Solute mobility

The ability of an enzyme to bind its substrate, a carbonyl to condense with an amine, or a Pd catalyst to couple two alkenyl halides, all depends upon the reactants encountering each other in solution. The rate of the encounters depends upon the mobility of the solutes. Thus, before exploring reactivity (Part II of this book) or the structures of molecular complexes (Chapter 4), it is best to understand how molecular encounters occur. Here we present a brief introduction into the molecular details and mathematics of diffusion and molecular encounters. 

The diffusion of a molecule through a solvent is best described as a random walk . The molecule collides with solvent molecules, changing direction and speed with each collision. Each little step (jostling) is smaller even than atomic sizes, because there is little space in a solvent for the solute to hop around in. Yet, the speed at which molecules diffuse is relatively rapid (see below). Adding up all the random motions leads to what is referred to as Brownian motion. 

Molecules with charges or dipoles diffuse slower in polar solvents. This slower diffusion is because polar molecules are well solvated in polar solvents, and hence must shed and interchange solvent molecules as they diffuse, or they must take the solvent with them. Shedding the solvent is costly. However, dragging the solvent is also costly because it results in increased friction due to the larger size of the entity that is moving. The friction that a solute feels as it diffuses through a solvent is related to its size, shape, and the viscosity of the solvent. This friction enters into the equations for translation in solution and determines how much solute molecules slow down in each step of the random walk. 

Diffusion of a solute in a solvent is caused by a concentration gradient. A thermodynamic driving force (F) exists for diffusion of a solute toward a uniform concentration of the solute, which is achieved throughout the solvent at equilibrium. However, on a microscopic level, even after bulk equilibrium has been achieved, a solute has a driving force for Brownian motion. This is because incremental movements (dx) take the solute to areas of incrementally different solute concentration (3c). The driving force (at constant pressure and temperature) for the diffusion of a solute in an ideal solution is given by Eq. 3.6, where c is concentration and x is a one-dimensional axis in space. After differentiation we get Eq. 3.7. 

To calculate the speed (rate) at which a solute will diffuse through a solution, we need to know the driving force for the diffusion, and the diffusion coefficient for the solute in the particular solvent. The diffusion coefficient depends upon the shape of the solute and the specific kinds of interacfions it has with the solvent. Further, the viscosity of the solvent itself affects the diffusion coefficienf. Table 3.5 shows several diffusion coefficients for different kinds of species in different solvents. In general, standard rate constants for diffusion of a solute through a solvent are on the order of 10 to 10 s h Therefore, diffusion controlled reactions occur on a timescale of ns. 

Soils are composed of inorganic and organic minerals with surfaces possessing sites capable of producing chemical or physical bonds with compounds or minerals dissolved in water (see Chapter 3). These solute-mineral surface reactions regulate the potential of chemicals in the soil-water environment to become mobile. Such chemicals include plant nutrients, pesticides, and/or other synthetic organics making up soil-water pollutants. The potential of chemical species to move in the soil-water system depends on the potential of soil to conduct water and on the potential of solution minerals to react with soil minerals. In the case of a nonreactive chemical species (nonreactive solute), its mobility in the soil system will be equal to that of water. However, the mobility of a reactive solute would be less than that of water. The rate of downward movement of a chemical species (e.g., a monovalent cation X+) can be predicted by the equation 

Therefore, the Kd of X+ in a given soil equals the ratio of adsorbed X (-S-X) to that in solution (X+). This can be established experimentally by meeting all of the condi- 

Based on Equation 10.3, chemical mobility differs from water mobility by a factor of 1 + (pb/x)Xd. This factor is also known as the retardation factor. The larger the retardation factor, the smaller is the velocity of the chemical species in relationship to the velocity of water. Note, however, that the retardation factor contains a reactivity factor (Kd) and two soil physical parameters, bulk density (pb) and porosity (t). The two parameters affect retardation by producing a wide range of total porosity in soils as well as various pore sizes. Pore size regulates the nature of solute flow. For example, in very small pores, solute movement is controlled by diffusion, while in large pores, solute flow is controlled by mass flow. 

Diffusion describes the number of molecules transferred across a boundary per unit time (e.g., seconds or minutes). It is given by Fick s law  

When a solution containing a particular chemical species is displaced from a porous medium with the same solution but without the particular chemical species, this miscible displacement produces a chemical species distribution that is dependent on (1) microscope velocities, (2) chemical species diffusion rates, (3) physicochemical reactions of the chemical species with the porous medium, (e.g., soil), and (4) volume of water not readily displaced at saturation (this not-readily displaced water increases as desaturation increases (Nielsen and Biggar, 1961). 

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Resolution depends upon differences in mobihties of the species. Background elec trolyte of low ionic strength is advantageous, not only to increase elec trophoretic (solute) mobilities, but also to achieve low elec trical conductivity and thereby to reduce the thermal-convec tion current for any given field [Finn, in Schoen (ed.). New Chemical Engineering Separation Techniques, Interscience, New York, 1962]. 

Katz et fl/.[l] searched the literature for data that could be used to identify the pertinent dispersion equation for a packed column in liquid chromatography. As a result of the search, no data was found that had been measured with the necessary accuracy and precision and under the sufficiently diverse solute/mobile phase conditions required to meet the second criteria given above. It became obvious that a... 

Figure 7.3 The positions occupied by LC and GC in a generic Type I phase diagram representing the mobile phase. Note that the GC mobile phase is shown as being composed of 100% component a, but this makes no difference chemically because there are no solute-mobile-phase interactions in GC. Reproduced by permission of the American Chemical Society.

Now, it was also shown on page 145 that for a given column, solute, mobile phase and flow rate, equation (l)can be reduced to an alternative abbreviated form which is given as follows,... 

