Aug 11, 1995 - minima for the mercury surface are found at dis- tances about 0.5A larger than for the platinum surface. While the dependence of the energy on ...
ElectrorhimiaAcra.Vol.41. No. 14. pp.2131-2144. 1996 Copyright% 1996 ElsevierScienceLtd. Printedin Great Britain.Allrightsreserved 0013-4686196 $15.00 + 0.00
Pergamon
STRUCTURE AND DYNAMICS OF WATER AND HYDRATED IONS NEAR PLATINUM AND MERCURY SURFACES AS STUDIED BY MD SIMULATIONS E.
SFQHR,~.*
G.
T~TH$
and K.
HEINZINGER~
7
Abteilung fiir Theoretische Chemie, Universitlt Ulm, D-89069 Ulm, Germany $ Max-Planck-Institut fiir Chemie (Otto-Hahn-Institut), D-55020 Mainz, Germany (Received 15 June 1995; in revised form 11 August 1995)
Abstract-Results of various MD simulations of pure water and those with either an additional lithium or iodide ion near a Pt( lOO),a rigid and a liquid mercury surface are reported. The potentials describing the interactions with the metal surfaces are based on ab initio calculations of a water molecule or an ion and metal clusters of different sizes. The flexible BJH and the rigid TIP4P models for water are employed and the ion-water interactions are also derived from ab initio calculations. The structure at the interfaces for pure water at the three different surfaces is described by oxygen, hydrogen and mercury atom density profiles. The effect of all three metal surfaces on the structure of the hydration shells of the lithium and the iodide ion are discussed in detail and the free energies are reported as a function of distance from the rigid mercury surface. The spectral densities of the hindered translational motions of both ions parallel and perpendicular to the Pt(100) and the liquid mercury surface are presented. Copyright (Q 1996 Elsevier Science Ltd Key words: molecular dynamics simulations. interfacial structure and dynamics, water, metal surfaces, electrochemical interfaces.
1. INTRODUCTION In two review papers in this journal we have reported on computer simulation studies of electrolyte solutions near non-polar walls[l] and of water near metal surfaces[2]. After it had been demonstrated that the use of the image charge model to describe the Coulombic part of the partly charged oxygen and hydrogen atoms of the water molecules with the metal wall led to contradictions with experimental results, potentials were introduced[3] which are based on extended Hiickel calculations of a five atom platinum cluster and a water molecule[4]. With these potentials a water lamella between Pt(100) surfaces has been simulated and the structural[S] as well as dynamic[6] properties of the water molecules have been reported. In a recent review paper all the results achieved for water near the Pt(100) surface have been reported[7], including those which describe the effects of applied external electrical fields[8]. In a more recent MD study, employing a similar potential for the platinum-water interactions, Raghavan et a/.[91 extended the investigation to a Pt( 111) surface (for details see the paper by Berkowitz et al. in this issue). In a similar way a potential describing the interaction between water and a mercury surface has been derived based on nb initio calculations of Nazmutdinov et al.[lO]. First results of MD simulations * Author to whom correspc)ndence should be addressed.
with this potential assuming a rigid mercury surface have been reported recently by Bijcker et a/.[1 11. In analogy to the water-metal potentials the description of the ion-platinum and ion-mercury interactions is derived from ab initio calculations of a metal cluster and an ion. In the case of the Pt(100) surface potentials have been reported for an Li+ and a I- where the clusters consisted of five and nine platinum atoms, respectively[12]. For the mercury surface the potentials have been calculated for the alkali and halide ion series with cluster sizes of nine or ten mercury atoms[ 131. With these interaction potentials MD simulations have been performed and first results have been reported so far for the lithium and the iodide ion near the Pt(100) surface[14]. Similar systems have been investigated by Perera and Berkowitz[15] while simulations with Na+ and Cl- at the Pt(100) surface were reported with and without external electrical field by Rose and Benjamin[16]. Glosli and Philpott reported results from simulations of lithium and the halide ion series with the ST2 model for water near a non-specific metal surface[17] (for details see the paper by Philpott in this issue). In the next two sections the potentials are collected which describe the interactions of water and ions with a platinum( 100) and a mercury surface and details of the simulations are given. In Section 4 the density profiles of the oxygen, hydrogen and mercury atoms as well as those of the lithium and the iodide ion near the Pt( lOO),the rigid and the liquid mercury
2131
E.
2132
SPOHR et
al.
