Associating fluid model

The first and earliest class of new approaches to polymer fluids is the associating fluid model pioneered by Wertheim. In the associating fluid model one considers a liquid of particles interacting with a potential given by... 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

The theory of inhomogeneous associating fluids evidently has benefited from the developments available for bulk associating models. The theory of... 

The present chapter is organized as follows. We focus first on a simple model of a nonuniform associating fluid with spherically symmetric associative forces between species. This model serves us to demonstrate the application of so-called first-order (singlet) and second-order (pair) integral equations for the density profile. Some examples of the solution of these equations for associating fluids in contact with structureless and crystalline solid surfaces are presented. Then we discuss one version of the density functional theory for a model of associating hard spheres. All aforementioned issues are discussed in Sec. II. 

Sec. Ill is concerned with the description of models with directional associative forces, introduced by Wertheim. Singlet and pair theories for these models are presented. However, the main part of this section describes the density functional methodology and shows its application in the studies of adsorption of associating fluids on partially permeable walls. In addition, the application of the density functional method in investigations of wettability of associating fluids on solid surfaces and of capillary condensation in slit-like pores is presented. 

The structure of the bulk associating fluid in the framework of the model in question can be determined by solving the common Ornstein-Zernike (OZ) equation... 

The singlet-level theories have also been applied to more sophisticated models of the fluid-solid interactions. In particular, the structure of associating fluids near partially permeable surfaces has been studied in Ref. 70. On the other hand, extensive studies of adsorption of associating fluids in a slit-like [71-74] and in spherical pores [75], as well as on the surface of spherical colloidal particles [29], have been undertaken. We proceed with the application of the theory to more sophisticated impermeable surfaces, such as those of crystalline solids. 

The singlet-level theory has also been used to describe the structure of associating fluids near crystalline surfaces [30,31,76,77]. The surface consists explicitly of atoms which are arranged on a lattice of a given symmetry. The fluid atom-surface atom potential can also involve an associative term, i.e., the chemical-type bonding of the adsorbate particles with the surface may be included into the model. However, we restrict ourselves to the case of a nonassociative crystalline surface first. 

Again, we consider the model of an associating fluid by Cummings and Stell [25-27]. The fluid is studied in contact with a hard wall Uq,(z) is given by Eq. (41). In this case Eq. (16) becomes [85,86]... 

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]. 

The geochemical interactions possible between an injected waste and the reservoir rock and its associated fluids can be quite complex. Thus a combination of computer modeling, laboratory experimentation, and field observation will inevitably be necessary to satisfy current regulatory requirements for a geochemical no-migration deep-well injection. This section covers the computer methods and models available for predicting geochemical fate. 

The Separated Associated Fluid Interaction Model for Polar + Nonpolar Mixtures... 

Figure 6. Comparison of the Separated Associated Fluid Interaction Model using...

Flow calorimetric measurements of the excess enthalpy of a steam + n-heptane mixture over the temperature range 373 to 698 K and at pressures up to 12.3 MPa are reported. The low pressure measurements are analysed in terms of the virial equation of state using an association model. An extension of this approach, the Separated Associated Fluid Interaction Model, fits the measurements at high pressures reasonably well. 

The contribution "Application of Meso-Scale Field-based Models to Predict Stability of Particle Dispersions in Polymer Melts" by Prasanna Jog, Valeriy Ginzburg, Rakesh Srivastava, Jeffrey Weinhold, Shekhar Jain, and Walter Chapman examines and compares Self Consistent Field Theory and interfacial Statistical Associating Fluid Theory for use in predicting the thermodynamic phase behavior of dispersions in polymer melts. Such dispersions are of quite some technological importance in the... 

Holten-Andersen et al. (1987) modified the Flory equation of state in order to develop an equation that is applicable to the vapor phase, to make it more applicable to associating fluids, and to introduce a group contribution approach. Chen et al. (1990) revised and improved the equation of state. The final model takes the following form. 

In Tab. 3 we show selected results for the homogeneous phase at typical liquid state points and also at supercritical temperatures. We see that the internal energies for the short-range and parent models agree surprisingly well, particularly for associating fluids. Somewhat larger discrepancy, about 10%, is... 

Figure 9. The coexistence densities of the full (solid lines and filled symbols) and short-range models of polar and associating fluids. The straight lines correspond to the rectilinear diameter rule.

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