Adsorption and desorption represent the initial processes of the interaction of gas species with the condensed phase. They have important implications for evaluating heterogeneous (gas-to-solid) and multiphase chemical kinetics involved in catalysis; environmental interfaces; and, in particular, aerosol particles. When describing gas uptake, gas-to-particle partitioning, and the chemical transformation of aerosol particles, parameters describing adsorption and desorption rates are crucial to assessing the underlying chemical kinetics such as surface reaction and surface-to-bulk transfer. For instance, the desorption lifetime, in turn, depends on the desorption free energy which is affected by the chosen adsorbate model. To assess the impact of those conditions on desorption energy and, thus, desorption lifetime, we provide a complete classical and statistical thermodynamic treatment of the adsorption and desorption process considering transition state theory for two typically applied adsorbate models, the 2D ideal gas and the 2D ideal lattice gas, the latter being equivalent to Langmuir adsorption. Both models apply to solid and liquid substrate surfaces. We derive the thermodynamic and microscopic relationships for adsorption and desorption equilibrium constants, adsorption and desorption rates, first-order adsorption and desorption rate coefficients, and the corresponding pre-exponential factors. Although some of these derivations can be found in the literature, this study aims to bring all derivations into one place to facilitate the interpretation and analysis of the variables driving adsorption and desorption for their application in multiphase chemical kinetics. This exercise allows for a microscopic interpretation of the underlying processes including the surface accommodation coefficient and highlights the importance of the choice of adsorbate model and standard states when analyzing and interpreting adsorption and desorption processes. We demonstrate how the choice of adsorbate model affects equilibrium surface concentrations and coverages, desorption rates, and decay of the adsorbate species with time. In addition, we show how those results differ when applying a concentration- or activity-based description. Our treatment demonstrates that the pre-exponential factor can differ by orders of magnitude depending on the choice of adsorbate model with similar effects on the desorption lifetime, yielding significant uncertainties in the desorption energy derived from experimentally derived desorption rates. Furthermore, uncertainties in surface coverage and assumptions about standard surface coverage can lead to significant changes in desorption energies derived from measured desorption rates. Providing a comprehensive thermodynamic and microscopic representation aims to guide theoretical and experimental assessments of desorption energies and estimate potential uncertainties in applied desorption energies and corresponding desorption lifetimes important for improving our understanding of multiphase chemical kinetics.

Any interaction between gas-phase species and condensed matter, including liquid, semi-solid, and solid phases, commences by adsorption and desorption processes (McNaught and Wilkinson, 2014; Langmuir, 1915, 1916, 1918). These are of importance in the research areas of catalysis and, in particular, multiphase chemical kinetics or phase transfer kinetics involving environmental surfaces and interfaces (Cussler, 2009; Chorkendorff and Niemantsverdriet, 2007; Finlayson-Pitts and Pitts, 2000; Ravishankara, 1997; Solomon, 1999). Surfaces including water bodies, ice, and terrestrial and anthropogenic structures can provide interfaces at which phase transfer processes and multiphase and heterogeneous reactions can take place. In the atmospheric sciences, multiphase chemical reactions have been the foci of research since the realization that heterogeneous reactions on the surface of polar stratospheric clouds lead to the activation of inert chlorine reservoir species that subsequently result in ozone depletion, manifested in the spring southern hemispheric ozone hole (Solomon, 1999; Rowland, 1991). By now it is well established that gas–particle interactions play crucial roles in particle growth by condensation, gas–particle partitioning, and the chemical evolution of particles during aerosol formation and aging (Pöschl et al., 2007; Kolb et al., 2010; Rudich et al., 2007; George and Abbatt, 2010; Pöschl and Shiraiwa, 2015; Moise et al., 2015; Ammann et al., 2013; Crowley et al., 2013; Kroll et al., 2011; Donahue et al., 2011; Jimenez et al., 2009). The role of reversible adsorption and desorption has been addressed in many studies of gas uptake and multiphase chemical reactions, in particular for the decoupling of mass transport and chemical reaction (Kolb et al., 1995, 2010; Hanson and Ravishankara, 1991; Ammann et al., 2013; Crowley et al., 2013; Pöschl and Shiraiwa, 2015).

