Stability thermodynamic condition

When the aldol reaction is carried Wt under thermodynamic conditions, the product selectivity is often not as high as under kinetic conditions. All the regioisomeric and stereoisomeric enolates may participate as nucleophiles. The adducts can return to reactants, and so the difference in stability of the stereoisomeric anti and syn products will determine the product composition. 

Under other reaction conditions, the product can result from thermodynamic control. Aldol reactions can be effected for many compounds using less than a stoichiometric amount of base. In these circumstances, the aldol reaction is reversible and the product ratio is determined by the relative stability of the various possible products. Thermodynamic conditions also permit equilibration among the enolates of the nucleophile. The conditions that lead to equilibration include higher reaction temperatures, protic or polar dissociating solvents, and the use of weakly coordinating cations. Thermodynamic conditions can be used to enrich the composition in the most stable of the isomeric products. 

The thermodynamic stabilities of phenonium ions have been determined based on bromide-transfer equilibria in the gas phase and, depending on the substituents, the bridged species (1) has been proposed as an intermediate or transition state on the potential-energy surface for the 1,2-aryl rearrangement of triarylvinyl cations (see Scheme 1). Phenonium ion (3) has been presented as an intermediate to account for the fact that lactonization of methyl 4-aryl-5-tosyloxy hexanoate (2) produces y-lactone (4) selectively under thermodynamic conditions, but affords 5-lactone (5) preferentially under kinetic conditions. It has been shown that anodic oxidation of frany-stilbene in alcohols in the presence of KF or BU4NBF4 is accompanied by its electro-oxidative rearrangement into diphenylacetaldehyde acetals. The mechanism outlined in Scheme 2 has been proposed" for the transformation. 

Note, however, that this thermodynamic condition alone is not sufficient to guarantee instability of the intermediates. One of the energy barriers may be so high that the faradaic potential region is shifted beyond the standard potential of the first electron transfer, i.e. the intermediate Y is stabilized kinetically. Similar reasoning applies to a non-linear mechanism. 

An extremum principle minimizes or maximizes a fundamental equation subject to certain constraints. For example, the principle of maximum entropy (dS)v = 0 and, (d2S)rj < 0, and the principle of minimum internal energy (dU)s = 0 and (d2U)s>0, are the fundamental principles of equilibrium, and can be associated with thermodynamic stability. The conditions of equilibrium can be established in terms of extensive parameters U and. S, or in terms of intensive parameters. Consider a composite system with two simple subsystems of A and B having a single species. Then the condition of equilibrium is... 

The Gibbs stability theory condition may be restrictive for nonequilibrium systems. For example, the differential form of Fourier s law together with the boundary conditions describe the evolution of heat conduction, and the stability theory at equilibrium refers to the asymptotic state reached after a sufficiently long time however, there exists no thermodynamic potential with a minimum at steady state. Therefore, a stability theory based on the entropy production is more general. 

Thermodynamic aspects of the stability of electroless plating solutions have been discussed by Vashkyalis [10]. Electroless plating solutions are thermodynamically unstable and subject to spontaneous decomposition, resulting in precipitation of metal throughout the solution. For the plating solution to be practically useful, the actual occurrence of spontaneous decomposition must be prevented. Thermodynamic conditions which must be met to prevent decomposition can be discussed on the basis of the Gibbs-Thomson equation, which relates the chemical potential of a substance to the curvature of its surface. It follows that the equilibrium potential of a metal particle... 

In the last chapter we established two powerful general theorems, those of Gibbs and Duhem, relating to heterogeneous systems. We shall now consider in more detail the quantitative behaviour of some simple systems, beginning with a study of the phase changes of a pure substance. A study of more complex heterogeneous systems will follow in later chapters after we have discussed the thermodynamic conditions of stability. 

