Physicochemical Properties Needed to Calculate the Nonretarded
Hamaker Function (Equation 3.4) for Some Materials Commonly
Found in Food Emulsions
Static relative Absorption dielectric constant Refractive index frequency
Water 80 1.333 3.0
Pure protein 5 1.56 2.9
x% protein in water 5x + 80(1 - x) 1.56x + 1.333(1 - x) 2.9
Pure Tween 20 1.468 2.9
Data compiled from Israelachvili (1992), Wei et al. (1994), and Hato et al. (1996).
suspended in an electrolyte solution because of the accumulation of counterions around the droplets (Section 3.4.2). Electrostatic screening causes the zero-frequency component to decrease with increasing droplet separation and with increasing electrolyte concentration (Mahanty and Ninham 1976; Marra 1986; Israelachvili 1992; Mishchuk et al. 1995, 1996). At high electrolyte concentrations, the zero-frequency contribution decays rapidly with distance and makes a negligible contribution to the overall interaction energy at distances greater than a few nanometers (Figure 3.3). On the other hand, the frequency-dependent component (Av>0) is unaffected by electrostatic screening because the ions in the electrolyte solution are so large that they do not have time to move in response to the rapidly fluctuating dipoles (Israelachvili 1992). Consequently, the van der Waals interaction may decrease by as much
as 42% in oil-in-water emulsions at high-ionic-strength solutions because the zero-frequency component is completely screened.
The strength of the van der Waals interaction between emulsion droplets is reduced because of a phenomenon known as retardation (Israelachvili 1992). The origin of retardation is the finite time taken for an electromagnetic field to travel from one droplet to another and back (Mahanty and Ninham 1976). The frequency-dependent contribution to the van der Waals interaction (wv>0) is the result of a transient dipole in one droplet inducing a dipole in another droplet, which then interacts with the first dipole (Section 2.3.3). The strength of the resulting attractive force is reduced if the time taken for the electromagnetic field to travel between the droplets is comparable to the lifetime of a transient dipole, because then the orientation of the first dipole will have changed by the time the field from the second dipole arrives (Israelachvili 1992). This effect becomes appreciable at dipole separations greater than a few nanometers and results in a decrease in the frequency-dependent (Av>0) contribution to the Hamaker function with droplet separation. The zero-frequency contribution (Av=0) is unaffected by retardation because it is electrostatic in origin (Mahanty and Ninham 1976). Consequently, the contribution of the Av>0 term becomes increasingly small as the separation between the droplets increases. For example, the retarded value of wv>0(tí) between two emulsion droplets at a separation of 20 nm is only 33% of the nonretarded value (Figure 3.3). Any accurate prediction of the van der Waals interaction between droplets should therefore include retardation effects. A number of authors have developed relatively simple correction functions which can be used to account for retardation effects (Schenkel and Kitchner 1960; Gregory 1969, 1981; Anandarajah and Chen 1995; Chen and Anandarajah 1996), although the most accurate method is to solve the full theory numerically (Mahanty and Ninham 1976, Pailthorpe and Russel 1982).
So far, we have assumed that the van der Waals interaction occurs between two homogeneous spheres separated by an intervening medium (Figure 3.1). In reality, emulsion droplets are normally surrounded by a thin layer of emulsifier molecules, and this interfacial layer has different physicochemical properties (eR, n, and v^ than either the oil or water phases (Figure 3.4). The molecules nearest the surface of a particle make the greatest contribution to the overall van der Waals interaction, and so the presence of an interfacial layer can have a large effect on the interactions between emulsion droplets, especially at close separations (Vold 1961, Israelachvili 1992, Parsegian 1993).
The influence of an adsorbed layer on the van der Waals interactions between emulsion droplets has been considered by Vold (1961):
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