surface are presented. The free energies of ion adsorption at the rigid mercury surface are discussed in Section 5. The oxygen-oxygen, Lif-oxygen and I--oxygen pair correlation functions in the layer adsorbed on the Pt(100) surface are depicted in the following section. In Sections 7 and 8 the hydration shell structures of the lithium and the iodide ions near the platinum and the rigid mercury surface are described. Finally, in Section 9 the hindered translational motions of the same two ions calculated separately for the motions parallel and perpendicular to the Pt(100) and the liquid mercury surface are presented. 2. POTENTIALS The water-water potentials employed in the simulations are described either by the flexible BJH model[ IS] which has proved its usefulness in various simulations of pure water and aqueous electrolyte solutions[19] or by the rigid TIP4P model[20]. The platinum-platinum and mercury-mercury interactions are modelled by a harmonic nearestneighbour potential in order to account for the coupling between motions of the water molecules and lattice vibrations[21]. These harmonic potentials between the metal atoms mean practically rigid surfaces. Based on this experience, the mercury atoms were kept frozen in their equilibrium positions in the studies of the potential of mean force. In addition, simulations have been started of a liquid mercury-water interface. In this case the mercurymercury potentials have been taken from a simulation of pure liquid mercury[22]. The ion-water potentials have been employed successfully in simulations of bulk electrolyte solutions. They are based on quantum mechanical calculations and can be found in the original publications cited. The platinum-water potential is based on extended Hilckel molecular orbital calculations of a water molecule and a five-atom platinum cluster by Holloway and Bennemann[4]. Figure la shows the quadratic arrangement of the platinum atoms on the (100) surface with a lattice constant of 2.77 A. The five atom (4 + 1) platinum cluster used in the ab initio calculations has been cut out of the Pt(100) surface as indicated in Fig. la. On the mercury surface the atoms are arranged rhombohedrally (Fig. lb) and for the a6 initio calculations only surface atoms were employed. The cluster used to study the adsorption of a water molecular consisted of seven mercury atoms for the case where the oxygen atom is positioned on top of a mercury atom while only six atoms are employed for hollow and bridge site positions[lO]. The denotations top, bridge and hollow site for the mercury surface are explained in Fig. lb. For the Pt(100) surface the definitions apply accordingly. The parameterized potentials based on adsorption energies of a water molecule on the Pt(100)[3] and the mercury[l l] surface are given for the oxygen atoms by: Vu_&, p) = [Aij exp(-aijr) x h(P) +
-
i?, exp(-bijr)]
cij exp(-cijr)Cl
-f&)1 (1)
‘top’
b
I
‘bridge’ ‘hollow’
Fig. 1. (a) Sketch of the arrangement of the platinum atoms in the first (circles) and the second (crosses) layer of the (100) surface which coincides with the xy-plane of the basic periodic box the border of which is marked by dashed lines. Form and size of the two clusters used for the ab initio calculations are indicated. (b) Relative positions of the water molecules (oxygen atoms) on the mercury surface. The denotations top, bridge and hollow site are used for the Pt( 100) surface accordingly.
where fo(n) = exp( - d, P*) with p = Jm. The metal-hydrogen V,_,(r)
= A,
(2)
potential can be written as: exp(-aijr)
-
Bij exp(-bijr).
(3)
The parameters are given in Table 1 and in Fig. 2 the potential energies between a water molecule and the infinitely extended platinum( 100) and mercury surfaces are depicted as a function of the oxygensurface distance z for different relative positions and orientations. Both potentials lead to the preferential adsorption site on top of a metal atom. The energetically most favourable orientation is the one where the dipole moment vector points away from the surface with a minimum of the total interaction energy of -35.7 and of -38.6 kJ mol-2 for the Pt and the Hg surface, respectively. The potential minima for the mercury surface are found at distances about 0.5A larger than for the platinum surface. While the dependence of the energy on the relative orientation of the dipole moment vector is
Water and hydrated ions near platinum and mercury surfaces
i\
a
-45 -
’
1
-
45-
!I:I
-
3O-
-
150.
4 ! I 41
-
-15-
-
-30 -
-
-45 -
I
I
II
b
-
,,i I\ : )I .. ‘I
45 -
30
1
1
I
V / kJ mol-’
I
45
2133
30 -
15
a
I
I
-
,
I
b -
0 -15 -30 -45 I
1
1
2
3
4
,
I
5
6
I
7 z/h
-45 1 I 1
, 2
3
4
I
I
I
5
6
7
1 I
z/h
Fig. 2. Water-platinum (left) and water-mercury (right) interaction potentials as a function of the oxygen-surface distance. (a) For water on top of a metal atom ( full line), on a bridge site (dashed), and on a hollow site (dotted). The dipole moment vector of the water molecule points away from the surface. in all three cases. (b) For different orientations of the dipole moment vector relative to the surface: pointing away ( full line), towards (dotted) and parallel with the proton-proton vector parallel (dashed) or perpendicular (dash-dotted) to the surface. In all four cases the oxygen atom is on top of a metal atom.
quite similar for both metals, the difference between top, bridge and hollow site is much smaller for the mercury compared with the platinum surface. The platinum-Iand platinum-Li+ potentials are derived from molecular orbital calculations of one ion and a platinum cluster consisting of nine and five atoms, respectively (see Fig. la). The platinum-Ipotential can also be expressed by equation (3). For the platinum-lithium potential a slightly different analytical expressions had to be used to achieve a
good fit: L_i(r)
- B, exp(-bijr)
= Aij exp(-ajjr)
+
1.06 x lo4 p.350
(4) Figure 3 shows that both ions are adsorbed preferentially opposite to a hollow site of the Pt(100)
Table 1. Potential parameters
Aij
i
i
Pt Hg Pt Hg Pt Pt Hg Hg Hg Hg Hg Hg Hg Hg Hg
0 0 H H I Li F Cl Br I Li Na R Rb Cs
(kJ mol-‘) 1894.2 25518 1.7142 2603.6 6.30 x lo6 1.87 x lo3 0.5648 x lo6 0.3305 x 106 0.5990 x lo6 0.3721 x 10’ 0.2754 x lo5 0.6649 x IO5 0.1435 x lo6 0.4044 X 106 0.5612 x lo6
$2,) 1.1004 2.0829 1.2777 2.2230 4.59 1.33 4.0420 3.2156 3.2909 2.9385 2.3415 2.5949 2.6167 2.8432 2.7872
-
Bij
cij
(kJ mol-‘) 1886.3 5508.2 0 - 2603.6 4.66 x 1.23 x 0.6289 0.3396 0.2387 0.2067 0.1261 0.5848 0.3663 0.1886 0.1540
lo2 10’ x lo3 x lo3 x lo3 x lo3 x lo4 x lo3 x lo3 x lo3 x lo3
($!i)
(kJ mot-‘) 1.0966 1.3922 2.6737 0.80 1.02 0.9195 0.7833 0.7137 0.6808 1.0791 0.9308 0.8612 0.7431 0.7091
lo6
5.3568 2.1759 -
8813.2
dij
(A -‘)’
-
0.5208 0.2213 -
-0.2023 x -0.2488 x -0.4797 x -0.1474 x 0.3894 x -0.7832 x -0.1005 x - 0.9631 x -0.9386 x
10’ 10’ 106 106 10s 10’ lo5 lo4 10.’
