Diffusion coefficient measurement techniques

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

Applications to fluorescent or fluorescently labeled proteins and nucleic acids, and to fluorescent lipid probes in phospholipid bilayers, have been reported. In the latter case, the diffusion coefficients measured above the chain melting temperature were found to be 10 7 cm2 s 1, which is in agreement with values obtained by other techniques. 

Fluorescein-labeled proteins are also used to measure the translational mobility of proteins and lipids by the Fluorescence Recovery After Photo-bleaching technique [54-59]. The uniformly labeled fluorescent sample is flashed with an intense light source to bleach a spot, thus producing a concentration gradient. The rate of recovery of fluorescence in that bleached area is measured and used to calculate the diffusion coefficient of the probe dye into the bleached zone. Such diffusion coefficient measurements have been used to determine the association constants of proteins in cells [60], to measure the exchange of tubulin between the cytoplasm and the microtubules [61,62], to study the polymerization-depolymerization process of actin [63-65] and to monitor the changes that occur upon cell maturation [66,67]. 

Figure 4.8 The tracer diffusion coefficient as a function of protein concentration. Tracer and mutual diffusion coefficients measured by a variety of techniques illustrate the dependence of protein diffusion on concentration, (a) Diffusion coefficients for hemoglobin [64] (b) diffusion coefficients for albumin [64] (c) diffusion coefficients for albumin [64, 65].

V. MICROBMULSION CHARACTERIZATION DIFFUSION COEFFICIENT MEASUREMENTS USING ELECTROCHEMICAL TECHNIQUES... 

Figure 8 Corrected diffiisivUies of methane, ethane and propane at various temp tures and sorbate concentrations as determined by single-step FR method (open symbols) and self-diffusion coefficients measured by the NMR pulsed-field gradient technique (filled symbols).

A cell for characterising the diffusion of small molecules through thin polymer films using attenuated total reflectance (ATR) FTIR spectroscopy was described. The cell was designed to be used with precast (commercially extruded) polymer films, thus enabling the as-processed transport properties of the film to be studied. The cell was used to measure the diffusion of carbon dioxide, amyl acetate and limonene, and simultaneous diffusion of the individual components from a 50/50 mixture of amyl acetate and limonene through the thin polymer films (HDPE, LDPE and PS). Diffusion coefficients measured with the ATR technique compared favourably with values obtained from gravimetric measurements with the same penetrants and polymer samples. 20 refs. 

One of the most important physicochemical applications of gas chromatography (GC) is for the measurement of diffusion coefficients of gases into gases, hquids, and on solids. The gas chromatographic subtechniques used for the measurement of diffusivities are briefly reviewed, focusing on their accuracy and precision, as well as on the corresponding sources of errors responsible for the deviation of the experimental diffusion coefficients measured by GC from those determined by other techniques or calculated from known empirical equations. 

Katsanos, N.A. Karaiskakis, G. Temperature variation of gas diffusion coefficients measured hy the reversed-flow sampling technique. J. Chromatogr. 1983, 254,15 25. 

Siddiqu and Wu [31] used a dynamic laser light scattering method to characterise an unfractionated PI in chloroform at 25 °C. The relatively small angular and concentration dependencies and translational diffusion coefficients measured by this technique enabled the PI to be characterised from only one measurement at a finite concentration and small scattering angle. Thus, this method could be used to characterise the molecular weight distribution of PI from the measured line-width distribution. 

This work involved the use of photothermal techniques for determining the diffusion coefficients of O2 and CO2 of commercial LDPE. The methodology involved the monitoring of diffused gas hy a photoacoustic analysen Diffusion coefficients measured for CO2 and O2 were 2.77 x 10 cm Vs and 16.8 x 10 cm Vs, respectively. To support the gas diffusion results, thermal properties were studied using photoacoustic spectroscopy and crystallinity was determined using X-ray diffraction. Values obtained for the thermal diffusivity and specific heat capacity were 0.00165 cm and 2.33 J/cm /K, respectively, which were in good agreement with the values found in the literature for pure LDPE and thus, assured the reliability of the diffusion coefficient values. 

