Reorientation models

The notable features of the pair-reorientation model (7) can be summarized as follows ... 

Reexamination of the pair-reorientation model is most conveniently carried out on the basis of mathematical formulations of all explicit and implicit assumptions. 

Based on simple pictorial arguments, the pair-reorientation model introduced the expression... 

By choosing different combinations of Hyps. 1 to 9, various "relations between the FeS2—P and FeS2—m type atomic arrangements may be deduced, but only those relevant to the judgement of the pair-reorientation model are presented here. The combination of Hyps. 1, 5, and 7 gives an expression... 

The relaxation times have been interpreted on the basis of a large-step isotropic reorientation model. The results show that in methylamine the internal reorientations of the methyl group are fast compared to the overall molecular rotations, whereas in dimethylamine they are of comparable magnitude and in trimethylamine the overall molecular motions are the faster. (171)... 

On the other hand, the number of possible states for adsorbed molecules, corresponding to different partial molar areas cOj, can be quite large. Theoretically one can assume a continuous change of co between cOmin and cOmax, and successive values varying from each other by an infinitesimal increment of the molar area Aco. The transition from a discrete to a continuous reorientation model can be performed formally, replacing the summation in Eqs. (2.78) and (2.89) by an integration. 

Let us consider now the dependence of the shape of surface pressure isotherms on the parameters of the reorientation model. The dependence of surface pressure on the maximum area C0 is illustrated in Fig. 2.5. Here Eqs. (2.84)-(2.88) are employed with (02 = const and a = 0. All calculated curves are normalised in such a way that for the concentration 1 O " mol/1, the surface pressure is 30 mN/m. One can see in Fig. 2.5 that with the increase of (Oj the inflection of the isotherm becomes more pronounced, however, for the ratio a)i/( 2 = 4 the calculated curve almost coincides with the one calculated from the von Szyszkowski-Langmuir equation (2.41) which assumes only one adsorption state with (Oo = < = const. 

Fig. 2.9 Equilibrium surface pressure for BHBCi solutions symbols - experimental data from [13,25], curves -theoretical calculations curve 1 - Langmuir-Szyszkowski equation curves 2 - 5 - reorientation model for 2, 3, 7 and over 50 adsorption states of the BHBCie molecule, respectively (n j =2.52 lO mVmol,...

Fig.2.10. Dependence of the Gibbs elasticity modulus CioEOg solutions on surface pressure reorientation model water/air interface (1) reorientation model water/hexane interface (2) von Szyszkowski-Langmuir equation for both interfaces (3).

The above analysis of the viscoelastic behaviour for adsorption layers of a reorientable surfactant leads to important conclusions. It is seen that the most important prerequisite for a realistic prediction of the elastic properties is the adequacy of the theoretical model used to describe the equilibrium adsorption of the surfactant. For example, when we use the von Szyszkowski-Langmuir equation instead of the reorientation model to describe the interfacial tension isotherm, this rather minor difference drastically affects the elasticity modulus of the surface layer. The elasticity modulus, therefore, can be regarded to as a much more sensitive parameter to find the correct equation of state and adsorption isotherm, rather than the surface or interfacial tension. Therefore the study of viscoelastic properties can give much more insight into the nature of subtle phenomena, like reorientation, aggregation etc. 

The reorientation model for molecules which can exist in two states (conformational changes) in the adsorption layer, 1 and 2, respectively (for definiteness we assume co, > CO2) involves the equation of state of the surface layer... 

The surface tension isotherms for alkyl dimethyl phosphine oxides (C DMPO) in the interval from Cj to Ci6 at 25 °C are shown in Fig. 3.11. It should be noted that the experimental data reported in [36] for Cj, Ciq, Cp and C[4 are in a good agreement with the data presented in [37, 38], and therefore the results for these experimental data are also shown in Fig. 3.11. The parameters of the Frumkin and reorientation models are summarised in Tables 3.6 and 3.7. Both isotherms agree well with the experimental data. Small differences between the calculated isotherms exist only for nc > 13, while for lower nc the curves for the two models perfectly coincide. It follows then that neither of the two models can be preferred if one takes into account only the agreement between the experimental and theoretical data. However, the negative values of the Frumkin constant a for lower homologues, and the unusual shape of this dependence on nc (cf Fig. 3.12) indicate that for the Frumkin model the coincidence with the experiment is only formal. 

Fig. 3.11. Dependence of equilibrium surface tension on concentration for C DMPO solutions, according to [36, 37], numbers denote the carbon atoms number, the theoretical curves are calculated from the Frumkin (solid line. Table 3.6) and reorientation models (dashed line. Table 3.7).

