Mobile diffusion

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

Shimizu, T. and Kenndler, E., Capillary electrophoresis of small solutes in linear polymer solutions Relation between ionic mobility, diffusion coefficient and viscosity, Electrophoresis, 20, 3364, 1999. 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

An indirect indication of the presence of interactions between micellar phase and drugs is given by molecular and dynamic parameters of the drug and the micelles (ionic mobility, diffusion coefficient, hydrodynamic radius, apparent molecular mass), which are altered by the solubilization of lipophilic substances in a significant manner. 

Stern combined the ideas of Helmholtz and that of a diffuse layer [64], In Stern theory we take a pragmatic, though somewhat artificial, approach and divide the double layer into two parts an inner part, the Stern layer, and an outer part, the Gouy or diffuse layer. Essentially the Stern layer is a layer of ions which is directly adsorbed to the surface and which is immobile. In contrast, the Gouy-Chapman layer consists of mobile ions, which obey Poisson-Boltzmann statistics. The potential at the point where the bound Stern layer ends and the mobile diffuse layer begins is the zeta potential (C potential). The zeta potential will be discussed in detail in Section 5.4. 

The striking advantages of STM are atomic resolution, its conceptional transparency and versatility, and the appeal of direct visualisation. STM can be applied to study anisotropic surface mobility, diffusion on inhomogeneous surfaces, or adsorbate interactions and collective transport effects on a local scale. It also a technique where a simultaneous characterization of tracer and chemical diffusion on single crystals is feasible [54]. Surface mobility studies using STM are currently progressing rapidly. 

Up till about 1921, it was often supposed that the potential could be identified with the single potential difference at the phase boundary. Freundlich and his collaborators1 showed that this is quite impossible, since the variation with concentration, and the influence of adsorbed substances, are entirely different in the two cases sometimes indeed the two potentials may have different signs. The phase boundary potential, if defined as the Volta potential, is the difference between the energy levels of the charged component, to which the phase boundary is permeable, inside the two phases when these are both at the same electrostatic potential. We have seen that it is difficult, or impossible, to define the phase boundary potential in any other way (see 2 and 3). It includes the work of extraction of the charged component from each phase, and this includes the part of the double layer which according to Stern s theory is fixed. The potential is merely the potential fall in the mobile, diffuse part of the double layer, and is wholly within one phase. 

Regarding the Stem-diffuse layer border, at low co the situation remains as In the static case. This situation has been discussed in sec. 3.13. At high frequency, polarization of the Stem layer may to a certain extent leak away via the, more mobile, diffuse part. Otherwise stated, the Stem layer is then shunted, or short-circuited, by the diffuse part. 

When the mean of the Poisson distribution A is plotted against the scan time 0 both the number of molecules N as well as their mobility (diffusion time) can be determined. Examples on the mobility of Green fluorescent protein expressed in SK-NM-C cells has been obtained and compared with classical confocal FCS. 

Using SI units, the velocity of the electro-osmotic flow is expressed in meters per second (m/s) and the electric field in volts per meter (V/m). Consequently, in analogy to the electrophoretic mobility, the electro-osmotic mobility has the dimension square meters per volt per second. Because electro-osmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomenon, the Hehnholtz-von Smoluchowski equation applies to electro-osmosis as well as to electrophoresis. In fact, when an electric field is applied to an ion, this moves relative to the electrolyte solution, whereas in the case of electro-osmosis, it is the mobile diffuse layer that moves under an appUed electric field, carrying the electrolyte solution with it. 

More generally, any force could be used to move the particles, so a more general definition of this type of transport coefficient will be the mobility diffusion coefficient, Du = ksTulci. Eq. (11.66)). Note that while this relationship between the conductivity and the diffusion coefficient was derived for noninteracting carriers, we now use this equation as a definition also in the presence of interparticle interactions, when o is given by Eq. (11.76). 

Late in 1969, Gaus and Hoinkis (30) published a paper in which they reevaluated the model of Hoinkis and Levi for zeolite A (35). They proposed that sited ions serve as a source for mobile diffusing ions and include a term in their equation describing a first-order process. However, they do not consider that the vacant cation sites are a sink and... 

The solution species were characterised in terms of ionic molar mobility, diffusivity, mobility, and hydrated ion radius prior to speciation. Equilibrium pH of the backffound solution was estimated as a function of gas type and operatingpressure. 

Estimate the ratio of the ionic conductivity to diffusion coefficient for a monovalent ion diffusing in an ionic solid. Take a typical value for the number of mobile diffusing ions as the number of vacancies present, approximately 10 defects per metre cubed, and Tas 1000 K. 

FIGURE 8.1 Dependence of A on EIN. (From Thomson et al.. Mobility, diffusion, and clustering of potassium(-r) in gases, J. Chem. Phys. 1973, 58, 2402-2411. With permission.)... 

Skullerud, H.R., Mobility, diffusion and interaction potential for potassium ions in argon, J. Phys. B 1973, 6, 918-928. 

Pick s laws also describe diffusion in solid phases. In solids transport properties can be considerably different than in liquid phases. Only one component can mobile diffuse in the matrix of the second component. At higher temperatures the diffusion coefficient can be more similar in size than in liquid phases, but the diffusion coefficient at room temperature can be orders of magnitudes smaller, e.g., D < 10 ° cm s k To overcome the time limitation one must make the diffusion length smaller. Ultra-thin layers or nanoparticles provide such small dimensions. Under such conditions the diffusion is not semi-infinite but has a restricted extension. This has to be considered in the boundary conditions. 

The surface characteristics of a microfluidic channel are very important in determining the flow in electrokinetically driven systems. In electrokinetically driven systems, the bulk flow is created by movement of the mobile diffuse layer near the channel wall/solution interface that is termed electroosmotic flow (EOF). The EOF is dependent on the surface of the microchannel walls. Roberts et al. demonstrated the generation of EOF on laser-ablated polymer substrates for the first time, using the parallel processing mode with a photomask and an ArF excimer laser at 193 nm [17]. A variety of polymer substrates such as polystyrene, polycarbonate, cellulose acetate, and poly(ethylene terephthalate) (PET) were ablated to fabricate microfluidic channels. The laser ablation process alters the surface chemistry of the machined regions and produced negatively charged. 

In conclusion, large differences exist in the behavior of small molecules and large (chain) macromolecules in the chromatographic systems. These mainly result from substantial role of conformational entropy of macromolecules and are augmented by distinctions in the viscosity, flow patterns, as well as in the mobility (diffusibility) of solutes of different sizes. It is necessary to consider these differences in order to devise the appropriate chromatographic system for efficient HPLC separation of particular polymer samples. 

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