Solvent Viscosities

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

As is inversely proportional to solvent viscosity, in sufficiently viscous solvents the rate constant k becomes equal to k y. This concerns, for example, reactions such as isomerizations involving significant rotation around single or double bonds, or dissociations requiring separation of fragments, altiiough it may be difficult to experimentally distinguish between effects due to local solvent structure and solvent friction. 

In the Smoluchowski limit, one usually assumes that the Stokes-Einstein relation (Dq//r7)a = C holds, which fonns the basis of taking the solvent viscosity as a measure for the zero-frequency friction coefficient appearing in Kramers expressions. Here C is a constant whose exact value depends on the type of boundary conditions used in deriving Stokes law. It follows that the diffiision coefficient ratio is given by ... 

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. 

To conclude this section it should be pointed out again that the friction coefficient has been considered to be frequency independent as implied in assuming a Markov process, and that zero-frequency friction as represented by solvent viscosity is an adequate parameter to describe the effect of friction on observed reaction rates. 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

Other Factors Affecting the Viscosity of Dispersions. Factors other than concentration affect the viscosity of dispersions. A dispersion of nonspherical particles tends to be more viscous than predicted if the Brownian motion is great enough to maintain a random orientation of the particles. However, at low temperatures or high solvent viscosities, the Brownian motion is small and the particle alignment in flow (streamlining) results in unexpectedly lower viscosities. This is a form of shear thinning. 

A parameter used to characterize ER fluids is the Mason number, Af, which describes the ratio of viscous to electrical forces, and is given by equation 14, where S is the solvent dielectric constant T q, the solvent viscosity 7, the strain or shear rate P, the effective polarizabiUty of the particles and E, the electric field (117). 

Component 1 is the diffusing gas, while component 2 is the solvent. The solvent viscosity l2 in Pa sec, the solute molar volume at the normal boihng point Vi in mVkmole, and the solvent association parameter Xo multiplied by the solvent... 

Rizzuti et al. [Chem. Eng. Sci, 36, 973 (1981)] examined the influence of solvent viscosity upon the effective interfacial area in packed columns and concluded that for the systems studied the effective interfacial area a was proportional to the kinematic viscosity raised to the 0.7 power. Thus, the hydrodynamic behavior of a packed absorber is strongly affected by viscosity effects. Surface-tension effects also are important, as expressed in the work of Onda et al. (see Table 5-28-D). 

The function f(k ) is shown plotted against the thermodynamic capacity ratio in Figure 1. It is seen that for peaks having capacity ratios greater than about 2, the magnitude of (k ) has only a small effect on the optimum particle diameter because the efficiency required to effect the separation tends to a constant value for strongly retained peaks. From equation (1) it is seen that the optimum particle diameter varies as the square root of the solute diffusivity and the solvent viscosity. As, in... 

Viscosity. Solvent viscosity of resins is influenced by the concentration of resin, the softening point, the molecular weight distribution, the chemical composition of the resin, and the type of solvent. The higher the resin concentration, the higher the viscosity. For a given concentration, solution viscosity depends on the softening point of the resin (Fig. 22). 

H type columns must be used at a flow rate and pressure drop below maximum values listed in Tables 4.12-4.16. Standard flow rates are also listed in these tables. They are flow rate range recommendable for long-term usage in tetrahydrofuran at 25°C and vary with temperature. H type columns can be operated at a higher flow rate at elevated temperatures. They also vary with solvent depending on the viscosity. They are approximately inversely proportional to the solvent viscosity. The maximum pressure drop listed in the tables is for one column. When some columns are used in series, the total maximum pressure drop is a summation of values of all columns. 

Of course these requirements cannot be fulfilled simultaneously. For example, a low vapor pressure of the liquid electrolyte is obtained only by using more viscous dipolar aprotic solvents such as propylene carbonate, but high solvent viscosity generally entails a low conductivity. Nevertheless, a large number of useful solvents and electrolytes is available, allowing a sufficiently good approximation to an ideal electrolyte. 

The Role of Solvent Viscosity, Ionic Radii, and Solvation... 

There have been numerous studies on the kinetics of decomposition of A IRK. AIBMe and other dialkyldiazenes.46 Solvent effects on are small by conventional standards but, nonetheless, significant. Data for AIBMe is presented in Table 3.3. The data come from a variety of sources and can be seen to increase in the series where the solvent is aliphatic < ester (including MMA) < aromatic (including styrene) < alcohol. There is a factor of two difference between kA in methanol and k< in ethyl acetate. The value of kA for AIBN is also reported to be higher in aromatic than in hydrocarbon solvents and to increase with the dielectric constant of the medium.31 79 80 Tlic kA of AIBMe and AIBN show no direct correlation with solvent viscosity (see also 3.3.1.1.3), which is consistent with the reaction being irreversible (Le. no cage return). 

While the rate of azo-compound decomposition shows only a small dependence on solvent viscosity, the amount of cage reaction (and hence f) varies dramatically with the viscosity of the reaction medium and hence with factors that determine the viscosity (conversion, temperature, solvent, etc.) 1... 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

A common approximation in many flow field computations at high fluid velocities is to consider that inertial forces dominate the flow and to neglect viscous forces (inviscid approximation). Since solvent viscosity is a variable in some of the experiments discussed here, the above approximation may be not be valid throughout and viscous forces are explicitly considered in the flow equations. Results of computations showed, nevertheless, that even with viscous solvents such as bis-(2-ethyl-hexyl)-phtalate with qi = 65 mPa s, viscous forces do not affect the flow field unless tbe fluid velocity drops below a few m s"1 at the orifice. This limit is generally more than one order of magnitude lower than the actual range used in the present investigations. 

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