1142
Langmuir 1988,4, 1142-1147
Theoretical Approach to the Dynamics of Cluster Morphology and the Electrochemical Faceting of Metals E. E. Mola, J. L. Vicente, E. Custidiano, and A. J. Arvia* Instituto de Inuestigaciones Fisicoquimicas Teciricas y Aplicadas (INIFTA),Facultad de Ciencias Exactas, UNLP, Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina Received September 9, 1987. I n Final Form: May 2, 1988 A simplified theoretical approach based on the tight-binding method is presented to account for the dynamics of metal ion detachment (electrooxidation reaction) and incorporation (electroreductionreaction) at clusters consisting of a cubium lattice. The model emphasizes either the charge density distribution (electrostatic aspects) or the energetics of the reactions at active sites (electrical potential aspects) and the role played by the influence of an applied potential on the metal ion detachment and incorporation. The model predicts that according to the cyclic withdrawal from and incorporation of ions to the clusters it results in the development of different preferred oriented atomic arrangements. Similar results are obtained for a cluster growth process including a relaxation time for ion incorporation. The conclusions from the simple model are in qualitative agreement with the basic processes involved in the electrochemical faceting of fcc metals and metal electrocrystallizationdespite the large difference between the model and the complex electrochemical processes.
I. Introduction The application of a periodic potential to fcc metal electrodes such as Pt, Rh, Au, and Pd in acid electrolyte produces different modifications at the metal surface according to the potential limits and frequency of the perturbing potential. In this way different procedures were developed to obtain (i) electrochemical faceting of either polycrystalline (pc) or polyfaceted single-crystal specimens with a particular preferred orientation such as (loo), (lll), or (l10);1-3(ii) electrodispersed metal electrode surfaces involving a supercluster-typestructure where each cluster of about 10 nm average diameter exhibits a large preferred crystallographic ~ r i e n t a t i o nand ; ~ ~(iii) the combination of procedures i and ii with the purpose of obtaining large active surface areas with a definite type of crystallographic orientation." The surface topography of these modified metal electrode surfaces was investigated through scanning electron microscopy (SEM) and scanning electron tunneling microscopy (STM) techniques, the latter comprising a resolution to 0.1 nm.&-'O The basic phenomena responsible for the electrochemical faceting and the metal electrodispersion in acid electrolytes can be briefly summarized as follows. In the first case, the application of the periodic perturbing potential under certain well-defined potential limits and frequency implies selective metal electrodissolution-electrodeposition cycles furnishing the progressive appearance of a preferred crystallographic orientation. In the second case the periodic perturbing potential extends up to relatively large (1) Cerviiio, R. M.; Triaca, W. E.; Arvia, A. J. J. Electrochem. SOC.
1986, 132, 266; J. Electroanal. Chem. 1985,182, 51. (2) Canullo, J. C.; Triaca, W. E.; Arvia, A. J. J. Electroanal. Chem. 1984, 175,337; 1986,200,397. (3) Arvia, A. J.; Canullo, J. C.; Custidiano, E.; Perdriel, C. L.; Triaca, W. E. Electrochim. Acta 1986,31, 1359. (4) Chialvo, A. C.; Triaca, W. E.; Arvia, A. J. J. Electroanal. Chem. 1983, 146, 93; 1984, 171, 303.
(5)VHsquez, L.; Gbmez, J.; Barb, A. M.; Garcia, N.; Marcos, M. L.; Gonzaez, J.; Vara, J. M.; Arvia, A. J.; Presa, J.; Garcia, A.; Aguilar, M. J. Am. Chem. SOC. 1987,109, 1730. (6)Gbmez, J.; VCquez, L.; Barb, A. M.; Alonso, C.; Gonzaez, E.; Gonzaez, J: Arvia, A. J. J. Electroanal. Chem., in press. (7) Visindn, A.; Triaca, W. E.; Arvia, A. J. J.Electroanal. Chem. 1987, 221, 239.
