Crossover studies of viscosity and light scattering

In order to determine the dependence of the cut-off wave numbers q_c and q_D from the background viscosity ηbg, parameters A_η, B_η and T_η the shear viscosity measurement have been evaluated for each ternary mixture. In Table (5.7) the parameters from a si-multaneous treatment of ηs and D data, taking crossover as well as background effects in account, according to Eqs.(4.29), are presented. The plots of parameter A_η, B_ηand T_η

weight fraction A_η±0.02 , B_η±200, T_η±20 ξ0±0.02, q_c, q_D±0.06, Γ0±2.5

of (3MP) ·10⁻⁶Pas K K nm nm⁻¹ nm⁻¹ ·10⁹s⁻¹

0.000 0.55 2537 -51 0.160 >1000 0.55 156

0.082 0.59 2958 -134 0.195 4.40(10) 0.80 124

0.200 0.61 3174 -174 0.213 14.40(77) 0.60 102

0.300 0.50 2818 -111 0.209 12.89(68) 0.52 117

0.534 0.23 2877 -84 0.230 1.30(12) 0.32 125

Table 5.7: Parameters from shear viscosity and light scattering measurements in depen-dence on the weight fraction of (3MP): the background viscosity was determined according to Eqs.(4.29).

versus the weight fraction of (3-MP) are presented in Fig.(5.42) and Fig.(5.43) according to Table (5.7). It is interesting to see that quantity A_η follows the inverse shape of the in Fig.(5.40) shown plait point temperature in dependence on (3MP) concentration. On the one hand similar situation can be observed in case of the parameter B_η in the limits of error. On the other hand, the quantity T_η relates to the plait point plot in Fig.(5.40). The central parameter the fluctuation correlation lengthξ0within the framework of analysis of shear viscosity and light scattering measurements is presented in Fig.(5.44). Within the limit of errors, it demonstrates an increase, controlled by the weight fraction of (3MP).

Along with the graph of Eq.(5.9) the dependence of the correlation length amplitude upon the scaled temperature is shown as bilogarithmic plot in Fig.(5.44) for each ternary as well as binary mixture (Table (5.7)). The fluctuation correlation length plots follow power law over significant range of reduced temperature. The amplitudeξ0, of the (NE-3MP) sys-tem is significantly larger than that of the (NE-CH) syssys-tem Table (5.7). This difference in the fluctuation correlation length of similar binary mixtures is obviously a reflection of their different shear viscosities, Fig.(5.45). This assumption is supported by the behavior of theξ0 values of the ternary mixtures α⁰, col andα⁰⁰, which are following of order of weight fraction likewise the shear viscosityηs. In Fig.(5.47), the characteristic relaxation

Figure 5.42: Plots of Table (5.7) resulted from the viscosity background determination with the aid of Eqs.(4.29) and the crossover formalism versus weight fraction of (3MP), lines are drawn to guide the eyes; Left Figure: plot of parameter A_η; Right figure: plot of parameter B_η.

Figure 5.43: Plots of Table (5.7) resulted from the viscosity background determination with the aid of Eqs.(4.29) and the crossover formalism versus weight fraction of (3MP), lines are drawn to guide the eyes; Left Figure: plot of parameter T_η; Right figure: semilogarithmic plot of the cut-off wave number q_c.

rate amplitudesΓ0are displayed. The presented data correspond once more with the plait point line in Fig.(5.40). Finally, the conclusion could be done, that in ternary mixtures of type 2a, the col point corresponds with the smallest value of the characteristic relaxation rateΓ0between two corresponding binary mixtures. Figure (5.48) shows three relaxation rates Γ(ε), of order of fluctuations which according to Eq.(4.11) have been calculated from the mutual diffusion coefficient Eq.(4.35) and the fluctuation correlation length of the critical ternary systemsα⁰, col andα⁰⁰. The diffusion coefficient data exhibit system-atic deviations from function Eq.(4.35). These deviations may result from the insufficient temperature control (±0.03 K). Especially in the case of the ternary mixtureα⁰⁰the relaxa-tion rate data exhibit small deviarelaxa-tions from the power-law behavior. However, the cut-off

Figure 5.44: Plots of Table (5.7) resulted from the viscosity background determination, ac-cording to Eqs.(4.29), lines are drawn to guide the eyes; Left Figure: plot of the cut-off wave number qD; Right figure: plot of the correlation length amplitudeξ0.

Figure 5.45: Shear viscosity plots versus reduced temperatureε: of (NE-CH),◦;α⁰,M; col,♦;α⁰⁰,⁵; (NE-3MP),•.

wave numbers in Fig.(5.43) and Fig.(5.44) display an unexpected shape. Especially the q_c parameter with value>1000 of the crossover function H(ξ(ε),q_c,q_D)in the case of (NE-CH) does not fit to the qualitative shape of the other values. Nevertheless, taken

Figure 5.46: Semilogarithmic plots of mutual diffusion coefficient, according to Eq.(4.35);Left Figure: ternary mixtureα⁰; Right figure: ternary mixtureα⁰⁰; Lower fig-ure: ternary mixture at col point.

into account that q_c is one of the parameters which are controlling the overlap between mean field and critical range, the unusual behavior corresponds with the anomaly of crit-ical amplitude (see Sec.(5.5.2)) S_BF in (NE-CH). However, this correspondence is only an assumption. Another question which should be treated within framework of dynamic light scattering is the behavior of critical exponents. The assumption has been made that adding a third component to a binary critical mixture does not only alter the critical expo-nents but also change or influence the correction to scaling. In fact, in literature this kind of behavior has been reported [41] in the case of the ternary mixture aniline-cyclohexane-p-xylene. In that work it was observed that, due to the existence of the third component, an enlargement of the critical static and dynamic exponents results. In the present thesis,

Figure 5.47: Plots of Table (5.7) resulted from the viscosity background determination, ac-cording to Eqs.(4.29), of investigated binary and ternary mixtures; Left Figure: bilogarithmic plot of the fluctuations correlation lengthξ0versus reduced temperatureε, (NE-CH),◦;α⁰, M; col,♦; α⁰⁰,⁵; (NE-3MP),•; Right figure: the characteristic relaxation rateΓ0versus weight fraction of (3MP),lines are drawn to guide the eyes.

as mentioned before, owing to insufficient temperature control(±0.03 K) in comparison with(±0.001 K) in [41], the determination of critical exponents was not possible. Hence, critical exponents from theory, listed in Chapter 2, have been used. However, the results in this section, support the critical exponents for binary mixtures.