Mobility on surfaces

A further aspect of the strength of the interactions between adsorbate and substrate is the mobility of the adsorbate. Mobility is often a vital feature of a catalyst’s activity, because a catalyst might be impotent if the reactant molecules adsorb so strongly that they cannot migrate. The activation energy for diffusion over a surface need not be the same as for desorption because the particles may be able to move through valleys between potential peaks without leaving the surface completely. In general, the activation energy for migration is about 10–20 per cent of the energy of the surface adsorbate bond, but the actual value depends on the extent of coverage. The defect structure of the sample (which depends on the temperature) may also play a domin ant role because the adsorbed molecules might find it easier to skip across a terrace than to roll along the foot of a step, and these molecules might become trapped in vacancies in an otherwise flat terrace. Diffusion may also be easier across one crystal face than another, and so the surface mobility depends on which lattice planes are exposed. Diffusion characteristics of an adsorbate can be examined by using STM to follow the change in surface characteristics or by field-ionization microscopy (FIM), which portrays the electrical characteristics of a surface by using the ionization of noble gas atoms to probe the surface (Fig. 25.24). An individual atom is imaged, the tempera ture is raised, and then lowered after a definite interval. A new image is then recorded, and the new position of the atom measured (Fig. 25.25). A sequence of images shows

Fig. 25.25 FIM micrographs showing the migration of Re atoms on rhenium during 3 s intervals at 375 K. (Photographs provided by Professor G. Ehrlich.)

that the atom makes a random walk across the surface, and the diffusion coefficient, D, can be inferred from the mean distance, d, travelled in an interval τ by using the two-dimensional random walk expression d = (Dτ)1/2. The value of D for different crystal planes at different temperatures can be determined directly in this way, and the activation energy for migration over each plane obtained from the Arrhenius-like expression

D=D₀^e−ED/RT

Where E_D is the activation energy for diffusion. Typical values for W atoms on tungsten have E_D in the range 57–87 kJ mol⁻¹ and D0 ≈ 3.8 × 10⁻¹¹ m² s⁻¹. For CO on tungsten, the activation energy falls from 144 kJ mol⁻¹ at low surface coverage to 88 kJ mol⁻¹ when the coverage is high.

Biosensor analysis is a very sensitive and sophisticated optical technique that is now used routinely to measure the kinetics and thermodynamics of interactions between biopolymers. A biosensor detects changes in the optical properties of a surface in con tact with a biopolymer. The mobility of delocalized valence electrons accounts for the electrical conductivity of metals and these mobile electrons form a plasma, a dense gas of charged particles. Bombardment of the plasma by light or an electron beam can cause transient changes in the distribution of electrons, with some regions becoming slightly more dense than others. Coulomb repulsion in the regions of high density causes electrons to move away from each other, so lowering their density. The resulting oscillations in electron density, called plasmons, can be excited both in the bulk and on the surface of a metal. Plasmons in the bulk may be visualized as waves that propagate through the solid. A surface plasmon also propagates away from the surface, but the amplitude of the wave, also called an evanescent wave, decreases sharply with distance from the surface. Biosensor analysis is based on the phenomenon of surface plasmon resonance (SPR), the absorption of energy from an incident beam of electromagnetic radiation by surface plasmons. Absorption, or ‘resonance’, can be observed with appropriate choice of the wavelength and angle of incidence of the excitation beam. It is common practice to use a monochromatic beam and to vary the angle of incidence θ (Fig. 25.26). The beam passes through a prism that strikes one side of a thin film of gold or silver. The angle corresponding to light absorption depends on the refractive index of the medium in direct contact with the opposing side of the metallic film. This variation of the resonance angle with the state of the surface arises from the ability of the evanescent wave to interact with material a short distance away from the surface. As an illustration of biosensor analysis, we consider the association of two polymers, A and B. In a typical experiment, a stream of solution containing a known concentration of A flows above the surface to which B is chemisorbed. Figure 25.27 shows that the kinetics of binding of A to B may be followed by monitoring the time dependence of the SPR signal, denoted by R, which is typically the shift in resonance angle. The system is normally allowed to reach equilibrium, which is denoted by the plateau in Fig. 25.27. Then, a solution containing no A is flowed above the surface and the AB complex dissociates. Again, analysis of the decay of the SPR signal reveals the kinetics of dissociation of the AB complex. The equilibrium constant for formation of the AB complex can be measured directly from data of the type displayed in Fig. 25.27. Consider the equilibrium

A+B5⇌AB K=

Where k_on and k_off are the rate constants for formation and dissociation of the AB com plex, and K is the equilibrium constant for formation of the AB complex. It follows that

In a typical experiment, the flow rate of A is sufficiently high that [A] = a0 is essentially constant. We can also write [B] = b0 − [AB] from mass-balance considerations, where b0 is the total concentration of B. Finally, the SPR signal is often observed to be proportional to [AB]. The maximum value that R can have is R_max ∝ b0, which would be measured if all B molecules were ligated to A. We may then write

At equilibrium R = Req and dR/dt = 0. It follows that (after some algebra)

Req = Rmax

Hence, the value of K can be obtained from measurements of Req for a series of a0. Biosensor analysis has been used in the study of thin films, metal–electrolyte sur faces, Langmuir–Blodgett films, and a number of biopolymer interactions, such as antibody–antigen and protein–DNA interactions. The most important advantage of the technique is its sensitivity; it is possible to measure the adsorption of nanograms of material on to a surface. For biological studies, the main disadvantage is the require ment for immobilization of at least one of the components of the system under study.

Fig. 25.26 The experimental arrangement for the observation of surface plasmon resonance, as explained in the text.

Fig. 25.27 The time dependence of a surface plasmon resonance signal, R, showing the effect of binding of a ligand to a biopolymer adsorbed on to a surface. Binding leads to an increase in R until an equilibrium value, Req, is obtained. Passing a solution containing no ligand over the surface leads to dissociation and decrease in R.

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مواضيع ذات صلة

Units

Names of quantities

Working galvanic cells

Electrolysis

Experimental techniques

The rate laws

The electric potential at the interface

The structure of the interface

Catalytic activity at surfaces

Mechanisms of heterogeneous catalysis

The rate of desorption

The rate of adsorption