(8) Cervifio, R. M.; Arvia, A. J.; Vielstich, W. E. Surf. Sci. 1985, 154, 623. (9) Gbmez, J.; Vizquez, L.; Barb, A. M.; Garcia, N.; Perdriel, C. L.; Triaca, W. E.; Arvia, A. J. Nature (London) 1986, 323, 612.
(IO) VCquez, L.; Gbmez, J.; Gbmez, J. M.; Barb, A. M.; Garcia, N.; Canullo, J. C.; Arvia, A. J. Surf. Sci. 1987, 181, 98.
positive values, that is, in the order of 2.0 V referred to the standard hydrogen electrode scale, promoting the accumulation of an oxide layer that can be subsequently electroreduced under proper conditions. This yields an electrodispersed metal electrode structure particularly interesting for electrocatalysis. In both cases, the triggering reaction is the decomposition of water yielding adsorbed OH species and proton in solution. The kinetics of the subsequent reaction, i.e., the metal ion detachment during the electrooxidation half-cycle and the metal ion incorporation during the electroreduction half-cycle, are influenced by surface processes, which become of critical importance in defining the resulting metal morphology. The recent attempt at modeling the development of electrochemical faceting was based upon the application of Monte Carlo simulation." These results for the first time demonstrate the importance of surface diffusion length and symmetry rules in the growth mode of the new metal surface. Nevertheless, the statistical base of these calculations precluded further understanding of fundamental aspects of those processes such as the nature of centers of attack and growth a t the metal surface during the oxidation-reduction cycles (ORC) and the dynamics of the surface morphology along the potential cycling in relation to ib dependence on the number of metal particles participating in the overall process. The present paper attempts to answer the posed questions by using a simple quantum mechanical model that explains qualitatively the electrochemical faceting of metals. The model consists of a cluster approach for the metal surface under ORC for an ideal gas phase type environment where the presence of solvent molecules and ion-ion interactions beyond the cluster boundaries is specifically ignored. To simplify the attack of the problem, only main processes are considered as occurring during the application of the periodic perturbing potential, namely, the metal electrodetachment and the metal electrodeposition reactions, which can be considered as equivalent to the sublimation and condensation of atoms at the solid surface in contact with the gas phase. The model developed to deal with these processes emphasizes either the electrostatic aspects, i.e., charge distribution (sections IV and V.2), or the energetics of the reactions (sections I11 and V.l). (11)Albano, E. V.; MHrtin, H. 0.; Arvia, A. J. Phya. Rev. B: Condens. Matter 1987, 35, 9341.
0743-7463/88/2404-1142$01.50/0 0 1988 American Chemical Society
-0
Dynamics of Cluster Morphology
li-1; 1
0
0
0
I
0
0
0
0
0
0
0
c
0
c . * * * a
*
c c
Figure 1. Types of 2D clusters used for the calculations. Different kind of nodes can be distinguished: ( 0 )surface, (0) inner, and (*) first coordination sites.
11. The Model The Schrodinger equation is solved by using the LCAO method
AI*)
= El*)
(1)
where (Q) is given in terms of atomic orbitals li), according to
I*)
= Caili)
(2)
I
so that eq 1 results (3)
where Hik denotes the matrix elements
Hik = (klfili)
(4)
and Sik refers to the overlapping integrals:
(5)
Sik = (kli)
The minimum condition derived from eq 3 yields the following expression for coefficients ai:
c(Hik - ESik)ai = 0; k = 1, 2, i
...,n
(6)
The nontrivial solution of eq 6 is given for values of E satisfying det(Hik- ES,k) = 0 (7) Each cluster is made of n model atoms in a simple cubic lattice array, the locus of each atom being a node of the network and each node comprising a single atomic orbital (cubium).*2 The matrix elements in eq 4 and 5 are defined through the tight-binding approach; that is, the elements Hikare not 0 for i and k corresponding to orbitals of the nearest-neighbor sites in the duster. For arbitrary 2D clusters (Figure 1)different sites can be immediately distinguished, that is, those corresponding to surface nodes which involve a coordination number lower than 4,those related to the inner nodes which are fully coordinated, and those comprising the first coordination sites (FCS) which involve the outer neighbors nearest to surface nodes. The initial shape of the cluster, either regular or irregular, has been arbitrarily chosen (Figure 1). The total energy of the cluster ( E ) and the net charge density (qk) of the k-atom is obtained from the equations occ
E=2CEj j=1
(12) Messmer, R. P. In The Nature of the Surface Chemical Bond; Rhodin, T. N., Ertl, G., Eds.; North-Holland Amsterdam, 1979; p 70.
