Attractive interaction energy Hamaker constant

Surface Coating. A dense surface coating (encapsulation) that contains no occluded solvent decreases interparticle attraction provided that the coating has a Hamaker constant intermediate between the particle and the Hquid. This is called semisteric stabilization (ST). The energy of interaction between coated spheres is as follows (26) ... 

Figure 6.11 Gibbs free interaction energy (in units of ki>T) versus distance for two identical spherical particles of R = 100 nm radius in water, containing different concentrations of monovalent salt. The calculation is based on DLVO theory using Eqs. (6.57) and (6.32). The Hamaker constant was Ah = 7 x 10 21 J, the surface potential was set to )/>o = 30 mV. The insert shows the weak attractive interaction (secondary energy minimum) at very large distances.

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) ... 

Zeta potentials of slun particles and wafer surfaces were measured to calculate the DLVO total interaction energy between them at various pHs. Instead of the Debye-Huckel low potential approximation, Overbeek s approximate was applied to the calculation. The repulsive energy was calculated between silica and TEOS wafers. Particle dip test also showed no deposition of particles on TEOS wafer. Due to the low cell constant of conductive W plate, it was not possible to measure the zeta potentials of W. The Hamaker constants of A1 and W were calculated and applied to the calculation of total interaction energy. The theoretical calculation was agreed well with the experimental results. The strong attractive interaction between metal surfaces and alumina particles were observed in both the calculation and experiments. 

The variation of the potential energy of interaction between colloidal particles and sohd surfaces can be also succeeded by the addition of a detergent to the suspending medium, which leads to a decrease in the Hamaker constant and, consequently, in the potential energy of attraction. 

The van der Waals interaction due to the polarization of the metal cores constitutes the attractive term and the steric interaction between the thiol molecules on the two surfaces forms the repulsive term, where t is the interpartide distance. The Hamaker constant, A, for Pd nanocrystals, in toluene for instance, has been estimated to be 1.95 eV [140]. The calculated diameter of the area occupied by the thiol molecule (sa) on the particle surface is 4.3A [112]. The total energy is attractive... 

Fig. 3 Electrostatic repulsive thick line), van der Waals attractive dotted line) and total thin line) interaction energies of two approaching spherical particles. Particle radius, R=100 nm Stern potential, Pd=10 niV Hamaker constant, A=0.5xl0" J...

The attractive interaction depends largely on the Hamaker constant A, as shown in Eq. (2). The larger the value of A, the greater is the attractive energy between the particles. The net interaction energy is then the sum of Vr and Va-Equations (1) and (2) show that a better dispersion of fine particles must come from systems having large tj/rf and small A. 

The attractive van der Waals energy of interaction (Va) for spheres in the 10- to l(X3-nm size range for silica sols discussed here varies as the inverse of the separation distance, and at any separation Va is directly proportional to particle size. The Hamaker constant (A), which controls the magnitude of the variation of van der Waals attraction with particle radius (a) and separation (Hq) between surfaces, is for silica-water-silica not a large number. Further, the known hydration-polysilicic acid formation at silica-water interfaces will further reduce the overall Hamaker constant in the silica sol-water-silica sol system. 

If we want to create a colloidally stable system, some type of interparticle repulsion needs to be introduced to overcome the van der Waals attraction. In a stable system, the maximum attractive interparticle energy should be less than 1 -2 kT to allow thermal motion to readily break all particle-particle bonds. Since the magnitude and range of the attractive van der Waals interaction scales with the effective Hamaker constant, a relatively long-range repulsion is needed to stabilize suspensions of ceramic powders such as alumina and silicon carbide silica, however, is stabilized by a very short-range repulsion. 

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