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Interfacial thickness calculated

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid-liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. [Pg.424]

Once the free energy of an inhomogeneous system is given, one can calculate by standard methods the properties of the interface—for example, the interfacial tension or the density profile perpendicular the interface [285]. Weiss and Schroer compared the various approximations within square-gradient theory discussed earlier in Section IV.F for studying the interfacial properties for pure DH and FL theory [241, 242], In theories based on local density approximations the interfacial thickness and the interfacial tension were found to differ by up to a factor of four in the various approximations. This contrasts with nonionic fluids, where the density profiles and interfacial... [Pg.46]

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. [Pg.51]

Figure 4.14. The four-layer model used for the calculations of the interfacial thickness, nj designates the refractive index, 0j the incidence angle, r. the Fresnel reflection coefficient, Rj the reflection coefficient in the incident plane and dj the thickness of the layer. Figure 4.14. The four-layer model used for the calculations of the interfacial thickness, nj designates the refractive index, 0j the incidence angle, r. the Fresnel reflection coefficient, Rj the reflection coefficient in the incident plane and dj the thickness of the layer.
Small angle X-ray scattering (SAXS) has been used by many authors to determine the interfacial thickness. An excellent review of this subject can be found in Perrin and Prud homme [1994]. Many methods of calculations can be used. One of these involves an analysis of the deviation from Porod s law, in which the desmearing procedure is avoided. This procedure was applied to blends of PS with PMMA added with a P(S-b-MMA) block copolymer. Upon addition of copolymer the interface thickness changed from A1 = 2 to 6 nm [Perrin and Prud homme, 1994]. [Pg.316]

Helfand and Tagami [1971, 1972] model is based on self-consistent field that determines the configurational statistics of the macromolecules in the interfacial region. The interactions between the statistic segments of polymers A and B are determined by the thermodynamic binary interaction parameter, The isothermal segmental density profile shown in Figure 9.12, Pj (i = A or B), was calculated for infinitely long macromolecules, M — oo. The interfacial thickness, A1, and the interfacial tension coefficient, v, were expressed as ... [Pg.591]

The annealing temperature dependence of such a surface mobile layer will now be discussed. At 370 K, the thickness of the surface mobile layer was 10 2.8 nm. It should be of interest to compare the thickness with the chain dimension. Twice the radius of gyration (2/fg) of an unperturbed PS with Mn of 29k is calculated to be 9.3 nm. This value is comparable to the surface layer thickness. At 365 and 355 K, the interfacial thicknesses similarly increased with time at first and then became invariant with respect to the annealing time, as shown in Fig. 8c, d. The evolved interfacial thickness at 365 and 355 K were 9.6 2.5 and 11.4 0.9 nm, respectively. Half of these values, namely surface mobile layer thicknesses, are much... [Pg.11]

The experimental setup of the ellipsometry provides directly temperature dependent data of the interfacial thickness X, which can be used to calculate the polymer-polymer interaction parameter Xab as a function of temperature The temperature dependence in the system PS/PMMA can independently be confirmed by measuring phase diagrams of oligomers and their PVT data. Having these data, it is possible to calculate XAh(T) by using the Flory- Huggins theory or an equation-of-state (EOS) theory. [Pg.562]

Figure 1 showed the temperature dependence of the interfacial thickness for PS/PMMA and two PMMA/SAN blends. Using equation (7) it is then possible to calculate the polymer-polymer interaction parameter Xab as a function of the temperature. The interaction parameter Xab between PMMA(A) and SAN(B) is then given by ... [Pg.572]

Figure 3.33 shows how the weight fraction of the interface increases with time, whilst Figure 3.34 shows how >a and co, the weight fractions of PMA and PVAc, respectively, in the interface change with time. The changes of (Op, and (o with time are similar, which indicates that interdiffusion in this particular polymer pair is symmetrical. The change of thickness of the interface with diffusion time is shown in Figure 3.35. Here, the room temperature densities of PMA and PVAc were used to calculate the average density, p. Thus, for both symmetrical and asymmetrical interfaces, the growth of interfacial thickness can be described by Eq. (22). Figure 3.33 shows how the weight fraction of the interface increases with time, whilst Figure 3.34 shows how >a and co, the weight fractions of PMA and PVAc, respectively, in the interface change with time. The changes of (Op, and (o with time are similar, which indicates that interdiffusion in this particular polymer pair is symmetrical. The change of thickness of the interface with diffusion time is shown in Figure 3.35. Here, the room temperature densities of PMA and PVAc were used to calculate the average density, p. Thus, for both symmetrical and asymmetrical interfaces, the growth of interfacial thickness can be described by Eq. (22).
The ellipsometric method has been developed by Yukioka and Inoue (1991, 1994). The principles of the technique and the model used for calculating the thickness of the interphase are schematically illustrated in Figs. 4.13 and 4.14, respectively. The retardation (A) and reflection ratio (tan(i/<)) can be determined from the ellipsometric readings. The adopted model assumes the existence of four layers air, thin polymer-1, interphase, and thick polymer-2 (see Fig. 4.14). In the interphase the refractive index is assumed to be an average n = iti+ ni)H. Thus, one can compute the best value of the interfacial thickness, do, to fit the observed values of A and tan( ). The following relations were derived for the computation of d ... [Pg.480]

