Diffusion, coefficients in membranes

M. F. Blackwell, K. Gounaris, S. J. Zara, and J. Barber, A method for estimating lateral diffusion coefficients in membranes from steady-state fluorescence quenching studies, Biophys. J. 51, 735-744 (1987). 

In this chapter we describe more advanced topics in quenching. Quenching in membranes is desoibed in some detail because of the numerous applications. These include localization of membrane-bound probes, estimation of diffusion coefficients in membranes, and the effect of quencher partitioning into membranes. We also describe transient effects in quenching, which result in nonexponential decays whenever diffusive quenching occurs. These effects can complicate the interpretation of the time-resolved data, but they also provide additional information about the diffusion coefficient of die quencher, the interaction radius, and the medianism of quendiing. For those interested in an introduction to fluorescence, the reading of this chi ter can be postponed. 

But for very heterogeneous systems or for flow reactions (e.g. columns [54] or tubes [55]) the practically useful information such as the amount of substrate transformed in function of time can also be obtained by the engineering approach one uses mass transfer equations (e.g. permeabilities or mass transfer coefficients instead of diffusion coefficients in membranes or unstirred layers and Reynolds, Nusselt and Schmidt numbers for the hydrodynamics [56, 57]) and the turn-over (or mean speed) of the reactions together with the dimensions of the parts constituting the system and obtains their inter-relations. 

With regard to the enantioselective transport through the membrane, one advantage of liquid membrane separation is the fact that the diffusion coefficient of a solute in a liquid is orders of magnitude higher as compared to the diffusion coefficient in a solid. The flux through the membrane depends linearly on the diffusion coefficient and concentration of the solute, and inversely on the thickness of the membrane [7]. 

The Desmopressin diffusion coefficient in the cubic phase at 40 C (D=0.24 x 10-10 m2s-l) is about a factor 9 smaller than in 2H20-solution at 25 C (D=2.25 x 10-10 m s" ), a difference which is larger than what is expected from pure obstruction effects a reduction factor of three is expected from the inclusion of a solute in the water channels of the cubic phase (13). Thus, the results indicate an interaction between the peptide and the lipid matrix and/or membrane surface, especially since the peptide and lipid diffusion coefficients are very similar in the cubic phase (Table... 

In general, it is easier to measure the permeability coefficient than the partition coefficient, diffusion coefficient, and membrane thickness. Once permeability is measured, it is difficult to separate the contributions of the individual variables. We often see permeability coefficients being reported in the literature instead of the more fundamental partition coefficient and diffusion coefficient being reported separately. 

Figure 19 Free volume plot for co(polyether)polyurethane membranes at 37°C for model drugs. D is the diffusion coefficient in cm2/sec, and H is the hydration expressed as (wet volume — dry volume)/wet volume. (Reproduced with permission from Ref. 59.)...

Sampling rates for the case of total boundary layer-control can be expected to be nearly independent of temperature, since both the diffusion coefficients in air, and the kinematic viscosity of air are only weak functions of temperature (Shoeib and Harner, 2002). This leaves the air-flow velocity as the major factor that can be responsible for the seasonal differences among sampling rates observed by Ockenden et al. (1998). The absence of large R differences between indoor and outdoor exposures may be indicative of membrane-control, but it may also reflect the efficient damping of high flow velocities by the deployment devices used for SPMD air exposures (Ockenden et al., 2001). 

Nafion absorbs MeOH more selectively than water, and the MeOH diffusion flow is higher than the osmotic water flow in Nafion membranes. Diffusion coefficients of Nafion 117 determined by different techniques have been reported. Ren et al. measured MeOH diffusion coefficients in Nafion 117 membranes exposed to 1.0 M MeOH solutions using pulsed field gradient (PPG) NMR techniques. The MeOH self-diffusion coefficient was 6 x 10 cm S and roughly independent of concentration over the range of 0.5-8.0 M at 30°C. A similar diffusion coefficient was obtained for Nafion 117 at 22°C by Hietala, Maunu, and Sundholm with the same technique. Kauranen and Skou determined the MeOH diffusion coefficient of 4.9 x 10 cm for Nafion... 

The MeOH diffusion coefficients in BPSH 40 exhibit remarkably different behavior. At low MeOH concentrations, the diffusion coefficienf is 7.7 x 10 cm s, buf if drops significanfly to 2.5 x 10 cm s at 4 M. In the range of 4-8 M, MeOH diffusion coefficienfs of both Nation 117 and BPSH 40 are roughly independent of MeOH concentration. This trend of decreasing MeOH diffusion coefficients upon increasing MeOH concentration is, on the face of it, ideal for DMFCs. The necessary corollary proviso is that the concentration in the membrane increases to a lesser extent than the diffusion coefficient decreases, yielding a net permeability decrease. 

In dense membranes, no pore space is available for diffusion. Transport in these membranes is achieved by the solution diffusion mechanism. Gases are to a certain extent soluble in the membrane matrix and dissolve. Due to a concentration gradient the dissolved species diffuses through the matrix. Due to differences in solubility and diffusivity of gases in the membrane, separation occurs. The selectivities of these separations can be very high, but the permeability is typically quite low, in comparison to that in porous membranes, primarily due to the low values of diffusion coefficients in the solid membrane phase. 

Solvents used in liquid membranes should have special characteristics such as low aqueous solubility, as a thin film of solvent is in contact with large volumes of aqueous solutions, and low viscosity to provide large diffusion coefficients in the liquid membrane. Furthermore, the analyte should have large partition coefficients between the donor and the membrane phase to give good extraction recovery and, at the same time, interfering substances in the sample should have low partition coefficients for efficient cleanup. 

It may be noted that data on the diffusion coefficient of the salt and on the limiting transport numbers permit the individual ionic mobilities and diffusion coefficients in the membrane to be evaluated by conventional means. 

The first theory of transport through nonporous gels was presented by Yasuda et al. [150] and was proposed as a result of previous experimental results [151, 152]. This theory relates the ratio of diffusion coefficient in the polymer membrane and diffusion coefficient in the pure solvent to the volume fraction of solvent in the gel membrane or in Yasuda s terminology, the degree of hydration of the membrane, H (g water/g swollen polymer). Yasuda et al. use the... 

Peppas and Reinhart have also proposed a model to describe the transport of solutes through highly swollen nonporous polymer membranes [155], In highly swollen networks, one may assume that the diffusional jump length of a solute molecule in the membrane is approximately the same as that in pure solvent. Their model relates the diffusion coefficient in the membrane to solute size as well as to structural parameters such as the degree of swelling and the molecular weight between crosslinks. The final form of the equation by Peppas and Reinhart is... 

One should take into account the specific features of gas diffusion in porous solids when measuring effective diffusion coefficients in the pores of catalysts. The measurements are usually carried out with a flat membrane of the porous material. The membrane is washed on one side by one gas and on the other side by another gas, the pressure on both sides being kept... 

Another important set of observations is related to the detection limit dynamic range and sensitivity. For the expected values of the diffusion coefficient (in the gel) of approximately 10-6cm2 s and substrate molecular weights about 300, the detection limit is approximately 10 4M. This is due to the fact that the product of the enzymatic reaction is being removed from the membrane by diffusion at approximately the same rate as it is being supplied. The dynamic range of the sensor... 

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%. 

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