Slope variation with solute

The slope of fluorescence lifetime variation with temperature of FMN in the absence of AMP differs from that observed in the presence of AMP, thus indicating that an interaction exists between FMN and AMP. The quantum yield of FMN free in solution varies identically to fluorescence lifetime. However, in the presence of AMP, the quantum yield increases, while the lifetime decreases, thus indicating that a static complex (nonfluorescent) is formed between FMN and AMP. 

For the van der Waals component no such analytical theory exists. Aqvist and co-workers assumed that a similar linear treatment would work for these interactions but with a different empirical factor, to be determined from calibration experiments. There was some indirect evidence that this approach would be reasonable. For example, the experimental free energies of solvation for various hydrocarbons (e.g. n-alkanes) depend in an approximately linear fashion on the length of the carbon chain. In addition, the mean van der Waals solute-solvent energies from molecular dynamics simulations did show a linear variation with chain length (the slope of the line varying according to the solvent). 

Figure 13. Variation of peak potential with solution pH at a slow sweep rate (ca. 10 mV s"1). Slope values, mV/pH unit (SHE scale) Anodic, 137 cathodic, 87 (from Ref. 218, with permission).

Equation (19) relates the dependence of the pzc on the concentration of the electrolyte solution in the presence of specific adsorption (F 0 when au = 0) and its variation with the electrode charge. The dependence of the pzc of a mercury electrode on the logarithm of KI concentration was used for the first time for studying the iodide specific adsorption in [17] and later was named the Esin-Markov effect. As follows from the model theories of the electric double layer (see Sect. 3.2), the limiting slope of the aforementioned dependence should tend to the value —RT/kF, where the coefficient X(0 < X < 1) characterizes the discrete nature of the charge of specifically adsorbed anions. 

The equation reproduces the limiting slopes of A-Ce curves very satisfactorily over a wide range of conditions. For instance, for KCl the calculated slopes agree with the experimental at 273 K (S = 47.3) and at 373 K (S = 313.4) the equation also reproduces the large effects of changing valency (see conductance of aqueous solutions) and of variations in the dielectric constant and viscosity of the solvent (see non-aqueous solutions). The equation is accurate at concentrations up to Ce = 0.002 g-equiv. dm for uniunivalent salts in water. For multivalent salts and for electrolytes in non-aqueous solvents, its range is more restricted. 

An important quantity whieh has been frequently studied is the mean ehain length, (L), and the variation of (L) with the energy J, following Eq. (12), has been neatly eonfirmed [58,65] for dense solutions (melts), whereas at small density the deviations from Eq. (12) are signifieant. This is demonstrated in Fig. 6, where the slopes and nieely eonfirm the expeeted behavior from Eq. (17) in the dilute and semi-dilute regimes. The predieted exponents 0.46 0.01 and 0.50 0.005 ean be reeovered with high preeision. Also, the variation of (L) at the threshold (p, denoted by L, shows a slope equal to... 

The general picture emerging from the pzc in aqueous solutions is that the major variation of <7-0 between two metals is due to with a minor contribution from AX that is governed by metal-solvent interactions. If this is also the case in nonaqueous solvents, a similar picture should be obtained. This is confirmed by Fig. 20 in which the data in DMSO are reported. As in aqueous solution, all points lie to the left of the point of Hg. Bi, In(Ga), and Tl(Ga) lie with Hg on a common line deviating from the unit slope. As in aqueous solution, Ga is further apart. Au is in the same position, relatively close to the Hg line. Finally, the point of Pt is (tentatively) much farther than all the other metals. 

For semi-dilute solutions, two regimes with different slopes are similarly obtained the powers of M, however, can be lower than 1.0 and 3.4. Furthermore, the transition region from the lower to the higher slope is broadened. The critical molar mass, Mc, for polymer solutions is found to be dependent on concentration (decreasing as c increases), although in some cases the variation appears to be very small [60,63]. 

The concentration effects. This term describes variations in Vr of the polymer samples due to changes of injected concentration, Cj. The retention volumes as a rule increase with raising Cj in the area of practical concentrations [104-107]. This is mainly due to the crowding effects when the concentration of macromolecules is high enough so that they touch each other in solution and shrink due to their mutual repulsive interactions. The concentration effects in SEC are expressed by the slopes k of the mostly linear dependences of Vr on c,. K values rise with the molar mass of samples up to the exclusion limit of the SEC column. 

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