Viscosity correlations, reaction

This power will be uniquely determined by viscosity, and the reaction can be stopped at a given degree of polymerization (viscosity), once the desired power-draw/viscosity correlation is known. 

Theoretical treatment of this polymerization is difficult because of the presence of both primary and secondary amine reactions as well as tertiary amine catalyzed epoxy homopolymerization. To obtain kinetic and viscosity correlations, empirical methods were utilized. Various techniques that fully or partially characterize such a system by experimental means are described in the literature ( - ). These methods Include measuring cure by differential scanning calorimetry, infra-red spectrometry, vlsco-metry, and by monitoring electrical properties. The presence of multiple reaction mechanisms with different activation energies and reaction orders (10) makes accurate characterizations difficult, but such complexities should be quantified. A dual Arrhenius expression was adopted here for that purpose. 

Figure 10.15 A correlation between viscosity of reaction medium rig and fractal dimension of microgels D for system 2DPP + HCE/DDM.

This experimental observation can also be correlated with the pressure dependency of the viscosity. The reaction medium tends to be more viscous at higher reaction pressures, thus slowing the rate of termination ie, the activation volume of the termination rate coefficient is very close to the corresponding activation volume that characterizes the pressure dependence of the inverse of the monomer viscosity (356). It is important to note that the pressure dependencies of the termination and propagation rate coefficients display opposite behavior, ie allowing for increased rates of polymerization at elevated pressures. 

SSP mns were conducted at 160 and 200 ° C imder nitrogen flow, resulting in process acceleration when the phosphonates were present, especially at the high SSP temperature. Indicatively, the solution relative viscosity of the products increased by up to 288% (200 °C, 4h, 0.5% Irgamod 195), while the relevant value for pure PA 66 was 144%. The SSP kinetics was estimated using a linear correlation of relative viscosity vs. reaction time and the calculated rate constants are shown in Figure 12. 

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). 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

Figure 19 shows the rate-constant curves for the reaction of [Co(IIIXen)2LCl]2+ (L = PVMI or N-ethylimidazole(NEI)) with Fe-edta2- in H20-alcohol mixed solvents. An increase in the alcohol content brings about the enhancement of the reactivity of the Co(III) complex however, maxima and minima appeared in the reaction between PVMI-Co(ni) and Fe-edta2-. The viscosity behavior of the PVMI-Co(III) complex solution is also shown as a function of ethanol concentration in Fig. 19. There is good correlation between the reactivity curve and the viscosity curve, with the maximum (minimum) point of the reactivity precisely coincident with the minimum (maximum) point of the viscosity. The decrease in viscosity reflects a contraction in the PVMI chain caused by the suppression of charge dissociation of the Co(III) complexes or of electrostatic repulsion due to the nonpolar ethanol solvent. At intermediate ethanol concentration (5—7 mol%) the hydro-...

The two methods described herein are inherently different in that one is a traditional initial velocity assay that attempts to quantitatively measure rates of product formation (see Basic Protocol 1), whereas the other correlates the activity of an enzyme preparation with its ability to change the rheological properties (i.e., viscosity) of a substrate solution (see Basic Protocol 2). For both assays, it is presumed that the analyst is using soluble substrate and enzyme preparations, appropriate buffer systems, and a method to control the reaction mixture temperature. The ultimate goal of both assays is the same to obtain a quantitative estimate of the PGase activity of a test solution. 

Figure 7.10 Typical (steady-state) viscosity rise curve for the free-radical copolymerization of mono- and multiunsaturated monomers, correlated with the steps of the reaction mechanism.

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

Knowing the viscosity and density of the reaction mixture, the flow channel diameter, void fraction of the bed, and the superficial fluid velocity, it is possible to determine the Reynolds number, estimate the intensity of dispersion from the appropriate correlation, and use the resulting value to determine the effective dispersion coefficient Del or I). Figures 8-32 and 8-33 illustrate the correlations for flow of fluids in empty tubes and through pipes in the laminar flow region, respectively. The dimensionless group De l/udt = De l/2uR depends on the Reynolds number (NRe) and on the molecular diffusivity as measured by the Schmidt number (NSc). For laminar flow region, DeJ is expressed by ... 

Measurements of dielectric properties have been used to monitor chemical reactions in organic materials for more than fifty years. In 1934, Kienle and Race 11 reported the use of dielectric measurements to study polyesterification reactions. Remarkably, many of the major issues that are the subject of this review were identified in that early paper the fact that ionic conductivity often dominates the observed dielectric properties the equivalence between the conductivity measured with both DC and AC methods the correlation between viscosity and conductivity early in cure the fact that conductivity does not show an abrupt change at gelation the possible contribution of orientable dipoles and sample heterogeneities to measured dielectric properties and the importance of electrode polarization at low frequencies. 

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