Langmuir, Vol. 4 , No. 5, 1988 1143 where (cI1,c , ~..., , cj,) is the eigenvector for EP When the metal cluster is subjected to the periodic perturbing potential, during the electrooxidation half-cycle, a metal atom is drawn from a node at the surface: Me, AE, Mensl+ Me (loa)
+
-
where Me, denotes a metal cluster composed of n atoms, Me a metal atom separated from the cluster, and AEa the corresponding energy change associated with the process, as given by the difference AE, = E f - Ei (lob) where Ei is the energy of the initial cluster formed by n + 1 atoms and Ef the energy of the cluster of n atoms. Analogously, during the electroreduction half-cycle a metal atom incorporates to a FCS according to the reaction Me, + Me = Men+l + AE, (W The energy change AE, is the difference between the energy of the initial cluster formed by n atoms (Ei)and the energy of the new one containing n + 1 atoms (Ef): AE, = Ei - E f (1lb) The addition of the Me atom may involve either AE, > 0, energy deliverance to the surrondings, or AE, < 0, the opposite effect. The same conditions with a change in sign apply for the reverse process.
111. Energetic Approach In this section let us assume that any surface relaxation process is much faster than either detachment or incorporation of metal atom reactions themselves; hence, these processes must occur at the energetically most favorable FCSs. The model allows calculations of the energy variation associated with the metal atom: either incorporation or detachment at any FCS. Therefore, to account for the new hypothesis into the model, the metal atom incorporation to FCSs should occur within an energy change range close to the maximum energy change Wm. Hence, from a quantitative standpoint as W, the energy change associated with the reaction at FCS, which is related to AE,, the most favorable sites should comprise W values between w”,the maximal values for W, and Wm + A W, where A W is another parameter. The same hypothesis can be extended to the metal atom detachment from the cluster surface, In this case, those atoms involving energy changes (w) comprised between the maximum value wm and wm Aw are able to be detached. Aw is also a preset parameter. The energetic approach was particularly useful to follow the influence of the potential applied to the metal cluster on the development of definite lattice configurations. Values of AW (Aw) employed in section I11 were in the range 0.01-0.02 Ha (1 Ha = 27.2 eV).
+
IV. Electrostatic Approach For the electrostatic approach one assumes that the incorporation of the metal atom occurs at the FCSs. In principle, the incorporation of atoms to the cluster can occur at any available FCS site with the required charge density sign. However, in the present model one assumes that the rate of atom incorporation to the cluster strongly depends on the charge density value at each FCS site; that is, the atom attachment probability to a certain site increases according to the negative charge density value. On the basis of this assumption the atom attachment has been restricted to those sites which imply negative charge density values only very slightly different from the maximum charge density value.
Mola et al.
1144 Langmuir, Vol. 4, No. 5, 1988
Figure 2. Charge-density contours calculated a t V = -0.6 V. It is assumed that each q k (eq 9) has a spherical distribution a t the site k . There is no uniform potential distribution in the lattice. Note that positive charge-density contours are inside the cluster because of the sign of the potential applied.