In the context of atmospheric sciences, adsorption is commonly described by
the surface accommodation coefficient,

Equation (1) does not explicitly show that the desorption rate depends on
the choice of adsorbate model and standard states. The same applies to the
surface accommodation coefficient, which is not referring to the adsorbate
model. Once the pre-exponential factor

The difference in adsorbate models reflects the treatment of the potential
well in which the adsorbate “sits” (Hill, 1986; Campbell et al.,
2016). The most commonly applied adsorbate model is the 2D ideal gas which
lacks 1 translational degree of freedom compared to the 3D ideal gas
(Hill, 1986). It is defined by the condition of negligible lateral
potential wells; thus, it can freely move parallel across the surface. The
other extreme is the 2D ideal lattice gas where the absorbate cannot
overcome the potential well of the adsorption site. Thus, it exerts only
vibrational movements parallel and vertically to the surface. A model that can
describe both extremes is, e.g., the ideal hindered translator model
(Hill, 1986; Campbell et al., 2016; Sprowl et al., 2016). Which of the two
models, the 2D ideal gas and the 2D ideal lattice gas, is realized will depend
on the activation barrier for adsorbate diffusion parallel to the surface.
If this activation barrier is above

The purpose of this study is to provide a holistic description of the
thermodynamic functions derived from microscopic principles (i.e.,
corresponding partition functions) that allow for the calculation of the
pre-exponential factor of the desorption rate based on transition state (TS)
theory for the case of the 2D ideal gas and 2D ideal lattice gas. We will
apply statistical thermodynamics to describe the microscopic, i.e., on the
molecular level, processes and classical thermodynamics that define the
overall energy and equilibrium conditions. The presented framework only
considers physisorptive processes, within the general framework of treating
adsorption in atmospheric chemistry (Kolb et al., 2010; Pöschl et al.,
2007). Although many aspects of the presented derivations can be found in
statistical thermodynamic textbooks (Hill, 1986; Kolasinski, 2012)
and articles (Campbell et al., 2016; Donaldson et al., 2012; Savara, 2013),
a complete treatment of adsorption and desorption including the TS and
respective standard states is not readily available in the literature, as
far as the authors are aware of. An outcome of this exercise is an improved
understanding of the defining parameters that govern typically measured and
reported thermodynamic parameters and their dependency on chosen standard
states. For example, the presented derivations demonstrate that the
pre-exponential factor, commonly assumed to be around

The outline of this study is guided by ways to derive the
thermodynamic functions. TS theory assumes thermodynamic equilibrium between
the adsorbed state and the TS for desorption (Kolasinski,
2012; Eyring, 1935). The description of this equilibrium in terms of the
basic thermodynamic functions is based on adsorption thermodynamics. Since
the desorption rate and the pre-exponential factor are expressed in terms of
molecular properties (i.e., the microscopic picture), the linkage between
statistical thermodynamics and the thermodynamic functions has to be
considered and applied. However, the foundational derivations for the
thermodynamics and statistical thermodynamics of adsorption are not well
established and not treated in comprehensive ways in textbooks. We therefore
retrace this theory first for the case of desorption as an overall process.
This will then serve as the basis for applying this theory to the TS theory
for desorption and adsorption and to derive the pre-exponential factor for
desorption. A great part of those derivations follows the treatment by
Campbell et al. (2016). Subsequently, combination of the rate
expressions of desorption and adsorption establishes the links between the
overall adsorption thermodynamics and the microscopic kinetic parameters
including the interpretation of the surface accommodation coefficient. In
this study, the surface accommodation coefficient follows the definition by
Kolb et al. (2010) valid for physisorptive processes and consistent with
the Langmuir adsorption description but not necessarily the same as the
sticking coefficient used in surface sciences or catalysis, which is often
inconsistently defined and sometimes lumps or sometimes does not lump physisorption
and chemisorption together. There are alternative descriptions such as the
Kisliuk-type precursor mechanism that consider more complex configurations
of the adsorbate (Kisliuk, 1957; Tully, 1994; Campbell et al., 2016), not
discussed in this study. Lastly, we evaluate how our findings impact
interpretation and analysis of measured or theoretically derived

