K-M theory

Seme of the problems and limitations of the K-M theory have been discussed by Stenius (17-19). The great sensitivity of the absorption coefficient to small errors in the reflectivity measurement is particularly remarkable. Even though the derivation of K-M assumes perfectly diffuse illumination and reflectivity measurement, the optical geometry of practical measuring apparatus has been a point of discussion (20-24). 

In a collaborative effort with Marcus, we used quantum calculations of the density of states to obtain the rates that are in accord with the R.R.K.M. theory. We have found the following First it can be shown that the Eq obtained from our experiments (k against EJ can be correlated with that obtained from solution-phase studies (ktii Secondly, deviations from R.R.K.M. can be handled by... 

For the dissociation of IQ-water and IQ-methanol good agreement with R.R.K.M. theory was found. In these systems there are numerous low-frequency modes due to complexation, and the density of B-typc modes (states) is very large. This work will be published elsewhere. 

Kubelka-Munk theory n. A theory describing the optical behavior of materials containing small particles, which scatter and absorb radiant energy. It is widely used for color matching calculations. The mathematical equation describes the reflectance or transmittance in terms of an absorption coefficient, K, and a scattering coefficient, S. The K-M theory is based on the assumption of... 

DRS is based on the reflection of light by a powdered sample, when the diffuse-reflected photons are scattered in all directions. Quantitative treatment of the spectra is based on the Schuster-Kubelka-Munk (S-K-M) theory. It has to be emphasized that this approach is valid under the following conditions of... 

In later work, Kubelka [22] published a treatment that is applicable to spectroscopy, which is generally referred to as the K-M theory. It is this later work that we will describe here, following the... 

Other scientists in the field [24-28] derived expressions similar to those of Schuster [20] and Kubelka and Munk [21]. Earlier theories developed by Gurevic [29] and Judd [30,31] were shown by Kubelka [22] to be special cases of the K-M theory, while Ingle [32] showed that the formulas derived by Smith [33], Amy [34], and Bruce [35] can be derived from the equations of Kubelka and Munk. 

FIGURE 3.5 Diffuse reflectance i oo of an isotropic, optically thick sample according to the three-flux approximation, the diffusion approximation, GiovaneUi and the K-M theory. 

Utilizing the Kubelka-Munk (K-M) theory we then can relate the reflectance (R) to the absorption (K) and the scattering coefficient (S) by the equation ... 

For diffuse reflectance spectroscopy the Kubelka-Munk function, f Roo), is most appropriate [128, 129]. The K-M theory indicates that linear relationships of band intensity vs. concentration should result when intensities are plotted as the K-M function f Roo) = k/S, where k is the absorption coefficient and S is the scattering coefficient (cfr. Chp. 1.2.1.3). The use of the K-M equation for quantitative analysis by diffuse reflectance spectroscopy is common for measurements in the visible, mid-IR and far-IR regions of the spectrum. Measurement of scattered light (ELSD) allows quantitative analysis. 

The rate of decomposition of C2H4F is controlled by the rate of passage into the transition state, C2H4F, and this step is the one calculated by R.R.K.M. theory. 

There are several levels of approximation possible in the consideration of the NA transition. First there is the self-consistent mean field formulation due to Kobayashi and McMillan [8-10]. This is an extension to the smectic-A phase of the self-consistent mean-field formulation for nematics ( Maier-Saupe theory [11]). Kobayashi-McMillan (K-M) theory takes into account the coupling between the nematic order parameter magnitude S with a mean-field smectic order parameter. In Maier-Saupe theory, the key feature of the nematic phase - the spontaneously broken orientational symmetry - is put in by hand by making the pair potential anisotropic. In the same spirit, the K-M formulation puts in by hand a sinusoidal density modulation as well as the nematic-smectic coupling. 

In the mean-field picture one expects the phase transition to be genetically second order. However, as one adjust materials parameters to reduce the temperature width of the nematic phase, parametrized in K-M theory by the dimensionless ratio the coupling drives the transition first order, with the point in material-parameter space where this happens being termed the Landau Tricritical Point (LTP). 

Molecular order in the smectic-A phase was probed recently via a proton NMR study of three aromatic solutes in the liquid crystal 8CB [35]. The results were analyzed in the context of a simple modification of K-M theory for dissolved non-uniaxial solutes. The smectic solute Hamiltonian was written in the form ... 

---