Interfacial thickness comparison

From the results of MD simulations, the non-linear susceptibility, Xs p. can be calculated for each interfacial species of water molecule as a function of distance along the simulation cell (see Figure 2.13) to determine how each species contributes to the SF signal and to the depdi that SF intensity is generated. Although this representation is only a first approximation of the SF probe depth, it is the most relevant measure of interfacial thickness for SF experiments because it indicates the depth to which water molecules are affected by the presence of the interface. To make a direct comparison to experiment, the contribution from each OH oscillator to the total xisp is multiplied by a factor, linear in frequency, that accounts for the IR vibrational response dependency on frequency. For example, an OH vibration at 3400 cm is approximately 12 times stronger in SF intensity than the free OH. 

If interfacial thickness is small in comparison with the radii of curvature of S, and if the body force at any lateral position is approximately uniform between 5a and we can write... 

When presented in this fashion, even the sample PTMO-1000-MDI-31-DCA indicates a less phase separated structure in comparison to PTMO- 00- MDI-31-DCA. Polyether polyurethane based on MDI/BD (ESTANe ), which had indicated a smaller interfacial thickness, shows a considerable amount of mixing between the two types of segments. In general, a good correlation can be found between the degree of phase separation as determined by x-ray analysis and mechanical and thermal characteristics observed earlier. 

In spite of the wide variety of interfacial media encountered, it is possible in many cases to obtain surface balance equations, which are representative and unrestrictive in comparison to actual phenomena. The constitutive laws can be established by dimensional analysis. They relate to surface variables, to flux and rates of production. The phenomenological coefficients can be determined experimentally, or by detailed analysis over the interfacial thickness. The solution implies a coupling between these equations and those for volumes in contact. In the examples presented here, the results are in perfect agreement with those of simple classical theory. 

INVESTIGATION OF LAMELLAR SPACING AND INTERFACIAL THICKNESS OF STYRENE-ISOPRENE BLOCK COPOLYMER FILMS CAST FROM SOLUTIONS AND ITS COMPARISON WITH CURENT THEORIES... 

Figs. 3 and 4 show comparison of the domain properties, the lamellar spacing D and the interfacial thickness At,... 

Fig. 4. Comparison of observed interfacial thickness with calculated ones...

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

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. 

Fig. 3. Interfacial slip of an entangled melt at a non-adsorbing perfectly smooth surface, where the dots represent an organic surface (e.g., obtained by a fluoropolymer coating), which invites little chain adsorption. Lack of polymer adsorption produces an enormous shear rate jiat the entanglement-free interface between the dots and the first layer of (thick) chains. y-x=vs/a is much greater than the shear rate y present in the entangled bulk. This yields an extrapolation length b, which is too large in comparison to the chain dimensions to be depicted here...

Generally, for the interpretation of reflectivity data, models are used in which the interfacial region is divided into a number of parallel homogeneous and optically isotropic layers with sharp boundaries, onto which the Fresnel equations are applied ). Comparison with the data lets us verify the assumed profile and assign parameter values, like the thicknesses of subsequent layers and their refractive indices. An intrinsic problem is that the solution obtained is not unique different profiles may match the same experimental data. For adsorption layers the parameters obtained from the model fit allow for the calculation of the adsorbed amount r. It is generally found that this result is hardly dependent on tlie chosen profile ), so that Tcan be calculated in an easy way by assuming an... 

Eq. (54). These are film thickness D/(aN1/2), interaction parameter %/%c> the chemical potential difference NAp, and bare surface energies N1/2/a fsL and N1/2/a fsR. They enable [60] an easy comparison of finite size effects observed in different systems. Sometimes two such parameters, D/(aN1/2) and %/%c, are combined into the film thickness-to-interfacial width ratio D/w=3(7/7r-l)1/2D/(aN1/2). 

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],... 

According to Gibbs [1], one can view an interface as a layer of finite thickness within which the composition and thermodynamic characteristics are different from those in the bulk of phases in contact. This approach allows one to describe the properties of interfaces phenomenologically in terms of excesses of the thermodynamic functions in the interfacial layer in comparison with the bulk of individual phases. With this approach one does not need to introduce any model considerations regarding the molecular structure of the interfacial layer or utilize particular values of layer thickness. 

Figure 25 shows the temperature dependence of relaxation time for the relaxation processes in the internal and interfacial regions of the ultrathin PS1.46M film sandwiched between the SiO layers. Since it was hard to distinguish the temperature-Ta relations between the vacuum deposited and laminated films, each data point was averaged over six independent measurements including both vacuum deposited and laminated films. The average thickness was about 40 nm. For comparison, the dashed curve in Fig. 25 denotes the bulk data obtained by the Vogel-Fulcher equation [72, 73] ... 

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