Langmuir 1999, 15, 5141-5149
5141
Adsorption Isotherms of Water Vapor on Calcite: A Molecular Dynamics-Monte Carlo Hybrid Simulation Using a Polarizable Water Model Elmar Sto¨ckelmann and Reinhard Hentschke* Max-Planck-Institut fu¨ r Polymerforschung, Postfach 3148, D-55021 Mainz, Germany Received December 31, 1998. In Final Form: April 26, 1999 We model adsorption isotherms of water on the calcite (101 h 4) surface using a polarizable water model in a variable particle number simulation. The sampling procedure employs a molecular dynamics-Monte Carlo hybrid technique, which consists of a classical molecular dynamics simulation combined with spatially random removal and insertion trials. The fluctuating charge algorithm is used to describe the many-body interaction of induced polarization during the simulations. We obtain the isotherms and isosteric heats of adsorption at 278 and 298 K. For the higher temperature we present a detailed analysis of the adsorbate structure for coverages ranging from the monolayer regime to the bulk interface.
Introduction The effects of induced polarization make quantitative force field simulations of polar molecules in strongly heterogeneous environments difficult. Electrostatic interactions in phenomenological force fields are commonly modeled via partial charges, which are distributed throughout the molecules in a way that reproduces their electric fields at the relevant distances as closely as possible. In the case of homogeneous systems the charges usually are determined via independent phenomenological or quantum mechanical approaches prior to the simulation. These charges are then kept fixed during the simulation, and polarization commonly is included in a mean field sense by scaling the charges uniformly. Probably the most intensively studied system in this respect is water, where in all fixed charge models (beginning with the first molecular model by Bernal and Fowler1 and including all up to the more recent models like the WK model2) the vacuum charges are increased to account for the higher dipole moment in the liquid phase (cf. ref 3 for a listing of references providing a detailed discussion of phenomenological interaction potentials for liquid water). Explicit inclusion of polarization mostly has been very time consuming, and therefore it is usually avoided. When polarization is included, two approaches are common. The µind B (0) first approach adds an induction term, -1/2∑i b i ‚E i , to ind µ i ) R iE B i is the induced dipole the Hamiltonian. Here b B (0) B i are the electric moment of atom (or molecule) i. E i and E fields of only the fixed partial charges and of the fixed partial charges including the surrounding induced dipole moments, respectively. Ri is the isotropic polarizability of atom (or molecule) i. During a molecular dynamics µind is determined iteratively after each time simulation b i step. This makes the algorithm rather time consuming. The, second approach treats the partial charges themselves as dynamic variables which are computed according to their own equations of motion4 (the above induced dipole * Corresponding author. Permanent address: Bergische Universita¨t Gesamthochschule, FB8 Physik, Postfach 100127, D-42097 Wuppertal, Germany. (1) Bernal, J. D.; Fowler, R. H. J. Phys. Chem. 1933, 1, 515. (2) Watanabe, K.; Klein, M. L. J. Chem. Phys. 1989, 103, 157. (3) Sto¨ckelmann, E.; Hentschke, R. J. Chem. Phys. 1999, in press.
Table 1. Positions of the Atoms in the Calcite (101 h 4) Unit Cell Used in the Calculation of the Surface Potential in Eqs 4 and 5 s 1 2 3 4 5 6 7 8 9 10
atom
xs (Å)
ys (Å)
zs (Å)
O O O O C C Ca Ca O O
2.8138 6.8618 2.0239 6.0719 2.0239 6.0719 0.0000 4.0479 1.2341 5.2820
1.8542 3.1358 3.7765 1.2135 2.4950 2.4950 0.0000 0.0000 1.8542 3.1358
-0.7796 -0.7796 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7796 0.7796
Table 2. Model Parameters Used in This Work Lennard-Jones Parameters σOj (Å) Oj (kJ/mol)
j ) Owater
j ) Ca2+
j ) CCO3
j ) OCO3
3.245 0.377
3.00 0.628
3.32 0.368
3.22 0.573
Electrostatic Parameters χ˜ ° mq ζ q (fixed) [kJ/(mol‚e)] [×10-5 (ps/e)2 kJ/mol] n (Å-1) (e) H2O H O CO32- C O Ca2+ Ca2+ a
0.0 340.34
28.9 28.9
1 2 1 1 3
1.89 3.19 2.65 +0.9193a 3.19 -0.9731a 3.50 +2.0a
Taken from ref 23.