Each FCS is associated with a charge density Q, see Figure 2, equal to the sum of the charge densities q k (eq 9) of surface node's nearest neighbors to the FCS. Hence, the FCSs electrostatically most favorable for metal atom incorporation are those involving a value of Q comprised between Q", the maximal charge density value, and Q" + AQ, where AQ is a parameter. Similarly, for metal atom detachment from the cluster surface, the greatest probability of this event corresponds to those surface atoms whose positive charge density lies between a maximum value (4") and qm + Aq, where Aq is another parameter. Values of AQ (Aq) employed in section I1 (10-3-10-2),which correspond to 1-10% the value of Q" (q"), were chosen in such a way that due to the inhomogeneous surface charge density distribution one assumes that the atom detachment will occur with a different probability over the surface, i.e., atom detachment will occur at sites of highest positive charge density. Only for values of AQ ( A q ) falling in the 10-3-10-2 range could changes in surface atom arrangement with the development of definite lattice configurations be achieved. The resulting effect of the atom incorporation-atom detachment cycle is a certain atomic ordering at the cluster surface. According to the results obtained with the model, this atomic ordering can no longer be observed for AQ ( A q ) values greater than those referred to above. V. Results 1. Energetic Approach. The influence of the applied potential was accounted for through the application of the method originally developed for simulating the influence of the applied potential to 3D metal cluster^.'^-'^ Thus the effect of V , the potential applied to the metal cluster, is introduced by changing the diagonal matrix elements Hii = a into a* for all atoms in the cluster except the surface atoms according to a* = cy - 27.2/eV (12) where e is the absolute electron charge, a and a* are given in atomic units, and V is in volts; a = -0.175 Ha, whereas for the matrix elements Hik # 0 a constant value was assumed; that is, H i k = 0. For the calculations the value 0 = 0.046 Ha reproduces the bandwidth of a series of typical metals.13-15 The effect of the applied potential V as seen from eq 12 is to push down (V > 0) the occupied eigenvalues of the metal cluster and consequently the Fermi energy level ("anodic"), whereas a negative potential (V < 0) has the (13)Leban, M.A.;Hubbard, A. T . J. Electroanal. Chem. 1976, 74, 253. (14) Lee, W.; Reilley, Ch. N. J. Electroanal. Chem. 1981, 121, 29. (15) Mola, E. E. Electrochim. Acta 1981, 26, 1253. (16)Dohnert, D.; Kouteck?, J.; Scultze, J. W. Surf. Sci. 1977, 82, 81.
..... ..... ..... ..... .....
I wo12
a I O
Ira
iq -12
-06
I
I
..... ..... ::::: .4,..
-01
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..... ....... ..... ... w
a
P
08-1
..... ........ ..... ...
-
, 1;
I
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01
; I
I
06
12
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~
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a
....... ..... :P
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;2i;"la 120
~
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a
15
15. -12
-06 . O I v, I Y o l l l -
01
06 v"iYolll
12
Figure 3. AEc and AEa, energy changes (in 0 units) associated with the particle incorporation and detachment processes (ORC), respectively (eq I l a and loa), as a function of the applied potential, for different site positions.
opposite effect ("cathodic"). This can be considered as a possible way to account for coulombic interactions between ions at the cluster lattice and those in the neighbor phase. In this way the original problem (eq 10a and l l a ) can be dealt with as a simple atomic system. In the present case, oxidation-reduction cycles (ORCs) are promoted by applying a periodic square wave perturbing potential characterized by an upper ( Vu) and lower (VI)potential limits and frequency #. The values of Vu and VIare set above and below the thermodynamic potential of the metal/ metal ion electrode, respectively. Hence, one considers that a potential difference between the surface and the bulk metal ions in the cluster strongly influences the dynamics of detachment and incorporation of ions at the lattice. Certainly, it is possible to improve the model by further assuming that there is a smooth change of the potential (i.e., exponential-like) either from the border into the bulk metal side15-17 or from the border outward (i.e., to the gas-phase side)ls or both together. Although it is a fairly (17) Mola, E. E.; Vicente, J. L. Surf. Sci. 1986, 172, 533; Int. J. Quantum Chem. 1987,21, 355.
