ROLE OF ADSORBATE INTERACTIONS IN SURFACE DYNAMICS AND PHASE-TRANSFORMATIONS - MEAN-FIELD AND QUASI-CHEMICAL APPROXIMATION APPROACHES

The significant influence of adsorbate interactions in surface dynamic s is quantified using mean-field approximation (MFA) and quasichemical approximation (QCA) approaches and two typical situations (i) T > T-c (critical temperature for surface phase transformation) and (ii) T < T-c are analyzed. The formulation involves transition state theory (TS T) and the key parameters involved are: (1) the sign and magnitude of the pairwise adsorbate interaction energy (w > 0, w < 0 meaning repuls ive and attractive interactions, respectively) (2) W-A#, the interacti on energy between a molecule in the ground state and the activated com plex. W-A#(A) is in turn related to w by a coupling parameter sigma. s igma=0, sigma=1 are shown to result in extreme divergence of the rate behavior for both repulsive and attractive interactions. First T > T-c is considered. For sigma=0, attractive interactions retard and repuls ive interactions enhance the surface rates. The rates display nonmonot onic behavior for attractive interactions and steady increase with sur face coverage for repulsive interactions. However, when sigma=1, the r ates monotonically increase for both types of forces. In addition the attractive forces show an instability of the slope due to a cooperativ e catalytic effect. Both attractive and repulsive forces display maxim a when plotted against temperature, the maxima being sharper for the f ormer case. The case T < T-c is more interesting, as a discontinuous p hase separation can occur for attractive interactions. The density and internal energy differences between the coexisting phases are compute d proceeding from closed-form expressions of the canonical ensemble pa rtition functions and employing standard methods of statistical mechan ics. Since repulsive forces can only show continuous order-disorder tr ansitions, they are not considered for T < T-c. The surface rate expre ssions (both corrected and uncorrected for ground-state internal energ y differences between the phases) display a symmetric rate curve (symm etric about theta=0.5) vs surface coverage with a maximum at theta=0.5 . A certain type of hole-particle symmetry is present in the rate expr ession as the rate expression is invariant with respect to the exchang e of an occupied and vacant site. This conclusion is valid for both si gma=0, sigma=1. The appearance of symmetry in the rate curve is sugges tive of the phase separation. The qualitative differences between the rate predictions of MFA and QCA are significant enough to warrant refi nement in the analysis of surface dynamics.