The slope of the dependence for the data calculated for the Frumkin isotherm is lower than that for the reorientation model. The increment of the free energy of adsorption calculated from the reorientation model, = —3.0 kJ/mol, is almost equal to the value obtained for normal... 

Table 3.9. Reorientation model parameters, Eqs. (3.3)-(3.7), calculated for CnBHB.

Fig. 3.18. Dependence of adsorption equilibrium constant b on nC for CnBHB calculated from the Frumkin ( ) and reorientation (<>) models, ( ) - data for fatty acids as in Fig. 3.10.

It is seen that for the Frumkin model, the two methods give somewhat different values of the standard free energy of adsorption, while for the reorientation model the values obtained by these two methods are equal. This fact can be easily explained equating the AG values given by Eqs. (3.11) and (3.16) to each other, one obtains ... 

Therefore, for the reorientation model the two methods lead to similar values of AG , because, on the one hand, this model transforms into the ideal (Langmuir - von Szyszkowski) model at high surface pressure, when only one of two possible adsorption states exists, namely that possessing the minimum area, cf. Eq. (3.7). On the other hand, this coincidence also indicates that the CMC and the adsorption characteristics (b and CO2) calculated from the fitting program, are reliable. 

Maleic acid mono[2-(4-alkylpiperazinyl)ethyI esters] (CnPIP) also are amphoteric surfactants and the ionic form depends on the pH, [44, 45]. Four ionic forms are known, of which the most surface active one is similar to the betain, with two oppositely charged atoms bF and 0 . At pH = 6.2 approximately 99.6% of all CnPIP molecules in solution exist in the betain form, while each of the other two forms, containing one ionised atom (either N or O ) is represented by 0.2% [45]. The experimental and theoretical surface tension isotherms of C PIP solutions at pH = 6.2 and 24"C are presented in Fig. 3.21. The theoretical curves calculated from the Frumkin and reorientation models are essentially the same with similar deviations, and therefore neither model could be preferred. The dependencies of the main parameters on n for the two models are shown in Figs. 3.22 - 3.24. 

Considering the data shown in Tables 3.12 and 3.13, one notes the significant difference between the values of calculated for the two models for the Langmuir model these values are 2 to 10 times higher than for the reorientation model. This difference becomes more pronounced with increasing n and m in the C EO molecule. 

Comparing the experimental data with the calculated surface tension isotherms one can see that perfect agreement exists between the predictions given by the reorientation model and the experimental results, while the correspondence with the Langmuir model is rather poor. 

It is seen from these dependencies that, with the increase of m, the onset of surface tension decrease (or the surface pressure increase) corresponds to lower surfactant concentrations at the same time, the decrease of the isotherm slope at high concentrations takes place. The increase of surface activity with the increase of m for low pressure in the framework of reorientation model can be qualitatively explained by strong increase of the molar area of C EO, molecule in the state 1 (coj), while the decrease of the isotherm slope (and also the decrease of surface activity) at high concentrations can be ascribed to slight increase of the CO2 value. Therefore, the Intersection of the isotherms which is observed for the oxyethylated alcohols with different m values is the consequence of the fact that these two molar areas are increased with the increase of m, but the rate of this increase is different for CO2 and coj values. 

The significant increase in co, with increasing m is caused by the localisation of the oxyethylene chain in the surface layer. This result which is implied by the reorientation model also agrees with the neutron reflection data. It was shown in [14] that, with the increase of the area per C EO , molecule in the adsoiption layer, i.e., with surface pressure deerease, the thickness of the layer occupied by the oxyethylene groups of C EO, becomes lower. At the same time, a decrease in the tilt angle of the oxyethylene groups to the interface is observed. These results were discussed in [14] in the context of the adsorption of oxyethylene groups in the non-saturated adsorption layer of oxyethylated alcohols. The dependence of molar areas in the two states on n is shown in Fig. 3.32. 

We compare now the adsorption behaviour of oxyethylated alcohols (with C,oEOg as an example) at the water/air and water/hexane interfaces, with reference to the data reported in [57]. The experimental and theoretic isotherms at the water/hexane interface are shown in Fig. 3.33. It was mentioned above that the experimental data agree satisfactorily with the Frumkin model for a physically unrealistic value of a = -10.8. Comparing the reorientation model parameters for CiqEOj at the two interfaces (cf. Fig. 3.33 and Table 3.13), one can see that the molar areas are almost the same, while the value of a for the water/hexane interface is 2.5 times higher than that for the water/air interface. Thus the adsorption activity of the oxyethylene groups at the water/hexane interface is significantly higher than that at the water/air interface. 

Fig. 3.33. Surface tension isotherm for CjoEOg at water/liexane interface, solid line - reorientation model for two states (CO2 = 4.0-10 mVmol, co, = l.l-lO m /mol, a = 7.5, b=2.25-10 l/mol).

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