Molecular analysis diffusion coefficient

P. Stilbs, Molecular self-diffusion coefficients in Fourier-transform nuclear magnetic resonance spectrometric analysis of complex mixtures. Anal Chem., 53 (1981) 2135-2137. 

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

The low molecular diffusion coefficients of proteins and other biopolymers reduces the efficiency of mass transfer and compromises efficiency as flow rate is increased. Therefore, high-performance SEC columns are usually operated at modest flow rates, e.g., 1 ml/min or less. However, operation at very low flow rates is undesirable due to excessive analysis times, loss of efficiency due to axial analyte diffusion, and the risk of poor recovery due to analyte adsorption. 

Moller, K. and Gevert, T. 1994, An FTIR solid-state analysis of the diffusion of hindered phenols in low-density polyethylene (LDPE) the effect of molecular size on the diffusion coefficient. J. Appl. Polym. Sci. 51 895-903. 

Consequently the use of very flne particles, liner than thuiSe presently available with a reasonably good size distribution would pernitt significant improvement in the analysis of high molecular weight solutes which have low diffusion coefficients and for which the optimum reduced velocity, vq. is attained at a very low value of the actual flow velocity, in columns packed with particles having the usual size ... 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

In this Appendix, the equivalence of the diffusion equation treatment and the molecular pair analysis is proved (see Chap, 8, Sect. 3.2) for the situation where there is a potential energy E/(r) between the reactants and the diffusion coefficient is tensorial and position-dependent. This Appendix is effectively a generalisation of the analysis of Berg [278]. The diffusion equation has a Green s function G(r, f r0, t0) which satisfies eqn. (161)... 

Sir Geoffrey Taylor has recently discussed the dispersion of a solute under the simultaneous action of molecular diffusion and variation of the velocity of the solvent. A new basis for his analysis is presented here which removes the restrictions imposed on some of the parameters at the expense of describing the distribution of solute in terms of its moments in the direction of flow. It is shown that the rate of growth of the variance is proportional to the sum of the molecular diffusion coefficient, D, and the Taylor diffusion coefficient ko2U2/D, where U is the mean velocity and a is a dimension characteristic of the cross-section of the tube. An expression for k is given in the most general case, and it is shown that a finite distribution of solute tends to become normally distributed. 

This shows that the mean of the temperature wave moves with the kinematic wave velocity and that an apparent diffusion coefficient may be defined to describe the dispersion. This coefficient is the sum of the diffusion coefficients which would be obtained if each effect were considered independently. Such an additivity has been demonstrated by the author for the molecular and Taylor diffusion coefficients elsewhere (Aris 1956) and is assumed in a paper by Klinkenberg and others (van Deemter, Zuiderweg Klinkenberg 1956) in their analysis of the dispersion of a chromatogram. 

From a detailed analysis of molecular motion in dilute gases a much better prediction of diffusion coefficients results with the Chapman-Enskog equation. This equation, which describes a mixture of two solutes A and B (binary gas system) is ... 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

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