Diffusion equilibrium techniques

CE is a technique with a very high power of resolution. This is attributed to low diffusion and high plate numbers obtained from the absence of band-broadening factors (e.g., eddy diffusion, equilibrium dynamics, etc.) other than diffusion, which is also minimized by short analysis time. 

When a state of sedimentation-diffusion equilibrium has been reached, the molecular or particle mass can, therefore, be evaluated without a knowledge of the diffusion coefficient (and, hence, independently of shape and solvation) by determining relative concentrations at various distances from the axis of rotation. Molecules as small as sugars have been studied by this technique. 

Leermakers, M., Y. Gao, C. Gabeille, et al. 2005a. Determination of high resolution pore water profiles of trace metals in sediments of the Rupel River (Belgium) using DET (diffusive equilibrium in thin films) and DGT (diffusive gradients in thin films) techniques. Water Air Soil Pollut. 166 265-286. 

Two experimental runs were performed. The H2S- and CO2 mole fluxes were obtained from the measured concentration curves by numerical differentiation and are plotted in figure 8a,b together with penetration and film model calculations. It is evident that forced desorption can be realized under practical conditions and can be predicted by the model. In general, measured H2S mole fluxes are between the values predicted by the models, whereas the CO2 forced desorption flux is larger than calculated by the models. The CO2 absorption flux, on the other hand, can correctly be calculated by the models. This probably implies that the rate of the reverse reaction, incorporated in equation (5), is underestimated. Moreover, it should be kept in mind that especially the results of the calculations in the forced desorption range are very sensitive to indirectly obtained parameters (diffusion, equilibrium constants and mass transfer coefficients) and the numerical differentiation technique applied. 

The mass of a protein can be directly determined by sedimentation equilibrium, in which a sample is centrifuged at relatively low speed so that sedimentation is counterbalanced by diffusion. The sedimentation-equilibrium technique for determining mass is very accurate and can be applied under nondenaturing conditions in which the native quaternary structure of multimeric proteins is preserved. In contrast, SDS-polyacrylamide gel electrophoresis (Section 4.1.4) provides an estimate of the mass of dissociated polypeptide chains under denaturing conditions. Note that, if we know the mass of the dissociated components of a multimeric protein as determined by SDS-polyacrylamide analysis and the mass of the intact multimeric protein as determined by sedimentation equilibrium analysis, we can determine how many copies of each polypeptide chain is present in the multimeric protein. 

Thermal desorption is a dynamic (non-equilibrium) technique in which a sample of hydrated corneum is heated at a constant rate in a dry atmosphere. The water desorption rate is plotted as a function of temperature. The general shape and temperature maxima of the desorption rate vs. temperature curves (Figure 12) are characteristic of the material s diffusion and equilibrium sorption behavior as well as experimental conditions such as heating rate. In a simple desorption process where... 

The mass of a protein can be directly determined by sedimentation equilibrium, in which a sample is centrifuged at relatively low speed so that sedimentation is counterbalanced by diffusion. The sedimentation-equilibrium technique for determining mass is very accurate and can be applied without denaturing the protein. Thus the native quaternary structure of multimeric proteins is preserved In contrast, SDS-polyacrylamide gel electrophoresis... 

Diffusion Gradient in Thin films (DGT) and equilibrium techniques such as Peepers and DETs... 

We have modified the diffusion cloud technique to study the vibrational energy dependence of reactions of alkali metals with polyatomic molecules. A steady-state reaction is prepared by the standard method, and the vibrational energy of the polyatomic reactant is then perturbed by absorption of energy from a g-switched COj laser. The effect of the added energy is determined by following the rate of departure from equilibrium sodium concentration after the laser pulse, on a time scale when the energy is still localized within the vibrational modes. The main reaction studied to date... 

There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

Finally, although both temperature-programmed desorption and reaction are indispensable techniques in catalysis and surface chemistry, they do have limitations. First, TPD experiments are not performed at equilibrium, since the temperature increases constantly. Secondly, the kinetic parameters change during TPD, due to changes in both temperature and coverage. Thirdly, temperature-dependent surface processes such as diffusion or surface reconstruction may accompany desorption and exert an influence. Hence, the technique should be used judiciously and the derived kinetic data should be treated with care ... 

This technique was employed to study the binding dynamics of Pyronine Y (31) and B (32) with /)-CD/ s The theoretical background for this particular system has been discussed with the description of the technique above. Separate analysis of the individual correlation curves obtained was difficult since the diffusion time for the complex could not be determined directly because, even at the highest concentration of CD employed, about 20% of the guest molecules were still free in solution. The curves were therefore analyzed using global analysis to obtain the dissociation rate constant for the 1 1 complex (Table 12). The association rate constant was then calculated from the definition of the equilibrium constant. 

Atoms are not rigidly bound to the lattice, but vibrate around their equilibrium positions. If we were able to look at the crystal with a very short observation time, we would see a slightly disordered lattice. Incident electrons see these deviations, and this, for example, is the reason that in LEED the spot intensities of diffracted beams depend on temperature at high temperatures the atoms deviate more from their equilibrium position than at low temperatures, and a considerable number of atoms are not at the equilibrium position necessary for diffraction. Thus, spot intensities are low and the diffuse background high. Similar considerations apply in other scattering techniques, as well as in EXAFS and in Mossbauer spectroscopy. 

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