3.1631 2.8523 3.7839 3.2344 2.5451 1.9004 3.1154 3.0118 3.3035
* For the metal-oxygen interactions p = 2 and for the mercury-ion ones p is defined in equation (6).
0.1614 x 0.1779 x 0.1353 x 0.9490 x 0.1326 x 0.7515 x 0.8668 X 0.2268 x 0.1280 x
1O-3 lo-* lo-* lo-* lo-’ 1o-6 10-G 1O-9 1O-6
E. SPOHR et al.
2134
E&l
* mol-’
0
-150 -200 -250 -
!!fG
-300 -
Li+
-60
!
-120
Fig. 3. Potential energy of a lithium and an iodide ion as a function of distance from an infinitely extended Pt(100) surface for ion positions on top of a platinum atom (---j. on a bridge site (- -) and a hollow site (-)[ 121.
II
Vlon-Hg(r,/I) =
Aij exp( - Uijr) +fr&)cij
Bij
exp( -
bij
exd - cij 4
r)
’
’
’
’
-.-.-...--.-.-.. . -- --.--.-.._...._ -._-_- ..__ ___
0
cs+
-25
surface and the lowest potential minima for Li+ and I- are found at -265 and -319kJ mol-‘, respectively[l2]. All ion-mercury interactions have been derived from molecular orbital calculations of one ion and a mercury cluster, consisting of either nine or ten atoms. Except for the lithium ion, the interaction potentials can be described by:
m’
-50
0
1
2
3
4
5
6
7
8
9
IO
TIA Fig. 4. Potential energies for various alkali and halide ions as a function of distance from an infinitely extended Hg(I11) surface for ion positions on top of a mercury atom (. ,), on a bridge site (---) and a hollow site (-).
(5)
where &,(P) = exp( - dij P’) with p =
I~“~~,“,,~
dij.
(6j
Again a slightly different analytical form had to be used for the mercury-lithium potential: V&(r,
p) = Aij expf - aijr) - B,, exp( - bijr)
+AOAP)Ccij exp(-cijr)
- Aij exp( -aij 41 (7)
The constants in p are chosen such that f = 1 if p = 0 and f = 0.01 if p corresponds to the nearest mercury atoms of the cluster when the ion is located
above the hollow site. The parameters are given also in Table 1 and in Fig. 4 the potential energies of selected alkali and halide ions as a function of distance from an infinitely extended mercury surface are presented[13]. The comparison of Figs 3 and 4 shows that for the lithium and the iodide ions the potential minima are much deeper and are about 1 A closer to the Pt( 100) surface when compared with the mercury surface. For further details of the potentials the reader is referred to the original publications cited. The calculations of the potential of mean force of ion adsorption and hydration shell structure near the rigid mercury surface (Sections 5 and 8) were performed according to the method of Ciccotti er aI.[23]. During the simulation all image contribu-
Water and hydrated ions near platinum and mercury surfaces
tions between ion and water charges are taken into account. The total potential of mean force is obtained by adding the ion self-image energy. As the very short ion-surface distances are not of interest here, no short range repulsion potential terms have been included.
3. DETAILS
OF THE
SIMULATIONS
The rectangular basic box for the MD simulations of pure water at the Pt(100) surface is shown in Fig. 5. Between the five layers of platinum atoms on each side-altogether 55Gremains space for about six layers of water molecules. In accord with the lattice constant for the Pt(100) surface the sidelengths of the rectangular box L, = L, = 19.6A and L, = 45 A result. The number of 305 water molecules between the two platinum surfaces was reached by adding water molecules until the density in the centre of the box became that of bulk water. In this way agreement with the usual experimental conditions was achieved[5]. The results of this simulation are presented and discussed in Sections 4 and 6. For the simulation of the rigid mercury/water interface a similar rectangular box was chosen. The 440 mercury atoms on each side are arranged rhombohedrally with a nearest neighbour distance of 3 and 3.6A in the x, y and the z directions, respectively. Here 551 water molecules occupy the space between the two mercury surfaces. The resultin dimensions of the basic box are L, = 24 A, L, = 26 x and L, = 60.2 A[1 11. The density profiles from this simulation are presented and compared with those at the Pt( 100) surface in Section 4.
Fig. 5. Sketch of the basic tetragonal simulation cell. The water molecules are located in the centre of the box, and the platinum atoms are represented by the circles. The coordinate system which is used throughout the paper is inserted in the centre[S].
