Transfer of molecules

Here p is the chemical potential just as the pressure is a mechanical potential and the temperature Jis a thennal potential. A difference in chemical potential Ap is a driving force that results in the transfer of molecules tlnough a penneable wall, just as a pressure difference Ap results in a change in position of a movable wall and a temperaPire difference AT produces a transfer of energy in the fonn of heat across a diathennic wall. Similarly equilibrium between two systems separated by a penneable wall must require equality of tire chemical potential on the two sides. For a multicomponent system, the obvious extension of equation (A2.1.22) can be written... 

The condition for the pressure or molar concentration to remain constant in such a system is that there should be no net transference of molecules. The process is then referred to... 

Substituting this result in Eq. (53), we have for the free energy change associated with the transfer of molecule I from infinity to a distance a from molecule k... 

As a result of Eq. (11) we are able to calculate the chemical potential of any molecule X in any liquid system S, relative to the chemical potential in a conductor, i.e. at the North Pole. Hence, COSMO-RS provides us with a vehicle that allows us to bring any molecule from its Uquid state island to the North Pole and from there to any other liquid state, e.g. to aqueous solution. Thus, given a liquid, or a reasonable estimate of AGjis of a soUd, COSMO-RS is able to predict the solubility of the compound in any solvent, not only in water. The accuracy of the predicted AG of transfer of molecules between different Uquid states is roughly 0.3 log units (RMSE) [19, 22] with the exception of amine systems, for which larger errors occur [16, 19]. Quantitative comparisons with other methods will be presented later in this article. 

The discussion of moisture uptake by hygroscopic materials must include a description of the thermodynamics of vapor-liquid equilibria. For gas (g) and liquid (1) phases to be in equilibrium, the infinitesimal transfer of molecules between phases (dng and dn ) must lead to a free energy change of zero. 

When chemisorption is involved, or when some additional surface chemical reaction occurs, the process is more complicated. The most common combinations of surface mechanisms have been expressed in the Langmuir-Hinshelwood relationships 36). Since the adsorption process results in the net transfer of molecules from the gas to the adsorbed phase, it is accompanied by a bulk flow of fluid which keeps the total pressure constant. The effect is small and usually neglected. As adsorption proceeds, diffusing molecules may be denied access to parts of the internal surface because the pore system becomes blocked at critical points with condensate. Complex as the situation may be in theory,... 

At all positions in the bed, concentrations in the fluid and adsorbed phases are related by the adsorption isotherm. This implies that there is no resistance to the transfer of molecules of adsorbate from bulk fluid to adsorption site. 

Returning to our A-B dissociation process, the vibrational levels of the molecule can only be excited by collisions with other molecules. Consider the energy transfer of molecule A by collision with other A molecules as a chemical reaction... 

From the theoretical point of view, it is necessary to show that no microphysical difference exists between the processes of diffusion, i.e. the transfer of molecules according to a gradient of their chemical potential or concentration, and self-diffusion, i.e. the re-distribution of molecules in space due to their random walk at equilibrium. The corresponding coefficients... 

This can be solved assuming that the concentration in the bulk liquid is 0 inside the drop at time t = 0 as well as at x = x at longer times, and that the concentration in the thin layer at the interface is in Henry s law equilibrium with the adjacent gas (Danckwerts, 1970, pp. 33-37). Under these conditions, the rate of transfer of molecules across a... 

Show that the expression for rran given in Eq. (KKK) can be obtained from the expression in Eq. (JJJ) for the rate of transfer of molecules across a plane. 

The mechanisms of transfer of molecules and ions across the wall of tubules are more complicated than in the artificial apparatus. In addition to osmosis and simple passive transport viz., ordinary downhill mass transfer due to concentration gradients), renal mass transfer involves active transport viz., uphill mass transport against gradients). The mechanism of active transport, which often occurs in living systems, is beyond the scope of this text. Active transport requires a certain amount of energy, as can be seen from the fact that live kidneys require an efficient oxygen supply. 

