Solvent viscosity models

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]. 

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 [ ]... 

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

A model that can take these findings into account is based on the idea that the screening of hydrodynamic interactions is incomplete and that a residual part is still active on distances r > H(c) [40,117]. As a consequence the solvent viscosity r s in the Oseen tensor is replaced by an effective... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

ARe>s is the Reynolds number based on the solvent properties, /zs is the solvent viscosity, D is the pipe diameter, F is the velocity in the pipe, and A is the fluid time constant (from the Carreau model fit of the viscosity curve). 

At low frequencies the loss modulus is linear in frequency and the storage modulus is quadratic for both models. As the frequency exceeds the reciprocal of the relaxation time ii the Rouse model approaches a square root dependence on frequency. The Zimm model varies as the 2/3rd power in frequency. At high frequencies there is some experimental evidence that suggests the storage modulus reaches a plateau value. The loss modulus has a linear dependence on frequency with a slope controlled by the solvent viscosity. Hearst and Tschoegl32 have both illustrated how a parameter h can be introduced into a bead spring... 

In this model, whether kq is a function of the solvent viscosity depends upon the relative magnitudes of Mint) and Mext). If Mint) Mext),then kq will depend upon viscosity if Mint) > Mext), the structural fluctuations in the protein allowing penetration of the quencher determine the magnitude of M and change in bulk viscosity may not affect this rate. Simulation of protein penetration behavior suggests that the penetration rate should be extremely sensitive to the size and charge of the quencher.(65)... 

The dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

As the results of Schwander and Cerf (188) and of Leray (180,181), which were obtained on samples of DNA from calf thymus, have been reproduced already in several review articles (1,3), the present discussion can be kept rather short. When the viscosity of the solvent (1.0 molar aquous solution of sodium chloride) is increased by replacing part of the water by glycerol, the behaviour of the initial slope of the extinction angle curve follows the qualitative pattern, as given by Fig. 5.10. At low solvent viscosities the molecules seem to behave like frozen molecules, at high solvent viscosities they seem to become flexible coils exhibiting internal friction. These results have been considered to prove the correctness of Cerf s theoretical model. 

This model combines different approaches of existing models by introducing at the same time the solvent viscosity, the molar volume Vm (as a measure for the molecular size), the surface tension of the solid membrane material and a sorption value ( > (as a measure for membrane-solvent interactions). Other SD-based transport models were presented by White [14], providing a predictive model for feed solutions with a high concentration of aromatics, by Scarpello et al. [67] and by Gibbins et al. [68]. A slightly modified equation was proposed by Geens et al. [69] ... 

The photoisomerization of stilbene is one of the most extensively studied photoreactions (25). Solvent effects have been thoroughly investigated for both the direct and photosensitized isomerizations, and a model has been developed which attributes these effects to solvent viscosity (26). Increased viscosity inhibits direct photoisomerization of the cis isomer, but facilitates that of trans-stilbene. As a result, the cis/trans ratio of the photostationary state increases with increasing solvent viscosity. The wide range of viscosities which are attainable by pressure manipulation of supercritical carbon dioxide provides an excellent opportunity to probe the effect of viscosity on stilbene photochemistry in the same solvent. 

New models for the prediction of molecular diffusion coefficients are described, and compared to previously established ones. These are based on solute molecular size, solvent viscosity solvent molecular size, and temperature. The data set of diffusion coefficients used was primarily the one developed by Wilke and Chang and upon which their commonly used diffusion model is based (A.I.Ch.E. Journal, 1 (1955), 264). 

Models of colloidal electrohydrodynamics relate the electrophoretic mobility /t to the zeta potential , the particle radius / , the composition of the solution via the Debye length /k, and the solvent viscosity and permittivity, // and f. Dimensional analysis shows that these variables must be related by... 

Quadrupole coupling constants were derived from the temperature dependence of the line-widths. With the aid of the Debye relationship, which should be a reasonable model for these symmetric compounds, the quadrupole coupling constant was derived from plots of the line-width against the ratio where ly and Trepresent bulk solvent viscosity... 

The ratio of the solvent viscosity to the total viscosity retained in the model is 1/9, generally used in most of the papers on tiie subject. 

How rapidly diffusion occurs is characterized by the diffusion coefficient D, a parameter that provides a measure of the mean of the squared displacement x of a molecule per unit time f. For diffusion in two dimensions such as a membrane, this is given by = 4Ht. The Saffman-Delbrtlck model of Brownian motion in biologic membranes describes the relationship between membrane viscosity, solvent viscosity, the radius R and height of the diffusing species, and D for both lateral and rotational diffusion of proteins in membranes (3, 4). This model predicts for example that for lateral diffusion, D should be relatively insensitive to the radius of the diffusing species, scaling with log (1/R). 

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