Replica Ornstein-Zernike self-consistent theory for mixtures in random pores G. Pellicane and C. Caccamo Dipartimento di Fisica, Università di Messina and Istituto Nazionale per la Fisica della Materia (INFM), Messina, Italy D. S. Wilson and L. L. Lee * School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, Oklahoma 73019, USA (Received 4 December 2003; published 4 June 2004) We present a self-consistent integral equation theory for a binary liquid in equilibrium with a disordered medium, based on the formalism of the replica Ornstein-Zernike (ROZ) equations. Specifically, we derive direct formulas for the chemical potentials and the zero-separation theorems (the latter provide a connection between the chemical potentials and the fluid cavity distribution functions). Next we solve a modified-Verlet closure to ROZ equations, which has built-in parameters that can be adjusted to satisfy the zero-separation theorems. The degree of thermodynamic consistency of the theory is also kept under control. We model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard-sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction, at different mixture concentrations. We compare the theoretical structural properties as obtained through the present approach with Percus-Yevick and Martinov-Sarkisov integral equation theories, and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical Monte Carlo simulations. Our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials. This feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general. DOI: 10.1103/PhysRevE.69.061202 PACS number(s): 61.20.Gy, 61.20.Ja, 64.70.Ja I. INTRODUCTION Phase changes of liquids inside porous media are of both scientific and technological interest. Porous materials, such as activated carbon, silica gels, zeolites, pillared clay and more recently, aerogels, aminosilicates, aluminophosphate, carbon nanotubes, Vycor glass, microporous BN, and star- burst dendrimers have been extensively used in industry for adsorption, dehumidification, catalysis, gas separation [1], and gas storage [2,3]. Many of these systems have an amor- phous structure, that is, they consist of microsized pores that are irregularly distributed throughout the material. For ex- ample, aerogels have a cobweblike structure that is made up of cross interconnecting inorganic/organic colloidal-like par- ticles or polymeric chains with high porosity s75-99% d [4]. When fluids invade the interior of such materials, the con- finement in narrow dimensions deeply changes the bulk phase behavior, as has been well documented [5]. Only a few theoretical studies have looked into binary fluid mixtures in random pores [6]. The simplest model for these systems, exhibiting a stable phase separation, is exemplified by the nonadditive hard sphere mixture (NAHSM). In this paper we employ both integral equations (IE) of the replica type [7] and computer simulations in order to characterize the structure and the thermodynamics of NAHSM under confinement. The effect of confinement is assured by the presence of a disordered, rigid matrix of hard spheres. The study of this basic model should help in under- standing both the effects of nonadditivity and of porosity on phase properties in general. In our approach, we improve the performance of the replica-Ornstein-Zernike (OZ) integral equations by requir- ing both conformity to the zero-separation theorems and a partial thermodynamic consistency. This combined method- ology has been applied and tested in a number of previous studies: on pure hard spheres in bulk [8] and in pores [9], additive [10] and nonadditive [11] hard sphere mixtures in bulk, Lennard-Jones molecules [12], and diatomic hard dumbbells [13]. In all cases, close agreement was obtained between IE and simulation. The essence of such an approach is the use of the zero separation theorems (ZST)[14], in addition to the usual thermodynamic consistencies [15]. The values of correlation functions at zero distance (when two particles coincide) obey certain exact conditions that tie them to the thermodynamic properties of the system under study, such as the chemical potentials and the isothermal compress- ibility. This is, in a way, similar to the contact value theorem for hard-core systems [16]. The difference between ZST and thermodynamic consistencies is in the “local” (specific val- ues of the correlation functions are required at some dis- tances) nature of the former versus the “global” (almost ev- erywhere) nature of the latter. Both types of consistencies reinforce the “accuracy” of the integral equation formulation based on the replica OZ equations. For the aforementioned reason, we specifically develop zero-separation theorems of model mixtures in random pores, and we adapt them to our particular model system. Next, we solve a modified-Verlet closure [17] to the replica OZ equations which has built-in, adjustable parameters and we tune them so as to satisfy the zero-separation theorems (ZSEP closure). We refer to the present implementation of ZSEP as a self-consistent closure only to the satisfaction of zero-separation theorems; on the other hand, its degree of thermodynamic consistency is *Corresponding author. Email address: lle@ou.edu PHYSICAL REVIEW E 69, 061202 (2004) 1539-3755/2004/69(6)/061202(10)/$22.50 ©2004 The American Physical Society 69 061202-1