In a second study, they evaluated the interfacial thickness of twopoly(isoprene-b-methyl methacrylate) block copolymers (Pl-PMMA) using the same approach. Small-angle X-ray scattering experiments showed that films of the mixed diblock copolymers have a lamellar morphology with a spacing that varies with composition from 24 to 26 nm. Fluorescence decay profiles from these films were analyzed in terms of an energy transfer model that takes into account the distribution of junctions across the interface and calculated an interface thickness of 1.6 + — 0.1 nm. This value was independent of the acceptor/donor ratio (i.e., the acceptor concentration) in the films. [Pg.485]

More recently, Karian (1) used DSC methodology to determine the magnitude of interfacial thickness and correlate calculated values with measured tensile strength for a spectrum of composite materials having varying degrees of chemical coupling. This thermodynamic probe of the interphase microstructure is based on the Lipatov model (22) of the interphase microstructure. [Pg.436]

The theory was originally compared to three polymer pairs, namely PS/PMMA PMMA/poly(n-butyl methacrylate), PnBMA and PnBMA/poly(vinyl acetate), PVA. The calculated interfacial tension agreed exactly with the experimental value for PnBMA/PVA it compared well for PMMA/EhiBMA and differed by 50% for PS/PMMA. Helfand and Tagami suggested that, if z is too large, then the characteristic interfacial thickness is too small for the mean-field theory to be appropriate. The theory has been widely used to estimate the interfacial tensimi in many different polymer-polymer systems with acceptable success. [Pg.146]

Ellipsometry is a powerful tool [16] for measuring the interfacial thickness between two polymers, whether in the case of immiscible or miscible polymer blends. In the case of miscible blends, investigations of changes in interfadal thickness with time at a fixed temperature allow the calculation of mutual diffusion coefficients [22]. In contrast, for immiscible blends the Flory-Huggins interadion parameter x can be deduced by measuring the interfacial thickness in an equilibrium state, and using the theory of Helfand [41] and its extended version [42]. [Pg.305]

The characteristic interfacial thickness t is calculated using t = (2jt) o [1]. Results are summarized in Table 18.6. The interfacial thickness and the surface area are found to increase with the addition of MA-g-SEBS. These results can be interpreted as the compatibilizer effect. However, this system does not indicate enough impact strength because the domain size is too large. Thus, it is necessary to make the domains much smaller by adjusting the primary structure of the polyolefin and the compatibilizer. [Pg.390]

Fig. 4. Comparison of observed interfacial thickness with calculated ones... Fig. 4. Comparison of observed interfacial thickness with calculated ones...
In principle, Qc appearing in (9) must be obtained from the solution of (8). Owing to the practical difficulty Helfand and Wasserman [8] had in calculating Qc rigorously from (9), they applied the Narrow Interphase Approximation (NLA) method to calculate Qc. Note that the NLA method is only valid for the situations where the interfacial thickness Aj between block A and block B is very small compared to the domain spacing D, i.e., Xi/D -C 1. Specifically, in place of (9), based on the NIA method Helfand and Wasserman employed the following expression to calculate Qc. ... [Pg.85]

Lattice calculations have been made by Roe and Helfand which give the interfacial tension and interfacial thickness, a, (defined as the difference in composition of the phases divided by the gradient at the midpoint). These theories have the disadvantage that the result depends on the size and coordination number of the lattice which are unknown. [Pg.152]

This relation between the interfacial thickness of an interphase and correlation length could allow calculation of 8 if the density of an interphase were known. However, the density of an interphase is not known. [Pg.51]

Referring to Fig. IV-4, the angles a and /3 for a lens of isobutyl alcohol on water are 42.5° and 3°, respectively. The surface tension of water saturated with the alcohol is 24.5 dyn/cm the interfacial tension between the two liquids is 2.0 dyn/cm, and the surface tension of n-heptyl alcohol is 23.0 dyn/cm. Calculate the value of the angle 7 in the figure. Which equation, IV-6 or IV-9, represents these data better Calculate the thickness of an infinite lens of isobutyl alcohol on water. [Pg.157]

Templeton obtained data of the following type for the rate of displacement of water in a 30-/im capillary by oil (n-cetane) (the capillary having previously been wet by water). The capillary was 10 cm long, and the driving pressure was 45 cm of water. When the meniscus was 2 cm from the oil end of the capillary, the velocity of motion of the meniscus was 3.6 x 10 cm/sec, and when the meniscus was 8 cm from the oil end, its velocity was 1 x 10 cm/sec. Water wet the capillary, and the water-oil interfacial tension was 30 dyn/cm. Calculate the apparent viscosities of the oil and the water. Assuming that both come out to be 0.9 of the actual bulk viscosities, calculate the thickness of the stagnant annular film of liquid in the capillary. [Pg.489]

Calculate the film thickness for the Marongoni instability shown in Fig. Xlll-2 using the relationship in Eq. XIIl-3, assuming that the interfacial tension is 20 mN/m. [Pg.490]


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