~ f -- y o Langmuir, Vol. 4, No. 5, 1988 1145
Dynamics of Cluster Morphology trivial matter to reinterpret the model by including these modifications, they can be neglected at the present stage until the goodness of the simple model has been demonstrated. The values of AEc and AE, were calculated for 2D clusters with three different configurations: two of them involving homogeneous arrays of border atoms, in (11)and (10) directions, respectively, and a third one having an inhomogeneous array of atoms (Figure 3). Values of AZ3, have been obtained for three potentials (“cathodic”),that is, Vi = -0.1, -0.6, and -1.2 V. As seen in Figure 3, the value of AEc required to attach one metal ion to a specific cluster border site depends to some extent on the applied potential. Likewise, the influence of Vl on AEc depends on the successive ion attachment events, that is, on the site involved in those processes as they involve changes in the external crystallographic habit along the cluster growth. Similarly, AE, values were also obtained for three potentials (“anodic”),namely, Vu = 0.1, 0.6, and 1.2 V, respectively. The value of AE, appears to be directly proportional to the number of metal-metal bonds which are broken during the metal ion withdrawal. In this case, only a slight influence of Vu on AE, can be noticed. For a particular number of metal-metal bonds which are broken per detached metal ion, the values of AE, change only slightly with Vu in a way which can hardly be made explicit either qualitatively or quantitatively. From these results based upon the energetic approach, one can conclude that there is a clear specificity of AEc on the type of site involved in both ion detachment and incorporation. 2. Electrostatic Approach. Following the electrostatic approach the cluster growth under the applied potential Vl can be described through successive stages; that is, the initial metal ion attachment is subsequently followed by a cluster relaxation in which the metal ion on the surface moves into the FCS. This description of the process implies that the number of metal ions involved in the incorporation stage turns out to be determined by the AQ value. The evolution of each cluster of atoms subjected to oxidation and reduction cycles from the upper potential Vu to the lower potential Vi depends on the chosen AQ (Aq) value. The influence of the latter was inspected for different sets of Vu and Vl values in the range already considered in the previous section. According to the preset AQ (Aq) value the effect of the oxidation and reduction cycles is either the cluster growth, the decrease of its size, or a reaccommodation of the atoms in the cluster. Occasionally, a quasi-steady configuration of atoms can be observed, where the atomic arrangement after a certain number of ORCs begins to oscillate, so that for each cycle the same number of atoms is detached and incorporated at the same border sites. Therefore, the value of AQ (Aq) determines the number of atoms participating at each cycle. Calculation is performed on the basis that during the reduction (oxidation) half-cycle a certain number of atoms are incorporated (detached) at once. Furthermore, it is also assumed that the incorporation (detachment) of atoms to (from) the cluster border is much faster than the proper atom relaxation processes at the cluster. Certainly, the model also offers another possible approach which corresponds to the reverse situation; that is, the relaxation processes become faster than atom incorporation (detachment). This situation can be achieved by running the (18) Schmickler, W.; Henderson, D. Phys. Rev. B: Condens. Mutter
1984, B-30, 3081; J . Chem. Phys. 1984,80, 3381.
(19)Kern, R.;Lelay, G.; Metoism, J. J. In Current Topics in Materials Science; Kaldis, E., Ed.; North-Holland: Amsterdam, 1979; Vol. 3, p 131.
0
0
0
0
(a1
0
0
(b)
(C)
Figure 4. Evolution of a square cluster along the ORC for Vl = -0.1 V, Vu = 0.1 V, AQ = 10”. Note that the contour moves from a, the initial (10) configuration, to b, an intermediate (11) (10) configuration, and finally oscillates between b and c, a (11) configuration.
+
0 0
0
0
0
0
0
0
lb)
(0)
IC1
Figure 5. Evolution of a rhombic cluster along the ORC for Vl = -1.2 V, Vu = 0.1 V,AQ = The contour moves from a, the initial (11)configuration, to b, a quasi-(10) configuration, and finally oscillates between b and c, an intermediate (11)+ (10) configuration.
0+IL.
0 0 0 0
0 0 0
lbl
101
IO
Figure 6. Evolution of an asymmetric cluster, a, along the ORC The cluster for Vl = -0.1 V, Vu = 0.1 V, and AQ = 3 X boundary moves to b and oscillates between b and c, two quasi-(11) configurations.
