For electron transfer at surfaces, see:  electransfer.pdf

Forces acting on adsorption

See class notes in surface_bonds.pdf

Physisorption: Weak  — few tenths of an eV or less

Chemisorption: Strong — eV or more

Physisorption

The electric field outside the surface, produced by the spill out of the electrons, polarizes the adsorbed atom, creating an induced dipole.  The interaction of the induced dipole with the surface charge is attractive, and similar to the Lennard-Jones interaction. 

              V_LJ = - C/r³

first discussed by John Bardeen (Twice Noble prize winner for transistor and superconductivity).

The so-called dispersion forces due to oscillating charges fall faster, according to the London potential:

            V_L= - a₁a₂/r⁶

where a₁ and a₂ are the polarizabilities.

Polarizabilities (in ų)

Molecules with permanent dipole moments m can further polarize each other and give a potential:

             V_Debye = -a₁m₂²/r⁶ - a₂m₁²/r⁶

 Direct dipole interaction gives:

             V_Keesom = -(2/3kT) m₁²m₂²/r⁶

Dipole moments (in Debyes) 

Adsorption is governed also by the interaction between the adsorbed molecules, which have the same origin.

The main aspects of the adsorption process is the bonding of the incoming molecule to the surface, its motion across it or to the interior (diffusion) and the evaporation (desorption).

Chemisorption

Chemisorption is characterized by high binding energies. The surface chemical bond results from charge transfer or charge redistribution involving the surface and the absorbate. High adsorption energies are found for transition metals, due to their incomplete d-bands. See Somorjai's Fig. 6.1 for adsorption energies of hydrogen and oxygen on transition metals.  Notice the range of energies for hydrogen adsorption (around 2.5 eV) and oxygen adsorption (4 to 10 eV).

  Noble metals like gold are noble partially because they do not contain empty localized levels, which can participate in the chemical bonding.  In addition, the large electron cloud of gold strongly repels the electron cloud of the incoming atom or molecule, and also leads to the population of anti-bonding (repulsive) states that provides a repulsive force to the gold.

   In dissociative chemisorption the internal molecular bond is broken by interactions with the substrate.  In the interaction of the generic molecule X₂ with the surface S, the electronic potential curve X₂ - S, describing the energy of the system as a function of the distance X₂ to the surface crosses the corresponding potential curve X + X - S. which describes the interaction of the dissociated fragments with the surface.  At the crossing, there can be a dissociative transition, unless the energy at the crossing is positive (there is a barrier).  In that case, X₂ - S might stay at a local minimum (precursor state) until the barrier may be overcome by "activation" (thermal, absorption of light, etc.)

   Description of chemisorption in terms of energy-distance curve is an oversimplification since more coordinates are needed.  Not only depends also on the coordinate along the surface (e.g., top site vs. hollow site) but also on the interatomic distance in the molecule, its orientation with respect to the surface, and individual coordinates of the dissociation products.  Thus, the problem of obtaining the relevant energies for the chemisorption process is extremely complicated.

  The chemisorbed state can be studied in several ways.  Changes in work function give information on charge transfer.  An increase (decrease) in work function corresponds to a dipole with the positive (negative) side towards the surface.  Changes in the electronic density of states are best studied by ultraviolet photoelectron spectroscopy.  The location may be obtained in single crystals by LEED or ISS.  Other techniques like XPS, AES, STM also provide useful information.

Adsorption kinetics

Experiments of adsorption are most usually done with a sample exposed to an ambient gas at pressure p. Usually all angles of incidence of the molecules are allowed and the molecules are characterized by a Maxwell-Boltzmann distribution of velocities, vibrations and rotations corresponding to the temperature of the gas (complications may arise if the surface is surrounded by surfaces at different temperatures). Another way of studying, more controlled, consists in the use of directed molecular beam. Here the direction is fixed. A narrow range of molecular velocities is possible if there is a velocity selector. The rotations are not controlled while the vibrations will depend on the temperature of the gas source.

In the first case, the number of molecules bombarding the surface is given by the impingement rate

I = dN/dt = p (2pmkT)^-1/2

where m is the mass of the molecule, k the Boltzmann constant and T the absolute temperature. The adsorption rate u is the number of adsorbed molecules N_a per unit time:

u = dN_a/dt = S I

which defines S, the sticking coefficient (probability of sticking). S is an average value. Molecules may stick for a while and then desorb. In general, S depends on the number of molecules on the surface, N_a.