Since the basis for describing desorption by TS theory requires
consideration of thermodynamic equilibria, in Sects. 2 to 5 and the
Supplement, we introduce first the overall desorption thermodynamics in more
detail to provide the necessary equations and terminology. Section 2
discusses the general thermodynamic functions for describing adsorption and
desorption, their derivations from microscopic properties (partition
functions), and definitions of the standard states. Section 3 provides the
derivation of equilibrium thermodynamic functions that describe the
desorption process for the two different adsorbate models. The results so
far are applied in Sect. 4 to derive the desorption rates and
associated pre-exponential factors for the different adsorbate models in
terms of thermodynamic and microscopic quantities. Section 5 presents the
derivation of the adsorption rate including thermodynamic and microscopic
treatment and evaluation of the surface accommodation coefficient. In
Sect. 6, by combination of the previous results we consider the
equilibrium between adsorption and desorption to derive the corresponding
equilibrium constants demonstrating that the derivations are internally
consistent. Section 7 provides the derivation of the kinetic parameters from
equilibrium between adsorption and desorption. Section 8 discusses how the
choices made for standard states and the type of adsorbate model impact
surface concentration, activity, and coverage; adsorption and desorption
rates;

To fundamentally follow all derivations presented in this document, an excess number of equations would have needed to be shown, which would have rendered this document difficult to read. In the Supplement we provided all necessary definitions, equations, and derivations from first principles to follow the thoughts in the main document. The reader is encouraged to study this document side by side with the Supplement that contains all information leading to the results shown here. We apply the definitions of parameters and standard states given in the Supplement. The Supplement includes all necessary detailed derivations of the thermodynamic equations for 3D ideal gas, 2D ideal gas, 2D ideal lattice gas, and TS. It includes the following sections: (S1) Definition of desorption and adsorption equilibrium constants; (S2) Derivation of thermodynamic functions for desorption and adsorption; (S3) Standard molar enthalpies, entropies, and Gibbs free energies; (S4) Derivation of equilibrium constants; (S5) Standard molar Gibbs free energy change and equilibrium constant between the 3D ideal gas and the transition state for adsorption; and (S6) Adsorption–desorption equilibrium.

In this section we define the nomenclature, signage, and units involved in partition functions, thermodynamic quantities, and standard states when describing adsorption and desorption processes.

The spontaneous occurrence of adsorption implies an exergonic process with
the thermodynamic condition (Bolis, 2013):

Since adsorption of a gas on a substrate results in an increase in molecular
ordering and

For the remainder of the text, the subscripts denote the process direction in the order of (from left to right) process (adsorption or desorption), educt (e.g., adsorbate), and product (e.g., gas species). Subscript m denotes molar quantities.

Potential energy curve for adsorption and desorption processes
expressed by the heat of desorption,

We define the energy reference as the internal energy,

We treat the general case of activated adsorption–desorption here, meaning
that the TS's internal energy is elevated by the barrier height above the
reference level. The TS for adsorption–desorption is assumed to exist at
some fixed distance from the surface but within a very thin layer of
thickness

We use statistical thermodynamics to relate the microscopic properties to
the matter's bulk properties. Via the partition function

As introduced below for the cases of 3D ideal gas, 2D ideal gas, 2D ideal
lattice gas, and TS for desorption, we will apply the appropriate partition
functions (see also Sect. S3 in the Supplement). For the 3D and 2D ideal gases we will
use the canonical partition function, expressed for indistinguishable and
independent molecules as