10
I
ib)
IO
Figure 7. Evolution of a, the same initial cluster iven in Figure 6, for Vl = -1.2 V, Vu = 0.6 V, and AQ = 1 X 10-93 . In this case the cluster boundary finally oscillates between b and c, two quasi-(10) configurations.
process in single-atom steps and by dividing the duration of each half-cycle into n steps, with the calculation proceeding n times for each half-cycle. The evolution of two symmetric clusters along the oxidation reduction cycleg, for Vl = -0.1 V, Vu = 0.1 V, AQ = and Vi = 1.2 V, Vu = 0.1 V, AQ = is depicted in Figures 4 and 5. In one case (Figure 4) the contour of the cluster moves from the initial (10) configuration (Figure 4a) to an intermediate (11)+ (10) configuration (Figure 4b), and after the nth cycle the system oscillates between the configuration shown in Figure 4b and the (11)configuration depicted in Figure 4c. When the starting contour corresponds to a (11)configuration (Figure 5a), it first moves to an intermediate stage (Figure 5b) involving a predominant (10) array of ions at the border, and after the nth cycle a quasi-stable situation is reached in which the system oscillates between two intermediate (11) + (10)
1146 Langmuir, Vol. 4, No. 5, 1988
..... ..... ..... ..... ............................. ............ -...... -.............................. .... .... .*.. .... ..... ..... ..... ........ ............................. - ........................ .......... ......- ...... ..... -........... ..... .............. ............ ...... - .................................... .................. ...... .................. .................................. ........ ........ ........ ...... +z........ .................... - ........ ...... - ....... ........ .......... .......... 0.
0..
0..
0..
0.0
(C)
(d)
process continues by repeating the sequence of the stages referred to above in a progressively large scale. In this case, the overall process can be compared to metal electrocrystallization through a layer by layer growth mechanism as observed experimentally from the gas phase.18
0.0
(a1
(b)
.e...
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0..
(e)
(g)
( f )
(h)
0
0
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(1)
(k)
0.0
0 .
0.0
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0.
0.
0.0
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(m)
-
........ ........ .......... 0
0 0 0.000.
0.0
.
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( 0 )
’
’
Mola et al.
’
0
(PI Figure 8. Step growth under a constant-energycondition from an initial asymmetric cluster, a, to f, where the smoothing of borders can be observed, and then to k, a (10) configuration. The following incorporation events repeat at a large scale: first the incorporationat corners takes place (l),followed by step growth (m, n) to (10) configurations (0).
configurations (Figure 5b,c), the former comprising a (11)/(10) border ratio smaller than the latter. When an asymmetric starting metal cluster is considered (Figure 6a), for VI = -0.1 V, Vu = 0.1 V, and AQ = 3 X and VI = -1.2 V, Vu = 0.6 V, and A Q = 1 X lo4 (Figure 7), the initial ORCs produce a clear elimination of defects a t borders (Figure 6b), and after the nth cycle again the system oscillates steadily between the two definite structures shown in Figure 6b and Figure 6c. The border of these structures exhibits a remarkable trend to develop a particular orientation either in the (11)direction in one case (Figure 6c) or in the (10) direction in the other (Figure 7c). Let us consider the growth of the starting asymmetric cluster in terms of a sum of single events (Figure 8). In this case for the entire process it is assumed that the dynamics of atoms at the border is the rate-controlling step. The resulting scheme clearly shows various stages in the cluster growth. Thus, initially surface defects are successively removed, producing a smoothing effect of cluster borders (Figure 8a-f). This effect is accompanied by a gradual development of a preferred orientation in the (10) direction a t cluster borders. Later, the ion incorporation takes place at 2D steps (i.e., step and kinks in 3D space) with further development of extended borders (i.e., terraces in 3D space) (Figure 8g-j), finally yielding a regular array of ions with (10) preferred orientation a t cluster borders (Figure 8k). Further incorporation of ions (Figure 81-11] undergoes a t corner sites with the development of newly growing 2D steps and preferred oriented borders, which in turn repeat the regular square figure (Figure 80) with a larger number of particles. In this way the cluster growth
