Relative Stabilities of the Various Forms

Relative Stabilities of the Various Forms 1. The Pyranose Form 

Further attempts have been made to explain and predict the proportions of the pyranose forms in solution. It is not difficult to calculate, by various methods, the relative free energies in vacuum or in inert solvents it is not, however, easy to take the effect of solvation into account. Clearly, solvation has a substantial effect on the composition, and the variation of the dielectric permittivity between different solvents does not fully account for this effect. 

AM 1 semi-empirical molecular-orbital calculations have been carried out on several sugars in order to establish energy minima and favored conformations.22 However, Tvaroska and Carter23 showed that this method does not provide the correct energy differences between anomers. The difficulty lies in the comparatively small energy differences (—1-2 kJ/mol) between anomers much-more refined calculations are necessary for this to emerge 

An ingenious examination of the hydrophilicity of the eight aldohex-oses (that is, their hydrophilic volume in water) allowed a rationalization of their a / pyranose ratios in aqueous solution.28 

Another example of the observation that the side chain attached to the anomeric carbon atom in ketoses affects the proportion of one furanose form [p. 29] is afforded by the series 1-deoxy-D-fructose JV-substituted 1-amino- 

Before discussing the composition of solutions of individual sugars, it will be instructive to look at the relative stabilities of the various forms of the sugars. These considerations will give a general overview, and also provide explanations for some of the results. 

Pyranoses are the most stable forms of most sugars in aqueous solution,50 The difference between the free energies of pyranoses and fura-noses is quite substantial when neither of them has serious steric interactions, it is about 8 kj/mol. This is to be expected, as six-membered, saturated rings are more stable than five- (or seven-) membered ones and the substituents of a six-membered ring are all fully staggered, whereas this is not possible in other ring systems. 

It appears that the conditions favoring the stability of the pyranose form are precisely those under which the equilibrium is usually observed aqueous solutions, ambient temperature, free hydroxyl groups. 

The calculated, relative free-energies of the aldo-hexo- and -pento-py-ranoses are shown in Table I these values are relative to an imaginary aldopyranose in which there are no conformational interactions. From these values, the a / ratio can be calculated despite the simplicity and 

Calculated Conformational Free Energies and the Proportion of the a Anomer in Aqueous Equilibrium Solution of Aldopyranoses 

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Enamines derived from 1-azabicycloalkanes, readily accessible by mercuric acetate oxidation of saturated bases (112), have been extensively studied recently (113-115). Since an immonium salt is formed during dehydrogenation, the composition of the liberated enamine mixture shows the relative stability of the various possible isomers. The study of infrared and NMR spectra has shown that the position of the enamine double bond is determined by factors similar to those determining the relative stability of simple olefins. 

The nature of the substituent group X plays an important role in determining the relative stability of the various tautomeric forms. In aliphatic systems the tendency of C—XH to become CH— C 1=X increases markedly in the order X = CHz < NH < O, and certainly hydroxy compounds show less inclination to exist as such than do amino compounds. The position of S in this series is not completely... 

The success of the multifunctional initiators in the preparation of block and graft copolymers depends critically on the kinetics and mechanism of radical production. In particular, the initiator efficiency, the susceptibility to and mechanism of transfer to initiator, and the relative stability of the various radical generating functions. Each of these factors has a substantial influence on the nature and homogeneity of the polymer formed. Features of the kinetics of polymerizations initiated by multifunctional initiators have been modeled by O Driscoll and Bevington 64 and Choi and Lei.265... 

The hydroxide so formed will react with the metal ion to form the metal hydroxide, hydrated oxide, or oxide, depending on the relative stability of the various oxides and hydroxides. (The resulting hydroxides or oxy hydroxides can be heated in air or oxygen to form the oxides.) In addition, insoluble carbonates may also form. The competition between hydroxide and carbonate will depend on their solubility products. Carbonates tend to be more solnble than hydroxides of the same metal ion. On the other hand, the valne of K for equilibrium (3.32) (1.8 X 10 " ) means that the concentration of hydroxide will be ca. four orders of magnitude less than that of carbonate (assnming no other pH-determining species is present). 

