INTERFACIAL LAYER THICKNESS

A simple test to estimate the interfacial layer thickness is to measure the thickness of the bottom layer before and after spinning, exposure, and development of the top layer. The difference is taken to be the thickness of the interfacial layer for comparison purposes. In reality, the mixing is continuous and the development of the top layer stops inside the interfacial layer instead of at its edges precisely. Furthermore, the test in Reference 26 relies on the IBM Film Thickness Analyzer to measure the resist thickness for convenience. Since this tool operates on the principle of spectral reflectivity changes caused by film thickness changes, a uniform refractive index is important. When some part of the interfacial layer still remains, the measurement can be erroneous in principle. 

Figure 33. The interfacial layer thickness as a function of AZ1350J prebake temperature with an AZ dilution of 60% and an 8000-rpm spin speed, resulting in a 0.32-pm film.

Figure 35. The interfacial layer thickness as a function of spin speed.

If hydrogen bonding is involved, both Eqnations 2.C3 and 2.C5 must be replaced by more appropriate equations. In this case the above derivatives may not lead to analytical expressions and numerical differentiation may be needed. Still, however, Eqnations 2.C7 and 2.C12 can be used for making a rongh estimation of the effective interfacial layer thickness, which could prove useful for development of semiempirical models. 

As can be easily derived from the concentration pattern, the reaction takes place either mainly in the bulk of the well-mixed liquid phase or in the liquid-phase boundary layer. In reactions which occur in the bulk of the liquid phase, the concentration of gaseous educts decreases only within the interfacial layer (thickness d) to the concentration cAj by physical diffusion processes. Only in the case of mass transport processes that are fast relative to the reaction rate is the latter proportional to the cAl j in the liquid phase. If the catalytic reaction is fast enough a reaction surface may develop within the boundary layer which may even move into the interface itself and, thus, neither the bulk of the liquid nor the liquid-phase boundary layer is utilized any more for the reaction. A simple approach in order to determine the regime of the overall reaction rate can be performed by comparison of the intrinsic kinetics with the rate of mass transfer according to Table 2 [22],... 

Thus, the aforementioned used nanoscopic methodics allow estimating both interfacial layer and structural special features in polymer nanocomposites and its sizes and properties. For the first time it has been shown that two consecutive interfacial layers are formed in elastomeric particulate-filled nanocomposites, which are reinforcing elements for the indicated nanocomposites. The proposed theoretical methodics of interfacial layer thickness estimation, elaborated within the fiamewoiks of finctal analysis, give well enough correspondence to the experiment. 

This fraction is estimated approximately by the ratio 37/Z), where is interfacial layer thickness. As mentioned earlier, the data of Figure 6.1 gave the average experimental value 8.7 nm. Furthermore, from the condition 3/yZ) = 0.5 let us obtain D 52 nm, which is shown in Figure... 

In Fig. 6.1, the obtained according to the original methodics results of elasticity moduli calculation for nanocomposite butadiene-styrene rub-ber/nanoshungite components (matrix, nanofiller particle and interfacial layers), received in interpolation process of nanoindentation data, are presented. The processed in SPIP pol5mier nanocomposite image with shimgite nanoparticles allows experimental determination of interfacial layer thickness which is presented in Fig. 6.1 as steps on elastomeric... 

The calculation according to the Eqs. (4)-(6) gives d =2A4. Further, using the calculated by the indicated mode parameters, let us obtain from the equation (1) the theoretical value of interfacial layer thickness i[f=l A nm. This value is close enough to the obtained one experimentally (their discrepancy makes up 10%). 

Therefore, the interfacial layer thickness, between the pure liquid ant its vapours, could be determined only be the surface energy of a condensed phase and the corresponding energies ... 

Let us consider further diffiisive processes influence on interfacial regions formation in the studied nanocomposites. In Refs. [12, 13], the treatment of depositions structure formation on fibers and surfaces within the frameworks of irreversible aggregation models was proposed. Within the framework of this treatment the relationship between mean-square deposition (interfacial layer) thickness and particles (statistical segments) number . in it atwas proposed [13] ... 

FIGURE 7.4 The dependence of interfacial layer thickness /jj on statistical segments number n. in it for nanocomposites on the basis of BSR in double logarithmic coordinates. 

The coefficient c value in the Eq. (5) can be calculated as follows [4], First the interfacial layer thickness / is determined according to the equation [6] ... 

In Figure 2.20, the experimental [110,111] surface tensions of the 1-propanol + n-hexane mixture at 298.15 K with the predicted ones by the present combined model are compared. In view of the strong nonideality of this system, the agreement is again rather satisfactory. For the same system, we have calculated the interfacial layer thickness as a function of composition of the liquid phase. The calculations are shown in Figure 2.21. This is an azeotropic system, and it is worth observing that the calculated maximum in Figure 2.21 is close to the azeotropic composition. In Ref. [106], we have shown that the interfacial layer thickness increases with the vapor pressure of the system. 

FIGURE 2.21 The calculated interfacial layer thickness as a function of composition for 1-propanol (l)-n-hexane (2) mixture at 298.15 K. 

Fig, 13.2 The photo-voltage Vp as a function of the output voltage V for various interfacial layer thicknesses (S. The parameters of Table 13.1 have been used. 

A similar method was used for improving the reactivity of polyamide-6 (PA-6) in the experimental work of Dedecker and co-workers [69]. They also demonstrated, using optimum curves, that the PA-co-MA content had an effect on the equilibrium interfacial layer thickness. The maximum value of the equilibrium interfacial layer thickness ( 50 nm) was found when the PA-co-MA contained 15% MA. 

Equilibrium interfadal thickness at 180 °C shows a maximum as a function of the copolymer composition at 25% AN content for PC/SAN film, which allows the most compatible polymer pair to be defined. There was a correlation between the compatibility (interfacial layer thickness) and the degree of dispersion in bulk, since the... 

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