2135
For the simulation of the liquid mercury-water interface the basic box contained 750 water molecules and 880 mercury atoms with side-len ths of L, = 24.00& L, = 25.98A and L, = 69.80 1 . The interface simulation was started from a configuration where the basic periodic boxes from a pure mercury and a pure water simulation were combined at a distance of 3A, which is approximately the position of the potential minimum for the water-mercury interaction. During the equilibration period the dimensions of the combined box were changed until the average density at the centre of the water as well as that of the mercury phase showed the density of the pure substances[24]. For the results see Section 4. For the investigation of the effect of the Pt(lO0) surface on the hydration shell properties of the Li+ and I- a rectangular basic box with side-lengths of L, = L, = 19.6A and L, = 25 A was used. In the range - 11.76 < z < 0 seven metal layers were located, the seventh one being immobilized. The liquid phase extended up to z = 13.24& where a Lennard-Jones potential prevented the evaporation of the water molecules. The system contained altogether 350 platinum atoms, 150 water molecules and one ion, either an Li+ or an II. The results are presented and discussed in Sections 4,6, I and 9. In the simulation of the Li+ and I- adsorption at the liquid mercury/water interface a similar arrangement was used as in the case of pure water. The sidelengths of the basic periodic box were L, = L, = 19.32 A and LZ = 65A. It contained 400 mercury atoms, 499 water molecules and one ion. At the beginning of the calculations the ions were placed in the middle of the water phase. After an intermediate time of 20-60~s both ions moved to the metal surface and remained there adsorbed for the rest of the simulation. Some preliminary results of these investigations can be found in Sections 4 and 9. In the calculation of the potential of mean force of ion adsorption on the mercury surface, the system consists of a film of 259 TIP4P water molecules and one ion, deposited on a rigid mercury slab. In these calculations, in addition to the liquid/metal interface a liquid-gas interface exists. The dimensions of the basic periodic cell are L, = 18.OA and L, = 20.78 A. The ion is constrained to specified distances from the surface, but is allowed to move parallel to it. Simulations for various fixed ion-surface distances lasted between 50 and 100~s with periodic temperature resealing. For more details see Ref. [25]. Periodic boundary conditions have been introduced in all three directions in all simulations except for the one with the ions adsorbed at the Pt(100) surface where they were applied only in two directions because of the Lennard-Jones wall. In this way an infinitely extended water lamella between metal walls or, equivalently, a metal lamella between water layers have been simulated. As long as no external electrical field is applied both interfaces are equivalent and the comparison of the results indicates the statistical significance of the calculated properties. The simulations were performed at room temperature either for an NVE or an NVT ensemble. For further details the reader is referred to the original papers cited. In all simulations reported here, the length of the time step was chosen between 0.1
2136
E. SPOHR et al.
and 0.25fs for the BJH model and 2.5 fs for the TIP4P model.
4. DENSITY
PROFILES
The first properties to be calculated as far as the structure of a water/metal interface is concerned are the oxygen and hydrogen atom density profiles. They are shown in Fig. 6 for the Pt(100) and the rigid Hg surface. The first maxima of the 0 and H profiles almost coincide at distances of about 2.5 and 3.0A from the Pt and the Hg surface, respectively. The reduced oxygen atom densities are significantly higher than those of the hydrogen atoms. After much less pronounced second peaks in the density profiles the distributions become uniform except for statistical noise. The higher and narrower peaks near the mercury surface are a consequence of the more pronounced potential minima for this surface when compared with the Pt(100) surface (Fig:2). The coincidence of the positions of the first peaks indicates a strong preference for a water molecule orientation parallel to the metal surface. As the potential minimum for a single water molecule is found for an orientation where the dipole moment vector points away from the surface, this coincidence demonstrates that the water-water interactions predominantly determine the structure of even the first
5 4
&%ulk
i
____ H
-0
1
-I
_
0
2
I
,
4
6
10
P
-
= 1.0 + 1.2 exp(0.152) cos(2.4~).
(8)
PO
Both the oxygen and the hydrogen density profiles, show two pronounced maxima and small third ones. The height of the first two maxima is significantly reduced compared to those at the solid mercury surface or the platinum(100) surface (Fig. 6). As the oxygen and hydrogen density profiles do not coincide, it follows that the potential drop at the interface is significantly different from zero. With 72 mercury atoms and 73 water molecules in the first layers nearly each mercury atom is in contact with one adsorbed water molecule. The mercury density profile can be compared with a theoretical study of a mercury vapour interface[26] and an experimental investigation of a mercury/ water interface[27]. These studies showed an oscillatory density profile with a frequency which is similar to that of our study, but with a significantly smaller decay length.
I
1
8
water layer. This is also reflected in the significantly shallower minimum for the average water-metal potential energy when compared with the potential energy for a single water molecule[5]. For the density profiles near the Pt(100) surface the excess of negative charge is indicated by shaded areas (Fig. 6). This charge distribution leads to an electrostatic potential drop at the Pt(100) surface in good agreement with the measured value. The running integration number for the oxygen atoms at the rigid Hg surface leads to 76 water molecules in the adsorbed layer. This result shows that almost every one of the 80 mercury atoms on the surface has a directly adsorbed water molecule. The density profiles for the mercury, oxygen and hydrogen atoms from the simulation of the liquid mercury-water interface, averaged over both interfaces, are depicted in Fig. 7. The xy plane at z = 0 is defined as the average position of the mercury atoms in the first layer. The mercury density profile can be presented by the following analytical form
z/h I 2.8
7
280
6
240
5
200
4
160
3
120
2
80
0.8
1
40
0.4 -
I
\
PIP0
2.4 21.6 1.2 _..~_
. . . . _._ . . .../. __..._.I
_......
-12
0
i
0
2
4
6
8
lo
z/A
Fig. 6. Normalized oxygen and hydrogen atom densities as a function of distance from the Pt(100) (top) and the rigid mercury (bottom) surface. The shaded areas indicate an excess of negative charges, while N(z) gives the number of the oxygen or half that of the hydrogen atoms in the volume between the mercury surface and a distance Z.
