INDEX Hamaker constant

Keywords Swelling of La-phases Refractive index Hamaker constant... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Effective Hamaker constant, 234 Emulsifying activity index, 186,188/ Emulsions, concentrated oil-in-water, effea of interdroplet forces on centrifugal stability, 229-245 Enhancers of taste. See Taste enhancers Enzymatic modification of soy proteins, 181-190... 

Table 10.5 shows a few numerical examples of how well this attempt at unification succeeds. Equations (28), (32), and (62) have been used to calculate values of the Hamaker constant from refractive index data at visible wavelengths. These values have then been used along with yd values from Chapter 6 to calculate d0 values according to Equation (68). The resulting values of d0 are seen to be physically reasonable. That such plausible values for d0 are obtained is especially noteworthy in view of the approximations made in the calculations. 

Polarizability Attraction. All matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaker constant for interaction eneigy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where Vg is the frequency of the principal electronic absorption... 

Here, n is the refractive index and is the ise the mean ionization frequency of the material. Typically this is ve k, 3x1015 Hz. If the absorption frequencies of all three materials are assumed to be the same, we obtain the following approximation for the non-retarded Hamaker constant ... 

The analysis of Knowles and Turan (2000) of 7 -BN-amorphous silica-3C SiC interfaces showed that Eq. (17.3)could be used to calculate values of the Hamaker constant as a function of the orientation of / -BN with respect to a planar interface containing a thin amorphous silica film, provided that the effective values of static dielectric constant and refractive index for / -BN, /,., and / bx respectively, were taken to be... 

The resulting Hamaker constant is alwa3rs positive r ardless of the relative magnitures of A i and A22- For two different spherical particles (index 1 and 2) interacting in a liquid (index 3), the Hamaker constant mixing rule is given by... 

Several implications can be drawn directly from Eq. (2-39). First, A // is always positive. Thus, the rule like attracts like, inferred from Eq. (2-30) for molecular mixtures, should also hold at the continuum level. Second, when dispersion forces are dominant, the Hamaker constant is small when ha= b—that is when the dispersed phase (A) has an index of refraction close to that of the medium (B), These rules also apply to molecular mixtures. Nevertheless, small molecules with a significant difference in index of refraction often mix because of the large entropy thereby gained. But particles lose too little entropy on coagulation to resist doing so when there is an attractive van der Waals interaction, and so particle-particle clumping is the norm in suspensions, unless countermeasures are taken to stop it (see Section 7.1). Analogous considerations explain the prevalence of phase separation in polymer blends (see Section 2.3.1.2). 

In the case where the medium and the solids have the same index of refraction ( i = 2 1 = 2). the Hamaker constant A132 goes to zero. This method is... 

When the Hamaker constant is positive, it corresponds to attraction between molecules, and when it is negative, it corresponds to repulsion. By definition, 3 = 1 and n3 = 1 for a vacuum. As we know from McLachlan s equation (Equation (92)), the presence of a solvent medium (3) rather than a free space considerably reduces the magnitude of van der Waals interactions. However, the interaction between identical molecules in a solvent is always attractive due to the square factor in Equation (567). On the other hand, the interaction between two dissimilar molecules can be attractive or repulsive depending on dielectric constant and refractive index values. Repulsive van der Waals interactions occur when n is intermediate between nx and n2 in Equation (566). If two bodies interact across a vacuum (or practically in a gas such as air at low pressure), the van der Waals forces are also attractive. When repulsive forces are present within a liquid film on a surface, the thickness of the film increases, thus favoring its spread on the solid. However, if the attractive forces are present within this film, the thickness decreases and favors contraction as a liquid drop on the solid (see Chapter 9). 

Table 7.1 Dielectric constant (e), refractive index (n), main absorption frequency in the UV region (ve) and non-retarded Hamaker constants (/ n) for two identical liquids, solids and polymers at 20°C interacting across vacuum (or air), calculated using Equation (567), where e3 = 1 and n3 = 1. From Equation (569)...

This is because the refractive index of the solvent and that of the bilayers becomes closer, so that the Hamaker constant in the expression of van der Waals forces gets close to zero ... 

By reducing the density, solvent incorporation lowers the refractive index, which, in turn, affects the Van der Waals interaction, as shown in eq 1, and therefore leads to a decrease in the Hamaker constant. 

The Van der Waals force between the glass substrate and the sUica sphere is given by the superposition of the forces between (i) the glass substrate and the sUica sphere acting across an adsorbed layer of 8CB, (ii) the forces between the adsorbed layers and the prenematic 8CB, and (iii) the glass and prenematic 8CB acting across the adsorbed layer [8]. These different interactions are accounted for via the Hamaker constant Ah. A precise determination of the Hamaker constant is difficult, because it depends on the optical properties of the medium between the two surfaces, i.e. on the temperature and distance dependent anisotropic dielectric constants. To estimate Ah we ignored the anisotropy of the dielectric constant [8]. Dependent on the dielectric constant, the refractive index and the substrate, the Hamaker constant varies between 0.5 x 10-21 J < Ah < 10 X 10-21 J. 

Micellar stmctures from surfactants have a higher refractive index than water. For this reason, micellar solutions scatter light. The differences between the refractive index of micellar stmctures and the solvent water can be eliminated by adding hydrophilic co-solvents such as glycerol to the aqueous phase. The change of the refractive index of the mixed solvent has also consequences on the interaction between the micelles. With the matching of the refractive index between solvent and micellar stmctures, the attractive forces between the stmctures disappear because the Hamaker constant in the DLVO theory decreases towards zero. The consequence of this is that L -phases in two-phase Li/ La-systems swell until the La-phase takes up the whole volume of the sample. 

From a knowledge of the adsorption, immersion, and wetting properties of solid particles, we have examined the influence of particle-particle and particle-liquid interactions on the stability and structure formation of suspensions of hydrophobic and hydrophilic Aerosil particles in benzene-n-heptane and methanol-benzene mixtures. For the binary mixtures, the Hamaker constants have been determined by optical dispersion measurements over the entire composition range by calculation of the characteristic frequency (Vk) from refractive index measurements [7,29,36,64], The Hamaker constant of an adsorption layer whose composition is different from that of the bulk has been calculated for several mixture compositions on the basis of the above results. Having the excess isotherms available enabled us to determine the adsorption layer thickness as a function of the mixture composition. For interparticle attractive potentials, calculations were done on the basis of the Vincent model [3-5,39]. In the case of hydrophobic particles dispersed in benzene- -heptane and methanol-benzene mixtures, it was established that the change in the attractive potential was in accordance with the interactions obtained from rheological measurements. 

For non-polar polymers interacting with a silica probe under perfluorodecalin the Hamaker constant scales with the refractive index. This leads to the observation that the polymer with the highest refractive index shows the largest pull-off force. In fact, calculating the work of adhesion, W, from Eq. 1, and plotting the measured pull-off forces against this quantity, one sees a reasonable correlation (Figure 4), as would be expected from the appropriate contact mechanical models (25). 

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