Hamaker constant different materials

Here, we used the fact that the major contribution to the Hamaker constant comes from frequencies in the visible or UV. The refractive indices of the materials are n1 n2, and n3. Values of , n, and is, for different materials are listed in Table 6.2. 

Equation (6.25) not only allows us to calculate the Hamaker constant, it also allows us to easily predict whether we can expect attraction or repulsion. An attractive van der Waals force corresponds to a positive sign of the Hamaker constant, repulsion corresponds to a negative Hamaker constant. Van der Waals forces between similar materials are always attractive. This can easily be deduced from the last equation for 1 = e2 and n = n2 the Hamaker constant is positive, which corresponds to an attractive force. If two different media interact across vacuum ( 3 = n3 = 1), or practically a gas, the van der Waals force is also attractive. Van der Waals forces between different materials across a condensed phase can be repulsive. Repulsive van der Waals forces occur, when medium 3 is more strongly attracted to medium 1 than medium 2. Repulsive forces were, for instance, measured for the interaction of silicon nitride with silicon oxide in diiodomethane [121]. Repulsive van der Waals forces can also occur across thin films on solid surfaces. In the case of thin liquid films on solid surfaces there is often a repulsive van der Waals force between the solid-liquid and the liquid-gas interface [122],... 

In Table 6.3 non-retarded Hamaker constants are listed for different material combinations. Hamaker constants, calculated from spectroscopic data, are found in many publications [124-128], A review is given in Ref. [129],... 

Hamaker constants for single materials usually vary between about 10" 20 J and 10 19 J. Some examples are given in Table 8.3. Where a range of values is quoted for a given material, this reflects different methods of calculation within the basic microscopic or macroscopic method. 

Knowles and Turan (2000) and Knowles (2005) have used the approach of Parsegian and Weiss (1972) to examine the effect of anisotropy on Hamaker constants. Such calculations are relevant for materials such as 7 -BN and rutile, Ti02, which exhibit strong anisotropy in their refractive indices because of their crystal structure. They make little difference to predicted values of Hamaker constants as a function of grain orientation for materials such as Si3N4 and SiC which, by comparison, exhibit modest values of birefringence. 

Unless aggregation is studied, potential-barrier FFF is restricted only to particles which fully adsorb in a reversible way on the channel wall. Thus, the material of the channel walls needs to be properly selected which is a difficult task. One major advantage of potential-barrier FFF is the possibility to separate and characterize dilute colloidal samples of the same size but differing surface potentials or Hamaker constants. 

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. 

The (Qp2) term for the same type of molecule-surface and the (C1dp1p2) term for different types of molecule-surface are the material-related constants for an interaction. Hamaker collected these material constants in Hamaker interaction constants, (An), (A22) and (Ai2) so that... 

The Hamaker constant for a material composed of two different kinds of atoms can be calculated by replacing the quantity in Equation (4.44) by ( -I- nlal + Ithriiaiai). Explain why this formulation should be correct and calculate Ah for ice, taking the polarizabihty of H and O to be 0.67 X lO and 3.0 x 10 cm, respectively. Calculate the expected force between two thick flat slabs of ice 1 nm apart. Do the same for two spherical particles of ice 2000 nm in diameter and 1 nm apart. 

As a general conclusion, one could say that the proposed PBSdFFF concentration procedure works quite successfully in dealing with highly dilute samples, separating them according to size, surface potential, and Hamaker constant. At the same time, as separation occurs, the particle sizes of the colloidal materials of the diluted mixture can be determined. The major advantage of the proposed concentration procedure is that the method can concentrate and analyze dilute mixtures of colloidal particles even of the same size but with different surface potentials and/or Hamaker constants. The method has considerable promise for the separation and characterization, in terms of particle size, of dilute complex colloidal materials, where particles are present in low concentration. 

The first term is the disjoining pressure in the film with A the Hamaker constant describing the van der Waals interaction of the film with the surrounding media. The second term represents the electrostatic pressure exerted on the film by an electrostatic potential difference, U, between the conducting media cladding the film, with s being the dielectric constant of the film material. Finally the third term describes the Laplace pressure in the film with cr donating the interface tension between the film and the upper (liquid) medium. 

The difference between the two materials is that the Hamaker constant for the alumina is much greater than for the oil and thus the attraction between alumina particles is much stronger between alumina than between oil droplets. Thus, it is possible to just stabilize the oil droplets with 30 mV zeta potential, whereas when the alumina has 30 mV zeta potential, there is still attraction between the particles. Hence 60 mV is needed to stabilize the alumina to the same extent that 30 mV was able to stabilize oil droplets. 

Table 1 Examples of Hamaker constants for different materials [13]...

The value of A corresponds to the effective Hamaker cmistant for the interaction between particles i and j in the dispersion medium. The values of the Hamaker constant are presented for different materials in Table 1. 

It is well known from colloid science that two particles, labeled 1 and 2, immersed in a fluid, designated as 3, may either attract or repel each other, even over distances (h) of many tens of nanometers. Such long-range interaction may be due to apolar vdW forces, which can be described by a product of two terms. " The first term is accounting for the energetic properties of the different materials, expressed by an effective Hamaker constant A 22- The second term describes the geometry of the system. 1,5,10,56,57 is... 

Table 10.1 Examples of non-retarded (distance-independent) Hamaker constants for two identical materials interacting in a vacuum at room temperature. It should be emphasized that values for the same material can differ significantly from one source to another. The Hamaker constant of water is very low due to water being a small molecule. Additional values can be found in, for example, Bergstrom (1997) and IsraelachvUi (2011)...

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. 

In this case, the Hamaker constant, A, has been replaced by an effective Hamaker constant, A123, which is valid for two different materials in a liquid medium. The value of A123 can be calculated from Equation 10.7 ... 

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