-8
-4
! 4
8
12
16
z/A
Fig. 7. Relative densities of mercury (dotted line). oxygen (solid line) and hydrogen (dashed line) atoms as a function of distance from the mercury surface. The surface at z = OA is defined as the average position of the mercury atoms in the first layer.
Water and hydrated ions near platinum and mercury surfaces
2137
60
40
20
I 0
2
4
6
I 0
8
2
4
6
z/A
Fig. 8. Normalized ion (-), oxygen (- -), hydrogen (---) and mercury (. . .) atom densities as functions of distance from the Pt( 100) (left) and the liquid mercury (right) surface, calculated from simulations with a lithium ion (top) or an iodide ion (bottom) in the boundary layer. The arrows indicate the relevant scale[14].
The normalized density profiles for Li+ and Itogether with those for the oxygen and the hydrogen atoms at the Pt(100) surface are depicted in Fig. 8 (left). The positions and the heights in the 0- and H-profiles are not significantly different from those for pure water. The ion profiles show that over the whole simulation time of about 20~s neither of the ions leaves the boundary layer. The I- profile extends only over the very narrow distance range 1.8 < z < 2.4i(. Its maximum at 2.0A coincides with the potential minimum for a position of the iodide ion above of a hollow site of the Pt( 100) surface (Fig. 3). Therefore, the I- can be called “contact adsorbed” on the Pt(100) surface, although the platinum crystal-iodide ion interaction energy is slightly less negative than the lowest potential minimum. The I--O first neighbour interaction prevents the I- from occupying an exact hollow site position (Fig. 10). The density profile of Li+ is quite different from that of I-. In spite of the smaller size of the lithium ion the range of distances from the surface 2.0 < z < 3.2 A is almost completely beyond that for the iodide ion and is much broader. The maxima of the 0- and H-atom profiles coincide with that of Li+ at 2.5 A. It can be seen from Fig. 3 that at this distance the potential energy of Li+ is independent of its position relative to the platinum atoms of the surface layer. It does not exhibit a surface potential corrugation any more. Very different from I-, it is obvious that both the distance range of Li+ from the surface and its position relative to the surface platinum atoms is determined by the Li+-water and not by the Li+-Pt crystal interactions. Therefore, it is justified to say that the Li+ is “not contact adsorbed”. For
comparison
the
preliminary
normalized
density profiles for Li+ and I- at the liquid mercury surface are depicted on the right side of Fig. 8 together with those for the oxygen, hydrogen and mercury atoms[28]. The surface is defined as the average position of the first layer mercury atoms.
4 6 2 6 10 Z/A 0 Fig. 9. The free energy of adsorption of Li+ (dashed line) and I- (full line) as a function of the distance from the mercury surface (at z = 0). The data have been calculated from two series of simulations of one ion dissolved in 259 TIP4P water molecules (top). The normalized oxygen density profile for the same system (bottom).
2138
E.
SFQHRet al.
XV8
Xl/A
Fig. 10. Oxygen-oxygen, lithium-oxygen and iodide-oxygen pair correlation functions in the adsorbed layer of the Pt( 100) surface (AZ < 4.2 A for all particles). Ax and Ay are the projections of the interatomic distances in the x and y directions. respectively, of the laboratory coordinate system (left). Projection of the trajectories of the lithium ions (top), iodide ions (bottom) and the oxygen atoms onto the xy-plane. The positions are marked by a dot every 0.05 ps. Only the oxygen atoms of the adsorbed water layer are taken into account, and the platinum atoms which are not covered with water are denoted by a cross (right)[14].
The positions of the maxima of both ion profiles almost coincide with the first ones for the oxygen
and hydrogen atoms but for different reasons. The same arguments as for the Pt(lOO) surface hold for the liquid mercury surface. The position of the maximum of the I- profile is determined by the iodide-mercury interactions, the minimum of which is found at almost 3 8, (Fig. 4), while that of the Li+ is a consequence of the strong interactions between the small lithium ion and its first shell water molecules. Similarly, the I- can be called contact adsorbed on the liquid mercury surface and the Li+ not. 5. FREE ENERGY AT THE RIGID In an extensive
OF ION ADSORPTION MERCURY SURFACE
series of calculations
of the free
energy of ion adsorption from aqueous solution onto the rigid mercury surface, the adsorption of the halide ions F-, Cl-, I- and of Li+ was studied[25, 291. In all cases, the solvent by itself forms a barrier for ion adsorption. The reasons have been determined to be (i) the driving force towards ion hydra-
tion and (ii) the steric repulsion by the layer of adsorbed water molecules. Figure 9 shows the free energy of adsorption of I- and Li+ on the mercury surface located at z = 0 (top) together with the oxygen density profile (bottom). The data are from a series of simulations in which the ions interact with the surface according to the image charge model. The static image plane is also located at z = 0. The long-range interactions have been calculated by Ewald summation in two dimensions[29]. The influence of the solvent on the large I- is mostly steric in nature. The free energy profile has the form of a generalized step function. The height can be rationalized by the energetic expense to remove between two and three water molecules from the surface prior to ion adsorption[30]. The depth of the small region of stability (negative free energy) relative to the bulk phase around z = 98, is hardly outside the limits of statistical uncertainties. There are two solvent-induced local minima for Li+ adsorption. In a bulk solution, the hydration shell of Li+ forms a rather rigid octahedral complex. The Li+ and the water molecules in its hydration shell move cooperatively. Consequently, the hydra-
Water and hydrated ions near platinum and mercury surfaces
tion complex is sensitive to the barriers formed by the two pronounced layers of water molecules around z = 6 A and z = 3 A. This leads to a local free energy minimum on the solution side of each of the two maxima in the oxygen density profiles. The total potentials of mean force in Fig. 9, without the inclusion of specific ion-surface interactions, are rather similar to the solvent contributions of the potential of mean force at the Pt(100) surface, as discussed in Refs [31,32]. 6. PAIR CORRELATION
FUNCTIONS THE Pt(100) SURFACE
AT