When transfers of molecules from media where the microorganisms do not occur (e.g., solids, NAPLs, gases) to phases where they are present (e.g., in water) are not rate-limiting, then it is possible that uptake by the microorganisms can be the slowest step in the sequence. Such a situation implies that the chemical fiigacity of the chemical of interest in that system is not equal to the chemical fugacity inside the cells where the relevant enzymatic apparatus occurs. Now we have a case in which the rate of biodegradation is expressed ... 

Figure A1.8 Nuclear spin states and spectrum for product 5. At the top the four states are again shown in an energy-level diagram. Heavy lines are the states with enhanced populations. A downward-pointing arrow indicates a net transfer of molecules from an overpopulated higher spin state to a less populated lower one, and corresponds to net emission. The spectrum shows the multiplet effect of type El A. From S. H. Pine, J. Chem. Educ., 49, 664 (1972). Reproduced by permission of the Division of Chemical Education.

Discrete and continuum models of transfer of molecules over various sorption sites of a microheterogeneous membrane were considered for systems with weak intermolecular interactions and membranes with constant composition and structure. An equation for estimating size effects on permeability coefficient II of microheterogeneous membranes was derived [188], and the possibility of applying the continuum model to calculate the n value in thin films of thickness L is numerically analyzed. The effect of the composition and structure of a uniformly microheterogeneous membrane on the permeability coefficients II was studied. The dependence of n on the composition is a convex function if the migration between different sorption sites proceeds more quickly than between identical sites and a concave one in the opposite case [189],... 

Kohen, E. and Kohen, C. Rapid automated multichannel microspectrofluorometry. A new method for studies on the cell-to-cell transfer of molecules. Exptl. Cell Res. 107 261-268, 1971. 

Kohen, E. and Kohen, C. The intercellular transfer of molecules in tissue culture cells A kinetic study by multichannel microfluorometry. In The Tenth Miami Winter Symposia, 9-13 January 1978. Differentiation and Development. W. Whelan and J. Schultz (eds.)pp. 411-439. Academic Press, New York, 1978. 

Since the reaction rate per unit reactor volume depends on the transfer of molecules from the gas to the liquid, the mass-transfer coefficient is... 

The transfer of molecules back and forth between velocity states is a two-way random process thus step distance / may be positive or negative. The random sequence of positive and negative steps constitutes a random walk (see Section 5.3). The total number n of such steps, forward and backward, is the total time (retention time) of the process tr over exchange time t q... 

Most theories have the common feature that they explain the phenomenon of heat conductivity (in melts and amorphous solids) on the basis of the so-called "phonon" model. The process is supposed to occur in such a way that energy is passed quantumwise from layer to layer with sonic velocity and the amount of energy transferred is assumed to be proportional to density and heat capacity. No large-scale transfer of molecules takes place. 

Molecular clusters can be considered to be the smallest size range of an aerosol particle size distribution. Nucleation from the gas phase to particles or droplets involves, in the initial stages, the formation of clusters. Research on clusters provides a valuable approach to understanding, on a molecular level, the details of the transfer of molecules from the gaseous to the condensed state by either new particle formation or heterogeneous processes including adsorption onto or dissolution into particles. 

We define a as the fraction of the energy difference transferred upon impact between a molecule and a plate. Thus if a molecule has a mean temperature T and strikes a plate at temperature T, it will rebound with a mean temperature T -f a(T — T ). Since the energy transfer of molecules is given by the product Cv AT, the energy transfer will be aCv(T — T ). In the above we will assume that T2 is the temperature of the molecules after striking the plate T2. 

Permeability across epithelial cells can be affected by the presence of influx or efflux transporters (saturable integral membrane proteins that catalyze the transfer of molecules through a biological membrane). For example, in the gastrointestinal... 

When a liquid is placed in a closed container, the amount of liquid at first decreases but eventually becomes constant. The decrease occurs because there is an initial net transfer of molecules from the liquid to the vapor phase (Fig. 16.44). However, as the number of vapor molecules increases, so does the rate of return of these molecules to the liquid. The process by which vapor molecules re-form a liquid is called condensation. Eventually, enough vapor molecules are present above the liquid so that the rate of condensation equals the rate of evaporation (see Fig. 16.45). At this point no further net change occurs in the amount of liquid or vapor because the two opposite processes exactly balance each other the system is at equilibrium. Note that this system is highly dynamic on the molecular level—molecules are constantly escaping from and entering the liquid at a high rate. However, there is no net change, because the two opposite processes just balance each other. 

