Stability ratio theoretical

Discuss the agreements and disagreements between the theoretical predictions for the stability ratio with what is observed experimentally. 

A theoretical expression relating the stability ratio to the potential energy of interaction has been derived by Fuchs110 ... 

Theoretical relationships between the stability ratio and electrolyte concentration can be obtained by numerical solution of this integral for given values of A and if/a- Figure 8.7 shows the results of... 

Figure 8,7 Theoretical dependence of stability ratio on electrolyte concentration calculated from equation (8.2) for a = 1CT8 m, A = 2 x 10 19 J and fa = 76.8 mV = 3kT/e> At high electrolyte concentrations W < 1 owing to coagulation being accelerated by van der Waals attractive forces (reduced flow rate in the narrow inter-particle gap has not been allowed for) (By courtesy of Elsevier Publishing Company)...

Fig. 8 Comparison of theoretical and experimental stability ratios for TiO (0.05g/L) and AI2O3 (0.15 g/L) colloids in 10 M KNO3.

Fig. VIII-18. Effect of the surface charge segregation on the stability of polystyrene latex. Experimentally measured (symbols and dashed line) and theoretically computed (solid lines) stability ratios as a function of ionic strength. Different degrees of surface charge segregation were assumed in the evaluation of theoretical stability ratio a - 0 (totally smoothed out surface charges) b - 10% c - 20% d - 30% e - 40%. (From ref. [71] with pennission)...

First, the observed dependence of stability ratio on salt concentration tends to be much weaker than predicted. Second, the variation of the stability ratio with particle size is not reproduced experimentally. Recently, however, it was reported that for model particles with a low surface charge, where the DLVO theory is expected to hold, the aggregation kinetics do agree with the theoretical predictions (see [60], and references therein). 

These results also suggest that there is a close parallelism between the stability ratio and the potential, especially near the critical stability region. Indeed, a semiquantitative correlation between the stability ratio and the potential can be made using the DLVO theory. Reerink and Overbeek [36] provided the following theoretical justification based on the normal distribution approximation for the shape of potential energy curve ... 

Figure 25 Experimenlal and theoretical (DLVO and extended DLVO approaches) stability ratios of A

D.N.L. McGown, G.D. Parfitt, Improved theoretical calculation of the stability ratio for colloidal systems. J. Phys. Chem. 71(2), 449 50 (1967). doi 10.1021/jl00861a041... 

A wide range of nitroxidcs and derived alkoxyamincs has now been explored for application in NMP. Experimental work and theoretical studies have been carried out to establish structure-property correlations and provide further understanding of the kinetics and mechanism. Important parameters are the value of the activation-deactivation equilibrium constant K and the values of kaa and (Scheme 9.17), the combination disproportionation ratio for the reaction of the nilroxide with Ihe propagating radical (Section 9.3.6.3) and the intrinsic stability of the nitroxide and the alkoxyamine under the polymerization conditions (Section 9.3.6.4). The values of K, k3Cl and ktieact are influenced by several factors.11-1 "7-"9 ... 

A PEIT of 50/50 (molar ratio) composition is synthesized by a two-step reaction sequence as follows. In the first step, 97.10 g (0.5 mol) dimethyl terephthalate (DMT), 97.10 g (0.5 mol) dimethyl isophthalate (DMI), 136.55 g (2.2 mol) 1,2-ethanediol, and zinc acetate dihydrate ester interchange catalyst (2.7 x 10 4% mass of the total amount of DMI and DMT mixture) are weighed into a threenecked flask fitted with a mechanical stirrer, a nitrogen inlet, and a condenser. The medium is stirred for 2.0-2.5 h at 180-210°C under nitrogen. Ninety-two percent of the theoretical amount of methanol is removed by distillation. In the second step, antimony acetate polycondensation catalyst and trimethyl phosphate thermal stabilizer (9.9 x 10-4 and 1.5 x 10 3% mass of the total amount of DMI... 

Ruzic [278 ] considered the theoretical aspects of the direct titration of copper in seawaters and the information this technique provides regarding copper speciation. The method is based on a graph of the ratio between the free and bound metal concentration versus the free metal concentration. The application of this method, which is based on a 1 1 complex formation model, is discussed with respect to trace metal speciation in natural waters. Procedures for interpretation of experimental results are proposed for those cases in which two types of complexes with different conditional stability constants are formed, or om which the metal is adsorbed on colloidal particles. The advantages of the method in comparison with earlier methods are presented theoretically and illustrated with some experiments on copper (II) in seawater. The limitations of the method are also discussed. 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and /Cred of a complex in different oxidation states with experimentally measurable redox potentials EH and EHa. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if Kted is known or vice versa. 

Early theoretical treatments of bluff-body stabilized flame spreading have been based, in general, on the assumption that the flame is a discontinuous surface separating gas streams of different densities and temperatures [1, 15-17]. These theories neglect the finite thickness of turbulent flame zone and predict the increase of the spreading rate both with the density ratio across the flame, and with the increase in the laminar flame velocity of fuel-air mixture. This does not correspond to experimental observations (e.g., [8, 10]). 

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