Ostwald stage rule

Keywords Cryotropic gelation Poly (vinyl alcohol) hydrogels Time-resolving small angle neutron scattering Ostwald stage-rule Confined polymer crystallization... 

The formation of a gel and the concept of a gel as a metastable state of matter fits quite well with the Ostwald stage rule [33]. This mle was formulated at the end of the nineteenth century and states that a phase transformation from one stable state to another proceeds via metastable states, whenever such states exist, in stages of increasing stability. Although this rule does not explain why phase transitions evolve in this way, it is considered an intrinsic property of matter. 

Compound Physical Form Ostwald s Rule of Stages... 

The Ostwald Step Rule, or the rule of stages postulates that the precipitate with the highest solubility, i.e., the least stable solid phase will form first in a consecutive precipitation reaction. This rule is very well documented mineral formation via precursors and intermediates can be explained by the kinetics of the nucleation process. The precipitation sequence results because the nucleation of a more soluble... 

Metastable crystalline phases frequently crystallise to a more stable phase in accordance with Ostwald s rule of stages, and the more common types of phase transformation that occur in crystallising and precipitating systems include those between polymorphs and solvates. Transformations can occur in the solid state, particularly at temperatures near the melting point of the crystalline solid, and because of the intervention of a solvent. A stable phase has a lower solubility than a metastable phase, as indicated by the solubility curves in Figures 15.7a and 15.7/ for enantiotropic and monotropic systems respectively and,... 

In 1897, Friedrich Wilhelm Ostwald (1853-1932) published his now famous study of crystallization processes, which led to the Ostwald rule of stages or Ostwald step rule (Ostwald, 1897). Ostwald noticed that the course of transformation of unstable (or metastable) states into stable states normally occurs in stages,... 

These reactions will proceed without heating under nitrogen, where the driving force is the more favorable iron oxide precipitate. Following Ostwald s rule of stages, the hydroxide would be the kinetic product and the oxide would be the thermodynamic product. 

Ojala etal. (1998) reported on the crystallization of two conformational polymorphs (Bernstein 1987) (see Chapter 5) of acetone tosyUiydrazone 3-XX. A triclinic form and a monoclinic form are both obtained from anhydrous ethanol—sometimes together. If the crystallizing solution is allowed to evaporate completely, only the monoclinic form is obtained, suggesting that it is the thermodynamically preferred form at room temperature. This is consistent with Ostwald s Rule of Stages and McCrone s (1965) test for relative stability of polymorphs according to which the more stable polymorph... 

S-transferase from rat liver (Fig. 3.4). Day and McPherson (1991) reported crystallization of two crystalline forms in stages in accord with Ostwald s Rule for cytochrome c from Valida membran-aefaciens (Fig. 3.5). In every case of crystallization they obtained arrays of thin triclinic plates (Fig. 3.5a), some of which grew up to 0.5 mm in the largest physical dimension (Fig. 3.5b). In some cases, some of these dissolved (in accord with Ostwald s Rule of Stages (Section 2.3)) to give rectangular prisms (Fig. 3.5c), which turned out to be orthorhombic. 

The Ostwald step rule, or the mle of stages, postulates that the precipitate with the highest solubility (i.e., the least stable solid phase) will form first in a consecutive precipitation reaction. This mle is very well documented mineral formation via precursors and intermediates can be explained by the kinetics of the nucleation process. The precipitation sequence results because the nucleation of a more soluble phase is kinetically favored over that of a less soluble phase because the more soluble phase has the lower solid-solution interfacial tension (7cw) than the less soluble phase (equation 50). In other words, a supersaturated solution will nucleate first the least stable phase (often an amorphous solid phase) because its nucleation rate is larger than that of the more stable phase (Figure 13.26). While the Ostwald step mle can be explained on the basis of nucleation kinetics, there is no thermodynamic contradiction in the initial formation of a finely divided precursor. 

This is supported by the empirical Ostwald s rule of stages, which states that the most stable state does not necessarily form when an unstable solution crystallises." ... 

Reactive crystallization operations are subject to oiling out and/or agglomeration because of the inherently high local supersaturations encountered. As indicated in Section 10.3, the formation of a crystal may be preceded by oiling out as the first physical form that may or may not be observed (see also Chapter 5, Section 5.4). This oil may separate as a second phase because of the normally extremely low solubilities of the reaction products that result from the chemical reaction. This low solubility can cause a second liquid phase to form on a time scale that is shorter than the nucleation induction time. These issues are considered in Ostwald s Rule of Stages. 

A major consideration for a polymorph screen needs to be addressed at this stage. A polymorph screen, no matter how extensive, cannot guarantee that a new polymorphic form will not appear in the future. Stories of appearing and disappearing polymorphs are plentiful (48). Such occurrences are likely related to seeding. The first step in crystallization is formation of a seed, which involves collection of disordered molecules into an ordered array. Seed formation is the rate-determining step in a crystallization process. Now consider Ostwald s rule, which states that in passing from a less stable state (disordered) to a more stable... 

Following Ostwald s rule of stages the metastable diamond... 

Atmospheric dust frequently contains particles of the crystalline product itself, especially in industrial plants or in laboratories where quantities of the material have been handled. Fortuitous seeding from this source can serve to prevent the crystallization of thermodynamic unstable phases, e.g., hydrates or polymorphs, that might otherwise appear (Ostwald s rule of stages, section 5.7). 

It is not uncommon in crystallization processes for the first crystalline phase to make its appearance to be metastable, e.g. a polymorph or hydrate (Ostwald s rule of stages - section 5.7). Some metastable phases rapidly transform to a more stable phase while others can exhibit apparent stability for an exceptionally long time. Some transformations are reversible (enantiotropic) while others are irreversible (monotropic), as explained in sections 1.8 and 4.2.1. In some cases, the metastable phase may have more desirable properties than the stable phase, e.g., a metastable pharmaceutical product may be more pharmacologically active than the stable form. If the required metastable form is first to crystallize, it is important to isolate and dry it quickly to prevent it transforming to the stable form. Once in the dry condition a metastable form can often remain unchanged indefinitely. If the stable polymorph is required, it is essential to create conditions and allow sufficient time in the crystallizer for total transformation to the more stable phase to be ensured. 

Another frequent occurrence is the first-precipitation of a metastable phase (Ostwald s rule of stages section 5.7) followed by a phase transformation to the final product. The metastable phase may be an amorphous precipitate, a polymorph of the final material, a hydrated species or some system-contaminated substance. 

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