The O-O, Li+-0 and I--O pair correlation functions in the adsorbate layer, depicted in Fig. 10, show that the enhancement of the hydration shell structure of Li+ and the decrease for I- in the surface layer results from the formation of a pronounced quadratic water overlayer with a lattice constant of the Pt( 100) surface of 2.77 A. The origin (Ax = 0, Ay = 0) coincides with the changing position of an 0, a Li+ or an I- particle in the surface layer (z < 4.2 A), and 1Ax 1and 1Ay ) are the absolute values of the projection of the distances of the 0 atoms in the surface layer from these reference particles. Both the reference particle and the 0 atoms referred to, move with respect to the Pt lattice, and the shape of the peaks results from both movements. The plot of go,, reflects the positions of the oxygen atoms on the top site of the platinum lattice, and the pronounced form of the peaks refers to their relatively small displacement. The sharper peaks for gLio 20
show that the displacement of Lit at its hollow site is smaller than those of the oxygen atoms at their top sites, and the significantly broader ones for g,. than for go0 show that the displacements of I- are much larger than those of the oxygen atoms. Indeed the I- moves in a relatively widespread area between a hollow and a bridge site. In Fig. 10 also the trajectories of Li+ and I- are drawn and the x- and y-coordinates of the oxygen atoms of the water molecules with z < 4.2i( are marked by a dot after every 0.05~s. The positions of those Pt atoms which are not covered by oxygen atoms are indicated by crosses. Over the whole simulation time of 20~s the Li+ remains very near to the hollow site of the Pt(100) surface at x, y = 1. In accordance with the pair correlation functions the distribution of the neighbouring oxygen atoms above their respective Pt atoms is very narrow. The larger I- moves during this time in the area -4.0~~ < -2.5h and O 0.8 which results from the finite size of the water molecules. As the I- is contact adsorbed the excluded volume effect of the Pt surface amounts to almost one half and is responsible for the reduction of the hydration number of I- from 9.2 in the bulk solution to 5.1 in the boundary layer.
8
8. IONIC 6 4 2 0 2
4
6
8
10 a/A
Fig. 13. Average coordination number of Li+ (dashed line) and I- (full line) as a function of the distance from the mercury surface (at 2 = 0).
HYDRATION NEAR THE RIGID MERCURY SURFACE
Adsorption of ions on the surface is governed in part by the energetics of removal of water molecules from and rearrangement of water molecules within the hydration shell upon approach to the surface. As an example, the hydration shell structures around Iand Li+ near the mercury surface are analysed. Figure 13 shows the average coordination number of Li+ and I- as a function of ion position (the mercury surface is located at z = 0). Here, the coordination number is defined as the number of water
Water and hydrated
ions near platinum
molecules whose ion oxygen distance is smaller than 2.5 A and 4.2A for Li+ and I-, respectively, corresponding roughly to the minima of the ion-oxygen pair correlation functions in the bulk (see Fig. 11). The hydration number of iodide as a function of ion position is roughly constant beyond about z = 6.5 A. The penetration of the ion into the layers of adsorbed water leads to an increased coordination number up to about z = 4SA. At smaller distances from the surface, the hydration number decreases as expected due to geometrical reasons. The increase in hydration number coincides with the rise in the repulsive solvent free-energy barrier (see Fig. 9). The hydration number of the Li+ is slightly lower than 6 far from the surface and at most distances >4.5 A. Around z = 6.5 A there is a significant reduction of the hydration number to a value well below 5. This position coincides with an increase in the free energy (see Fig. 9). Apparently, the penetration of the Li+ into the second layer of water molecules around z = 6A is associated with partial dehydration (see also the discussion of Fig. 14 below). For small ion-surface distances (z < 4.5 A) the hydration number is reduced once more when the ion penetrates the contact layer of water molecules. Figure 14 demonstrates the changes in the hydration shell as a function of ion position. Each of the frames contains the normalized distribution function p(cos 9) where cos 3 is the angle of the ion-oxygen vector relative to the laboratory z-axis, which points towards the surface in this case. Only water molecules in the hydration shell of Li+ and I- (ir with ion-oxygen distance smaller than 2.5 and 4.2A, respectively) are taken into account. Cos 3 = - 1 corresponds to the arrangement where the ion is P(cOS8)
8-
9.oA
,,
5.58,
7.5‘4
,,_..-’
2141
between the hydrating molecule and the surface, whereas cos 9 = 1 indicates the situation where the hydrating water molecule is located between the ion and the surface. The dashed lines indicate the running integration of p(cos 9). normalized in such a way that the total integral yields the hydration number at the specified position. In the bulk of the lamina (z > 10 A) the hydration shells of both ions (not shown here for Li+) are isotropic in the external coordinate system as must be the case far from the surface in an isotropic liquid phase. For z < 9.08, the hydration shell of I- exhibits preferential orientations (Fig. 14, left). There are now more hydrating molecules towards the surface than in other directions. The maximum at cos 9 x 0.9 reflects the higher water density in the second layer of the density profile around z = 6A (see Fig. 9). At z = 7.5 A and z = 6.5 A about one half of the hydration shell (cos 9 < 0) remains nearly isotropic. The anisotropy of the hydration shell in the direction towards the surface shows an increasing contribution by the layer of directly adsorbed water to the hydration shell (as indicated by the increase of the rightmost maximum in the distribution function). The reorientation of the hydration shell is possible at almost no change in the free energy (see Fig. 9). This is in accord with the analysis of the iodide hydration shell in bulk solution which shows that the arrangement of water molecules around the ion is rather flexible and no regular polyhedral structure can be assigned to the hydration complex (see Fig. 12). For z < 6.5 A the hydration shell becomes increasingly anisotropic. Simultaneously, the free energy and the coordination number increase due to coordination with molecules in the first and second water layers. Already at z = 5.5 A there are no more water Li+
,,’
#’ ,: -
_/’
8-
surfaces
P(cosfl)/ nhyd
I-
/ nhyd
and mercury
3.5A I’--------
,’
6-
I:
Fig. 14. Normalized distributions of the cosine of the angle between the I--oxygen (left) and Lie-oxygen (right) vector and the inward directed surface normal (full line) and the running integral of p(cos 9) (dashed line) at various positions relative to the metal surface. The running integral is normalized to yield the total hydration number at a given distance for cos 9 = 1. Only oxygen atoms in the first hydration shells of the ions contribute.