VI. Conclusions 1. Preliminary Conclusions from the Simple Cluster Model. The simple model described above for simulating the 2D faceting of the cluster metal surface offers a reasonable explanation to some energetic aspects related to that process and throws further light on some mechanistic aspects a t the atomic level. The “iso-charge”profiles resulting for the metal cluster (Figure 2) indicate that for a cubium lattice containing a number of charged particles as large as 100 ions the charge per ion is not a constant, and therefore, no uniform potential distribution a t ion sites in the lattice can be considered. These nonuniform charge and potential distributions are consistent with the fact that the properties of this size of metal clusters differ substantially from bulk metal properties.20 This difference becomes more remarkably when the number of ions on the cluster is made progressively smaller. Consequently, the probability of either an ion detachment or incorporation should be related to either the greater (more positive) or the smaller (more negative) charge density a t reacting sites, respectively. Consequently, the reactivity of each border site is determined by the effective charge density at that site, and those processes become highly selective. For a constant number of ions, the development of preferred oriented borders implies, in principle, no substantial change in the cluster border length. This conclusion as extended to 3D clusters means that preferred orientation a t 3D cluster surfaces should occur without appreciable change in surface roughness. From the mechanistic standpoint, different subsequent stages can be distinguished along the ORC. These stages can be put forward in the following order: (i) elimination of defects at the borders and (ii) development of step-like growing centers with preferred orientation. Furthermore, when the change in cluster size is limited, the particle array steadily fluctuates between two quasi-stable configurations, in phase with the ORC. Likewise, when there is no limit in cluster size growth the mechanism of growth becomes comparable to a layer by layer metal growth mechanism from the gas phase.l9 The final product in both cases is a cluster configuration with a very stable and reproducible particle array at cluster borders. The final display of ions in the cluster is conditioned by the preset parameters of the perturbing potential. From the model, however, it can also be concluded that the number of bonds which are broken for each ion participating in ORC is by far more important than the influence of the potential applied to the metal cluster. The model predicts that ion diffusion a t borders (i.e., surface diffusion at a 3D model) plays also an important role in the development of preferred orientation. 2. Correlation between Model Conclusions and Electrochemical Faceting of fcc Metals. Despite the large difference between the simplified model presented in this work and the structure and reactions at the metal electrode/electrolyte solution interface involved in electrochemical faceting, there is a surprising qualitative correlation between the conclusions from the model and (20) Poltorak, 0.M.; Boronin, V. S. Russ. J.Phys. Chen. 1966, 40,
1436.
Langmuir 1988,4, 1147-1151 experimental results recently reported for a series of fcc metals.lg Thus, the surface images of metals such as Pt, Pd, Au, and Rh as revealed through STM at the nanometer s ~ a l show e ~ ~that ~ the early stages of electrochemical faceting imply a metal smoothing, which is later followed by the incipient formation of nuclei. The latter become centers for the development or preferred ~ r i e n t a t i o n . ~ These changes, which occur under preset fast electrodissolution-electrodeposition cycles, involve no change in real surface roughness. These facts are consistent with the conclusions derived from the model. Furthermore, the stable and reproducible preferred oriented surfaces resulting for real systems after a prolonged electrochemical faceting treatment keep an interesting parallelism with the quasi-stationary and reproducible configurations predicted by the model after a large number of ORCs. The correlations between the model and real systems can still be further extended to supercluster-like metal electrode^^^^ consisting of an approximately uniform distribution of sticking nearly spherical preferred crystallographically oriented metal clusters of about 10 nm average diameter each. The STM images Of these surfaces at the 0.1 nm level exhibit a clear development
1147
of steps and terraces with kinks at the atomic level which closely resemble the metal ion arrays depicted in Figure 8, where incipient step formation can be noticed. In conclusion, the simplified model described in this work constitutes the first quantum mechanical attempt to deal with the dynamics of metal surface crystallographic modifications promoted through ORC, in terms of both type of active centers and real surface-active area. The conclusions of the model can also be extended to account for atomic aspects related to electrocrystallization of metals,21*22 which are obviously implicit in the mechanism of electrochemical faceting of fcc metals.