The basic concepts in forming a molecularly imprinted polymer are therefore rather simple. Indeed this apparent simplicity has misled some would-be users of this approach who have failed to appreciate that realising this in practice, particularly with any degree of efficiency, has proved enormously difficult. Not the least, most polymer chemists would appreciate that to produce a crosslinked polymeric network sufficiently rigid to retain some memory of an imprint molecule, and yet allow ready mass transfer of molecules to and from the memory cavities, is no small undertaking. The early workers in the field have made enormous efforts to bring the technique to a point where materials capable of application and exploitation are now becoming available, and this is as much a tribute to their tenacity as it is to their scientific invention. 

The mechanism of evaporation of a liquid depends on the relative values of the vapor pressure of the liquid and the total system pressure. If evaporation takes place at a temperature such that p < P, the process involves transfer of molecules from the surface of the liquid to the gas above the surface, while if p = P, vapor bubbles form throughout the entire liquid, but predominantly at the heated container walls that is, the liquid boils. The temperature at which p = Pis the boiling point of the liquid at the given pressure. 

In arriving at this distribution E t) it was assumed that there was no transfer of molecules in the radial direetion between streamlines. Consequently, with the aid of Equation 13-44), we know that the moleeules on the center streamline (r = 0) exited the reaetor at a time t = t/2, and moleeules traveling on the streamline at r = 3R A exited the reaetor at time... 

Random transfer of molecules between tire two boxes. These moves alter compositions and chemical potentials /ij of tire species in tire boxes, ultimately bringing about equality of tire chemical potentials for each species in tire two boxes. These moves also contribute to tire evolntion of tire tliennodynamic properties of tire molecules in tire boxes. 

On a macroscopic scale, the interface can be regarded as a discrete boundary. On the molecular scale, however, the change from one place to another takes place over several molecular diameters. Due to movement of molecules, this region is in a state of violent change, the whole surface layer changing many times a second. Transfer of molecules at the actual interface is, therefore, virtually instantaneous and the two phases are, at this point in equilibrium. 

We recall first the definition of independent reactions introduced in chapter I, 6. If we have a system containing c constituents, which can undergo r reactions other than transfers of molecules from one phase to another, then we have (c/. 1.62) for each reaction a stoichiometric equation ... 

The preparative separations of certain polar (e.g., strongly basic) compounds and of many large molecular compotmds e.g., peptides and proteins) usually involve a complex mass transfer mechanism that is often slower than the mass transfer kinetics of small molecules. This slow kinetics influences strongly the band profiles and its mechanism must be accovmted for quantitatively. The accurate prediction of band profiles for optimization purposes requires a correct mathematical model of the various mass transfer processes involved. The piupose of the general rate model (GRM) is to accormt for the contributions of all the sources of mass transfer resistances to the band profiles [52,62,94,95]. The mass transfer of molecules from the bulk of the mobile phase percolating through the bed to the surface of an adsorbent or the mass of a permeable resin particle involves several steps that must be identified. 

This term covers the use of electric pulses to assist transfer of molecules into cells. In principle a membrane would not necessarily need to be measurably porated or permeabilized, possibly only sufficiently destabilized or perturbed to allow electrophoretic transfer across it. Examples of uses are DNA eiectrotransfer, siRNA eiectrotransfer, etc. 

In absorption, the transfer of molecules from the vapor to the liquid is a condensation process that is accompanied by the release of an amount of heat equivalent to the latent heat of condensation of the components being absorbed. If the process is adiabatic, where no heat crosses the system boundaries, the heat released by absorption is converted to sensible heat, resulting in a temperature rise. This thermal effect is reversed in stripping since the stripped components are transferred from the liquid state to the vapor state. The latent heat of vaporization is responsible for a temperature drop in adiabatic stripping processes. 

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