Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Capillaries within compartments: Microvascular interpretation of dynamic positron emission tomography data

Measurement of exchange of substances between blood and tissue has been a long-lasting challenge to physiologists, and considerable theoretical and experimental accomplishments were achieved before the development of the positron emission tomography (PET). Today, when modeling data from modern PET scanners, little use is made of earlier microvascular research in the compartmental models, which have become the standard model by which the vast majority of dynamic PET data are analysed. However, modern PET scanners provide data with a sufficient temporal resolution and good counting statistics to allow estimation of parameters in models with more physiological realism. We explore the standard compartmental model and find that incorporation of blood flow leads to paradoxes, such as kinetic rate constants being time-dependent, and tracers being cleared from a capillary faster than they can be supplied by blood flow. The inability of the standard model to incorporate blood flow consequently raises a need for models that include more physiology, and we develop microvascular models which remove the inconsistencies. The microvascular models can be regarded as a revision of the input function. Whereas the standard model uses the organ inlet concentration as the concentration throughout the vascular compartment, we consider models that make use of spatial averaging of the concentrations in the capillary volume, which is what the PET scanner actually registers. The microvascular models are developed for both single- and multi-capillary systems and include effects of non-exchanging vessels. They are suitable for analysing dynamic PET data from any capillary bed using either intravascular or diffusible tracers, in terms of physiological parameters which include regional blood flow. (C) 2003 Elsevier Ltd. All rights reserved.