This paper draws on the substantial literature concerning the metal sulfides (2,3), particularly that which concerns the relative stabilities of the various iron-sulfur and iron-oxygen forms. The intention is to build a framework within which to organize the current stock of observations concerning liquefaction residues from coal liquefaction experiments at the Pittsburgh Energy Technology Center. The presentation will display the experimental results, provide a framework for their interpretation and deal with the... 

A very important area of research in complex chemistry today is the correlation of data on the relative stabilities of the various complexes with their structure. The experimental methods used in such studies are described in elementary textbooks on physical chemistry and need not be discussed here. When more than one complex is formed between two reagents, mathematical treatment of the data may become complicated, but very often it is still possible to evaluate dissociation constants for all complexes that are detected. A summary of the conclusions, especially as applied to chelates, offers some points of interest. 

One generally finds, therefore, that absolute values for thermodynamic parameters are less important than are relationships that predict the relative stability of the various phases of a polymorphic system. Although it is possible to calculate such energy differences from considerations of the lattice energies of the different structures,most workers instead employ the time-honored empirical rules that have been developed over time. For instance, since Gmetastabie > G tabie, then the vapor pressure of the stable form must be less than the vapor pressure of the metastable form. 

Many factors must be considered to explain these facts, not least the relative stabilities of the various possible excimers or exciplexes and the accessibility of the pericyclic funnels. (Cf. Scheme 3 in Section 6.2.3.) In addition, the geometrical structure at the funnel and the ground-state relaxation pathways originating in the decay region determine which products will be formed. 

From thermodynamic principles, under specified conditions only one polymorph is the stable form (except at a transition point) [5], In practice, however, due to kinetic considerations, metastable forms can exist or coexist in the presence of more stable forms. Such is the case for diamond, which is metastable with regard to graphite, the thermodynamically stable form of carbon under ambient conditions. In practice, the relative stability of the various crystal forms and the possibility of interconversion between crystal forms, between crystals with a different degree of solvation and between an amorphous phase and a crystalline phase, can have very serious consequences on the life and effectiveness of a polymorphic product and the persistence over time of the desired properties (therapeutic effectiveness in the case of a drug, chromatic properties in the case of pigment, etc). 

The exploration of the crystal form space (polymorph screening) of a substance is the search of the polymorphs and solvates with a twofold purpose (i) identification of the relative thermodynamic stability of the various forms including the existence of enantiotropic crystalline forms (that interconvert as a function of the temperature) or of monotropic forms (that do not interconvert) and of amorphous and solvate forms and (ii) physical characterization of the crystal forms with as many analytical techniques as possible. The relationships between the various phases and commonly used industrial and research laboratory processes are illustrated schematically in Fig. 3.3.3. 

Since different crystal forms have different structures, they can, potentially, exhibit different physical properties and different responses to experimental analytical methods. Some of the more commonly used of these methods have been demonstrated above. A central question for any polymorphic system is the relative stability of the various crystal forms. As noted above, these may be investigated qualitatively by HSM methods, and more quantitatively using thermal analytical techniques. The combined results of these measurements are conveniently summarized on a semi-empirical energy-temperature diagram [31], as shown in Fig. 3.3.16. The thermal... 

Under the mild conditions of the reaction, there is no equilibration of the alkenes, so the product composition is governed by the relative stabilities of the various transition states. Usually, more of the trans olefin than of its cis isomer is formed, presumably because steric repulsion raises the energy of the transition state leading to cis olefin. The selectivity is not high, however, since the ratio of trans cis from some simple cases is in the range 3 1 to 2 1. In cyclic systems, conformational... 

The nature of the substituent group X plays an important role in determining the relative stability of the various tautomeric forms. In aliphatic systems the tendency of — XH to become CH—C=X... 

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