The concentration of the 3D ideal gas in the gas phase is given by

We define the concentration for the adsorbate representing a 2D ideal gas as

We define the concentration for the molecule in the TS for desorption as

For many applications, it has been common to normalize the surface
concentration,

For the 2D ideal lattice gas case, the maximum number of equivalent but
distinguishable sites is

We derive the desorption equilibrium constants for the 2D ideal gas and 2D ideal lattice gas in equilibrium with the gas phase considering the corresponding standard states and partition functions. See also general definitions for equilibrium constants outlined in Sect. S1 in the Supplement. For both adsorbate models we also derive the change in enthalpy and entropy between the adsorbed and the gas molecule. The derivations in this section will demonstrate the importance of standard states when calculating the equilibrium constants for the desorption processes.

The adsorbed 2D ideal gas is characterized by molecules moving freely
parallel to the surface with a constant binding energy to the surface. In
other words, the adsorbate vibrates in all directions but has free
translational motion only in the horizontal plane. The thermodynamic desorption
equilibrium constant is defined by the ratio of the activity in the gas
phase (

As indicated by the definition of the adsorbate surface activity,

The standard free energy change (and the equilibrium constant) is also
related to the adsorption entropy and enthalpy via (Eqs.
S119–S121 in the Supplement)

As derived in the Supplement (Eq. S16) from statistical thermodynamics, the
entropy in the gas phase is given by the Sackur–Tetrode equation
(Campbell et al., 2016; Atkins and de Paula, 2006; Hill, 1986) as

Substituting the definition of

In contrast to the adsorbate being equivalent to a 2D ideal gas, where
molecules freely diffuse parallel across the surface, the adsorbed molecule
could also randomly populate a fixed number of adsorption sites, where the
adsorbates have only vibrational degrees of freedom in three directions.
This adsorption model is generally referred to as Langmuir adsorption
(Langmuir, 1915, 1916, 1932). It is worthwhile noting that this concept
holds for solid and liquid surfaces as long as the number of adsorption
sites is given by

Since

We can now obtain the relationship between the desorption energy and the
adsorption enthalpy as

For the entropy of the adsorbed 2D ideal lattice gas (Eqs. S54
and S103 in the Supplement), we can write (Campbell et al., 2016)

For the change in entropy upon desorption, we can derive (Eq. S135 in
the Supplement; Campbell et al., 2016)

We can now use the results in Sect. 3.1 and 3.2 to evaluate the
equilibrium conditions between gas-phase and surface concentrations and
activities and respective coverages for the 2D ideal gas and 2D ideal
lattice gas, presented in Figs. 2–4. The thermodynamic quantities to
reproduce these figures are given in Table S1. Figure 2 illustrates the
behavior of the adsorption equilibria for the 2D ideal gas and the 2D ideal
lattice gas cases in terms of surface concentration versus gas-phase
concentration. As intuitively clear from the defining equations, for the 2D
ideal gas case, the surface concentration increases linearly with gas-phase
concentration without a limitation, thus increasing beyond a monolayer
coverage, here assumed as

Equilibrium adsorbate surface concentration as a function of gas-phase concentration for the case of a 2D ideal gas (blue line) and 2D ideal
lattice gas (red line). Applied

Equilibrium surface coverage as a function of gas-phase concentration for the case of a 2D ideal gas (blue line) and 2D ideal lattice gas (red line). The data are the same as used for the derivation of Fig. 2, but surface coverages are derived by normalization with the maximum number of adsorption sites. Thermodynamic quantities and standard states necessary for calculation are given in Table S1.

In contrast to Figs. 2 and 3, when considered in terms of activities, both
adsorbate models exhibit a linear relationship between the surface activity
and the gas-phase activity as shown in Fig. 4. While trivial for the 2D
ideal gas case, for the 2D ideal lattice gas case, this is related to the
definition of the activity as being proportional to

Equilibrium surface activity as a function of gas-phase activity for the case of a 2D ideal gas (blue line) and 2D ideal lattice gas (red line). The data are the same as used for the derivation of Fig. 2. Thermodynamic quantities and standard states necessary for calculation are given in Table S1.