N_a= ò udt = ò S dN/dt dt

From the measurements of N_a vs time, or dosage or exposure

    F = ò Idt

one can determine S:

    S = u/I = I^-1 dN_a/dt

as a function of F, where N_a can be measured by different techniques, i. e., AES, ISS, desorption (to be discussed later).

  Notice that the literature is a bit confusing since the symbol q is used often for number of molecules and for the more usual coverage (N_a/N_s where N_s is the number of surface atoms).

Microscopic Picture

Sticking depends on different parameters.

Monolayer adsorption

If the adsorption of only one monolayer can occur with significant probability (q £ 1), one can write:

    S = s f(q) exp(-E_act/kT)

where s is a condensation coefficient, which includes the effect of the orientation of the molecule and energy loss to substrate. If the molecule sticks only if landing site is empty,

    f(q) = 1 - q

usually valid for gases on metals. For dissociative chemisorption of a molecule that breaks up into two fragments, two sites are needed to accept the fragments.

    f(q) = (1 - q)²

If molecules diffuses, it can search the surface for a binding site, so

    f(q) = 1 for q < 1 and 0 otherwise

If the adsorption occurs in the perimeter of a cluster or an island, the initial sticking is zero or very small (if there are nucleation sites). f(q) increases with q until the island start to touch and coalesce, causing f(q) to decrease with further coverage.

These are simple cases. Often, the bonding type changes with q and so the situation is more complex.

Surface diffusion

The motion of atoms across the surface is subject to a periodic potential determined by the individual atoms, which is affected by defects like vacancies, steps, etc. This periodic potential can be considered as a succession of wells and barriers. The motion across a diffusion barrier, E_dif, is thermally activated. The frequency of escape from the well is given by

n = n_o z exp(-E_dif/kT)

where n_o is of the order of a vibration period (~10^-13 sec) and z is the number of equivalent neighboring sites. In the absence of electric fields, diffusion occurs by a random walk. The distance moved from the initial site, r, is given by:

r = (<r²(t)>)^1/2 = (nt)^1/2 d

where t is time and d the mean jump length. The diffusion coefficient D is defined as the limit of D = r²/2bt for large t, where b is the dimensionality of the diffusion b=2 for surface diffusion and 3 for bulk.

D = nd²/4

for surface diffusion and:

r = (4Dt)^1/2

D can be determined by measuring r(t) with different methods, including the STM in atomic scales.

D = D₀ exp(-E_dif /kT) = (n₀ d²/4) exp(-E_dif /kT)

At 600 K, a diffusion barrier E_dif = 2 eV, d=0.3 nm, gives:

D ~ 0.2 exp(-2/0.05) = 10^-18 cm²/s

and in one hour, r = 1,2 nm or only a few lattice spacing.

A useful rule of thumb is that the activation energy for surface diffusion is one tenth of the desorption energy.

Desorption

Let E_d be the desorption barrier, E_d = E_B + E_act where E_B is the binding energy of the molecule (or heat of adsorption) and E_act the activation barrier. The probability of escape (desorption) per unit time is

n_d = n₀ f exp(-E_d/kT)

where f is a statistical factor (the underline is used to denote desorption). If there are many sites from which desorption can occur, the one with the lowest E_d will dominate since the exponential is a very rapidly varying function of E_d. Atoms will diffuse more readily than desorb because the barrier for diffusion is smaller than for desorption, and they will desorb preferentially when the diffusion path takes them to the sites with smaller E_d.

In general, the rate of desorption is:

v = s(q)f(q) exp(-E_d/kT)

The mean surface lifetime is t = 1/n_d = t_o exp(E_d/kT). E_d is usually given in kcal/mol or (preferred) kJ/mol, which can be converted to eV by using 1 eV = 23.07 kcal/mol = 96.48 kJ/mol.

u = v

since E_d= E_B+E_act,

since I = p (2pmkT)^-1/2 the equilibrium pressure is:

p = (s(q)/s(q)) (2pmkT)^1/2 exp(-E_B/kT) f(q)/f(q) or

This is the general form of the Langmuir isotherm (constant T). For non-dissociative adsorption of a monolayer,

therefore,

or

where A is a constant at a given pressure. Measurement of q(p) thus allow the determination of A and, therefore E_B.

  The assumptions in the Langmuir model are that 1) only a fixed number of states is available (such as for monolayer adsorption) and 2) that there is no surface diffusion.

  For multilayer adsorption, a well known model is the BET (Brunauer, Emmett and Teller).

Copyright 2002, by Raúl Baragiola, University of Virginia. All rights reserved.