Article pubs.acs.org/JPCC
Condensation and Evaporation in Slit-Shaped Pores: Effects of Adsorbate Layer Structure and Temperature Yonghong Zeng,† Chunyan Fan,‡ D. D. Do,*,† and D. Nicholson† †
School of Chemical Engineering, University of Queensland, St. Lucia, QLD 4072, Australia Department of Chemical Engineering, Curtin University, Perth, WA 6845, Australia
‡
ABSTRACT: We have carried out an extensive computer simulation study of the effects of temperature on adsorption and desorption of argon in two slit mesopores; one of which has both ends open to the surroundings, and the other with one end closed, to explore the fundamental reasons for the disappearance of the hysteresis loop as the temperature approaches the critical hysteresis temperature, Tch. Detailed mechanisms are presented for adsorption and desorption. At temperatures below Tch, both adsorption and desorption branches of the isotherm are metastable resulting in a hysteresis loop. As the temperature is increased, waves, due to thermal fluctuations, appear at the boundary between the dense adsorbed phase close to the pore walls and the gas-like phase in the core. For temperatures above Tch, these thermal fluctuations override the formation and subsequent movement of the meniscus (interface); adsorption is entirely due to the densification of the adsorbate, and desorption proceeds by rarefaction of the adsorbate. This mechanism gives rise to reversible isotherms in open ended pores and in the corresponding closed end pores; consequently, the critical hysteresis temperature in open and closed pores is the same; a result that has not been previously noted in the literature. studies8,14−16 both support this view. Molecular simulation studies have confirmed that in general, both the adsorption and desorption branches of a hysteresis loop are metastable,17,18 as first suggested by Everett in 1975,19 and that the equilibrium path therefore falls between the adsorption and desorption boundaries of the loop.20−24 As well as predicting that hysteresis will not be found in closed end pores, the Cohan−Kelvin mechanism also predicts that hysteresis would occur at all temperatures. However, experimental measurements on materials with cylindrical mesopores (MCM) and other geometries (SBA and silica gel),25−28 have shown that the hysteresis loop is a function of temperature and always shifts to higher pressures and shrinks in size, as the temperature is increased, eventually disappearing at the critical hysteresis temperature (Tch). This observation has been confirmed by a simulation study of pore models with different geometries and topologies with closed cross sections.29 To our best knowledge, this is the first simulation study to examine this problem for materials that have slit-like pore structure. Everett and Haynes30 discussed the stability of a capillary fluid in a simple cylindrical system. They argued that the equilibrium state is one where the effective area of the fluid−gas boundary is a minimum with respect to an external perturbation, and that this
1. INTRODUCTION Advances in the synthesis of ordered mesoporous materials and the use of high resolution apparatus for the measurement of physical adsorption,1 supplemented by computer simulation studies,2,3 have stimulated an increased interest in adsorption hysteresis and led to reconciliation of simulation results with reliable experimental data, enabling the development of molecular models of physical significance for prediction purposes.4,5 Most of the early work on capillary condensation was focused on cylindrical pore models and based on the Kelvin equation.6 A mechanism for pore-filling and emptying in cylinders that offered a plausible explanation for hysteresis was proposed by Cohan7 in which both adsorption and desorption were supposed to follow equilibrium rather than metastable paths, each being governed by different curvatures (1/r and 2/r, respectively) at the interface between the gas-like region and the dense adsorbate. According to Cohan’s theory, the shapes of the menisci in cylindrical pores with one closed end would be the same for adsorption and desorption, and therefore hysteresis would be absent. Recent molecular simulation studies suggest, however, that hysteresis is possible in pores that are open to the adsorptive at one end, but closed at the other because the adsorbate structure during adsorption is different from its structure during desorption.8,9 In this paper we shall refer to pores with this type of structures as “closed end pores”. Experimental evidence that reports hysteresis in long closed end pores10−13 and molecular simulation © XXXX American Chemical Society
Received: December 18, 2013 Revised: January 16, 2014
A
dx.doi.org/10.1021/jp412376w | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
Figure 1. Schematics of two pore models: (a) open end pore; (b) closed end pore. Bulk gas regions are shown as the gray area. Periodic boundary conditions are applied in the x-direction.
models with both open and closed ends. Our aim is to investigate adsorbate structure in these systems at a microscopic level, and especially to shed further light on temperature dependence. Our conjecture is that increasing thermal fluctuations eventually destroy any stable unduloid structures and are the principle reason for the advent of reversible isotherms at Tch. If this proposal is correct, then the presence of a closed end would not affect the approach to reversibility. The application of simulation and its relevance to experimental studies, to adsorption, hysteresis, and capillary condensation in pores, has been recently reviewed.36 The existence of hysteresis in the models with closed ends is consistent with our results from earlier simulations8,9 for adsorption in closed pores but is in conflict with other theoretical studies.37,38 In our previous work we have suggested that hysteresis can be found in simulation studies of closed pores because structures are modified during the filling process and can become stabilized as adsorption proceeds, due to the existence of the highly nonuniform adsorbent field at the base of the pore. Although these structures can be manifested in simulation studies they are unlikely to be detected by most other methods. For example, the original Cohan−Kelvin mechanism, is still frequently invoked as an argument against the existence of hysteresis in closed pores. Cohan’s model, however, perceived the adsorbate as a simple annulus of fluid having the same properties as a bulk fluid and unresponsive to the existence of an adsorbent field. As observed above, the model cannot account for a critical hysteresis temperature and although it is a possible stable conformation, Everett and Haynes30 showed that it is not necessarily the most stable conformation for the adsorbate, a conclusion later examined in detail for cylinders by Kornev et al.39 who also extended the theory to take account of the external adsorbent field, following Derjaguin.40 As mentioned above, no capillary condensation would occur in planar slit pores on the basis of the Cohan−Kelvin model. Later statistical theories are also subject to limitations that are not imposed on simulation studies. For example, a mean field overrides local correlations, and treatments employing this type of approximation may be oblivious to highly localized structural heterogeneities. In a similar vein, lattice based models, such as the Ising model, localize molecular centers on an underlying framework and thereby impose limitations on the detailed configurations of molecules. The same kind of restriction can apply to several methods, such as DFT, which employ potential energy models that forbid molecules to approach beyond a hard sphere limit, thereby inhibiting certain local molecular structures that may form at high densities. The picture is further complicated by the fact that the size of the hysteresis loop may diminish and even disappear in pore widths approaching macroscopic size and can also be modified by potential energy corrugations along the direction of the pore axis. These issues will be addressed in our later work.
condition is satisfied if the mean curvature of the interface is the same at all points on the surface. The mechanical equilibrium condition for the difference between liquid and gas phase pressures is given by the Laplace equation, pl − pg = γ1gC1g, in which γlg is the interfacial tension and Clg is the curvature (=1/r at a cylindrical interface and 2/r at a spherical interface (as in the Cohan−Kelvin theory)). The cylindrical interface is only stable when the length of the fluid cylinder is