Above we have outlined the determination of the equilibrium constant

In general, the desorption rate can be expressed as

According to conventional transition state theory (CTST) (Kolasinski,
2012),

Within this CTST approach, the desorption rate can be obtained by assuming
that the TS has a finite width

As further discussed in Sect. S3.4, the activation process can
be conceptually envisioned by bringing the molecules in the 2D ideal gas
from the zero-point energy to the actual energy level that allows for the
formation of the TS. Thus, activation does not include the energy of the
motion along the desorption coordinate and as such is less than the energy
associated with the TS. When defining the

Following Campbell et al. (2016) defining

The above derivations include the definition of the free energy of
desorption (i.e., the free energy change between the adsorbed state and the TS)
and, thus, allow us to evaluate the pre-exponential factor

Equation (78) demonstrates the relevance of knowing the standard state. The
first expression on the right-hand side, the formulation in terms of the
molecular partition functions (

Above derivations (Eq. 77) now allow for the interpretation of

For the case of the adsorbate being a 2D ideal lattice gas but the TS being a 2D
ideal gas, the associated equilibrium constant is related to the free energy
change between the TS and the absorbed state, each expressed with the
corresponding standard molar partition function,

The change in the desorption rate for the assumption of a 2D ideal
gas (solid lines) and 2D ideal lattice gas (dashed lines) is plotted as a
function of the adsorbate fractional surface coverage

Equation (82) highlights that the desorption rate is not proportional to the
surface concentration but depends non-linearly on the surface coverage

We now follow a similar derivation as for the 2D ideal gas. We define the

The activity-based desorption rate expression becomes

Therefore, the desorption rate coefficient (in units of

While the activity-based desorption rate expression (Eq. 86) clearly
displays the first-order decay behavior of the activity, driven by

We can now express the desorption rate coefficient as

The activity-based desorption rate for the case of a 2D ideal gas

We can establish the link between the entropy and the pre-exponential factor
by taking the expression for

Since, strictly speaking, the desorption rate law is representing a first-order process acting on the surface activity, it is also straightforward to understand that the desorption rate, when expressed as rate of change of activity per unit time is proportional to the surface activity, as shown in Fig. 6, independent of the adsorbate model. Thus, even when the surface coverage becomes high, the activity-based first-order desorption rate coefficient remains constant. The consequence of this becomes then directly apparent in Fig. 7, showing the desorption rate expressed as the rate of change of surface concentration per unit area and unit time, as a function of the surface coverage. For the 2D ideal gas case, the linear relationship is maintained; i.e., the surface concentration-based desorption rate coefficient is constant and thus independent of the surface coverage. In contrast, for the 2D ideal lattice gas case, the desorption rate rapidly increases towards high surface coverages, clearly demonstrating the non-first-order behavior of desorption when expressed in terms of surface concentration. This behavior is a consequence of the high configurational entropy at high coverages and naturally results from a consistent description of the surface activity. Therefore, the dependency of the desorption rate on coverage is not due to surface sites with different desorption energies but is a consequence of the applied lattice gas adsorption model that entails a limited number of equivalent sites. In other words, the lifetime of an individual adsorbate molecule depends on the overall surface coverage, exerting shorter adsorbate lifetimes for greater surface coverages. Therefore, as also pointed out by Campbell et al. (2016), experimental desorption rate measurements need to be analyzed with care when deriving the desorption energy from measured desorption rates.

