Probing the Origins of Linear Free Energy Relationships with Molecular Theory and Simulation
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Probing the Origins of Linear Free Energy Relationships with Molecular Theory and Simulation DAVID M. FORD Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA [email protected]
Abstract. Linear free energy relationships (also known as entropy-energy compensation) are seen in a range of physical processes, including adsorption and diffusion. The most interesting compensation effects presumably arise from geometric and energetic effects at the molecular level, but their origins are not well understood. We utilize molecular modeling of simple adsorbate-adsorbent systems to discover these origins in a semi-quantitative way. Sets of calculations were constructed to represent certain experimental processes, e.g. adsorption of a homologous series of molecules, for which linear free energy relationships might be expected. We find that the general correlation between energy and entropy is often much more complex than a simple linear relationship, although a linear approximation might be sufficient across limited ranges. Keywords: linear adsorption
1.
free
energy
relationship,
entropy-enthalpy
Introduction
In thermodynamics, chemical and physical changes are typically described in terms of free energy changes, such as A = E − T S
(1)
where A is the Helmholtz free energy, E is the energy, and S is the entropy. This relationship is derived from the first and second laws of thermodynamics and thus has a solid grounding in first-principles theory. In certain types of physical and chemical processes, researchers have consistently observed a linear relationship between the energetic and entropic contributions to the free energy, as E = a + bS
(2)
where a and b are constants. This so-called linear free energy relationship (LFER) has no grounding in
compensation,
molecular
simulation,
first-principles theory, but it has nevertheless been observed experimentally in widely varied classes of physicochemical processes, sometimes under different names (e.g. isoequilibrium effect, enthalpy-entropy compensation). A recent comprehensive review paper (Liu and Guo, 2001) summarizes the different fields in which LFERs have been observed and current thoughts on their interpretation. Of particular interest here is that LFERs have been observed in adsorption (Denayer et al., 1998; Ruthven and Kaul, 1998; Rudzinski et al., 2000) and diffusion (Fletcher and Thomas, 2000) of small molecules in microporous materials and polymers (Freeman, 1999). The purpose of this paper is to explore the possible origins of LFERs with molecular modeling techniques. The next section describes the basic molecular model, the necessary concepts in statistical mechanics and links to macroscopic observables, and the calculation procedure. Section 3 contains results for three different “processes” which might be expected to produce a LFER. Section 4 summarizes our conclusions.
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Ford
Figure 1.
2.
largest pore, L/σ = 5.0, are each 1.0 ε deep. The next smaller pore, L/σ = 2.245, has the deepest possib
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