Diffusion constant measurement methods

Several mechanisms are involved in the permeability through Caco-2 cells. In order to obtain a more pure measure of membrane permeability, an experimental method based on ghost erythrocytes (red blood cells which have been emptied of their intracellular content) and diffusion constant measurements using nuclear magnetic resonance (NMR) has been proposed [108]. 

Devaux et al. have described in some detail the use of the Bloch equations to relate electron spin-spin interactions between spin-labeled lipids to diffusion constants. This method was originally employed by Trauble and Sackmann,50 Scandella et al.,42 Devaux and McConnell,10 and Devaux et al.11 to measure diffusion constants in multibilayer model membranes and in biological membranes. In all cases diffusion constants of the order of those reported previously were obtained. 

Euringer (24), who measured the evolution of hydrogen from nickel wires, gave a method for measuring both the solubility and the diffusion constant. The method, which should be of general applicability, was based upon the following solution of Tick s law (Chap. I) ... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

A Poison. New method for measuring diffusion constants of biologically active substances. Nature 154 823, 1944. 

Fig. 4. Schematic representation of transient method employed by Devaux and McConnell9 to measure the rates of lateral diffusion of phospholipids in model membranes. The upper diagram represents a concentrated patch of labels at the beginning of the experiment, time f = 0. At later times f>0, the molecules diffuse laterally, as shown in the lower two drawings. The paramagnetic resonance spectra depend on the spin-label concentration in the plane of the membrane, and an analysis of the time dependence of these spectra yielded the diffusion constant. [Reprinted with permission from P. Devaux and H. M. McConnell, J. Am. Chem. Soc., 94, 4475 (1972). Copyright by American Chemical Society.]...

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

So, here is the summary of what we can do to help the experimenter be sure that his or her measurement reflects interfacial and not transport control.3 (1) Working at short times (microseconds up to a millisecond, say), increases iL and therefore lengthens the current density range in which diffusion-free measurements can be made. (2) Working at times > about 10 s means that natural convection tends to make 8 constant, i. e., independent of time. However, this time-independent value can still be reduced (and hence iL helpfully increased by methods already reviewed (Chapter 7),... 

Other indirect methods for measuring lifetimes often involve device structures such as p-n junctions. The electron-beam-induced current (EBIC) technique, for example, measures the increase injunction current as an impinging electron beam moves close to the junction, i.e., within a few minority-carrier diffusion lengths. If a diffusion constant can be estimated, say by knowledge of the minority-carrier mobility, then the minority-carrier lifetime can be calculated. However, SI GaAs does not form good junctions, so such methods are really not applicable. 

The test cell is similar to that for the constant volume method, the test piece dividing the cell into high and low pressure cavities. The essential difference is that the low pressure side is connected to a device to measure the volume increase as gas diffuses to the low pressure side whilst maintaining constant pressure. In ISO 2782, a graduated capillary tube is used to measure the volume change and the tube may be arranged either vertically or horizontally. In the vertical arrangement, a U-tube capillary... 

A recent study has employed the new technique of quasi-elastic light scattering for estimation of diffusion constants (257). The result for the native enzyme at 24° is in close agreement with the data given in the tabulation. The value of D as a function of temperature was measured through the thermal transition. The method was also used to follow the kinetics of the urea-induced transition. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

The galvanostatic intermittent titration technique (GITT) has been first proposed by Weppner and Huggins in 1977 [22], This method is of particular interest for the measurement of ion transport properties in solid intercalation electrodes, used in lithium-ion batteries, for instance [18]. The determination of the diffusion constants relies on Fick s law. The GITT method records the transient potential response of a system to a perturbation signal a current step (/s) is applied for a set time xs, and the change of the potential (E) versus time (0 is recorded (Figure 1.11) [18,22],... 

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