For further discussion of experimental methods for determination of electrophoretic titration curves of proteins, see the recent study by Gianazza et al. [129], For discussion of the free solution mobility of DNA see Stellwagen et al. [368],... 

It can be noted that in general this result predicts that the ratio of the dispersion coefficient to the free-solution diffusion coefficient is different from the ratio of the effective mobility to the free-solution mobility. In the case of gel electrophoresis, where it is expected that the (3 phase is impermeable (i.e., the gel fibers), the medium is isotropic, and the a phase is the space between fibers, the transport coefficients reduce to... 

Stellwagen, NC, Apparent Pore Size of Polyacrylamide Gels Comparison of Gels Cast and Run in Tris-acetate-EDTA and Tris-borate-EDTA Buffers, Electrophoresis 19, 1542, 1998. Stellwagen, NC Gelfi, C Righetti, PG, The Free Solution Mobility of DNA, Biopolymers 42, 687, 1997. 

LCEC is a special case of hydrodynamic chronoamperometry (measuring current as a function of time at a fixed electrode potential in a flowing or stirred solution). In order to fully understand the operation of electrochemical detectors, it is necessary to also appreciate hydrodynamic voltammetry. Hydrodynamic voltammetry, from which amperometry is derived, is a steady-state technique in which the electrode potential is scanned while the solution is stirred and the current is plotted as a function of the potential. Idealized hydrodynamic voltammograms (HDVs) for the case of electrolyte solution (mobile phase) alone and with an oxidizable species added are shown in Fig. 9. The HDV of a compound begins at a potential where the compound is not electroactive and therefore no faradaic current occurs, goes through a region... 

The conceptual basis for understanding the connection between isocratic and gradient elution is well established and is called "linear solvent strength theory".22 27 Linear solvent strength theory proposes that, for a given solute, mobile phase, and column, if one measures the retention time of an analyte at two organic component concentrations, it will be possible to predict the retention time with any other mobile phase composition. The k value that would be observed in pure water, kw, is related to the actual k by the relationship... 

Hoagland, D.A., Arvanitidou E., and Welch C., Capillary Electrophoresis measurements of the free solution mobility for several model polyelectrolyte systems, Macromolecules, 32, 6180, 1999. 

For multivalent ions, an equation representing the solute mobility must be derived that considers all the existing ionic species. For instance, the following equilibrium was established for an ampholyte, BH A ... 

Figure 3.25 — Electrolytic flow-cell of the tubular type. (A) Whole cell. (B) Detail of working micro-electrode 1 Working electrode 2 reference electrode (Ag/AgCl) 3 counter-electrode (Pt wire) 4 acrylic tube 5 rubber cup 6 electrolyte solution (mobile phase) 7 fused-silica tube (50- or 100-/tm ID) 8 Ni wire (diameter 25 or 50 im, length 5 mm) 9 PTFE tube (0.1-mm ID, 2-mm OD) 10 hole 11 adhesive resin 12 glass pipette 13 silver paste 14 insulator 15 electric wire, (Reproduced from [184] with permission of Elsevier Science Publishers).

Thus, the approximate value of Hmin, for a well retained solute eluted from a well packed column and operated at the optimum linear mobile phase velocity, can be expected to be about 2.48dp, Furthermore, to the first approximation, this value will be independent of the nature of the solute, mobile phase or stationary phase. For the accurate design of the optimum columns lor a particular separation however, this approximation can not be made, nevertheless, the value of 2.48 for Hmin is a useful guide for assessing the quality of a column. 

The relative migration rate of the peak concentration of strontium at a solution flow rate of 0.1 mL per minute was used to calculate the equilibrium fractionation of strontium between glauconite and solution. It was determined that at equilibrium 0.958 of the strontium would be adsorbed by the glauconite and 0.042 of the strontium would be in solution (mobile phase). 

This model attempts to integrate solute properties, vehicle composition, and electroosmosis [60-62], and derives an expression which includes as many as 12 determinants of iontophoretic transport (i) solute size (molecular weight and molecular volume), (ii) solute mobility,... 

The effects of temperature on a CE separation are severalfold. With increasing temperature, the viscosity of the running electrolyte decreases and analysis times are shorter. The high currents associated with elevated temperatures generates additional heat thus, the efficiency and resolution may be altered. Changes in selectivity are often observed with different temperatures because solute mobilities are a function of diffusion coefficients, which are, in turn, dependent on temperature. Changes in selectivity may result from alteration of solute pKa values with temperature changes. 

Fig. 5.5. Van Deemter plots obtained for Cib monolithic silica in a capillary in CEC (open symbols) and HPLC (solid symbols) with thiourea (A) and hexylbenzene (0,9) as a solute. Mobile phase acetonitrile-water (HPLC), acetonitrile-Tris.HCl buffer, 50 mM pH 8 (CEC), (a), 80 20 (b), 90 10. Column size 50 pm I.D. x 33.5 cm (effective length 25 cm).

Fig. 5.6. Plots of plate heights against k values obtained in CEC with alkyl-benzenes (O, ) and PAHs (<>, ) as solute. Mobile phase acetonitrile-Tris.HCl (buffer 50 mM, pH 8) 90 10 (solid symbols) and 80 20 (open symbols). Column size 100 pm I.D. x 33.5 cm (effective length 25 cm). Plate heights observed at around u= 1 mm/s were plotted.

The solubility parameter may be used to characterize the overall polarity of compounds (solutes, mobile and stationary phases) in chromatography. It may also be used to predict the polarity (solvent strength) of mixtures (see section 3.2). 

The polydentate nature of the ligand, whether it be the solution mobile ligand such as ethylcncdiaminc, or the rigid surface (=SiO) >, has a strong entropy effect on the stability of either the initial solution complex or the final grafted complex [61]. 

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