Hamaker constant negative values

For the aq.KOH-graphite system, the van der Waals interaction should be repulsive, because Lifshitz theory predicts a negative Hamaker constant A, which we calculated to be approximately -7.7 X 10 ° J. Using this value, the fit gives ... 

This review indicates that good solvent conditions (in terms of either x or 0) result in a positive value for AGR. This is what would be expected from a model that assumes that the first encounter between particles with adsorbed layers is dominated by the polymers. Conversely, in a poor solvent AGR is negative and amounts to a contribution to the attraction between the core particles as far as flocculation is concerned. Under these conditions the polymer itself is at the threshold of phase separation. Van der Waals attraction between the core particles further promotes aggregation, but it is possible that coagulation could be induced in a poor solvent even if the medium decreases the effective Hamaker constant to zero. 

For a molecule of gas, B is negative (the particles are attracted by the plates). However, if the particles are immersed in a medium, it is possible to have positive B values, depending on the Hamaker constants of the plates, particles and medium. Assuming a cut-off distance A for the interaction, the free energy per unit area (Eq. (8)) becomes, in the linear approximation (which is accurate if B is small or if the particle is sufficiently far from any interface) ... 

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). 

As mentioned in Section 12.1, the disjoining pressure is given by pdisj = — d V/d h. Differentiating Eq. (12.2) then yields />disj = —4/6 nh3. The disjoining pressure thus is negative, as it should be for an attractive force. According to Table 12.2, the value of An, i-e., for water across air, equals 37 10 21 J, and the value for air across water is virtually the same. We thus obtain />disj = —2000 Pa, a considerable pressure. The value of the Hamaker constant for oil across water depends on the type of oil and is... 

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. 

The Hamaker constant can be either positive (repulsion) or negative (attraction). Note that the precise value of the Hamaker constant according to direct summation can be wrong. This is a reason why a number of approximations have been developed to calculate the Hamaker constant using the exact theory [1]. 

Here, A is the absolute value of the (negative) Hamaker constant. Then the crossover reads ... 

Because, for most known cases, the Hamaker constant assumes positive values, one can deduce from Eqs. (68)-(75) that the dispersion contribution to the net interaction energy is negative (attraction) at all particle separations. Moreover, due to the insensitivity of the Hamaker constant on material properties (except for metals, it is usually confined within the range 5 X 10 to 5 X 10 J), the range of dispersion interactions is fairly fixed and equal to 10-... 

In the case of unlike particles, effective Hamaker constants can be positive or negative, and the latter imphes repulsive van der Waals forces which contribute to stabihty. One application of such repulsive vdW forces is in predicting solubihty for blend-solvent mixtures, as discussed by van Oss et al. (1980). Using the Hamaker constant values for some polymers and solvents, fill in Table 2.5 and compare... 

Thus, in the (often encountered) case of particles of the same type or when air/vacuum are the medium (zero Hamaker constant for vacuum and almost zero for air). Equations 10.6 and 10.7 lead always to a positive Hamaker constant and attractive van der Waals forces, which is the most usual case. However, in the case of unlike particles and when the Hamaker constant. A, of the medium has a value in between that of two different types of particles, the effective Hamaker constant can be negative, which implies repulsive van der Waals forces. In this case one material interacts more strongly with the medium than with the second body. 

Stable colloids are achieved if the Debye length (double layer thickness) is very high (i.e. low salt content, low valency ions), if the colloid particles are in a medium with high relative permittivity, if they have low (or even negative) Hamaker constants and high values of the surface or zeta potential. Control of the ionic concentration and surface charge are crucial. 

An increase in the Hamaker constant A makes increasingly negative and the maximum decreases. This factor should not be taken into account in the analysis of the stability of a system, because the value of A is fixed since it is a function of the characteristics of the materials. The same is true for particle size. If phenomena such as Oslwald ripening do not occur, the particle size is constant for any given system. However, it should be pointed out that the energy of Van Der Waals forces... 

According to Eq. (4.19), if Ci > 83 > C2, the value of A is negative, that is, there is a repulsive force. It is difficult to explain this in terms of the Hamaker method of pair-wise interactions. One might say that the intervening medium with dielectric constant likes itself more than the two bodies. 

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