Hamaker constant composite

The expression for the van der Waals attractive potential between two identical colloidal particles with adsorbed layers can be written in terms of a composite Hamaker constant A [17] as... 

TABLE 1 Accessible Force Measuring Range for vdW Interactions as a Function of Spring Constant. The Calculations Assume a Tip Radius of 5 x IO-h m and a Composite Hamaker Constant of l x lO-20 J... 

From this equation, it is seen that the force of attraction FJ is proportioual to a constant A commonly called the Hamaker constant. This constant is dependent upon the molecular composition of the materials. For example. 

Hamaker Constant In a description of the London-van der Waals attractive energy between two dispersed bodies, such as droplets, the Hamaker constant is a proportionality constant characteristic of the droplet composition. It depends on the internal atomic packing and polarizability of the droplets. 

The last equation shows that the energy in PBS-dFFF is a function of the size and of the surface potential of the particle, of the Hamaker constant, and of the ionic strength of the carrier solution, as the reciprocal double-layer thickness is immediately related to the ionic strength of the suspending medium. Thus, selectivity in PBSdFFF results from differences in particle size or chemical composition of the particles and of the suspending medium, where the latter will affect the surface potential and the Hamaker constant of the particle, as well as the medium s ionic strength. 

The chemical nature of a solid determines its adsorptive and wetting properties. Now, the energy of immersion mainly depends on the surface chemistry but also, to some extent, on the nature of the bulk solid. For example, the interaction between water and silica has contributions from the bulk Si02 together with contributions from the silanol groups of the interface. Polar molecules are very sensitive to the local surface chemistry, whereas nonpolar molecules are more sensitive to the bulk composition. Interactions between a bulk Hquid and a bulk solid through an interface are often described in terms of Hamaker constant [16]. Immersion calorimetry in apolar liquids was proposed to estimate the Hamaker constant [17]. The sensitivity of immersion calorimetry to the surface polarity has justified its use for characterising the surface sites. 

The fact that the solute (component 2) and the membrane (component 3) are made from two different materials separated by the solvent (component 1) will be reflected by the use of a composite Hamaker constant. 

Application. To apply the DLVO theory in practice, several pieces of information have to be collected. Particle size (distribution) and shape can generally be experimentally determined. Hamaker constants often are to be found in the literature or can be calculated from Lifshits theory. The surface potential can be approximated by the zeta potential obtained in electrophoretic experiments. The ionic strength is generally known (or can be calculated) from the composition of the salt solution. All the other variables needed are generally tabulated in handbooks. This then allows calculation of V(h). To arrive at an aggregation rate, more information is needed this is discussed in Section 13.2. 

Consequently, for symmetric films the molecular component of disjoining pressure is always negative, which corresponds to a tendency of dispersion medium layer separating identical phases to decrease its thickness. At the same time, one should emphasize that in such systems in the absence of non-dispersion interactions the lower the value of complex Hamaker constant is, the more similar in nature the interacting phases (dispersed phase and dispersion medium) are. If contacting phases are essentially similar in structure and chemical composition, the value of A may be as low as 10 21 J or even much lower. The so low Hamaker constants result in changes in the nature of colloidal stability. 

If the interaction energy between water and particle molecules exceeds that of water molecules with each other, i.e. A,, p > A, the composite Hamaker constant is negative and the molecular... 

The composite Hamaker constant can change its sign due to surfactant adsorption at the bubble and/or particle surfaces (see Appendix lOD). 

Here the first term expresses the contribution of dispersion forces of repulsion 11 > 0, where A,30 is the composite Hamaker constant. The second term represents the forces of electrostatic attraction n, < 0. 

The presence of a medium affects the value of the Hamaker constant and for this situation A has to be rewritten as a composite constant Ac in the form... 

Another consequence of Equation (10.34) is that as the Hamaker constant Ah increases, the ccc values of dispersions with the same electrical characteristics will decrease that is, the colloidal dispersions will become progressively less stable. As indicated previously, the Hamaker constant in a medium will be a composite of those of the dispersed particle and the medium in vacuum, so that as the characteristics of the medium and dispersed phase become more similar. Ah will decrease, leading to an additional stability for the system, in agreement with observation. 

Figure 5.13. (a) Rheological master curves of selected commercially available polymers which approach each other at 300 rad/s and 500 Pa.s, and (b) degree of dispersion derived from LM for composites with 1 vol% MWCNTs (prepared at the same shear level) plotted versus the effective Hamaker constant... 

The strength of the van der Waals interactions is determined by the size and the shape of the colloidal particles and by the chemical composition of the system, which is described by the Hamaker constant A. Between two similar particles, the van der Waals forces are always attractive and /I is a positive constant. For spherical particles of radius R at separation d, the van der Waals energy is given as... 

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. 

As noted before, A is typically of the order of 10 to 10 J and depends on the properties of particles (of composition 1) and suspending medium (composition 2). Accordingly, the effective Hamaker constant is given by... 

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