The desorption rate for the case of a 2D ideal gas (blue line) and
2D ideal lattice gas (red line). Applied

The features of the rate law for desorption acting as a first-order process on the surface activity then also become manifest in the time-dependent decay of the surface coverage for the two adsorbate models. As expected for the 2D ideal gas case, where surface activity and surface coverage are proportional to each other, the first order and thus single exponential decay of the surface activity leads to a corresponding single exponential decay of the surface coverage, as shown in Fig. 8. In contrast, as demonstrated in Fig. 9, the single exponential decay of the surface activity of the 2D ideal lattice gas case leads to a non-exponential decay of the surface coverage. This further emphasizes the need to carefully analyze experimental data of desorption rate measurements, especially if short timescales are considered.

The decay of surface activity

The decay of surface activity

As discussed above, the pre-exponential factor is often assumed to be

The pre-exponential factor

Adsorption is treated as a physisorptive process but might exert a non-zero
energy barrier

When considered from the gas-phase side, the equilibrium constant between
the gas phase and the adsorbed state is given by the inverse ratio of
activities compared to the case of desorption, as now the adsorbed state is
the product:

In general, the adsorption rate can be expressed as

The rate of change of surface activity for the 2D ideal gas is given by

TS theory for adsorption encompasses the same steps as those for
desorption but starting from the gas-phase side. Considered from the gas
phase, the equilibrium constant between the gas phase and the TS for
adsorption is related to the free energy change between the gas and the TS,
each expressed with the corresponding standard molar partition functions, as
defined by (Eqs. S193–S199 in the Supplement)

As in the case of desorption, the adsorption rate can be obtained by
assuming that the TS has the same finite width

When defining the

With this definition of

When using the definition of the adsorption rate coefficient linking the
loss rate from the gas phase with the gain in adsorbed species on the
surface, i.e.,

Defining

We can convert the standard molar partition functions back to the molecular
ones. For that, we consider that

In the case of adsorption, the Arrhenius term is only driven by the barrier
height. Therefore, the pre-exponential factor for adsorption is (since

The adsorption rate for the case of a 2D ideal gas and 2D ideal
lattice gas is depicted. We assume a non-activated adsorption process:

Thus, essentially, the gas loses 1 translational degree of freedom, and
the rate of adsorption (vibrations neglected) can be written as

As discussed in the previous section, the TS for adsorption is the same as
that for desorption and is considered a 2D ideal gas. This means that the
adsorptive flux, i.e., the adsorption rate in terms of gain in molecules per
surface area and time, is simply proportional to the gas-phase
concentration, independent of the adsorption model used to describe the
final state of adsorption, as shown in Fig. 11. For the same reason,
the rate of change of surface activity is also linearly related to the gas-phase
activity, as shown in Fig. 12. However, the meaning of the rate of change of
surface activity is entirely different for the two adsorbate models, as
discussed for the case of desorption. While for the 2D ideal gas model, the
rate of change of surface activity is linearly related to the rate of change
of surface coverage, for the 2D ideal lattice gas case, the same rate of
change of surface activity is governed by a strongly non-linear relationship
to the rate of change of surface coverage, thus depending on the actual
coverage. This explains the slight visible deviations between

The activity-based adsorption rates for the case of a 2D ideal
gas (blue line) and 2D ideal lattice gas (red line) are depicted. We assume
a non-activated adsorption process:

We can now look at the surface accommodation coefficient,

The dependency of the mass accommodation coefficient,

Figure 13 shows how

We consider equilibrium between adsorption and desorption and demonstrate that this results in the proper equilibrium constants for gas adsorption into a 2D ideal gas and a 2D ideal lattice gas, proving that the CTST formulation of the rates leads back to the equilibrium definition, from which we started. We also show that this works when using both partition functions and thermodynamic expressions. Hence, the derivations of all thermodynamic functions are internally consistent.

