Polanyi

A rather different approach is to investigate possible adsorption isotherm forms for use with Eq. X-43. As is discussed more fully in Section XVII-7, in about 1914 Polanyi proposed that adsorption be treated as a compression of a vapor in the potential held U x) of the solid with sufficient compression, condensation to liquid adsorbate would occur. If Uq(x) denotes the held necessary for this, then... 

In the second picture, an interfacial layer or region persists over several molecular diameters due to a more slowly decaying interaction potential with the solid (note Section X-7C). This situation would then be more like the physical adsorption of vapors (see Chapter XVII), which become multilayer near the saturation vapor pressure (e.g.. Fig. X-15). Adsorption from solution, from this point of view, corresponds to a partition between bulk and interfacial phases here the Polanyi potential concept may be used (see Sections X-7C, XI-1 A, and XVII-7). 

Alternative approaches treat the adsorbed layer as an ideal solution or in terms of a Polanyi potential model (see Refs. 12-14 and Section XVII-7) a related approach has been presented by Myers and Sircar [15]. Adsorption rates have been modeled as diffusion controlled [16,17]. 

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

The curve of Fig. XVII-15 is essentially a characteristic curve of the Polanyi theory, but in the form plotted in might better be called a characteristic isotherm. Furthermore, as would be expected from the Polanyi theory, if the data for a given adsorbate are plotted with RTln P/f ) as the abscissa instead of just ln(P/P ), then a nearly invariant shape is obtained for different temperatures. The plot might then be called the characteristic adsorption curve. 

Polanyi J C and Schreiber J L 1973 Physical Chemistry—An Advanced Treatise vol 6 (New York Academic)... 

Evans M G and Polanyi M 1935 Some applications of the transition state method to the calculation of reaction velocities, especially in solution Trans. Faraday Soc. 31 875-94... 

The first mfonnation on the HE vibrational distribution was obtained in two landmark studies by Pimentel [39] and Polanyi [24] in 1969 both studies showed extensive vibrational excitation of the HE product. Pimental found that tire F + H2 reaction could pump an infrared chemical laser, i.e. the vibrational distribution was inverted, with the HF(u = 2) population higher than that for the HF(u = 1) level. A more complete picture was obtained by Polanyi by measuring and spectrally analysing tlie spontaneous emission from vibrationally excited HE produced by the reaction. This infrared chemiluminescence experiment yielded relative populations of 0.29, 1 and 0.47 for the HF(u =1,2 and 3)... 

Polanyi J C and Rieley H 1991 Photochemistry in the adsorbed state Dynamics of Gas-Surface Interactions ed C T Rettner and M N R Ashfold (London Royal Society of Chemistry) p 329... 

Carrington T and Polanyi J C 1972 Chemiluminescent reactions Chemical Kinetics, Int. Rev. Sc/. Physical Chemistry senes 1, vol 9, ed J C Polanyi (London ButtenA/orths) pp 135-71... 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Generalized Correlations. Generalized correlations are often the only recourse when a property value cannot be determined from empirical correlations or by other means. Several powerful correlating techniques fall under this category, including the principle of corresponding states (3,17), reduced property models (1), and the Polanyi-type characteristic curve for microporous adsorbents (14). 

M. Polanyi, Uber eine Art Gitterstdrung, die einen Kristall Plastisch Machen Kdnnte, Z. Phys. 89, Nenntes and Zehntes Heft, 660-664 (1934). 

---