Diffusion coefficient modulation

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

The combination of microscopic and macroscopic information is made possible by what can be called parameter imaging . In the general sense, it consists of the encoding of properties such as spectral line shifts, relaxation times, diffusion coefficients, etc., in the image by suitable combination of corresponding modules into one pulse sequence. Parameter images are to be distinguished from mere... 

P. B. Garland, Phase and modulation optical spectroscopic methods for determining triplet lifetimes and slow rotational diffusion coefficients, Biochem. Soc. Trans. 15, 838-839 (1986). 

At low Q the experiments measure the collective diffusion coefficient D. of concentration fluctuations. Due to the repulsive interaction the effective diffusion increases 1/S(Q). Well beyond the interaction peak at high Q, where S(Q)=1, the measured diffusion tends to become equal to the self-diffusion D. A hydrodynamics factor H(Q) describes the additional effects on D ff=DaH(Q)/S Q) due to hydrodynamics interactions (see e.g. [342]). Variations of D(Q)S(Q) with Q (Fig. 6.28) may be attributed to the modulation with H(Q) displaying a peak, where S(Q) also has its maximum. For the transport in a crowded solution inside a cell the self-diffusion coefficient is the relevant parameter. It is strongly... 

Dp and D are surface diffusion coefficients parallel and normal to steps, respectively, and e is the step interaction energy. Obviously, two simple cases arise for /= 0 and / = Jt/2, i.e. for the profile modulation parallel and perpendicular to the intrinsic steps. Since the step energ>" is in general larger than the step interaction energy [24,28] and the diffusion parallel to steps faster than normal to steps [29,30], the decay rate of such profiles is expected to be much faster when the modulation is parallel to the steps. The dependence of B, D and E on... 

Besides kinetic applications, which are still to be fully realized, hydro-dynamic modulation is useful for Schmidt number and diffusion coefficient measurements not only in Newtonian fluids but also in viscoelastic polymer solutions (Ostwald fluids) [291]. 

The high frequency relaxation is attributed in part to the modulation of intermolecular dipolar interactions by the translational diffusion. The cutoff frequency (60 MHz at 55°C) corresponds to the local diffusive jump frequency that is estimated from measurements of the diffusion coefficient (D 10"6 cm2/sec at 55°) (19, 21). This cutoff frequency also varies in temperature with the same activation energy (Eact 0.25 eV) as the diffusion frequency. 

As organic and aqueous phases are macroscopically separated by the membrane, HFM offer several hydrodynamic advantages over other contactors, such as the absence of flooding and entrainment, or the reduction of feed consumption (160, 161). The flowsheets tested in HFM were similar to those developed for centrifugal contactor tests. Computer codes based on equilibrium (162) and kinetics data, diffusion coefficients (in both phases and in the membrane pores), and a hydrodynamic description of the module, were established to calculate transient and steady-state effluent concentrations. It was demonstrated that, by selecting appropriate flow rates (as mass transfer is mainly controlled by diffusion), very high DFs (DI A 11 = 20,000 and DFrm = 830) could be achieved. Am(III) and Cm(III) back-extraction efficiency was up to 99.87%. 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

From Equations (4.14) and (4.15), the value of the term >,75 at a fluid velocity of 30 cm/s is 1.6-1.8 x 10 2 cm/s. Based on a trichloroethane diffusion coefficient in the boundary layer of 2 x 10 5 cm2/s, this yields a boundary layer thickness of 10-15 pm. This boundary layer thickness is in the same range as values calculated for reverse osmosis with similar modules. 

Fluorescence Correlation Spectroscopy and Fluorescence Burst Analysis. Several nanoscopic chemical imaging approaches work very well for measurements of chemical kinetics, interactions, and mobility in solution. Fluorescence correlation spectroscopy (FCS) measures the temporal fluctuations of fluorescent markers as molecules diffuse or flow in solution through a femtoliter focal volume.54 Their average diffusive dwell times reveal their diffusion coefficients, and additional faster fluctuations can reveal chemical reactions and their kinetics if the reaction provides fluorescence modulation. Cross-correlation of the fluorescence of two distinguishable fluorophore types can very effectively reveal chemical binding kinetics and equilibria at nanomolar concentrations. 

To improve topical therapy, it is advantageous to use formulation additives (penetration enhancers) that will reversibly and safely modulate the barrier properties of the skin. Fick s first law of diffusion shows that two potential mechanisms are possible. The two constants that could be altered significantly are the diffusion coefficient in the stratum corneum and the concentration in the outer regions of the stratum corneum. Thus, one of mechanisms of action of an enhancer is for it to insert itself into the bilayer structures and disrupt the packing of the adjacent lipids, thereby, reducing the microviscosity. The diffusion coefficient of the permeant will increase This effect has been observed using ESR and fluorescence spectroscopy [16,17]. 

An important example of the system with an ideally permeable external interface is the diffusion of an electroactive species across the boundary layer in solution near the solid electrode surface, described within the framework of the Nernst diffusion layer model. Mathematically, an equivalent problem appears for the diffusion of a solute electroactive species to the electrode surface across a passive membrane layer. The non-stationary distribution of this species inside the layer corresponds to a finite - diffusion problem. Its solution for the film with an ideally permeable external boundary and with the concentration modulation at the electrode film contact in the course of the passage of an alternating current results in one of two expressions for finite-Warburg impedance for the contribution of the layer Ziayer = H(0) tanh(icard)1/2/(iwrd)1/2 containing the characteristic - diffusion time, Td = L2/D (L, layer thickness, D, - diffusion coefficient), and the low-frequency resistance of the layer, R(0) = dE/dl, this derivative corresponding to -> direct current conditions. 

The PERVAP simulator (tubular module) was developed by Alvarez (2005), using FORTRAN language (Compaq Visual Fortran Professional Edition 6.6.a). The mathematical model applied is based on the solution-diffusion mechanism. Activity coefficients of the components in the feed phase (jj) were determined using the UNIFAC method (Magnussen et al, 1981). The prediction of diffusion coefficient (Z) ) was carried out using the free-volume theory. 

The basic idea behind the DOSY concept is similar to the one behind multidimensional NMR. In 2-D NMR, a modulation in the phase or signal intensity with respect to a known time increment is recovered by inverse FT. In a DOSY experiment, the diffusion coefficient is recovered from the signal decay as a function of a diffusion increment by an ILT. In fact, the approximate ILT of the signal amplitude with respect to q, where q is defined as ygSf (t), yields the second dimension of the spectrum which correlates the chemical shift with the diffusion coefficient. Therefore, it was termed diffusion ordered spectroscopy (DOSY). However, unlike the FT of the time domain signal that yields a unique solution, ILT does not yield a unique solution. Therefore, several software packages were developed to overcome this problem. Readers interested in more details concerning the DOSY techniques can consult a recent extensive review on the subject [17]. 

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