Acknowledgment. This work was financially supporte$ by the Consejo Nacional de Investigaciones Cientificas y TBcnicas and the Comisidn de Investigaciones Cientificas de la Provincia de Buenos Aires. ,
(21) Budevski, E. B. In Comprehensiue Treatise of Electrochemistry; Conway, B., Bockris, J. O’M., Yeager, E., Khan, S. U. M., White, R. E., Eds.; New lga3; vO1. P 399. (22) Despic, A. R. In Comprehensiue Treatise of Electrochemistry; Conway, B.; Bockris, J. O’M., Yeager, E., Khan, S. U. M., White, R. E., Eds.; Plenum: New York, 1983; Vol. 7, p 518. 79
Substrate-Mediated Adsorbate-Adsorbate Interactions: Effect of Submonolayer Coverage and Coadsorbed Iodine on the Reversible Redox of 2,5-Dihydroxythiophenol Chemisorbed at Au and Pt Thomas Mebrahtu, Ginger M. Berry, Beatriz G. Bravo, Susan L. Michelhaugh, and Manuel P. Soriaga* Department of Chemistry, Texas A&M Uniuersity, College Station, Texas 77843 Received February 18, 1988. In Final Form: April 22, 1988 A close-packed monolayer of 2,5-dihydroxythiophenol (DHT) chemisorbed on gold and platinum exclusively through the sulfur atom displays reversible two-electron quinonefhydroquinone redox, due to the pendant diphenol, at the same potential where the unadsorbed molecule reacts. However, the cyclic voltammetric peaks are approximately twice as broad at Pt as at Au. Since the DHT surface packing densities are identical at the two surfaces, the differences in the redox peak widths can only be rationalized in terms of substrate-mediated adsorbateadsorbate interactions on Pt. The aim of the present study is to obtain empirical information with regards to the origins of this substrate mediation. Experiments were performed in which the coverage of and composition within the chemisorbed DHT layer were varied at smooth Au and Pt surfaces in acid media. When DHT is chemisorbed at submonolayer coverages on Pt, no redox peaks are observed. This signifies that the diphenolic group is no longer pendant but is directly bonded to the surface; an adsorbed molecule orientation which allows DHT to behave like a surface chelate is a strong possibility. In comparision, redox activity is still observed when submonolayer DHT is chemisorbed on Au. Even on a sparsely populated Au surface, the diphenolic moiety remains pendant; this means that diphenol-Au reactivity is not enhanced even by entropic or chelate effects. Reversible redox peaks reappear when DHT is coadsorbed at submonolayer coverages onto an iodine-pretreatedPt electrode. In the presence of coadsorbed iodine, the diphenol group is again pendant; evidently,direct interaction between the diphenol moiety and Pt surface is blocked by the surface iodine. The redox peaks are sharpened when surface iodine is present, indicating that the substrate-mediated DHT-DHT interactions are also suppressed by iodine coadsorption. On Au, essentially no changes in the peak widths are observed for the iodinefDHT mixed layer. The present results suggest that the driving force in the substrate-mediated intermolecular interactions which occur within the close-packed DHT layer is the inherent strong reactivity of the diphenolic moiety with the Pt surface. Although the phenomenon of substrate-mediated adsorbate-adsorbate interactions is not well understood, it may be possible to view it in terms of traditional concepts of mixed-valence metal complexes in which two metal ions separated by a common ligand are still able to interact with each other through the mediation of the delocalized electrons in the ligand.
Introduction We recently reported a comparative study of the surface electrochemical behavior of aromatic mercapto compounds
* Author t o whom correspondence should be addressed.
a t smooth polycrystalline platinum and gold electrodes.’ In that investigation, it was found that the maximum (1) Bravo, B. G.;Mebrahtu, T.; Soriaga, M. P.; Zapien, D. C.; Hubbard, A. T.; Stickney, J. L. Langmuir 1987,3, 595.
0743-7463/88/2404-ll47$01.50/0 0 1988 American Chemical Society
