Adsorption and Desorption Kinetics

Introduction

An equilibrium isotherm tells how much gas a surface holds after sufficient time. It does not say how quickly that state is reached or how long one molecule remains. Adsorption kinetics starts with molecules striking a surface and asks what fraction stick. Desorption kinetics asks how frequently bound molecules depart. Heating a loaded surface while monitoring released gas, called temperature-programmed desorption, can probe these processes if the experiment is interpreted with its kinetic assumptions.

Core explanation

Gas kinetic theory gives a molecular collision flux against a flat surface of roughly F = p/√(2πmk BT) for an ideal gas at equilibrium temperature T, where m is molecular mass, p pressure and k B Boltzmann's constant. Flux alone is not adsorption rate. Multiply by a sticking probability s, which can depend on incident energy, surface temperature, site occupancy and molecular orientation. In a simple vacant-site model the uptake rate per area can include sF(1−θ). If adsorption requires a pair of neighbouring sites, the vacancy factor differs.

For first-order molecular desorption from equivalent sites, −dθ/dt = k des θ at fixed temperature. The solution is θ(t)=θ₀ exp(−k des t), and the mean residence time is τ = 1/k des . A common activated-rate approximation is k des = ν exp[−E des/(RT)], with ν a frequency factor and E des a molar barrier. Increasing T normally increases k des and shortens τ. This describes an ideal first-order process; recombinative desorption from two adsorbed atoms can have second-order coverage dependence, and heterogeneous surfaces can produce several apparent residence times.

In temperature-programmed desorption, a surface is dosed with adsorbate, then heated at a controlled rate β = dT/dt while desorbed species are detected. The signal often has one or more peaks. A higher-temperature peak can suggest a more difficult desorption step, but peak position also depends on ν, β, coverage, desorption order, re-adsorption and transport. Peak area may reflect desorbed amount after detector calibration. One peak is not automatically one chemically unique binding site; overlapping processes can hide beneath it.

Kinetics and thermodynamics are linked through detailed balance for an equilibrated elementary process, but an equilibrium constant alone does not specify both forward and reverse rates. A high-affinity surface can still take time to load if molecules must diffuse through narrow pores. Conversely, fast exchange can occur at moderate equilibrium occupancy.

Step-by-step reasoning

Separate three stages: arrival at the surface, successful sticking and possible later departure. If given p, m and T, calculate collision flux with SI units and multiply by an appropriate sticking probability and vacancy factor. If given k des, compute τ and interpret it as a mean under the first-order model, not a fixed lifetime for every molecule. For a TPD trace, record heating rate and initial coverage before comparing peaks; ask what gas species the detector actually measures.

Visual explanation

Draw arrows of gas molecules striking a surface, with one reflecting and one entering an occupied adsorption site. Label incident flux F and sticking probability s. Next draw an exponential decay of coverage at constant temperature with θ = θ₀/e at t = τ. Finally show a TPD signal as a peak versus temperature during a linear heating ramp, with a note that changing heating rate can shift the peak.

Real-world analogy

A train platform may have many arriving passengers, but only a fraction decide to stay; that resembles collision flux times sticking probability. Those who stay leave after a distribution of waiting times rather than all departing exactly at the average. Heating the surface is like changing departure urgency continuously, so a peak in departures depends on the schedule of warming as well as attachment strength.

Real-world example

TPD of organic molecules on graphite has shown different kinetic behaviour for monolayer and multilayer desorption. Functional groups also shift desorption energetics. Such measurements help compare binding environments on well-defined surfaces. On a porous catalyst, however, molecules may re-adsorb while leaving, so the measured signal can include transport effects rather than a simple single-site barrier.

Why?

Why can a gas hit a surface and fail to adsorb? It may lack an open site, arrive with the wrong orientation, fail to transfer energy to the surface quickly enough, or face an activation barrier. The sticking probability is therefore not automatically one. Why does higher temperature shorten residence time in an activated model? More molecules can cross the desorption barrier per unit time as the thermal distribution broadens.

Common misconception

"Every collision leads to adsorption" ignores sticking probability. Another common error is to interpret a TPD peak temperature directly as an adsorption enthalpy. Peak position requires kinetic modelling and experimental details; desorption barrier and equilibrium adsorption enthalpy are related but not automatically identical signed quantities.

Worked example

Question: A bound species has ν = 1.0 × 10¹³ s⁻¹ and an assumed first-order desorption barrier of 80.0 kJ mol⁻¹ at 300 K. Estimate k des and mean residence time.

Reasoning: E des/(RT) = 80000/[(8.314)(300)] ≈ 32.1. Thus exp(−32.1) ≈ 1.18 × 10⁻¹⁴ and k des ≈ (1.0 × 10¹³)(1.18 × 10⁻¹⁴) = 0.118 s⁻¹. The mean τ = 1/0.118 ≈ 8.5 s. A different prefactor or barrier would change this substantially.

Answer: k des ≈ 0.12 s⁻¹ and mean residence time ≈ 8.5 s under the model assumptions.

Quick check

1. What additional factor is needed to turn gas collision flux into a successful adsorption flux? Answer: A sticking probability, together with any required vacant-site factor.

Exam focus

Distinguish flux, sticking and desorption. Use τ = 1/k des only for the stated first-order model and keep E des and RT in matching molar energy units. For TPD, state heating rate, coverage and kinetic order before assigning an energy to a peak. Never infer one unique site solely from one visible maximum.

Advanced insight

The Polanyi–Wigner framework writes desorption rate as νθⁿexp[−E des/(RT)], where n is kinetic order. For recombinative desorption, n may differ from one; for heterogeneous adsorbents, E des can depend on θ. A programmed-temperature spectrum is therefore an inverse problem: several combinations of energy distribution, rate order and re-adsorption can produce similar traces.

Summary

Adsorption kinetics combines incident molecular flux, sticking probability and site availability. First-order desorption produces exponential loss and a mean residence time equal to 1/k des. Temperature-programmed desorption probes how release changes during heating, but peak positions require kinetic interpretation. Equilibrium loading, adsorption speed and residence time are distinct quantities.

Practice questions

1. If F = 10²⁰ molecules m⁻² s⁻¹ and s = 0.01 on an empty surface, what initial successful flux is predicted? Answer: 10¹⁸ molecules m⁻² s⁻¹ under the simple model. 2. What is the mean residence time when k des = 0.50 s⁻¹? Answer: 2.0 s for first-order desorption. 3. Why might two TPD peaks not imply exactly two kinds of surface site? Answer: Overlapping kinetic orders, multilayers, reactions or transport and re-adsorption can also create multiple maxima. 4. Does a large equilibrium adsorption constant uniquely fix k des? Answer: No. The ratio of forward and reverse rates may be constrained, but either rate separately needs kinetic information.

Primary terminology and experiment: IUPAC sticking probability, IUPAC TPD and TPD study on graphite.