Experimental Concentration Dependences

Aqueous solutions of alkali halides have been extensively studied by chlorine, bromine and iodine NMR. Because of the considerable linebroadening for solid alkali halides and for liquids with covalent 

While remarks on line widths of chloride [257], bromide [12 13] 

Hertz and co-workers extend the previous studies of Br and I to higher concentrations for aqueous solutions of Lil, LiBr, Nal, 

Rbl and CsBr. An improved equation for the quadrupole relaxation resulting from ion-ion interactions is derived and used to analyze the experimental data in terms of distances of approach between the ions. Since it again was found that the electrostatic model used predicted relaxation rates much higher than those observed. Hertz [260] recently reexamined the theory. Although some terms in the expression for the relaxation rate are difficult to estimate, it appears now possible to rationalize experimental data reasonably well. In two further 

During a long period, Richards and co-workers [51 52 245 246 262j262] have studied alkali and halide ion relaxation in solutions of alkali halides and interpreted their data rather differently from Hertz. In their first paper, studies of NaBr and CsBr solutions were performed at different concentrations and the concentration dependence of relaxation compared with that of viscosity. For NaBr the line width was found to increase linearly with viscosity although direct proportionality between the two quantities is not displayed by the data. For CsBr solutions, where there is a minimum in the plot of viscosity versus concentration, the bromine line width divided by viscosity was found to increase approximately linearly with salt concentration. The interpretation of these findings was that in the case of NaBr, ion-solvent interactions dominate, whereas with CsBr also ion-ion interactions are of importance. The basis for comparing relaxation rate 

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Figure 3.90. The experimental concentration dependence of the Stern-Volmer constant for three different temperatures (points) fitted by DET with the single-channel Marcus transfer rate (thick lines). The thin lines represent the contact analogs of the curves above for the same temperatures (decreasing from top to bottom) and the diffusional control of quenching ( o = oo). (From Ref. 46.)...

In the highly simplified treatment of the diffusion potential that has just been presented, several drastic assumptions have been made. The one regarding the concentration variation within the transition region can be avoided. One may choose a more realistic concentration versus distance relationship either by thinking about it in more detail or by using experimental knowledge on the matter. Similarly, instead of assuming the activity coefficients to be unity, one can feed in the theoretical or experimental concentration dependence of the activity coefficients. Of course, the introduction of nonideality makes the mathematics awkward in principle,... 

Fig. 15. Experimental concentration dependence of S deduced from experimental data on T,.j in various solvents (1) CHClj, (3) CHjClCHjCl, (5) CH2CICHCICH2CI. The broken line gives the dependence proportional to c ...

Thus, in the fluid state, there are two relaxation processes, the a and the with relaxation times that scale with proximity to the critical point with differing exponents, -y and — l/2fl, respectively. For spherical particles, y — 2.58 and l/2a = 1.66 thus the a process is predicted to slow more dramatically as the transition is approached than the process. Figure 4-22 shows the relaxation times t and extracted from the relaxation data of Fig. 4-20 for the colloidal fluids. The power laws given by Eqns. (4-33) and (4-34) fit these experimental concentration dependencies well, supporting the mode-coupling theory of this transition. 

This definition of the CMC originates from the qualitative analysis of experimental concentration dependencies of physico-chemical properties, and is not quite strict. Indeed, the limits of the concentration range corresponding to the CMC depend on the error limits of the applied experimental method and on its sensitivity to micellar concentration. For instance, the equivalent conductivity of aqueous solutions of ionic surfactants decreases drastically just above the CMC. Sometimes other properties of surfactant solutions, for example, the intensity... 

Fig. 3.12. The experimental concentration dependence of the interaction parameter for aqueous solutions of (1) poly(vinyl pyrrolidone), PVP and (2) poly(vinyI methoxyacetal), PVMA.

This survey of the experimental concentration dependences around 25°C of halide ion quadrupole relaxation rate for aqueous alkali halide solutions can be summarized in the following general conclusions drawn from Figs. 5.1 - 5.3, which probably constitute the most... 

