained thin films. In Fig. 3, thin films of30 ML are coherently bonded to the hard substrates. The film phase has a misfit strain, e = 0.01, relative to the substrate phase, and the periodic length is equal to 200 a. The three interface energies are identical to each other = yiv = y = Y Both phases are elastically isotropic, but the shear modulus of the substrate is twice that of the film (p = 2p). On the left-hand side, an infinite-torque condition is imposed to the substrate-vapor and film-substrate interfaces, whereas torque terms are equal to zero on the right. In the absence of the coherency strain, these films are stable as their thickness is well over 16 ML. With a coherency strain, surface undulations induced by thermal fluctuations become growing waves. By the time of 2M, six waves are definitely seen to have established, and these numbers are in agreement with the continuum linear elasticity prediction [16]. 

Similarly, charged solid particles (such as latex spheres) —kinetically stable lyophobic colloids —may exist in colloidal crystalline phases (with body-centered or face-centered cubic structures) as a consequence of thermodynamically favored reduction in free energies (see Chapter 13). Even neutrally charged spherical particles ( hard spheres ) undergo a phase transition from a liquidlike isotropic structure to face-centered cubic crystalline structures due to entropic reasons. In this sense, the stability or instability is of thermodynamic origin. 

Swelling of Spherical Gels. Let us examine kinetics of the macroscopic instability at K = 0 in more details in a spherical gel with radius R immersed in solvent at zero osmotic pressure [18, 21, 46-49]. This should be appropriate because previous theories made no clear distinction between the two points, K = 0 and K + p = 0 [46-48]. The gel expands isotropically and the displacement vector u is assumed to be of the form,... 

In Fig. 7, we display Sc versus c. The gel surface is unstable in the region 8 <8C against the surface disturbances, because they decrease the free energy. Surprisingly, even in the isotropic case <5=1, the surface instability occurs at negative... 

Liquid crystals, as the name implies, are condensed phases in which molecules are neither isotropically oriented with respect to one another nor packed with as high a degree of order as crystals they can be made to flow like liquids but retain some of the intermolecular and intramolecular order of crystals (i.e., they are mesomorphic). Two basic types of liquid crystals are known lyotropic, which are usually formed by surfactants in the presence of a second component, frequently water, and thermotropic, which are formed by organic molecules. The thermotropic liquid-crystalline phases are emphasized here they exist within well-defined ranges of temperature, pressure, and composition. Outside these bounds, the phase may be isotropic (at higher temperatures), crystalline (at lower temperatures), or another type of liquid crystal. Liquid-crystalline phases may be thermodynamically stable (enantiotropic) or unstable (monotropic). Because of their thermodynamic instability, the period during which monotropic phases retain their mesomorphic properties cannot be predicted accurately. For this reason it is advantageous to perform photochemical reactions in enantiotropic liquid crystals. 

Fig. 2.42 Spinodal lines for a random multiblock copolymer melt of variable X (Fredrickson el al. 1992). On cooling a melt with X > AL —0.268, the first instability is predicted to be phase separation into two homogeneous liquid phases (x = %m)- On further cooling to % = the two liquid phases become unstable with respect to formation of a microphase. In contrast, a melt with X < XL first becomes absolutely unstable to the formation of microphases (x = fom)- At the critical composition of /= j, the point (AL, Xi) is an isotropic Lifshitz point.

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

Again, as with any RPA approach, this predicts an instability in the channel with the most negative V (Q0, ) In the case of the classical crossover, the RPA susceptibility is still given by Eq. (33) and corresponds to an isotropic interacting systems. 

When the temperature is further lowered below the 0 point, the density of rods in the isotropic globule increases, the instability of the metastable phase becomes more pronounced and finally the macromolecule undergoes the transition to the liquid-crystalline state. 

Experimental results (12) showed a transition to a lamellar liquid crystal for 14 added water molecules. Our calculations (to be reported at a later occasion) showed no discontinuity or any other indication of instability of the soap/acid water complex for the subsequent water molecules added in excess of 14. It appears reasonable to assume that the isotropic liquid/liquid crystal transition does not depend on the energy levels of the polar group interactions. The phase transition probably depends on the hydrophobic/hydrophilic volume ratio and estimations according to Israelachvili/Ninham (15) approach may offer a better potential for an understanding. 

Two-dimensional images of (Plane) Laser Induced Fluorescence (PLIF) have been used to study the turbulent mixing process in a vessel equipped with the Rushton turbine [654]. Particular attention has been paid to the bulk and to the stirrer stream regions at P/pV = 0.3 and 0.7 W/kg. The averaged concentration fields show a common two-dimensional steady circulation pattern. The probability density functions of concentration reflect well the instability of the flow in the two regions investigated and the non-isotropic distribution of these instabilities around the reference point when the feed port is situated in the bulk region only. 

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