Lennard-Jones fluids associating

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

In the context of liquid-vapor coexistence the particle number N (or equivalently the number density p = N/V) plays the role of an order parameter. Estimates of the distribution Po N p, T) are available from the simulation for all the points chosen to define the path. One may then identify the free energy difference from the integrated areas of the branches of this distribution associated with each phase and proceed to search for coexistence using the criterion that these integrated areas should be equal ((8) et seq.). Figure 2 show some explicit results [41] for a Lennard-Jones fluid. 

A very useful algorithm for the numerical integration of the large number of coupled differential equations associated with proteins was introduced by L. Verlet in 1964 for dynamical simulations of Lennard-Jones fluids [26]. The Verlet algorithm may be derived from the simple central difference of the Taylor series expansion for the atomic position at time t. For the vector position of atom i, fj, the algorithm is... 

A. Huerta, O. Pizio, S. Sokolowski, Phase transitions in an associating, network-forming, Lennard-Jones fluid in sfit-Hke pores. II. Extension of the density functional method, J. Chem. Phys. 112 (2000) 4286 295. 

B. M. Malo, L. Salazar, S. Sokolowski, O. Pizio, Application of the density functional method to study adsorption and phase transitions in two-site associating, Lennard-Jones fluids in cylindrical pores, J. Phys. Condens. Matt. 12 (2000) 8785-8800. 

The calculations have been carried out for a one-component, Lennard-Jones associating fluid with one associating site. The nonassociative van der Waals potential is thus given by Eq. (87) with = 2.5a, whereas the associative forces are described by means of Eq. (60), with d = 0.5contact with an attracting wall. The fluid-wall potential is given by the Lennard-Jones (9-3) function... 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

We report here some results for a simple model of a one-component fluid interacting via a slightly modified Lennard-Jones potential, with angular-dependent associative forces. The model is considered in contact with the adsorbing surface. The principal aim of the simulation is to investigate the... 

P. Bryk, A. Patrykiejew, O. Pizio, S. Sokolowski. The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations. Mol Phys 92 949, 1997 A method for the determination of chemical potential for associating liquids. Mol Phys 90 665, 1997. 

The simplest simulated system is a Stockmayer fluid structureless particles characterized by dipole-dipole and Lennard-Jones interactions, moving in a box (size L) with periodic botmdary conditions. The results described below were obtained using 400 such particles and in addition a solute atom A which can become an ion of charge q embedded in this solvent. The long range nature of the electrostatic interactions is handled within the effective dielectric environment seheme. In this approach the simulated system is taken to be surrounded by a continuum dielectric environment whose dielectric constant e is to be chosen self consistently with that eomputed from the simulation. Accordingly, the electrostatic potential between any two partieles is supplemented by the image interaction associated with a spherical dielectric boundary of radius (taken equal to L/2) placed so that one of these... 

The object of any statistical mechanical theory of polymer systems is ultimately to relate the measurable physical properties of the system to the properties of the constituent monomers and their mutual interactions. It is imperative that the initial statistical mechanical theories of these physical properties of polymer systems not depend on the exact details of a particular polymer. Instead, these theories should reflect those generic properties of polymer systems that are a result of the chainlike structures of polymer molecules. Once the properties of simple, yet general, models of polymers are well understood, it is natural to focus attention upon the particular aspects of a polymer of interest. The initial use of simple models of polymers is not solely dictated by an attempt to obtain those general features of polymer systems. The mathematical simplicity of the model is required so that we avoid the use of uncontrollable mathematical approximations which necessarily arise with the use of more complicated models. When the model is sufficiently simple, yet physically nontrivial, we are able to test different approximation schemes to find those that are useful. Presumably these methods of approximation would also be useful for more complicated models. This emphasis upon mathematical simplicity has its analog in the theory of fluids. First hard-core interactions can be used to test the physical principles associated with various methods of approximation. Once physically sound approximation schemes have been obtained with this model, they may be applied with more realistic potentials, e.g., the Lennard-Jones potential, which require subsequent numerical approximations. Thus we wish to separate approximations of a physical origin from those of purely a numerical nature. This separation... 

The main change in the SAFT version of Kraska and Gubbins is that they use Lennard-Jones (LJ) spheres for the reference term, rather than hard spheres. The remaining terms are unchanged, except that the radial distribution function used in the calculation of the chain and association contributions in Equations 3.25 and 3.31 is the radial distribution function for LJ spheres rather than hard spheres. Thus, an equation of state for LJ spheres is required. The equation used is that of Kolafa and Nezbeda. The Helmholtz energy for the reference (LJ) system is (for a pure fluid)... 

Here, we will describe in more detail the interesting example of an application of density functional theory to the very comphcated system, namely the four-bonding Lennard-Jones associating fluid confined in slitlike pore [255]. The fluid is confined in the slitlike pore of width H. The total external field is the sum of contributions from two pore walls, located at z = 0 and z = H ... 

Llovell, F. P mies, J.C. Vega, L.F. (2004). Thermodynamic properties of Lennard-Jones chain molecules Renormalization-group corrections to a modified statistical associating fluid theory. /. Chem, Phys, 121,10715-10724. 

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