We are now required to relate the antifoam concentration to the foam volume or F (= volume of air in foam in presence of antifoam/volume of air in foam in absence of antifoam) in order to make comparison between the implications of Equation 6.34 and observations of foam generation. The experimental concentration dependence of a commercial polydimethylsiloxane antifoam on foam volume, and therefore F, in the case of sparging solutions of sodium oleate, has been reported by Kulkami et al. [51]. Results for short-duration sparging (<200 s), where negligible deactivation of the antifoam is to be expected, have been shown by Garrett [23] to be represented by a simple exponential so that... 

The following two sections treat sedimentation of polymers in homogeneous solution, and sedimentation of probe chains and spheres through polymer solutions. A final section offers a systematic discussion of these results. Throughout, the analysis matches the experimental concentration dependence against the simple stretched-exponential form... 

We, therefore, conclude that the concentration dependence of the experimental rate gives the composition of the transition state in this example the transition state is composed of one molecule of A and one of B, for the experimental rate constant is first-order in each reactant. 

The reaction to the right, (R), proceeds with a rate that is found experimentally to depend upon the concentrations of the reactants as follows ... 

A comparison of values of yield stress for filled polymers of the same nature but of different molecular weights is of fundamental interest. An example of experimental results very clearly answering the question about the role of molecular weight is given in Fig. 9, where the concentration dependences of yield stress are presented for two filled poly(isobutilene)s with the viscosity differing by more than 103 times. As is seen, a difference between molecular weights and, as a result, a vast difference in the viscosity of a polymer, do not affect the values of yield stress. 

It seems however that this problem is not fully cleared up. Thus, it was stated in paper [19] on the basis of experimental data obtained earlier that Ye increased with a filler s concentration in proportion to cp4J. Such a law for the concentration dependence of yield stress at the shear Y(universal Value of the YJY ratio. It is quite probable however, that indicated discrepancies follow just from different ways of analytical approximation of particular experimental data. The only unquestionable fact is that Ye as well as Y grow very sharply with an increase in concentration. 

The full MSA expression for the capacitance is complex. However, at low ce it is composed of concentration-independent and concentration-dependent terms. 1 The concentration-independent term is not associated with any specific region of the interface, but quantitative agreement between experimental and theoretical values of capacitance at low ceJ is achieved only if the contribution of the metal phase is included. 

Figure 5 shows that EPM is able to reproduce fairly well the experimentally observed dependence of the particle number on surfactant concentration at a fixed initiator concentration (ammonium persulfate =... 

As an even more explicit example of this effect Figure 6 shows that EPM is able to reproduce fairly well the experimentally observed dependence of the particle number on surfactant concentration for a different monomer, namely methyl methacrylate (MMA). The polymerization was carried at 80°C at a fixed concentration of ammonium persulfate initiator (0.00635 mol dm 3). Because methyl methacrylate is much more water soluble than styrene, the drop off in particle number is not as steep around the critical micelle concentration (22.) In this instance the experimental data do show a leveling off of the particle number at high and low surfactant concentrations as expected from the theory of particle formation by coagulative nucleation of precursor particles formed by homogeneous nucleation, which has been incorporated into EPM. 

Using this equation we can calcnlate the concentration-dependent changes in (p (absolute values of (pQ and k, cannot be determined experimentally). 

There might be various reasons that lead to finding an apparent instead of the true activation energy. The use of power-law kinetic expressions can be one of the reasons. An apparent fractional reaction order can vary with the concentration, i.e. with conversion, in one experimental run. Depending upon the range of concentrations or, equivalently, conversions, different reaction orders may be observed. As an example, consider the a simple reaction ... 

E (A4>). This relation can be used to plot y (E ) from Fig. 5.7 as a function of the electrode potential, y [E (A(j))], for different electrolytes and concentrations, depending on which experimental capacity measurements have been used for the integration. Since these measurements were performed with an SCE, we have added a corresponding subscript to the electrode potential. 

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