Considering the equilibrium, for the case that the adsorbed state is a 2D
ideal gas, at low coverage

For the case of the activity-based adsorption and desorption rates, we
obtain

For the case when the adsorbed state on the surface is treated as a 2D ideal
lattice gas using Eqs. (92), (102), and (121),

For the case of the activity-based adsorption (Eq. 127) and desorption
rates (Eq. 86), we obtain

In previous studies (Bartels-Rausch et al.,
2005; Tabazadeh and Turco, 1993) equilibrium thermodynamic data or
equilibrium coverage data have been used to constrain kinetic parameters of
either adsorption or desorption. If

For the case of an adsorbed 2D ideal gas, we can derive the pre-exponential
factor from equilibrium,

For the case of an adsorbed 2D ideal lattice gas, we can derive the
pre-exponential factor from equilibrium,

As can be seen, the activity-based

The thermodynamic derivations above indicate that the underlying adsorption
model, i.e., 2D ideal gas or 2D ideal lattice gas, will have a significant
impact on desorption rates and the pre-exponential factor and, thus, on the
evaluation of

Figure 5 displays the variation in

As outlined above, Fig. 10 highlights how the underlying adsorbate model
impacts the pre-exponential factor. If the actual adsorbate system behaves more
like a 2D ideal lattice gas but is analyzed assuming a 2D
ideal gas, significant uncertainties in

Figure 14 presents estimates of

Estimates of

Figure 15 displays

Estimates of

Figures 5, 10, 14, and 15 highlight the potential uncertainties that arise
by the choice of the absorbate models for derivation of

Reversible adsorption is a key process for any gas–condensed-phase interaction and is particularly important when environmental interfaces are involved including aerosol particles. This study provides a comprehensive treatment of the classic and statistical thermodynamics of the adsorption and desorption processes considering transition state theory for two typically applied adsorbate models, the 2D ideal gas and the 2D ideal lattice gas, which apply to solid or liquid substrate surfaces. We established thermodynamic and microscopic relationships for adsorption and desorption equilibrium constants, adsorption and desorption rates, first-order adsorption and desorption rate coefficients, and corresponding pre-exponential factors. These derivations allow the interpretation of thermodynamic functions such as equilibrium constants in terms of their molecular properties, as well as the calculation of explicit numeric expressions for the latter. This exercise demonstrates the importance of applied assumptions of the adsorbate model and standard states when analyzing and interpreting adsorption and desorption processes, the latter often being ill-defined in experimental studies (Donaldson et al., 2012). The derivations allow for a microscopic interpretation of the surface accommodation coefficient including the entropic contribution. Our treatment demonstrates that the pre-exponential factor, when deriving the desorption lifetime from the desorption energy, can differ by orders of magnitude depending on the choice of adsorbate model. Clearly, such a difference yields similar effects on the desorption lifetime, and when used to estimate desorption energies (e.g., from interfacial residence times estimated from molecular dynamics simulations or from measured desorption rates) significant uncertainties in the desorption energy are incurred. Furthermore, uncertainties in surface coverage and assumptions about standard surface coverage can lead to significant changes in desorption rates and thus in evaluated desorption energies for the rather common case of a 2D ideal lattice gas. The objective of providing this comprehensive thermodynamic and microscopic treatment of the adsorption and desorption processes is to guide the theoretical and experimental assessments of adsorption and desorption rates, desorption energies, and choice of standard states with implications for the corresponding desorption lifetimes. This in turn will improve, specifically, the analyses and interpretation of surface layer reaction rates and surface-to-bulk transport and, thus, bulk mass accommodation. More generally, this provides a better basis for the prediction of gas–particle partitioning, multiphase chemical reactions, and the chemical evolution of atmospheric aerosols.

All data needed to draw the conclusions in the present study are shown in the paper and/or the Supplement.

The supplement related to this article is available online at:

DAK and MA envisioned this study and wrote this paper.

The authors are members of the editorial board of

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Daniel A. Knopf acknowledges support from the National Science Foundation. Markus Ammann appreciates support by the Swiss National Science Foundation. This study came out of an ongoing collaborative project with Manabu Shiraiwa and Ulrich Pöschl, and we appreciate discussions with both of our colleagues.

This research has been supported by the National Science Foundation (grant no. AGS-1446286) and the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. 188662).

This paper was edited by Andreas Hofzumahaus and reviewed by two anonymous referees.