Soft-repulsion effects

The column headed HSE uses an approximation made originally by Mansoori and Leland (3) that the diameter used in the hard sphere equations of state is c0o-, the LJ a parameter for each molecule multiplied by a universal constant for conformal fluids. This approximation then requires that be replaced by equations defining the HSE pseudo parameters, Equations 10 and 11. The results in the HSE column use c0 = 0.98, the value for LJ fluids obtained empirically by Mansoori and Leland. This procedure is correct only for a Kihara-type potential and it is not consistent with the LJ fluids in Table I. Furthermore, this causes only the high temperature limit of the repulsion effects to be included in the hard-sphere calculation. Soft repulsions are predicted by the reference fluid. 

The reduced density of 1.6 is considered to be the upper limit of the validity of Equation 36. At densities higher than this 8 and a2 decrease rapidly and a2 itself eventually becomes positive, interpreted as its domination by positive soft-repulsion effects. Diameters from Equation 36 give poor results in this region. There is no way that these soft effects can be separated from attraction effects and the optimal diameter cannot be calculated. 

The behavior of the quadratic and linear fit methods is shown in Figure 1. The interpretation of the a2 coefficient behavior in terms of soft-repulsion effects in the quadratic fit az(p) assumes that the data fitted... 

Somsen obtained individual AH iy(ion) data for the alkali metals and halides in the amides using the method of Halliwell and Nyburg. The quadrupole moments of the amides were obtained by modifying eqn. 2.11.21 to allow for repulsion effects. Considering a system of soft spheres , eqn. 2.11.21 becomes... 

The soft, repulsive effective interactions between polymer coils are also operative in the bulk. The analog considerations in the bulk yield the same recursion relation as in eqn [24] with d = 3. In this case, the solution is given by ... 

The quantity b has the dimension of a volume and is known as the excluded volume or the binary cluster integral. The mean force potential is a function of temperature (principally as a result of the soft interactions). For a given solvent or mixture of solvents, there exists a temperature (called the 0-temperature or Te) where the solvent is just poor enough so that the polymer feels an effective repulsion toward the solvent molecules and yet, good enough to balance the expansion of the coil caused by the excluded volume of the polymer chain. Under this condition of perfect balance, all the binary cluster integrals are equal to zero and the chain behaves like an ideal chain. 

To minimize effects of friction and other lateral forces in the topography measurements in contact-modes AFMs and to measure topography of the soft surface, AFMs can be operated in so-called tapping mode [53,54]. It is also referred to as intermittent-contact or the more general term Dynamic Force Mode" (DFM). A stiff cantilever is oscillated closer to the sample than in the noncontact mode. Part of the oscillation extends into the repulsive regime, so the tip intermittently touches or taps" the surface. Very stiff cantilevers are typically used, as tips can get stuck" in the water contamination layer. The advantage of tapping the surface is improved lateral resolution on soft samples. Lateral forces... 

The calculated Rayleigh mode (SJ, the lowest lying phonon branch, is in good agreement with the experimental data of Harten et al. for all three metals. Due to symmetry selection rules the shear horizontal mode just below the transverse bulk band edge can not be observed by scattering methods. The mode denoted by Sg is the anomalous acoustic phonon branch discussed above. Jayanthi et al. ascribed this anomalous soft resonance to an increased Coulomb attraction at the surface, reducing the effective ion-ion repulsion of surface atoms. The Coulomb attraction term is similar for all three metals... 

Exactly why this is, we are not certain. One can simply say that 0H is a hard base, whereas (Pt(II) is a class A metal or soft acid, and this hard-soft combination is unstable. It is also possible to suggest that the repulsive interaction between the filled d-orbitals on Pt(II) and the filled -orbitals on 0H make it a poor reagent. The same is true of F which is also a poor reagent. Other halide ions have low energy, vacant d-orbitals which can accept electrons and decrease the effect of the filled -orbitals. This makes these halide ions better reagents than F . 

The discussion of Kapral s kinetic theory analysis of chemical reaction has been considered in some detail because it provides an alternative and intrinsically more satisfactory route by which to describe molecular scale reactions in solution than using phenomenological Brownian motion equations. Detailed though this analysis is, there are still many other factors which should be incorporated. Some of the more notable are to consider the case of a reversible reaction, geminate pair recombination [286], inter-reactant pair potential [454], soft forces between solvent molecules and with the reactants, and the effect of hydrodynamic repulsion [456b, 544]. Kapral and co-workers have considered some of the points and these are discussed very briefly below [37, 285, 286, 454, 538]. 

The adhesion force increases linearly with the particle radius. Surprisingly, it is independent of the elasticity of the materials. This is because of two opposing effects. In a hard material the deformation of the solid is small. As a result the contact area and the total attractive surface energy are small. On the other hand, the repulsive elastic component is small. Both effects compensate each other. Soft materials are strongly deformed. Thus both the attractive surface energy term and the repulsive elastic term are high. 

We present how to treat the polarization effect on the static and dynamic properties in molten lithium iodide (Lil). Iodide anion has the biggest polarizability among all the halogen anions and lithium cation has the smallest polarizability among all the alkaline metal cations. The mass ratio of I to Li is 18.3 and the ion size ratio is 3.6, so we expect the most drastic characteristic motion of ions is observed. The softness of the iodide ion was examined by modifying the repulsive term in the Born-Mayer-Huggins type potential function in the previous workL In the present work we consider the polarizability of iodide ion with the dipole rod method in which the dipole rod is put at the center of mass and we solve the Euler-Lagrange equation. This method is one type of Car-Parrinello method. 

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