Effect of the Intervening Medium

Particles immersed in a liquid medium experience a smaller attractive force. The calculation of such forces and their relationship to the nature of the particles and of the dispersion medium has been, and continues to be, a major theoretical problem. Important advances towards its solution have been made in recent years, and they will be mentioned briefly in Chapter 15. For the present purposes it is sufficient to use a relatively simple approximate equation according to which the appropriate Hamaker constant to be employed when two particles of material 1 are separated by a medium 2 is given by 

In Chapter 1 it was stated that the particles in most colloidal dispersions in aqueous media carry an electric charge. We also learned that the stability of such dispersions is very sensitive to the addition of electrolytes. Evidence for the existence of charges on particles comes from the phenomenon of electrophoresis, which will be dealt with in Chapter 6. Meanwhile we accept their 

Surfaces may become electrically charged by a variety of mechanisms, the more important of which are the following  

To examine the way in which these charges affect the properties of colloids, it is first necessary to say a little about fundamental electrostatic theory. 

The fundamental law of electrostatics — Coulomb s law -expresses the inverse square law of force between two electric charges q and q2 separated by a distance if in a vacuum in the form  

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The closest contact distance, do, is normally taken to be 3 A (van der Waals contact of the edges of the donor and acceptor). The value of p is a measure of the effectiveness of the intervening medium in coupling the donor and acceptor [3, 30]. 

The Lifshitz theory, as outlined earlier, is fairly difficult, and we provide here only approximate relations for the effect of the intervening medium. If we consider two bodies with dielectric constants Ci and Cx separated by a medium with dielectric constant Cs, the theory predicts that the Hamaker constant A is proportional to a tom given by the equation... 

When considering long-range electron transfer in proteins, there has been some discussion of the influence of the intervening medium and in particular of whether the electron passes along a particular path or makes significant use of particular protein side chains. For instance it was postulated that aromatic side chains of proteins play an important role. However a recent study by Moser et of electron transfer in the bacterial photoreaction center reveals no such effects in that case. 

The equations for surface interactions given above were derived for the situation in which the interacting units were separated by a vacuum. Obviously, for practical purposes, that usually represents a rather unrealistic situation. Real life dictates that in all but a few situations, interacting units be separated by some medium that itself contains atoms or molecules that will impose their own effects on the system as a whole. How will the relevant equations be modified by the presence of the intervening medium ... 

One must keep in mind that the preceding discussion was couched in terms of interactions in a vacuum or other inert environment, which is not a very practical situation for most applications. In order to understand real colloidal systems, one must take into consideration the effects of an intervening medium, the continuous phase, on the above interactions. 

Dielectric constant A dimensionless constant that expresses the screening effect of an intervening medium on the interaction between two charged particles. Every medium (such as a water solution or an intervening portion of an organic molecule) has a characteristic dielectric constant. 

Clearly, if one takes a smaller value of D, one gets a higher value of IVj j, for a given distance Rufj. Kirkwood and Westheimer (1938), Westheimer and Kirkwood (1938), and Westiieimer and Shookhoff (1939) indeed argued that one should take a much smaller dielectric constant, since the intervening medium between the two protons more closely resembles a hydrocarbon liquid rather than water. In fact, for any dicarboxylic acid one can define an effective dielectric constant to fit the experimental value of W, by an equation of the form (4.8.13), with Dg being dependent on the proton-proton distance, the type and size of the acid and the solvent. 

If the charges are embedded in a medium, the electrical properties of the intervening molecules decrease the force from the value calculated by Equation (4). The relative dielectric constant of the medium er measures this effect quantitatively. In surroundings other than a vacuum, the force between two charges is given by... 

In reaching this conclusion we have assumed that no time lag affects the field that establishes the attraction between the particles. We have also considered particles under vacuum so no intervening medium enters the picture. Each of these simplifying approximations has the effect of overestimating the van der Waals attraction between particles at large separations from one another and embedded in a medium. We consider presently the effect of a time lapse between the interaction of a field with two different particles the effect of the medium is discussed in Section 10.8. 

If an intervening layer is now placed between the two media, the reflectivity will be modified due to interference effects between neutrons reflected from upper and lower interfaces. Apart from the incident angle, factors that determine the reflectivity are the scattering length density of the layer, the layer thickness, and the scattering length densities of the upper medium and the subphase. 

Fig. 1 shows the interference effects that occur when a thin film sample is irradiated on a substrate surface. (To clearly demonstrate the phenomenon, the reflective interference is illustrated here with angular incident light.) The reflection of vertically incident light of a specific wavelength depends on the film thickness, which can then be computed if the refractive indices for the intervening medium, film and substrate are all known [1]. 

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