Yukawa fluid

To illustrate a FT, we use the Dyson equation that is characteristic of helds and we focus on the local density fluctuations that is the most natural variable in this approach. Two systems are considered a homogeneous Yukawa fluid and an ionic soluhon near a hard wall. 

In [17] we have calculated (Ss(r)) and shown that the value of (,s(r)) on the wall verifies the contact theorem. The integral of (s(r)) gives the adsorption I. From the calculation of the free energy we have obtained the surface tension and shown that the Gibbs isotherm leads to the same F as the one calculated via the density profile. Thus, as in the case of the homogeneous Yukawa fluid we have a totally self consistent calculation. 

Brinkman, H. C. and J. J. Hermans. 1949. The effect of non-homogeneity of molecular weight on the scattering of hght by high polymer solutions. Journal of Chemical Physics. 17,574. Broccio, M., D. Costa, Y. Liu, and S. H. Chen. 2006. The structural properties of a two-Yukawa fluid Simulation and analytical results. Journal of Chemical Physics. 124,084501. Brooks, C. L., M. Kaiplus, and B. M. Pettitt. 1988. Proteins A Theoretical Perspective of Dynamics, Structure and Thermodynamics. Vol. 71, Advances in Chemical Physics Hoboken, NJ Wiley. 

Yu, Y.-X., You, F.-Q., Tang, Y., Gao, G.-H., and Li, Y.-G. 2006. J. Phys. Chem. B. Structure and adsorption of a hard-core multi-Yukawa fluid confined in a shthke pore Grand canonical Monte Carlo simulation and density functional smdy. 110 334. 

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. 

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... 

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]. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Steynberg, A. P., Shingles, T., Dry, M. E., Jager, B., and Yukawa, Y. Sasol commercial scale experience with Synthol [fixed fluid bed] and [circulating fluid bed] Fischer-Tropsch reactors, in Circulating Fluidized Bed Technology HI (P. Basu, M. Horio, and M. Hasatani, eds.), pp. 527-53Z Pergamon, New York, 1991. 

DFT has been much less successful for the soft repulsive sphere models. The definitive study of DFT for such potentials is that of Laird and Kroll [186] who considered both the inverse power potentials and the Yukawa potential. They showed that none of the theories existing at that time could describe the fluid to bcc transitions correctly. As yet, there is no satisfactory explanation for the failure of the DFTs considered by Laird and Kroll for soft potentials. However, it appears that some progress with such systems can be made within the context of Rosenfeld s fundamental measures functionals [130]. 

Rosenfeld, Y. 1993. Eree energy model for inhomogeneous fluid mixtures Yukawa-charged hard spheres, general interactions, and plasmas. The Journal of Chemical Physics 98, no. 10 8126. doi 10.1063/1.464569. 

Yu YX, Jin L (2008) Thermodynamic and structural properties of mixed colloids represented by a hardcore two-Yukawa mixture model fluid Monte Carlo simulations and an analytical theory. J Chem Phys 128 014901, 1-13... 

Liu Y, Chen X, Liu H, Hu Y,JiangJ A density functional theory for Yukawa chain fluids in a nanoslit. Mol Simul 36(4) 291—301, 2010a. 

The Gibbs-Duhem integration method excels in calculations of solid-fluid coexistence [48,49], for which other methods described in this chapter are not applicable. An extension of the method that assumes that the initial free energy difference between the two phases is known in advance, rather than requiring it to be zero, has been proposed by Meijer and El Azhar [51]. The procedure has been used in [51] to determine the coexistence lines of a hard-core Yukawa model for charge-stabilized colloids. 

Behzadi, B., Patel, B.H., Galindo, A., and Ghotbi, C., 2005. Modeling electrolyte solutions with the SAFT-VR equation using Yukawa potentials and the mean-spherical approximation. Fluid Phase Equilib., 236 241-255. 

To bring this subsection to a close some comments on the QHS system including attractive forces are in order. The introduction of attractive tails can modify greatly the structural and thermodynamic behavior of the underlying bare QHS system. This has been shown by the present author and L. Bailey [108] with the use of pair-wise Yukawa attractive tails and PIMC simulations. By doing so, the onset of critical behavior in the quantum hard-sphere Yukawa (QHSY) system was identified under conditions in which the QHS system remains in the normal fluid phase. The Hamiltonian for the QHSY system can be cast as... 

A number of simulation works carried out so far with PI and quantum effective pair potentials to study representative quantum fluids are considered later. Part of the related references have been cited throughout this chapter in connection with theoretical developments, and it seems fit to organize them under the quantum systems they deal with. These systems are as follows (i) the system composed of QHS, bare (QHS), and with attractive Yukawa tail (QHSY) (ii) liquid neon (iii) fluid hydrogen and (iv) fluid helium He and He). 

The phase behavior of the hard-core Yukawa potential has been studied experimentally and by numerical simulation, see e.g. Ref. [65, 66, 67]. The computed phase diagram of Ref. [67] shows a fluid-solid (bcc/fcc) and a solid-solid (bcc-fcc) coexistence line and it exhibits two fluid-bcc-fcc triple points, (see Fig. 19). The main difference between the phase diagram of the hard-core Yukawa model and that of the pure (i.e. point-particle) Yukawa potential [68] is the presence of the second triple point. This triple point sets a lower limit for the strength of the Yukawa interaction for which a bcc phase exists. 

The repulsive Yukawa system offers a unique opportunity to study the effect of meta-stable crystal phases on the pathway for crystal nucleation. To smdy the effect of meta-stable intermediates on crystallization, we analyzed the structure of the (pre)critical nucleus in different regions of the phase diagram. Note that the pressure range region where the bcc phase is stable is rather narrow. For these pressures, the supersaturation of the fluid phase is small, and hence the nucleation barrier is very high. As a consequence, we could only study the formation of pre-critical nuclei in... 

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