Overlap concentration 353 equilibrium

At equilibrium conditions, at very low concentration, the elution volume of a macromolecule should be independent of the flow rate. However, with increasing molar mass in the UHMM range, in the absence of degradation, the elution volume strongly depends on the molar mass of the sample. This result does not depend on the concentration of the sample. This retardation effect occurs also at very low concentrations below the overlapping concentration c. The retardation of UHMM macromolecules has been studied by several workers it is a very complex effect and substantially stiU not well understood. The retardation effect is particularly meaningful in proximity to the exclusion limit of the columns and when the pore size approximately equals or is lower than the sizes of the macromolecules. A trivial conclusion is that for a successful fractionation of UHMM macromolecules without retardation effects, one must use SEC columns with ultralarge pore sizes. 

In recent thermodynamic studies, laborious osmometry is scarcely used and instead of II, 5II/5c is measured by SLS or sedimentation equilibrium. Figure 17 illustrates the concentration dependence of 5II/5c (from SLS) for six samples of cellulose tris(phenyl carbamate) (CTC) in tetrahydrofuran (THF). The overlap concentration for the highest At sample (AI = 1.5 X 10 , = 20.9nm) is 6.5 x 10" gem" , so that... 

In an equilibrium study of the adsorption of molybdenum(VI) from aqueous solution onto activated carbon it has been found that the data are best explained in terms of an absorption model comprising the three species [HMo207] , Mo03(H20)3, and [HMo04] of which the dimer predominates by far (80). Computer treatment of potentiomet-ric (81) and spectrophotometric data (82) also indicated the possible existence of [HMo207] as a minor species in aqueous solution at low molybdenum concentration ( 2 X 104 Af). However, as its assumed stability region overlaps with several other polynuclear ions more direct evidence is needed before its existence can be accepted with certainty. 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

In a further study, Taniuchi et al. (1977) have shown that in the association of overlapping fragments of staphylococcal nuclease, two different species of active enzyme are formed. On the basis of the products of limited proteolysis, structures for the two species were deduced. In one case a structure is proposed in which fragment 1-126 assumes native-like structure over the sequence 1-48, and all of fragment 50-149 assumes native-like structure. In the other case the structure is one in which fragment 1-126 assumes native-like structure over the sequence 1-110, while that part of fragment 50-149 in the sequence interval 111-149 assumes native-like structure. The interest of these results is enhanced by the finding that the two active species initially form in relative concentrations substantially different from their equilibrium concentrations. Thus, both a mobile equilibrium and substantial kinetic control of the early products are evident. Taniuchi et al. did not reach a clear-cut mechanistic conclusion from their studies. 

Furthermore, equilibrium constants K2 for the formation of the adduct corresponding to Reaction 4 were determined by the overlap procedure in solutions containing fixed concentrations of the organic component, and the effect of solvent composition on the Hammett reaction constant p was followed. 

The second problem is somewhat more troublesome. The separation between the absorption maximum of the adduct and that of the free acid (or base) is seldom large and so there is considerable overlapping of bands (see Fig. 9.1). If the absorptivities of each of the species at each frequency were known, it would be a simple matter to ascribe a proportion of the total absorbance at a given frequency to each species. It is usually a relatively simple matter to measure the absorptivity, e, of the free acid (or base) over the entire working range. Since it is often impossible to prepare the pure adduct (in the absence of equilibrium concentrations of free acid and base), its absorptivity cannot be measured. However, if the equilibrium is studied at two different concentrations of acid (or base), it is possible to set up two simultaneous equations in terms of the two unknowns K and and solve for both.27... 

In contrast to spatial distribution, the equilibrium energy distribution of adsorbed particles cannot be violated to any substantial degree by reaction since energy is rapidly transferred between adsorbed particles and solids. Therefore, the activated complex method may be applied to rates of surface reactions. For this we consider the activated complex (transition state) of a surface reaction as a likeness of adsorbed particle (21). But, assuming that each adsorbed particle occupies only one site, it is necessary, even in the simplest kinetic model, to consider that activated complexes are able to occupy not only one, but also several surface sites (21). For example, the usual picture of a reaction between two particles adsorbed on neighboring sites involves, in fact, the notion that the activated complex occupies both sites. When the activated complex occupies several sites, this does not create any difficulty for the theory since the surface concentration of activated complexes is an infinitesimal quantity, and so the possibility of overlapping the required sites is excluded. 

Fig. 22 shows the results of photometry of plates similar to that illustrated in Fig. 21. The relative intensities of suitable transitions were determined from the asymptotic limit at long time delays when the system attains equilibrium. (These resemble, but are not identical to, the relative/ values because of the usual instrumental effects which depend on line width.) The time variation of the relative concentrations is shown in Fig. 23 the upper four levels attain Boltzmann equilibrium amongst themselves after 100 /isec, to form a coupled (by collision) system overpopulated with respect to the 5DA state. The equilibration of the upper four levels causes the initial rise (Fig. 22) in the population of Fe(a5D3). Thus relaxation amongst the sub-levels is formally similar to vibrational relaxation in most polyatomic molecules, in which excitation to the first vibrational level is the rate determining step. In both cases, this result is due to the translational overlap term, for example, in the simple form of equation (14) of Section 3.

In general, the flow of water due to a chemical potential gradient is called chemical osmosis. When compacted, clay can act as a semi-permeable membrane due to overlapping diffuse double layers. This means that the movement of solute particles is restricted across the membrane, while solvent is free to flow. To attain chemical equilibrium in case of an initial concentration gradient across the clay, water flows from low to high salt concentration. The degree of semi-permeability is described by the reflection coefficient a, which ranges from 0 (no osmosis) to 1 (no solute transport). 

The experiments demonstrate the development of a streaming potential in consolidated bentonite clay when flushed by a NaCl-solution of either low or high concentration. The streaming potential measured in our experiments is at least 5 to 10 times larger than values reported for bentonite in the literature. Apparently this is caused by a very low electric conductivity of the bentonite samples studied. This low conductivity might be ascribed to overlapping diffuse double layers on the clay particles, caused by the high compaction and the presence of monovalent ions in the equilibrium solution. The bentonite, thus compacted, will be a very effective medium for active application of electroosmosis. Compared with electrically shorted conditions, chemical osmosis will be reduced when the clay is not short-circuited. 

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