Adsorbed molecules intermolecular interaction

The present model has so f2ir assumed that interactions between molecules of solvent or solute in either phase can be ignored. Now we will examine the effects of these interactions on retention in various LSC systems. Equation (4) for the retention of a solute X in a mobile phase M recognizes intermolecular interactions in the mobile phase (n), but assumes that adsorbed-phase free energies ( ia) are not a function of intermolecular interactions within the adsorbed phase. We can recognize these adsorbed-phase intermolecular interactions by adding an energy term Eja" to Eq. (4) for each adsorbed species i ... 

A second criticism is that the model restricts attention to the forces between the adsorbent and the adsorbate molecules—the vertical interactions—and neglects the forces between an adsorbate molecule and its neighbours in the same layer—the horizontal interactions. From the nature of intermolecular forces (p. 5) it is certain that these adsorbate-adsorbate interactions must be far from negligible when a layer is approaching completion and the average separation of the molecules is therefore small in relation to their size. 

The Fowler-Guggenheim-Jovanovic model [3] assumes (as it was the earlier case also) the occurrence of intermolecular interactions among the molecules adsorbed as a monolayer but is based on the Jovanovic isotherm. The single-component isotherm is represented by the equation ... 

Snyder and Soczewinski created and published, at the same time, another model called the S-S model describing the adsorption chromatographic process [19,61]. This model takes into account the role of the mobile phase in the chromatographic separation of the mixture. It assumes that in the chromatographic system the whole surface of the adsorbent is covered by a monolayer of adsorbed molecules of the mobile phase and of the solute and that the molecules of the mobile phase components occupy sites of identical size. It is supposed that under chromatographic process conditions the solute concentrations are very low, and the adsorption layer consists mainly of molecules of the mobile phase solvents. According to the S-S model, intermolecular interactions are reduced in the mobile phase but only for the... 

One can further elaborate a model to have a concrete form of /(ft), depending on which aspect of the adsorption one wants to describe more precisely, e.g., a more rigorous treatment of intermolecular interactions between adsorbed species, the activity instead of the concentration of adsorbates, the competitive adsorption of multiple species, or the difference in the size of the molecule between the solvent and the adsorbate. An extension that may be particularly pertinent to liquid interfaces has been made by Markin and Volkov, who allowed for the replacement of solvent molecules and adsorbate molecules based on the surface solution model [33,34]. Their isotherm, the amphiphilic isotherm takes the form... 

The conformation of a polymer in solution is the consequence of a competition between solute intra- and intermolecular forces, solvent intramolecular forces, and solute-solvent intermolecular forces. Addition of a good solvent to a dry polymer causes polymer swelling and disaggregation as solvent molecules adsorb to sites which had previously been occupied by polymer intra- and intermolecular interaction. As swelling proceeds, individual chains are brought into bulk solution until an equilibrium solubility is attained. 

The question now arises of what simplification is possible in the treatment of orientationally structured adsorbates and what general model can be involved to rationalize, within a single framework, a diversity of their properties. Intermolecular interactions should include Coulomb, dispersion, and repulsive contributions, and the adsorption potential should depend on the substrate constitution and the nature of adsorbed molecules. However difficult it may seem, all these factors can be taken into account if we follow the description pattern put forward in this book. Its fundamentals are briefly sketched below. 

Intermolecular lateral interactions and resulting collectivized vibrations of individual adsorbed molecules greatly add to the complexity of description for local vibrational excitations in adsorbates. Fig. 4.5 schematically demonstrates that these interactions on a simple planar lattice of adsorbed molecules which vibrate with high (toh) and low (co/) frequencies lead to the emergence of the corresponding energy bands, with energy levels classified by the wave vector K. 

A fundamental question concerns the state of the adsorbed gas, namely whether it is closer to the gaseous or the liquid state. At 301 K, the solvent shift is mainly observed on the terminal carbon atoms which are more exposed to intermolecular interactions (22). The carbon Cj and C4 of 1-butene experience a small low field shift with respect to the gas, the carbon a small high field shift, while the methinic C2 carbon atom is much more influenced than the other carbon atoms (low field shift) suggesting a specific interaction at this site of the molecule. 

The situation is quite different for physisorbed molecules. In that case, there is no transfer of charge, the mechanical renormalization is weaker due to a much weaker metal-molecule bond and also the image interaction is smaller as the molecule probably is adsorbed further out from the surface. In a recent IRS investigation of CO physisorbed on Al(100) the measured frequency is only shifted down a few cm from the gasphase value. However, there is for this system also a short range intermolecular interaction that certainly will affect the vibrational frequency. As yet there exist no theoretical calculations for the van der Waals interaction between a CO molecule and a metal. 

The molecular approach, adopted throughout this book, starts from the statistical mechanical formulation of the problem. The interaction free energies are identified as correlation functions in the probability sense. As such, there is no reason to assume that these correlations are either short-range or additive. The main difference between direct and indirect correlations is that the former depend only on the interactions between the ligands. The latter depend on the maimer in which ligands affect the partition function of the adsorbent molecule (and, in general, of the solvent as well). The argument is essentially the same as that for the difference between the intermolecular potential and the potential of the mean force in liquids. 

In the same study, the SERS spectrum of adsorbed PhNC shows a v(N=C) peak at 2180cm, which is shifted 55cm" to higher values than that of free PhNC [31]. These results are in good agreement with other studies of PhNC adsorphon on gold [41] and indicate a molecule bonded to one Au atom in an on-top (t) ) position. The authors state, however, that a theorehcal calculation of molecular orientation that considers the adsorption of only one molecule is not entirely appropriate because it does not take into account intermolecular interactions among the adsorbates. 

The vibrational spectrum of a molecule adsorbed on a metal surface contains detailed information about the metal-adsorbate bonds, the local orientation of the molecule, and intermolecular interactions within the adsorbate layer. It is this detailed information about the adsorbate layer that makes vibrational spectroscopy and most prominently IR spectroscopy an important tool in heterogeneous catalysis research. 

The calculations with empirical potentials of the structure and dynamics of paraffin molecules adsorbed on graphite are presently being extended (27) to include the intermolecular interaction. This work together with elastic neutron diffraction experiments on deuterated paraffin films (see Sec. Ill) should provide a sounder basis for interpreting the inelastic neutron vibrational spectra. 

The experimental response may deviate from that expected under ideal conditions for the following reasons. First, there may be interactions between the adsorbed molecules that cause the surface activity to differ from the surface concentration [13,14]. Alternatively, double-layer effects, ion-pairing, acid-base dissociation, and dispersion of the formal potentials can cause similar deviations. A non-zero peak splitting may indicate intermolecular interactions between the redox centers or that switching the redox composition triggers a structural change within the supramolecular assembly, e.g. adsorbate reorientation or the formation of... 

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