Thermodynamic retardation

Relationship.s 80 and 81 reflect the law of so-called thermodynamic retardation near the critical point (van Hove, 1954 de Gennes, 1979, 1980), where concentration fluctuations practically do not disappear and they may be regarded as long-living colloidal particles which was discussed above with other systems as examples. 

I aking into account the relation of to the thermodynamic potential expansion coefficients in the general field theory (Equation 2.5-13), one can derive a state equation for a polymer mixture (Equation 3.7-36) with a gradient term, which involves the correlation of concentration fluctuations of the components. Using this state equation, in particular, an analytical expression for the coil relaxation time was obtained, which shows that near the critical point the effect of thermodynamic retardation must occur. 

It is accepted that, at normal pressures, mtile is the thermodynamically stable form of titanium dioxide at all temperatures. Calorimetric studies have demonstrated that mtile is more stable than anatase and that brookite and Ti02 (ii) have intermediate stabiHties, although the relative stabiHties of brookite and Ti02(ii) have not yet been defined. The transformation of anatase to mtile is exothermic, eg, 12.6 KJ/mol (9), although lower figures have also been reported (63). The rate of transformation is critically dependent on the detailed environment and may be either promoted or retarded by the presence of other substances. For example, phosphoms inhibits the transformation of anatase to mtile (64). 

In the presence of oxygen and water the oxides of most metals are more thermodynamically stable than the elemental form of the metal. Therefore, with the exception of gold, the only metal which is thermodynamically stable in the presence of oxygen, there is always a thermodynamic driving force for corrosion of metals. Most metals, however, exhibit some tendency to passivate, ie, to form a protective oxide film on the surface which retards further corrosion. 

Foams are thermodynamically unstable. To understand how defoamers operate, the various mechanisms that enable foams to persist must first be examined. There are four main explanations for foam stabiUty (/) surface elasticity (2) viscous drainage retardation effects (J) reduced gas diffusion between bubbles and (4) other thin-film stabilization effects from the iateraction of the opposite surfaces of the films. 

Nitroalkanes show a related relationship between kinetic acidity and thermodynamic acidity. Additional alkyl substituents on nitromethane retard the rate of proton removal although the equilibrium is more favorable for the more highly substituted derivatives. The alkyl groups have a strong stabilizing effect on the nitronate ion, but unfavorable steric effects are dominant at the transition state for proton removal. As a result, kinetic and thermodynamic acidity show opposite responses to alkyl substitution. 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

In the reaction with butanone, an equilibrium between the CH3-activated complex and the CH2-activated complex is observed and it is revealed that the former is a thermodynamic product and the latter is a kinetic product. These results indicate that the relative reactivity of the C-H bonds is in the order of 2>1>3, and the large and electron-withdrawing substituents retard the reaction. A plausible mechanism is shown in Scheme 63. When the oxy-... 

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

The final class of polymers containing carboranyl units to be mentioned here is the polyphosphazenes. These polymers comprise a backbone of alternating phosphorous and nitrogen atoms with a high degree of torsional mobility that accounts for their low glass-transition temperatures (-60°C to -80°C). The introduction of phenyl-carboranyl units into a polyphosphazene polymer results in a substantial improvement in their overall thermal stability. This is believed to be due to the steric hindrance offered by the phenyl-carborane functionality that inhibits coil formation, thereby retarding the preferred thermodynamic pathway of cyclic compound formation (see scheme 12). 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

This explanation advanced by Iredale cannot be considered as adequate or even thermodynamically possible. The change in density of the mercury vapour at the surface of the drop due to retardation of diffusion by the gas admitted, as well as alteration of the orientation of the surface layers may prove important factors. 

The reliable long-term safety assessment of a nuclear waste repository requires the quantification of all processes that may affect the isolation of the nuclear waste from the biosphere. The colloid-mediated radionuclide migration is discussed as a possible pathway for radionuclide release. As soon as groundwater has access to the nuclear waste, a complicated interactive network of physical and chemical reactions is initiated, and may lead to (1) radionuclide mobilization (2) radionuclide retardation by surface sorption and co-precipitation reactions and (3) radionuclide immobilization by mineralization reactions, that is, the inclusion of radionuclides into thermodynamically or kinetically stabilized solid host matrices. 

The origin of the deep localized states in the mobility gap that control the dark decay has been attributed to structural native thermodynamic defects [12]. Thermal cycling experiments show that the response of the depletion time to temperature steps is retarded, as would be expected when the structure relaxes toward its metastable liquid-like equilibrium state. As the structure relaxes toward the equilibrium state, t(j decreases further until the structure has reached equilibrium. The only possible inference is that must be controlled by structure-related thermodynamic defects. The generation of such defects is, therefore, thermally activated. We should note that because the depletion discharge mechanism involves the thermal emission of carriers... 

In addition to the above effects, the intermolecular interaction may affect polymer dynamics through the thermodynamic force. This force makes chains align parallel with each other, and retards the chain rotational diffusion. This slowing down in the isotropic solution is referred to as the pretransition effect. The thermodynamic force also governs the unique rheological behavior of liquid-crystalline solutions as will be explained in Sect. 9. For rodlike polymer solutions, Doi [100] treated the thermodynamic force effects by adding a self-consistent mean field or a molecular field Vscf (a) to the external field potential h in Eq. (40b). Using the second virial approximation (cf. Sect. 2), he formulated Vscf(a), as follows [4] ... 

Couples with E values outside the practical limits of stability do not necessarily cause the destruction of the solvent. Some reactions, although they may be thermodynamically feasible, are kinetically very slow. The Co3J"/Co2+ couple has an E value of + 1.92 V, and Co3+ should not exist in aqueous solution. However, its oxidation of water to oxygen is very slow, and solutions containing [Co(H20)6]3+ evolve dioxygen slowly. The value for the A13 + /A1 couple is -1.66 V, and indicates that aluminium should dissolve in acidic aqueous solutions. A stable protective oxide layer on the metal s surface normally retards the reaction, a circumstance gratefully acknowledged by aeroplane manufacturers. 

Effect of Propylene Pressure on Selectivity - The partial pressure of propylene is also one of key factors for selective formation of 4,4 -DIPB.22"25 The high partial pressure of propylene effectively enhanced the isopropylation, but the selectivity for 4,4 -DIPB decreased at lower partial pressures over HM(220), as shown in Figure 6.24-25 However, the isomerization of 4-IPBP did not occur at any propylene pressures. Because 3,4 -DIPB is a more thermodynamically stable isomer than 4,4 -DIPB,43 this decrease of the selectivity was ascribed to the isomerization of 4,4 -DIPB to 3,4 -DIPB, not to the lower selectivity to 4,4 -DIPB. Figure 7 shows the effect of propylene pressure on the selectivities for 4,4 -DIPB in bulk and encapsulated products. The selectivity of 4,4 -DIPB inside the pores was almost constant at every pressure. These results indicate that the isomerization does not occur inside the pores but at the external acid sites. The effect of the pressure on the isomerization of 4,4 -DIPB was similar to that on the isopropylation of biphenyl. 4,4 -DIPB itself isomerizes significantly to 3,3 - and 3,4 -DIPB over the catalyst in the absence of propylene. However, no significant isomerization of 4,4 -DIPB occurred in the presence of sufficient propylene pressure. On the other hand, the selectivity of 4,4 -DIPB in encapsulated DIPB isomers was almost constant at any pressure. These differences support the hypothesis that the isomerization of 4,4 -DIPB to 3,4 -DIPB occurs on the external surfaces. The isomerization of 4,4 -DIPB under high pressures is considered to be retarded by the preferential adsorption of propylene on acid... 

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