moments can also be treated in this fashion,5 but the algorithm remains time consuming). Berne and coworkers6,7 have developed an implementation of this idea, which is a Lagrangian version of the charge equilibration scheme.8 Their method incorporates two important features. The charges can be calculated on the basis of a simple phenomenological addition to the force field, which involves parameters of the individual atoms only, like the electronegativity. In addition, the calculation is fast; that (4) Sprik, M.; Klein, M. L. J. Chem. Phys. 1988, 89 (12), 7556. (5) Levesque, D.; Weis, J. J.; Patey, G. N. Mol. Phys. 1984, 51, 333. (6) Rick, S. W.; Stuart, S. J.; Berne, B. J. J. Chem. Phys. 1994, 101 (7), 6141. (7) Rick, S. W.; Berne, B. J. J. Am. Chem. Soc. 1996, 118, 672. (8) Rappe´, A. K.; Goddard, W. A., III. J. Phys. Chem. 1991, 95, 3358.
10.1021/la981790h CCC: $18.00 © 1999 American Chemical Society Published on Web 06/15/1999
5142 Langmuir, Vol. 15, No. 15, 1999
Sto¨ ckelmann and Hentschke
Figure 1. (Upper left and bottom) Structure of the calcite (101h 4) surface unit cell and view of the surface from the side. (Upper right) Simulation box of the interface: Lx ) 24.29 Å, Ly ) 24.95 Å, and Lz ) 51.5 Å (interface with bulk water) or Lz ) 100 Å (simulations of adsorbed vapor).
is, it increases the effort of usual fixed charge simulations by merely 10-15% and thus allows the dynamic incorporation of polarization during a simulation (cf. the discussion in ref 3). In a previous paper3 we have investigated the performance of a new polarizable water model based on the above work of Berne and co-workers for the simulation of neat water, ionic solutions, and water near an ionic surface. In this article we describe the application of our modified water model to the calculation of adsorption isotherms on calcite (101 h 4). We employ constant-µVT simulations (constant chemical potential, volume, and temperature) combining molecular dynamics translations and rotations of the water molecules with occasional Monte Carlo creation and destruction moves. The electrostatic interactions within the adsorbate and with the ionic substrate are treated using fluctuating water charges, as explained above; that is, we account for the large variations of the water dipole moment in the adsorbed layer near the calcite surface as compared to the gas phase. In the following, we first discuss the performance features of our combined molecular dynamics-Monte Carlo fluctuating charge algorithm. We then calculate two adsorption isotherms at 278 and 298 K including the coverage dependence of the isosteric heats of adsorption. For the higher temperature we characterize the molecular structure of the adsorbed film at coverages ranging from the monolayer regime to the bulk interface in terms of density, dipole
moment, dipole orientation order parameter, and oxygenoxygen pair correlation profiles. This provides a molecular picture of the isotherm, which is well described within the BET approximation, as a function of gas-phase activity. Combined with our earlier work,3 this completes a study of the present polarizable water model including static cluster properties (like the mean dipole moment or the cohesion energy as a function of cluster size), gas-phase and liquid-phase properties (like the second virial coefficient, the density, the molecular dipole moment, and the diffusion coefficient as a function of temperature), structural and dynamic properties of ionic solutions, and the interaction with ionic surfaces. Method We use the SPC/E-P water model, a polarizable rigid threecenter water model originally developed in ref 6, which is described in detail in ref 3. The potential energy of a system consisting of N atoms (distributed over Nmolec water molecules), using the fluctuating charge approach to include polarization is given by
[( ) ( ) ] ∑[ ]
U({r b},{q}) )
∑4 OO
N
i)1
σOO
OO
rOO
12
-
σOO rOO
6
N
+
∑J (r )q q + ij
ij
i j
i