Lipid domains and rafts in biological membranes are stabilized by several different interactions, including membrane-cytoskeleton, lipid-protein, and lipid-lipid interactions, and the organization can be both equilibrium and non-equilibrium in nature [27]. Lipid-domain formation caused by cooperative phenomena in the lipid bilayers is particularly important for the activation of SPLA2 [32-35]. The cooperative phenomena in lipid bilayers are caused by the fundamental interactions between the lipid molecules and are a consequence of the many-particle character of the supramolecular aggregate. The cooperativity leads to phase transitions and phase equilibria. The key cooperative event in many liposomal membranes is the so-called main phase transition, which takes the bilayer from a solid (gel) phase with conformationally ordered acyl chains to a fluid phase with conformationally disordered chains. The main transition in lipid bilayers is often accompanied by strong lateral density and compositional fluctuations. These fluctuations are manifested as dynamic lipid domains characterized by certain time and length scales that are determined by the thermodynamic conditions and the actual lipid species in question. 

When the aldol addition reaction is carried out under thermodynamic conditions, the difference in stability of the stereoisomeric anti and syn products determines the product composition. In the case of lithium enolates, the adducts can be equilibrated by keeping the reaction mixture at room temperature. This has been done, for example, for the product from the reaction of the enolate of ethyl r-butyl ketone and benzaldehyde. The greater stability of the anti isomer is attributed to the pseudoequatorial position of the methyl group in the chairlike product chelate. With larger substituent groups, the thermodynamic preference for the anti isomer is still greater. 

One problem with the Robinson annulation is the reversible nature of the initial Michael addition. One solution is to use a conjugated system that is particularly prone to Michael addition and forms the product, essentially irreversibly. a-Silyl vinyl ketones have been shown to be powerful Michael acceptors.The lithium enolate of cyclohexanone reacted with conjugated ketone 559 to produce the Michael product. 560.304b jn this case, the initially formed Michael adduct was stabilized by the presence of the silyl group at the a-position, driving the reaction toward the product. Hydrolysis produced 561, which was converted to the Robinson product (562) in 80% overall yield by treatment with NaOMe/MeOH under the requisite thermodynamic conditions.304b Pq,. this sequential process is justified when compared with normal treatment... 

Similar to most chemical systems of interest, the characterization of colloidal solutions requires the determination of the size, shape, structure, and stability of the particles present. This information is especially important for the understanding and utilization of organized assemblies of surfactants, in particular microemulsions, because the physical properties of the particles usually depend strongly on the thermodynamic conditions such as overall composition, temperature, and external force fields. This dependence is mainly due to the sensitivity to conditions of the monomer-aggregate equilibrium of the surfactant, which is responsible for the existence of the particles, and to the delicate balance of forces that maintain their integrity. For microemulsions, an additional complication arises from the compartmentalization of the systems, which is a source of possible phase transitions but is also a reason for most of their practical applications. 

Most studies have focused on ternary and quaternary systems (with an electrolyte as the fourth component or an alcohol as cosurfactant in the latter) of both ionic [6,37-41] and nonionic [28,42] surfactants. The shape of the transient birefringence signal and the number, amplitude, and rate of the relaxations typically depend on composition, temperature, and field strength. Since the thermodynamic conditions affect the aggregation number ( , size, and stability of the particles as well as the phase behavior of the system, the distance (Tc — T) from a critical temperature and the distance from a critical composition Cc also have a major influence. 

At variance with this new result, Bodak et al. (1978) reported the existence of ReSi at 800°C. It is, however, conceivable that ReSi is retained at low temperatures due to a slow decomposition reaction. In this case the phase equilibria involving ReSi at 800 °C as shown by Bodak et al. (1978) in fig. 60 merely represent metastable conditions (dashed lines in fig. 60). For the phase equilibria under stable thermodynamic conditions there will be two-phase equilibria in competition Re 3Si7-l-Y2Re3Sij and ReSi2 -I- YRe4Si2, whereby the latter, because of the higher thermodynamic stability of YRe4Si2, is supposed to be more likely. 

---