Viscosity of the solvent

Because the number of grazing encounters is a fimction of the diflfiision coefficient, CIDEP by the RPM mechanism is a strong fiinction of the viscosity of the solvent and, in general, the RPM becomes stronger with increasing viscosity. Pedersen and Freed [39] have developed analytical teclmiques for the fiinctional fonn of the viscosity dependence of the RPM. 

A frequently used example of Oldroyd-type constitutive equations is the Oldroyd-B model. The Oldroyd-B model can be thought of as a description of the constitutive behaviour of a fluid made by the dissolution of a (UCM) fluid in a Newtonian solvent . Here, the parameter A, called the retardation time is de.fined as A = A (r s/(ri + s), where 7]s is the viscosity of the solvent. Hence the extra stress tensor in the Oldroyd-B model is made up of Maxwell and solvent contributions. The Oldroyd-B constitutive equation is written as... 

The relative viscosity 77/770- This is obtained from Eq. (9.11) simply by dividing both sides of the equation through by the viscosity of the solvent (B = B/77o,etc.) ... 

Since 77/770 - 1 = (77 - Vo)IVo the specific viscosity describes the excess viscosity of the solution above the viscosity of the solvent relative to the latter. 

For predicting liquid diffiisivities of binary nonpolar liquid systems at high solute dilution, Umesi " developed a method that only depends on the viscosity of the solvent (2) and the radius of gyration of the solvent (2) and the solute (1). The Technical Data Book— Petroleum Refining gives the method and values of the radii of gyration for common hydrocarbons. Errors average 16 percent but reach 30 percent at times. 

Supercritical fluid chromatography (SFC) refers to the use of mobile phases at temperatures and pressures above the critical point (supercritical) or just below (sub-critical). SFC shows several features that can be advantageous for its application to large-scale separations [132-135]. One of the most interesting properties of this technique is the low viscosity of the solvents used that, combined with high diffusion coefficients for solutes, leads to a higher efficiency and a shorter analysis time than in HPLC. 

Owing to the enormous viscosity of the solvent, the result of these proton transfers is more striking than in other liquids. 

It is only when we come to examine ionic solutes in aqueous solution that we meet ionic solutes that decrease the viscosity of the solvent. 

The proportionality constant in this equation, D, is called the diffusion constant. A typical solute has D 1 X 10 9 m2 s . Values of D do not vary greatly with the solute but are inversely proportional to the viscosity of the solvent. 

Time-resolved optical absorption spectroscopy experiments have shown that arenesul-fonyl radicals decay with clean second-order kinetics14 the values of 2 k,/a h where s2 is the extinction coefficient at the monitoring wavelength, increased linearly with decreasing viscosity of the solvent, further indicating that reaction 16 is clearly a diffusion-controlled process. 

Po and rio are the densities and viscosities of the solvent, P2o,w and rj2o,w the corresponding values at 20.0 °C in water, v is the partial specific volume, which for neutral polysaccharides can often be reasonably estimated from the carbohydrate content [31] and takes on values between 0.5-0.7 ml/g for... 

In the relationship shown above, A and B are constants depending on temperature, viscosity of the solvent, and dielectric constant of the solvent, C is the concentration expressed in gram equivalents per liter, and Ac represents the equivalent conductance of the solution. A0 is the equivalent conductance at infinite dilution - that is, at C = 0, when the ions are infinitely apart from one another and there exists no interionic attraction, a represents the degree of dissociation of the electrolyte. For example, with the compound MN... 

Temperature variation may also be a relevant factor in flowrate stability. Since the viscosity of the solvent is temperature dependent, wide swings in the ambient temperature can directly affect pump performance. The direct effects of temperature on pump performance usually are far smaller, however, than the effects on retention and selectivity therefore, control of column temperature is generally sufficient to obtain high reproducibility. 

T divided by the viscosity of the solvent r s. For n-octane this number is 837 K/cP at T = 323 K. The results of the fitting process are all below this theoretical value. This is not surprising, since even in the case of dilute solutions of unattached linear chains, the theoretical values are never reached (see Sect. 5.1.2). In addition the experimental T/r s values differ considerably for the different labelling conditions and the different partial structure factors. Nevertheless, it is interesting to note that T/r s for the fully labelled stars is within experimental error the arithmetic mean of the corresponding core and shell values. 

The temporal evolution of P(r,t 0,0) is determined by the diffusion coefficient D. Owing to the movement of the particles the phase of the scattered light shifts and this leads to intensity fluctuations by interference of the scattered light on the detector, as illustrated in Figure 9. Depending on the size of the polymers and the viscosity of the solvent the polymer molecules diffuse more or less rapidly. From the intensity fluctuations the intensity autocorrelation function... 

Molecular rotors are fluorophores characteristic for having a fluorescent quantum yield that strongly depends on the viscosity of the solvent [50], This property relies on the ability to resume a twisted conformation in the excited state (twisted intramolecular charge transfer or TICT state) that has a lower energy than the planar conformation. The de-excitation from the twisted conformation happens via a non-radiative pathway. Since the formation of the TICT state is favored in viscous solvents or at low temperature, the probability of fluorescence emission is reduced under those conditions [51]. Molecular rotors have been used as viscosity and flow sensors for biological applications [52], Modifications on their structure have introduced new reactivity that might increase the diversity of their use in the future [53] (see Fig. 6.7). 

The yield of cage reaction products increases with increasing viscosity of the solvent. The decomposition of diacyl peroxides was the object of intensive study. The values of rate constants of diacyl peroxides (diacetyl and dibenzoyl) decomposition (kf and initiation (ki = 2ekd) are collected in Tables 3.4 and Table 3.5. The values of e are collected in the Handbook of Radical Initiators [4]. 

The rate constant of scrambling ksc was found to increase with increasing viscosity of the solvent [79] ... 

The higher the viscosity of the solvent, the longer the period of time of radical pair existence in the cage and the higher the observed value of scrambling rate constant [3,80-82]. The same phenomenon was observed during the photolysis of benzoyl peroxide and 1,1-dimethylethyl perbenzoate [3]. 

The higher the viscosity of the solvent, the higher the amount of the parent molecules formed due to the geminate recombination of radicals. The observed rate constant of decomposition of the initiator decreases with an increase in viscosity [3,90], This was observed in the decomposition of peresters and diacetyl peroxide in various solutions. Subsequently, the fraction fT of the radical pairs recombining to the parent molecule increases with an increase in the viscosity ... 

Khudyakov et al. [78] faced with unusual phenomena in his study of these reactions. He found that the rate constant of recombination is much lower (107— 10s L mol-1 s 1) than kD however, it depends on the viscosity of the solvent. It was found for the recombination of the following phenoxyl radical ... 

The steric factor P is high enough for the bimolecular reaction to occur when two radicals met in the cage. This reaction is limited only by translational diffusion of the reacting radicals and depends on the viscosity of the solvent. The rate constant of such reaction is close to the frequency of encounters of radicals, namely, k = a, kn = 0.25 x 47rrABZ)AB = RT 100007] where spin-statistical factor, rAB is the sum of radii of reactants A and B, and DAB is the sum of their diffusion coefficients. 

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