**1. Introduction**

518 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

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Interfacial processes are central to understanding many processes in environmental sciences and technologies, chemical engineering, earth sciences, ocean sciences and atmospheric sciences. Thermodynamics has been used as a classical method to describe interfacial equilibrium properties over the last century. Experimentally measurable macroscopic parameters of adsorption density and concentration are widely used as the basic parameters in many equations/models to describe the equilibrium characteristics of adsorption reactions at solid-water interfaces. For instance, methods of equilibrium adsorption constants or adsorption isotherms are commonly used to describe the equilibrium relationship between concentration in solution and adsorption density on solid surfaces.

However, thermodynamics has limitations in describing the equilibrium properties for surface adsorption reactions at solid-water interfaces. A fundamental principle has been missing in the conventional theoretical system where the microscopic structures on the solid surfaces are not taken into account in the conventional macroscopic methodology such as equilibrium adsorption constants and/or adsorption isotherms. The equilibrium properties for surface adsorption were conventionally described by macroscopic parameters such as adsorption density. Unfortunately, adsorption density is not a thermodynamic state variable and is generally affected by the microscopic metastable equilibrium surface structures, which make the equilibrium properties, such as equilibrium constants and/or adsorption isotherms, be fundamentally dependent on the kinetic paths and/or the reactant concentration conditions (e.g. the "adsorbent concentration effect" and "adsorbate concentration effect"). Failure in recognizing this theoretical gap has greatly hindered our understanding on many adsorption related issues especially in applied science and technology fields where the use of surface concentration (mol/m2) is common and inevitable.

With the application of spectroscopy and quantum chemical calculation techniques to solidliquid interface systems, such as synchrotron based X-ray absorption spectroscopy, it is now possible to develop new thermodynamic methodologies to describe the real equilibrium properties of surface adsorption reactions and to reveal the relationships between macroscopic equilibrium properties and the microscopic metastable equilibrium adsorption

Advances in Interfacial Adsorption Thermodynamics:

H2O for solvent in solution.

Thus,

since

Thus,

In step2

assuming

Metastable-Equilibrium Adsorption (MEA) Theory 521

where A stands for solute in solution, for adsorbed solvent, for adsorbed A, and

Since the Gibbs free energy is a state function and its change depends only on the initial and final states of the system, we can replace the real adsorption process of [1], which is generally thermodynamically irreversible, with two ideal reversible processes that lead to

where " " indicates that the real adsorption process can be irreversible. Step 1 represents an imagined reversible adsorption process where the final concentration of *A* on the solid surface is the same as that in the real irreversible process [1]. represents an ideal equilibrium stable state of adsorbed *A*, and represents a real metastable-equilibrium adsorption state. and represent different thermodynamic states of adsorbed *A*, although they have the same value of adsorption density. Δ*G*1 and *K*eq are the change in Gibbs free energy and equilibrium constant of step 1, respectively. Δ*G*2 of step 2 is the difference in Gibbs free energy between the reaction products of the real irreversible process

[1] and the ideal reversible process (step 1) . *K*me is the equilibrium constant of step 2.

*G RT K* ln

*K KK real e <sup>q</sup> me* (4)

2 2 <sup>2</sup>

 *H O*2 2 *H O real ideal G G*

<sup>2</sup> 0 *solid solid A A real ideal*

*solid solid HO A HO A real ideal*

*GG G G G* (5)

*GG G* (6)

*G GG real* 1 2 (3)

(2)

the same final state, in order to calculate the Gibbs free energy change,

(MEA) structures. These studies represent advances on how microscopic surface molecule structures affect the macroscopic relationships in surface adsorption thermodynamics. Surface microstructures greatly affect the local chemical properties, long-range interaction, surface reactivity, and bioavailability of pollutants in the environment. Both experimental techniques and thermodynamic theoretical development on interfacial processes are essential for the development of molecular environmental and geological sciences.

It has been a basic concept in traditional thermodynamic adsorption theories that adsorption density ( , mol/m2 ) is a state variable (a function that is only determined by the state and not affected by the path), so that the equilibrium adsorption constants defined by the ratio of equilibrium adsorption density on solid surfaces to the concentration in solution should be constant that is the reflection of the unique equilibrium characteristic of the reaction.1 Over the last century, the macroscopic methodology (e.g. surface complexation models) of equilibrium adsorption constants and adsorption isotherms are widely used to describe the equilibrium limits of adsorption reactions and predict the theoretical yield in many fields.2, 3 These relationships were deemed to obey the basic properties of chemical thermodynamics, i.e. the equilibrium constant should be constant and be independent of kinetics or initial reactant concentrations under fixed thermodynamic conditions.

However, an abnormal phenomenon called particle/adsorbent concentration effect (*C*<sup>p</sup> effect), i.e. the dependence of adsorption isotherms on one of the reactant concentrations *C*p, has caused great confusion over the last three decades because it cannot be interpreted by the existing thermodynamic theories.2, 4-8 Several hundreds of papers have been published on this issue but the underlined theoretical reason, which is far more important than the *C*<sup>p</sup> effect itself, still remains not clear to most researchers. Most studies so far attribute *C*p effect to various experimental artifacts.9, 10 However, after these artifacts are excluded from the experiments, *C*p effect may disappear in some systems,9 but still exist in other systems.3, 11 Thus, the problem becomes rather confused based on empirical or experimental analysis

only. Metastable-equilibrium adsorption (MEA) theory indicates that,12-14 for a given adsorption reaction under fixed thermodynamic conditions, a polyhedral adsorbate molecule is generally ended in various MEA states with different energies and geometries rather than a unique equilibrium state when the reaction reaches to the apparent equilibrium. Unlike concentration in solutions, adsorption density (mol/m2) on solid surfaces no longer unambiguously corresponds to thermodynamic state variables, because adsorption density can only count for the mass but not the chemical potentials/energies of different microscopic MEA states that construct the real equilibrium adsorption state. When the adsorption density is not treated as a thermodynamic state variable, a theoretical equation known as "MEA inequality" is deducted from the fundamental thermodynamic laws.12