Electroanalytical techniques, essentially similar to those employed in aqueous solutions, can be adapted for use in melts to provide data on solution equilibria by way of stability constant determinations, ion transport through diffusion coefficient measurements, as well as mechanistic analysis and product identification from mathematical data treatment. Indeed, techniques such as linear sweep voltammetry and chronopotentiometry may often be applied rapidly to assess or confirm general characteristics or overall stoichiometry of electrode processes in melts, prior to more detailed kinetic or mechanistic investigations requiring more elaborate instrumentation and equipment, e.g., as demanded by impedance studies. Thus, answers to such preliminary questions as... 

The short-time diffusion (a few picoseconds) of water molecules close to the Vycor surface has been described in terms of simple models for all the samples studied [80]. At short times, the water molecules, close to some hydrophilic surface, perform very local rotational jumps characterized by Z>t and Ti as in bulk water, but with a longer residence time Tq on a given site before diffusing to an adjacent site along the surface with a diffusion coefficient equal to ) ocai- This diffusion is limited to some volume estimated as spherical. For the 25% hydrated sample, the diffusion coefficient measured by NMR appears to be smaller than D, which is smaller than T iocai [81]. This is due to the fact that the NMR technique measures the long-time and long-range diffusion coefficient. 

The protein diffusion coefficient in hydrophilic polymers can be measured by a variety of experimental techniques. Since the type of diffusion coefficient measured by each technique can be different, the method of choice will depend on the desired information and variable. A summary of the advantages and disadvantages of techniques available for diffusivity measurements is presented in Table I. 

Miller et al. (139) have used NMR techniques to study the same system. NMR results suggest that only the outer carbons (near the headgroup) of SDS are affected by association with the gelatin polypeptide [as was found in the PEO/SDS system examined by Cabane (46) and referred to earlier] diffusion coefficients measured by the pulsed gradient spin echo (PGSE) NMR method indicated that interaction with gelatin lowers the diffusion rate of SDS by an order of magnitude. 

UMEs, planar diffusion occurs at short times because the diffusion distance is small compared to the electrode dimensions (Figure 19. Ic). At longer times the current becomes time-independent as radial diffusion dominates (Figure 19. Id). For diffusion coefficient measurements with UMEs, the steady-state current is normally measured, although some techniques utilize both short- and long-time current measurements. 

The critical micelle concentration (CMC) occurs at a fixed temperature as amphiphile concentration increases. The CMC is not a thermodynamic phase transition. It is defined phenomenologically from a sharp increase in the number of molecules associated into micelles. The precise location of the CMC thus depends on the technique used to measure it. Many physical properties exhibit abrupt changes at the CMC, as illustrated in Fig. 4.15. Some of these are colligative properties such as osmotic pressure or ionic conductivity. Other techniques are sensitive to changes in the dynamics of molecules at the CMC. For example, the self-diffusion coefficient measured by dynamic light scattering decreases discontinuously... 

Diffusion coefficients measured by the spin-echo technique provide a means of investigating the translational motion of molecules under the extremes of temperature and pressure. There have been numerous smdies of the self-diffusion coefficients of high-pressure liquids and supercritical fluids by NMR. As an illustration of the potential of these physicochemical measurements, we will focus on CO2 (3,28,33,38,39). The availability of a wide range of diffusion coefficients and viscosities allows one to test the Stokes-Einstein equation at the molecular level. From hydrodynamic theory,... 

Fig. 5. Linear plot of the diffusion coefficients as a function of concentration. The full lines and represent the behaviors of the diffusion coefficients in the liquid (L) and gel (G) regimes of Fig. 4. The symbols inside circles are obtained in the transition regime from L to G (see paragraph 4.3.). For the meaning of the symbols, see Table 1. (+) (M = 3.9 x 10 ) and ( m) (M = 8.6 X 10 ) correspond to the diffusion coefficient measured by the gradient concentration technique.

The values of the diffusion coefficients listed in Table 17.1 are similar to the gas kinetic diffusion coefficients measured by other techniques. However, the disorientation cross-sections are quite remarkable, being many orders of magnitude smaller than gas kinetic cross-sections. In the case of Rb-He collisions, for instance,... 

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