2142
E. SPOHR
1.0
I
1
1
6. f(v)HO%m
"II
0.8
6-
0.6 0.4 200
400
600 v/cm-'
-0.4 1.0 0.8
0.8
0.6
0.6
0.4
0.4 0.2 0 -0.2 -0.4 0
0.1
0.2
0.3
0.4
0.5 t t PS
0
0.1
0.2
0.3
0.4
0.5 t t
PS
Fig. 15. Normalized velocity autocorrelation functions and spectral densities of the lithium (left) and and the bulk (- -), calculated iodide ions (right) in the boundary layer of the Pt(100) surface (-) separately for the motions parallel (top) and perpendicular (bottom) to the surface. molecules in the direction towards the surface. At z = 3.5& the ion is incorporated into the adsorbate
layer and has an average of five neighbours in the plane of adsorption. Three more members of the hydration shell are located in the second layer of water molecules. The hydration shell structure of Li+ (Fig. 14, right) shows some interesting features. At z-values of 5.5 and 8.5A an octahedral arrangement is found with the octahedral plane parallel to the surface. For Li+ distances of 4.5 and l.OA the octahedron remains but is rotated in such way that two triangular planes are now parallel to the surface. At 3.5 and
200
400 600 y/cm-l
800
6.5 A, the first hydration shell consists of only about five water molecules in a pyramidal coordination with the base of the pyramid again parallel to the surface. For each of the three different configurations the structure of the hydration shell of Li+ is significantly more pronounced at the shorter distances from the surface. The pyramidal structure is found when the ion is positioned at the long distance side of the two pronounced peaks in the oxygen atom density profile, where also negative free energies are found in both cases (Fig. 9). The running integration in Fig. 14 shows that four out of five water molecules in the
20
40 60 y/cm-l
80
Fig. 16. Spectral densities of the hindered translational motions of the lithium (left) and the iodide (right) ion in the boundary layer of the liquid mercury interface calculated separately for the motions parallel (full line) and perpendicular to the surface (dashed line).
Water and hydrated
ions near platinum
first hydration shell belong to the high density region. The water molecules at the top of the pyramid at r-values of about 2 A larger than those of the ion are located in the second peak and in the only weakly indicated third maximum of the oxygen density profile. At these ion positions the octahedral structure expected from the bulk solution must remain incomplete because at distances about 2A smaller than those of the ion the oxygen atom density is nearly zero (Fig. 9). This result is similar to that found for the Li+ in the adsorbed layer on the Pt(100) surface (Fig. 12). The position of Li’ at 4.5 and 7.OA means that the two triangular planes coincide with the positions of the first and second peak and the second peak and the weak third maximum in the density profile. respectively, as a cosine value of about kO.6 corresponds to a z-distance from the ion of about 1.2A for a Lif-oxygen nearest neighbour distance of 28, as in a bulk solution. For c-values at 5.5 and 8.58, a complete octahedral arrangement of the water molecules in the first hydration shell is found again as in a bulk solution. The quadratic base planes of the octahedra coincide with the second peak and the weak third maximum for the small and large Zvalues, respectively. The remaining two oxygen atoms of each octahedron can be found at distances of + 2 A from the ion position in low density regions (Fig. 9). In short, the structural order of the hydration shell of the lithium ion at various distances from the mercury surface follows from the strong tendency of the Lif in a bulk solution to form an octahedral arrangement of the six nearest neighbour water molecules. This tendency has to be adjusted here to the densities determined by the mercury surface.
