Incommensurate adsorption

The adsorption and separation properties of a particular adsorbent largely depend on the adsorbate, including its morphology, composition, polarity, polarizability, diffusivity, and other properties. In the following sections we will describe adsorption and separation in MMOFs, focusing mainly on industrially important hydrocarbons and alcohols. We also discuss the concepts of commensurate and incommensurate adsorption in MMOFs and their implications toward adsorption-related properties. 

Incommensurate adsorption, or as the name suggests, non-commensurate adsorption, happens when there are size or symmetry mismatches between the adsorbate and the pores of the adsorbent. The phenomenon was first observed and quantified for the surface adsorption of organic molecules on layered substrates, with an incommensurate-commensurate transition occurring as a function of physical parameters such as temperature and pressure. ... 

Traditional zeolite-based molecular sieves most commonly exhibit incommensurate adsorption. This can be attributed to two main criteria (1) the dimensions of their channels or cages are, on average, much larger than that of the adsorbate molecules and (2) symmetry mismatches are often present. For example, zeolite-Y exhibits incommensurate adsorption for benzene and toluene molecules adsorbed within its super cage (Figure 4). The incommensurate adsorption type depends also on external parameters such as temperature. Single crystal and PXRD studies on the -hexane-loaded silicate-I MFI-type zeolite shows that at room temperature the adsorbed molecules are dynamically disordered and distributed over the entire channel, whereas at sufficiently low temperature, the adsorbate becomes well ordered within the channel, which is commensurate with the framework type. ... 

A transition to incommensurate adsorption is often observed in MMOFs that exhibit commensurate adsorption. A classic example is the aforementioned... 

The adsorption of alkali metals on single crystal surfaces can result in the formation of ordered structures (commensurate or incommensurate super-... 

Fig. IS. Phase diagram of the H/Fe(110) system, as detenniiied from LEED intensities. Fuli dots represent experimentally determined data points shaded areas correspond to incommensurate or antiphase domain regions. A possible interpretation for the ordered (2 x 1) and (3 x 1) phases is indicated in Fig. 16, assuming that the adsorption sites form a centered rectangular lattice as shown in Fig. lb. (From Imbihl et...

Fig. 4 The incommensurability versus electrode potential dependence for adsorption of Br on Au(lOO). Insets atomic models of Br adlayers corresponding to the potentials below and above the critical point of phase transition [59].

Adsorption in many different adsorption sites simultaneously is expected for overlayers with an incommensurate lattice (cf. Sect. III). This has been confirmed by LEED intensity analyses for the case of an incommensurate overlayer of Xe on Ag(l 11), where both the substrate and the overlayer consist of hexagonally close-packed layers (with unrelated unit cells) parallel to the surface. 

Adsorption processes on crystallographically well-defined substrate surfaces lead to the formation of 2D Meads phases with well-ordered structures denoted as overlayers". Generally, three different types of overlayers, depending on the degree of registry between overlayer and substrate, can be distinguished commensurate, higher-order commensurate or incommensurate overlayers, as illustrated schematically in Fig. 3.14. TTie term superlattice stmcture" is frequently used for commensurate overlayers which can be characterized by either the Wood or the matrix notation [3.271-3.274]. 

The specific adsorption of halide anions has been studied on Au and Ag single crystals [14]. On Au(l 11), these ions form incommensurate hexagonal monolayers that compress as the electrode potential is changed in the positive direction [19]. However, on Ag(lOO), Br adsorption occurs at the hollow site formed by four metal atoms in a square pattern. This type of commensurate monolayer has a c(2 X 2) surface structure. These studies demonstrate the role of atomic surface structure in determining the extent of adsorption. Differences between adsorption on Ag(lOO) and Au(lOO) are explained in terms of differences in the strengths of the metal-halide bonds [14]. 

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