Yukawa potential

The solution detennines c(r) inside the hard core from which g(r) outside this core is obtained via the Omstein-Zemike relation. For hard spheres, the approximation is identical to tire PY approximation. Analytic solutions have been obtained for hard spheres, charged hard spheres, dipolar hard spheres and for particles interacting witli the Yukawa potential. The MS approximation for point charges (charged hard spheres in the limit of zero size) yields the Debye-Fluckel limiting law distribution fiinction.  [c.480]

This r dependence is also known as a Yukawa potential. This type of potential has been used to describe the behaviour of latex suspensions at low ionic strength.  [c.2678]

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851.  [c.2687]

In the Yukawa potential, A is an inverse range parameter. The value A = 1.8 is appropriate for the inert gases. Each of the above potentials has a hard core. Real molecules are hard but not infinitely so. A slightly softer core is more desirable. The Lennard-Jones potential  [c.137]

Since the results for thermodynamics from the Yukawa potential, with A = 1.8, are similar to the results of the LJ potential, it is quite possible that the DHH closure may be applicable to the Yukawa potential. With A = 1.5, the thermodynamics of the square well fluid are also similar. Here, too, the DHH closure may be useful. However, the DHH closure has not been applied to either of these potentials.  [c.146]

The Yukawa potential is of interest in another connection. According to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, colloidal  [c.148]

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60].  [c.150]

The concentration profiles of colloidal particles [30] and of mixtures [31] in a charged cylindrical pore were considered. A fluid confined in a disordered porous material was simulated [32]. Symmetry-breaking density profiles were found [33]. The static and dynamical properties of hard spherical particles in 2d [34] and in 3d [35] confined to a spherical cavity (see Fig. 11) were investigated by molecular dynamics (MD) simulation. As this situation is also a challenge for theory, simulations where done to compare with density-functional theory [36,37]. For small systems the choice of ensemble matters, whether canonical or grand canonical. The effect of confinement on charge-stabilized colloidal suspensions between two charged plates was investigated [38]. The effective interaction and density profiles of charged colloids between parallel plates [39] was simulated using a model with a space-dependent Yukawa potential.  [c.757]

Coupling Eqs. (40) and (41) with the OZ equation gives an integral equation, which can be solved numerically. Perhaps the main reason for the interest in the MSA equation is that it can be solved analytically for several important fluids. For example, the PY approximation for the hard sphere fluid can be regarded as a special case of the MSA for a fluid with an infinitely hard core and no attractive interactions. Another case is the Yukawa fluid [30-37], whose potential is given by Eq. (6). Other fluids that yield analytic solutions are ionic fluids [38-41], where the ions interact with the Coulomb potential and the solvent molecules interact with a dipole-dipole interaction [42], and mixtures of fluids with these charged and dipolar potentials [43-47]. The MSA is very useful at higher densities, as long as the interactions are not too strong, but is less useful at low densities. Because of the linearization it can lead to negative values of g r).  [c.148]

See There it is again But even when this person sat down and contemplated the use of the P2P nothing but misery followed. This method has to work because its potential is massive. But it needs further study Yeesh  [c.93]

Product assembly is such a large area that focusing on the key operational issues, such as handling, fitting and joining, is justified at the design stage. Although much has been written about DFA, it was not appropriate to use the DFA indices directly for these assembly operations because they are based on relative cost, not potential variability. Where the knowledge and data cannot help, and where some of the more qualitative aspects of design commence, as well as expert knowledge, some Poka Yoke ideas were used, particularly for the component fitting chart. Poka Yoke is used to prevent an error being converted into a defect (Shingo, 1986). It is heavily involved in the development of any DFA process. Poka Yoke has two main steps preventing the occurrence of a defect, and detecting a defect (Dale and McQuater, 1998). Some of the assembly variability risks charts reflect these Poka Yoke philosophies.  [c.63]

Modem society has introduced or increased human exposure to thousands of chemicals in the environment. Examples are inorganic materials such as lead, mercury, arsenic, cadmium, and asbestos, and organic substances such as polychlorinated biphenyls (PCBs), vinyl chloride, and the pesticide DDT. Of particular concern is the delayed potential for these chemicals to produce cancer, as in the cases of lung cancer and mesothelioma caused by asbestos, liver cancer caused by vinyl chloride, and leukemia caused by benzene. Minamata disease, caused by food contaminated with mercury, and Yusho disease, from food contaminated with chlorinated furans, are examples of acute toxic illnesses occurring in nonoccupational settings. The full toxic potential of most environmental chemicals has not been completely tested. The extent and frequency of an illness are related to the dose of toxin, in degrees depending on the toxin. For chronic or delayed effects such as cancer or adverse reproductive effects, no "safe" dose threshold may exist below which disease is not produced. Thus, the cancer-producing potential of ubiquitous environmental contaminants such as DDT or the PCBs remains undefined.  [c.43]

Quite recently, Pini et al. [56] have reported a new, thermodynamically self-consistent approximation to the OZ relation for a fluid of spherical particles for a pair potential given by a hard-core repulsion and a Yukawa attractive tail (Eq. (6)). The closure to the OZ equation they have proposed has the form  [c.150]

See pages that mention the term Yukawa potential : [c.478]    [c.137]    [c.149]    [c.162]    [c.648]    [c.760]    [c.139]   
Computational methods in surface and colloid science (2000) -- [ c.137 , c.146 , c.148 , c.149 , c.307 , c.648 , c.757 , c.765 ]