Chemical-potential gradient

3 Chemical Potential Gradient With Eq. 3.72, Pick s law can be rewritten to 

In the right-hand side, k T In(c/c°) is the chemical potential in an ideal solution. This equation dictates a balance in the forces acting on the solute molecule at r. The friction v(r) is balanced by the chemical potential gradient, resulting in the velocity v(r) of the solute molecule. The chemical potential gradient causes a transfer of matter from a higher potential to a lower potential, just as a force on the particle moves it. 

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A reverse osmosis membrane acts as the semipermeable barrier to flow ia the RO process, aHowiag selective passage of a particular species, usually water, while partially or completely retaining other species, ie, solutes such as salts. Chemical potential gradients across the membrane provide the driving forces for solute and solvent transport across the membrane. The solute chemical potential gradient, —is usually expressed ia terms of concentration the water (solvent) chemical potential gradient, —Afi, is usually expressed ia terms of pressure difference across the membrane. 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to tire respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality tliroughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the elecuic potential gradient... 

The most important driving forces for the motion of ionic defects and electrons in solids are the migration in an electric field and the diffusion under the influence of a chemical potential gradient. Other forces, such as magnetic fields and temperature gradients, are commonly much less important in battery-type applications. It is assumed that the fluxes under the influence of an electric field and a concentration gradient are linearly superimposed, which... 

The ionic mobilities Uj depend on the retarding factor 0 valid for a particular medium [Eq. (1.8)]. It is evident that this factor also influences the diffusion coefficients. To find the connection, we shall assume that the driving force of diffusion is the chemical potential gradient that is, in an ideal solution,... 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

The self-diffusion coefficient is determined by measuring the diffusion rate of the labeled molecules in systems of uniform chemical composition. This is a true measure of the diffusional mobility of the subject species and is not complicated by bulk flow. It should be pointed out that this quantity differs from the intrinsic diffusion coefficient in that a chemical potential gradient exists in systems where diffusion takes place. It can be shown that the self-diffusion coefficient, Di, is related to the intrinsic diffusion coefficient, Df, by... 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

Pulsed field gradient NMR (PFG-NMR) spectroscopy has been successfully used for probing interactions in several research fields.44-53 The method was developed by Stejskal and Tanner more than 40 years ago54 and allows the measurement of self-diffusion coefficient, D, which is defined as the diffusion coefficient in absence of chemical potential gradient. 

Chemical potential gradients The chemical potential of a species can vary from place to place, e.g. inside and outside a cell, giving rise to a concentration difference and hence a concentration gradient. The inclusion of ions adds an electrochemical gradient and the two may oppose one another... 

Wagner pioneered the use of solid electrolytes for thermochemical studies of solids [62], Electrochemical methods for the determination of the Gibbs energy of solids utilize the measurement of the electromotive force set up across an electrolyte in a chemical potential gradient. The electrochemical potential of an electrochemical cell is given by ... 

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... 

For any change to occur a chemical potential gradient must exist. For a membrane system, such as the one under consideration, Haase(22) and Belfort(23) have derived the following simplified equation for constant temperature ... 

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