Tanaka plot

Fig. 2. a. BSF plot for estimation of unperturbed dimensions of polystyrene in n-butyl chloride at 25 °C. b Tanaka plot for the data of Fig. 2a. Notice that this plot is linear over the entire range o( excluded volumes investigated. Reprinted with permission from Maciomolecules, 24 199 (1991). Copyright 1991 American Chemical Society...

Caution is suggested when interpreting the results in Figure 18 for nylon 6,6. The Halpin-Tsai and Mori-Tanaka theoretical value plots seemed to be mislabeled. The dashed plot in Halpin and Tsai should probably be labeled with an aspect ratio of 28 and the solid line for the Mori-Tanaka plot should probably be labeled with an aspect ratio of 65. 

FIGURE 7.8 A contour plot obtained for 2D HPLC using two 2nd-D columns in a system shown in Figure 7.6c. Sampling every 15 s at the lst-D. Flow rate 0.8 mL/min for lst-D, and 10 mL/min for 2nd-D (reproduced from the reference, Tanaka et al. (2004) with permission from American Chemical Society). 

Problem 13. Plots of vs [Mo203L4]g in 1,2-dichIoro-ethane at 25°C. L = EtjNCSjfO), EtjNCSSefD), EtjNCSejfA). Reprinted with permission from T. Matsuda, K. Tanaka and T. Tanaka, Inorg. Chem. 18, 454 (1979). (1979) American Chemical Society. 

Fig. 10. Plot of normalized approach to equilibrium thickness against the square root of time for a temperature-sensitive 10x4 PNIPAAm gel sheet swelling and shrinking between 10 and 25 °C. Shown are the curve fits to the kinetic data of theory developed from equations of motion (Tanaka and Fillmore theory) [60]. The equilibrium degree of swelling is 17.0 at 10°Cand 11.1 at 25 °C the diffusion coefficients obtained from the curve fits are 2.3 x 10"7 ctn2/s for swelling and 3.6 x 10 7 cm2/s for shrinking [121]...

Figure 2.18 Diffusion and sorption coefficients plotted for gases in a family of 18 related polyimides. Data of Tanaka et al. [23]...

As a general rule, membrane material changes affect the diffusion coefficient of a permeant much more than the sorption coefficient. For example, Figure 2.18 shows some typical gas permeation data taken from a paper of Tanaka et al. [23], The diffusion and sorption coefficients of four gases in a family of 18 related polyimides are plotted against each other. Both sorption and diffusion coefficients... 

The second key factor determining permeability in polymers is the sorption coefficient. The data in Figure 2.18 show that sorption coefficients for a particular gas are relatively constant within a single family of related materials. In fact, sorption coefficients of gases in polymers are relatively constant for a wide range of chemically different polymers. Figure 2.25 plots sorption and diffusion coefficients of methane in Tanaka s fluorinated polyimides [23], carboxylated polyvinyl trimethylsiloxane [37] and substituted polyacetylenes [38], all amorphous glassy polymers, and a variety of substituted siloxanes [39], all rubbers. The diffusion... 

In Figure 4.10, values of ffLV for molten halides at TF are plotted versus the quantity C3.Le.vm 2/3 (Tanaka et al. 1996) (it should be noted that the constant C3 = 1.18 x 10 8 is similar but not equal to the constant Q of equation (4.1)). Fused halides have comparatively low surface energies (lying between 0.05 and 0.4 J/m2) for two main reasons (i) their heat of evaporation is low compared to that of metals (typical values being 30 as compared to 300 kJ/mole) and (ii) the coefficient of proportionality between (TLv and Le.vm 2/3 for halides is (as for oxides) only half of that for metals. 

Such pure ionic mechanisms have been severely criticized by several authors. Thus, Ishii et al. studying the reaction of various substituted benzoic acids with 1,2-epoxy-3-phenoxypropane in the presence of NMcj, determined values of Hammett s plot. They observed that q is positive and decreases with increasing reaction temperature. According to these authors, this shows that ionic dissociation of benzoic acid is not the rate-controlling factor, since q values relative to the dissociation constant of substituted benzoic acid do not change with temperature Even if Ishii s comments about the values of q are not clear, his experimental observations fit those of Kakiuchi and Tanaka... 

Tanaka interestingly discussed the factors which influence the stereochemistry of the transition-state species IV for the reaction of benzoic acid with l,2-epoxy-3-phenoxypropane catalyzed by substituted pyridines in xylene. As in Ref. it was shown that reaction (47) to (SO) do not take place and that the kinetics is second order with respect to acid and epoxide. The plot of the rate constant k against [Cat] is a straight line which does not pass through the origin ... 

The plot of the activation energy or of the logarithm of the rate constant vs. the basicity of these pyridines in water does not show any one relationship covering all the catalysts studied in this work. According to Tanaka the deviations from a linear relationship, which have been observed with other reactions, should not be due to the fact that the pK and the kinetic values were measured in different solvents, but to the difference in the steric requirements of these reactions. 

Studying the reaction of substituted l,2-epoxy-3-phenoxypropane with benzoic acid in the presence of a tertiary amine, Kakiuchi and Tanaka reported Hammett s plots obtained in solvents such as xylene, mono- and dichlorobenzene, and nitrobenzene. They obtained the following values of g ... 

In a comparative study five different thermochemical codes were used to calculate the equihbrium composition of five pyrotechnics including a particular MTV formulation described down below in Table 5.4 [17]. The results are given in the following tables (Tables 5.5-5.8). As is evident from the comparative temperature plot in Figure 5.9 all codes but the TANAKA code agree quite well and show only moderate deviation with respect to preferred reaction products. The predicted adiabatic combustion temperature is in good accord with experimental determination reported data (Chapter 9.3) (Figures 5.10-5.13). 

The c vs (10 /r -I- InM) plot proposed by Tanaka and Nishinari [7] and Tanaka and Stockmayer [9] is the method used to independently calculate the parameter s and C- It is an effective approach to characterize the crosslink structure of the thermoreversible gels. 

Figure 12.8 Plots of logiVj versus log ]> at 180 °C for neat PS (O) and carbon-black-filled PS composites with varying amounts of carbon black (wt %) ( ) 10, (A) 20, and (V) 30. The data were obtained using a cone-and-plate rheometer. (Reprinted from Tanaka and White, Polymer Engineering and Science 20 949. Copyright 1980, with permission from the Society of Plastics Engineers.)...

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