9. HINDERED
TRANSLATIONAL OF THE IONS
MOTIONS
and mercury
motions parallel to the surface show a strong blue shift. This reflects the enhanced Li+-water interactions as a result of the reduced water mobility, which is a consequence of the formation of the quadratic water overlayer. The motions of Li’ perpendicular to the surface are characterized by a shift of the main peak in the spectral density to lower frequencies. This is a consequence of the greater mobility of the Li+ because of the missing water molecule between the ion and the surface. Different results are found in the case of the iodide ions adsorbed on the metal surface. The blue shift of the frequency maximum for the transverse motions of the ions in the boundary region is about 20 cm ‘. This indicates a movement of the heavy ion parallel to the surface which is only slightly disturbed by collisions with neighbouring water molecules adsorbed at the Pt(100) surface. The perpendicular motions show a significant blue shift of the frequencies of the two main peaks, which demonstrates the strong interaction between the surface and the I- positioned near the energy minimum. In the same way the spectral densities for the ions in the boundary layer of the liquid mercury surface have been calculated and are shown in Fig. 16. The effect of the mercury surface on the hindered translational motions of Li+ is very similar to that of the Pt(100) surface in agreement with the similar hydration shell structures near the two surfaces as discussed above. In the I- case there is a difference as far as the motion perpendicular to the mercury surface is concerned. The blue shift is significantly smaller than at the Pt(100) surface, because the potential between the iodide ion and the mercury surface which determines the shift (see above) is significantly shallower than that at the Pt(100) surface. Ackno~cledgemfnrs-Financial support by Deutsche Forschungsgemeinschaft and the Fonds der Chemischen lndustrie is gratefully acknowledged.
To investigate the hindered translational motions, the velocity autocorrelation functions (a&) are calculated from the simulations according to
REFERENCES 1.
where N denotes the number of particles, N, the number of time averages and uj(t) the velocity of particle j at time t. From these acfs the power spectra have been calculated by Fourier transformation. Different from isotropic bulk systems the acfi of the particles in the lamella are functions both of the distance from the surface and the angle between the velocity vector and the normal vector. Therefore, the acfs have been calculated separately for the particles located in the boundary water layer and in the bulk region and separately for the motions parallel and perpendicular to the surface. They are depicted for Li+ and I- in the adsorbed layer of the Pt(lOO) surface in Fig. 15. The motions of the Lif in the boundary layer parallel and perpendicular to the metal surface are quite different from those in the isotropic solution. The frequencies of the hindered translational
2143
surfaces
E. Spohr and K. Heinzinger,
EIectrochimica Acta 33, 1211 (1988). 2. K. Heinzinger and E. Spohr. EIectrochimica Acta 34, 1849 (1989). 3. E. Spohr and K. Heinzinger. Eer Bunsenges. phys. Chem. 92, 1358 (1988). 4. S. Holloway and K. H. Bennemann. Surf. Sci. 101, 327 (1980). 5. E. Spohr. J. phvs. Chem.93,6171 (1989). 6. E. Spohr. Chem. Phys. 141,87 (1990). 7. K. Heinzinger. in Structure of Electr$ed Inter$res (Edited by J. Lipkowski and P. N. Ross), Frontiers of Electrochemistry, Vol. II, VCH Publishers, New York, 239 (1993). 8. G. Nagy. K. Heinzinger and E. Spohr, Faraday Discuss. 94, 307 (1992). 9. K. Raghavan, K. Foster, K. Motakabbir kowitz. J. Chem. Phys. 94, 2110 (1991).
10. R. R. Nazmutdinov. J. electroanaL
M. Probst
and
and M. BerK. Heinzineer.
Chem. 369, 227 (1994).
11. J. Backer, R. R. Nazmutdinov, zinger. Surj Sci. 335, 1 (1995). 12. J. Seitz-Beywl, M. Poxleitner,
Heinzinger, Int. J.
Quantum
E. Spohr
and K. Hein-
M. M. Probst
and
Chem. 42, 1141 (1992).
K.
2144
E. SPOHRet al.
13. Cl. T&h, E. Spohr and K. Heinzinger, Chem. Phys. 200, 347 (1995). 14. J. Seitz-Beywl, M. Poxleitner and K. Heinzinger, Z. Naturforsch. 46a, 876 (1991). 15. L. Perera and M. L. Berkowitz, J. Chem. Phys. 97, 13803 (1993). 16. D. A. Rose and I. Benjamin, J. Chem. Phys. 95, 6856 (1991); %I,2283 (1993). 17. J. N. Glosli and M. R. Philpott, J. Chem. Phys. 96,6962 (1991); !I&9995 (1993). 18. P. Bopp, G. Jancd and K. Heinzinger, Chem. Phys. Len. 9% 129 (1983). 19. K. Heinzinger, in Computer Modelling of Fluids, Polymers and Solids (Edited by C. R. A. Catlow, S. C. Parker and M. P. Allen), Kluwer Academic Publishers, Dordrecht, 1990, p. 357. 20. W. L. Jorgensen, J. Chandrasekhar, J. Madura, R. W. Impey and M. L. Klein, J. Chem. Phys. 79,926 (1983).
21. J. E. Black and P. Bopp, Surf. Sci. 140, 275 (1984). 22. J. Biicker, Z. Gurskii and K. Heinzinger, to be published. 23. G. Ciccotti, M. Ferrario, J. T. Hynes and R. Kapral, Chem. Phys. 129,241 (1989). 24. J. Backer, E. Spohr and K. Heinzinger, 2. Naturforsch. SOa, 611 (1995). 25. E. Spohr, Acta Chem. Stand. 49, 189 (1995). 26. J. Gbodisman, J. Chem. Phys. 82, 560 (1985). 27. L. Bosio. R. Cortes.. M. Denoziere and G. Folcher, Co!!. Phy;. C7, Suppl.‘lO, 50, 23 (1989). 28. G. Toth and K. Heinzinger, to be published. 29. B. Eck and E. Spohr, in preparation. 30. E. Snohr. J. Mo1. Liauids. 64.91 (1995). 31. E. Spohr; Chem. Phis. Len. 207,214 (1993). 32. L. Perera and M. L. Berkowitz, J. phys. Chem. 97, 13803 (1993).
