Homogeneous electric field diffusion

In summary, the advantages of low-pressure IMS are that ion trap injection can replace ion gates to improve sensitivity, and ion-focusing devices such as the ion funnel can be employed at low pressure to offset ion diffusion. Due to the complexity and size of the instrument, however, no commercially available low-pressure IMSs with static homogeneous electric fields are interfaced to MSs. Nevertheless, their performance in research laboratories has clearly demonstrated many advantages of coupling IMS to MS. 

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

Hong and Noolandi [72], Berg [278], and Pedersen and Sibani [359] have also noted the connection between the survival probability and homogeneous density distribution. Finally, the escape probability of an ion pair formed with a separation, r0, with an arbitrary monotonically decreasing potential energy of interaction and with electric field-dependent mobility and diffusion coefficient ions was found by Baird et al. [350] to be (see also Tachiya [357])... 

A membrane can essentially be defined as a barrier that separates two phases and selectively restricts the transport of various chemicals. It can be homogenous or heterogeneous, symmetric or asymmetric in structure, solid or liquid, and can carry a positive or negative charge, or be neutral or bipolar. Transport across a membrane can take place by convection or by diffusion of individual molecules, or it can be induced by an electric field or concentration, pressure or temperature gradient. The membrane thickness can vary from as little as 100 p.m to several millimeters. 

As a consequence of the collective motion of the neutral system across the homogeneous magnetic field, a motional Stark term with a constant electric field arises. This Stark term inherently couples the center of mass and internal degrees of freedom and hence any change of the internal dynamics leaves its fingerprints on the dynamics of the center of mass. In particular the transition from regularity to chaos in the classical dynamics of the internal motion is accompanied in the center of mass motion by a transition from bounded oscillations to an unbounded diffusional motion. Since these observations are based on classical dynamics, it is a priori not clear whether the observed classical diffusion will survive quantization. From both the theoretical as well as experimental point of view a challenging question is therefore whether quantum interference effects will lead to a suppression of the diffusional motion, i.e. to quantum localization, or not. 

Since the definition of E° in Eq. (96) refers to standard conditions, that is, conditions in which no external electrical field applies on the reactant or the product, it is more convenient to consider the act of electron transfer as a succession of three individual steps as outlined in Scheme 5, which is reminiscent of that in Scheme 3 established for the homogeneous analogous situation (Sec. II.C.l). In Scheme 5, Rq or Pq relates to R or P in the closest plane to the electrode where no electrical potential applies, that is, at the end of the diffuse layer, denoted Xq in Fig. 14d. Rd, and Pelectron transfer Xd, usually considered close to or slightly within the OHP, where an electrical potential Os (i.e., the electrical potential at the electron transfer site) applies. 

From the mathematical viewpoint, the diffusion problem (4.3.1)-(4.3.3) is equivalent to the problem on the electric field of a charged conductive body in a homogeneous charge-free dielectric medium. Therefore, the mean Sherwood number in a stagnant fluid coincides with the dimensionless electrostatic capacitance of the body and can be calculated or measured by methods of electrostatics. 

Membrane separation Pressure Electrical field Concentration gradient Heterogeneous Homogeneous Ultrafiltration (s — 1) Reverse osmosis (hyperfiltration) (s-1) Dialysis (s -1) Electrodialysis (s — 1) Electrophoresis (s — 1) Permeation (1 — 1, g - g) Gas diffusion (g - g)... 

According to Ohm s law, applying an electric field to an ionic solution leads to an ion current which creates a concentration gradient. This gradient immediately sets up a diffusive flow to attempt to restore homogeneity. Both processes involve ion flow the diffusive flux and the charge flux are... 

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