Leslie viscosities ratio

Using scattering and spectroscopy experiments, it has been shown that the physical quantities characterizing the wormlike micellar nematics such as the order parameter, Leslie viscosities ratio, or alignment angles can be determined. The main result of this section is the analogy between the wormlike micelles and the liquid-crystalline polymers, as far as their nematic states are concerned. Because these... 

The ratio of elastic constants Ku, calculated for the S-effect according to the equation (4) appeared to be (Kn (polymer XIV)/Kn (polymer XIII)) x 1 100 and (Ku (polymer XVI)/Kn (polymer XV)) x 1 36. Yet, as we have just indicated, taking into account molecular masses of the LC polymers and reducing k, values for various polymers to equal values of DP one may come to substantially different values for ratios of constants presented. It is necessary to note that up to date no quantitative data on the determination of elastic constants of LC polymers has been published (excluding the preliminary results on Leslie viscosity coefficients for LC comb-like polymer127)). Thus, one of the important tasks today is the investigation of elastic and visco-elastic properties of LC polymers and their quantitative description. 

Very few data exist for the viscosities or Frank constants of discotic nematics—that is, nematics composed of disc-Uke particles or molecules (Chandrasekhar 1992). One can estimate values of the Leslie viscosities from the Kuzuu-Doi equations (10-20) by setting the aspect ratio p equal to the ratio of the thickness to the diameter of the particles thus /j — 0 for highly anisotropic disks. This implies that R(p) —1, and Eq. (10-20b) implies that the viscosity o 2 is large and positive for discoidal nematics, while it is negative for ordinary nematics composed of prolate molecules or particles. If, as expected, is much smaller in magnitude than 0 2. the director (which is orthogonal to the disks) will tend... 

Here is a typical Leslie viscosity, AT is a Frank constant, V is a flow velocity, /i is a length scale of the flow geometry, such as the tube diameter in Poiseuille flow, and ftn is the average shear rate. The Ericksen number is the ratio of the flow-induced viscous stress 6Ye.fi = /h to the Frank stress K/h. The appropriate Leslie viscosity or Frank constant... 

With the Miesowicz technique one can measure three combinations of the Leslie viscosity coefficients from Eqs. (9.25) to (9.27). On account of the Parodi relationship, to find all five coefficients, one needs, at least, two additional measurements. In particular, the ratio of coefficients a3/a2 can be measured by observation of the director field distortion due to capillary flow of a nematic. The last combination yi = as — as can be found from the dynamics of director relaxation. 

A second requirement for this instability to occur is that the two Leslie viscosity coefficients tt2 and Oi are of opposite signs [276,312]. If the ratio between the two viscosities is positive, the director exhibits different dynamics it aligns with respect to the velocity at an angle 6I9 such that tan (6b) = a2/ 3- Note finally that, despite a complex microstructure, the classification in terms of flow-aligning and tumbling nematics, as defined for low molecular weight liquid-crystals, still applied to lyotropic systems. 

There are other reports on the study of pretransitional dynamics in polymeric and lyotropic nematics. Quantitative measurements of ratios of Frank elastic constants and Leslie viscosities in the pretransitional range of poly-y-benzyl-glutamate polymeric nematic are reported by Taratuta et al. [85]. McClymer and Keyes [86-88] report light scattering studies of pretransitional dynamics of potassium laurate-decanol-D20 system. An interesting study of a magnetic-field induced I N phase transition in a colloidal suspension is reported by Tang and Fraden [89]. 

The exdudedvolume factor at concentration q see 29 For i = 1-6, Ericksen-Leslie viscosity coeffidoit see Eq. 91 The exduded volume ratio at infinite dflution aS = R /(Lp/3)... 

From slow-shear-rate solutions of the Smoluchowski equation, Eq. (11-3), with the Onsager potential, Semenov (1987) and Kuzuu and Doi (1983, 1984) computed the theoretical Leslie-Ericksen viscosities. They predicted that ai/a2 < 0 (i.e., tumbling behavior) for all concentrations in the nematic state. The ratio jai is directly related to the tumbling parameter X by X = (1 -h a3/a2)/(l — aj/aa). Note the tumbling parameter X is not to be confused with the persistence length Xp.) Thus, X < I whenever ai/a2 < 0. As discussed in Section 10.2.4.1, an approximate solution of Eq. (11-3) predicts that for long, thin, stiff molecules, X is related to the second and fourth moments Sa and S4 of the molecular orientational distribution function (Stepanov 1983 Kroger and Sellers 1995 Archer and Larson 1995) ... 

At low enough shear rates, polymeric nematics ought to obey the same Leslie-Ericksen continuum theory that describes so well the behavior of small-molecule nematics. The main difference is that polymers have a much higher molecular aspect ratio than do small molecules, which leads to greater inequalities in the the numerical values of the various viscosities and Frank constants and to much higher viscosities. 

The conditions for the first two viscosity coefficient ratios correspond to Eq. (100). A discussion of the stability of the various solutions is presented in the paper of Saupe [59]. Brand and Pleiner [61] as well as Leslie [62] discuss the flow alignment without the restriction that one director is perpendicular to the shear plane. 

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