Adsorbed particles, coverage

In the last decade two-dimensional (2D) layers at surfaces have become an interesting field of research [13-27]. Many experimental studies of molecular adsorption have been done on metals [28-40], graphite [41-46], and other substrates [47-58]. The adsorbate particles experience intermolecular forces as well as forces due to the surface. The structure of the adsorbate is determined by the interplay of these forces as well as by the coverage (density of the adsorbate) and the temperature and pressure of the system. In consequence a variety of superstructures on the surfaces have been found experimentally [47-58], a typical example being the a/3 x a/3- structure of adsorbates on a graphite structure (see Fig. 1). 

The sticking coefficient at zero coverage, Sq T), contains the dynamic information about the energy transfer from the adsorbing particle to the sohd which gives rise to its temperature dependence, for instance, an exponential Boltzmann factor for activated adsorption. 

Finally, the probability factor rj, which is taken to be coverage-independent in the model of a homogeneous surface with no lateral interactions between adsorbed particles, will be expressed by means of the Arrhenius formalism based on the Boltzmann distribution, viz. 

In the case of monolayer adsorption, a limiting adsorption value exists that is attained when the surface is covered completely by particles of a given substance (i.e., at full monolayer coverage). The limiting adsorption value depends on the effective surface area Sj taken up by one particle 1/5. This parameter characterizes the number of sites that can be occupied by adsorbed particles on a given surface. 

At low values of the bulk concentration Bcy surface coverage is proportional to this concentration, but at high values it tends toward a limit of unity. This equation was derived by Irving Langmuir in 1918 with four basic assumptions (1) the adsorption is reversible (2) the number of adsorption sites is limited, and the value of adsorption cannot exceed A° (3) the surface is homogeneous aU adsorption sites have the same heat of adsorption and hence, the same coefficient B and (4) no interaction forces exist between the adsorbed particles. The rate of adsorption is proportional to the bulk concentration and to the fraction 1-9 of vacant sites on the surface = kjil - 9), while the rate of desorption is proportional to the fraction of sites occupied Vj = kjd. In the steady state these two rates are equal. With the notation kjk = B, we obtain Eq. (10.14). 

Frumkin Isotherm In 1928, Frumkin derived an eqnation for interaction between the adsorbed particles. Mntnal attraction leads to an increase in the heat of adsorption, whereas repnlsion leads to a decrease. Qnantitatively, these elfects depend on the degree of snrface coverage and can be written as = Qq whereis... 

Often, mnltistep reactions are enconntered where a reactant j first becomes adsorbed on the electrode, then is converted electrochemically (or chemically) to a desorbing prodnct. We shall consider the case where the electrochemical step involving adsorbed particles is rate determining. With a homogeneons electrode surface and without interaction forces between the adsorbed particles [i.e., in conditions when the Langmuir isotherm (10.14) can be apphed], the assumption can be made that the rate of this step is proportional not to the bulk concentration Cy j but to the surface concentration Aj or to the degree of surface coverage 0 hence. 

If the Gibbs energy of adsorption AG-M is considered as independent of the coverage the resulting formula is known as the Langmuir isotherm this assumption is reasonable when the interaction between the adsorbed particles is small. 

At small partial coverages the adsorbed particles are arranged randomly on the surface (Fig. 32a) and the rate of C02 formation is expected to follow a rate equation ... 

We assume a rapid surface migration this allows us to introduce the fugadty of adsorbed particles I, p1 common for all surface sites, although at a reaction following scheme (53), in contrast to mechanism (188), the coverage of the surface by particles I is in the general case not an equilibrium one, but a steady-state one. 

An increase in the sticking probability of adsorbed particles with a growth in the coverage at low coverages of a surface. 

If the adsorbed particles are packed to form a single layer on the surface, the coverage can be expressed as NML where ML denotes a mono-molecular layer (monolayer). If NML can be accommodated and N, have... 

Instead of c, for adsorption from the gas phase, it is custom to use the partial pressure. For that isotherm it has to be assumed (a) that a localized adsorption (i.e., finite and defined number of adsorption sites) takes place at an isotropic surface, (b) that the adsorbed particles do not interact with each other, and (c) that the maximum coverage is a monolayer of the adsorbed particles [iii]. About the importance of the Langmuir isotherm in electrochemistry see - adsorption isotherm. 

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