Ostwald's Rule Of Stages Research Articles

Ostwald Rule of Stages─Myth or Reality?

In 1897, following a number of crystallization studies, Ostwald suggested that if a system has a number of metastable states open to it then it proceeds sequentially by means of the nearest thermodynamic state and so on. This conjecture, which is known as Ostwald’s Rule of Stages (ORS), has gained traction with many researchers in many different fields. However, there has been no general proof of its validity. In this paper the specific case of batch solution crystallization of a polymorphic compound using classical nucleation and growth theory is examined in some detail and the ORS conjecture is found wanting. Classical nucleation theory presents not a sequential process, as in ORS, but a parallel process of multiphase nucleation and growth development of all metastable phases. What is observed is not the appearance of metastable phases sequentially but the disappearance of phases sequentially in the order of their metastability. If the crystallization kinetics of the metastable phases are suitably differentiated and advantageous the system might appear to be sequential under suitable conditions. This analysis does not exclude ORS from being applicable in other transformation cases. For instance, it is possible that systems where the subsequent phase changes are governed by solid-state transformations then the sequential model proposed by Ostwald might be appropriate but whether this covers all available metastable states is an open question.

Preference of High-Nitrogen-Content Compounds to Form Hydrates and the Tandem Contacts of Azide Groups

Under ambient conditions, the high-nitrogen-content compound, 6-azido-7-methyl[1,2,4]triazolo[4,3-b]pyridazine (C6H5N7), favorably crystallizes in the form of two concomitant monohydrate polymorphs: α-C6H5N7·H2O and β-C6H5N7·H2O; also anhydrate C6H7N7 is obtained from the acetone solution. High-pressure isochoric recrystallizations lead to new forms of these compounds. The α-hydrate can be reversibly isothermally compressed to 0.6 GPa at the least and the β-hydrate can be compressed to and from 1 GPa. However, the isochoric recrystallizations above 0.3 GPa favor the α-hydrate. This hydrate occurs as metastable phase, in accordance with the Ostwald rule of stages. Compound C7H7N7 could be recrystallized only from aqueous solution in the form of sesquihydrate C7H7N7·1.5H2O. The molecular packing in all hydrates is governed by hydrogen bonds OH···N and tandem contacts between azide groups.

Towards Predicting the Sequential Appearance of Zeolitic Imidazolate Frameworks Synthesized by Mechanochemistry.

We use computational materials methods to study the sequential appearance of zinc-based zeolitic imidazolate frameworks (ZIFs) generated in the mechanochemical conversion process. We consider nine ZIF topologies, namely RHO, ANA, QTZ, SOD, KAT, DIA, NEB, CAG and GIS, combined with the two ligands 2-methylimidazolate and 2-ethylimidazolate. Of the 18 combinations obtained, only six (three for each ligand) were actually observed during the mechanosynthesis process. Energy and porosity calculations based on density functional theory, in combination with the Ostwald rule of stages, were found to be insufficient to distinguish the experimentally observed ZIFs. We then show, using classical molecular dynamics, that only ZIFs withstanding quasi-hydrostatic pressure P ≥ 0.3 GPa without being destroyed were observed in the laboratory. This finding, along with the requirement that successive ZIFs be generated with decreasing porosity and/or energy, provides heuristic rules for predicting the sequences of mechanically generated ZIFs for the two ligands considered.

Exploring the role of crystal habit in the Ostwald rule of stages.

The crystallization of calcium carbonate is shown to be dictated by the Ostwald rule of stages (ORS), for high relative initial supersaturations (), under sweet (carbon dioxide saturated) and anoxic (oxygen depleted) solution conditions. Rhombohedral calcite crystals emerge after the sequential crystallization and dissolution of the metastable polymorphs: vaterite (snowflake-shaped) and aragonite (needle-shaped). However, the presence of certain cations, which can form trigonal carbonates (e.g. Fe2+ and Ni2+), in concentrations as low as 1.5 mM, triggers the emergence of calcite crystals, with a star-shaped crystal habit, first. These star-shaped crystals dissolve to yield needle-shaped aragonite crystals, which in turn dissolve to give the rhombohedral calcite crystals. The star-shaped crystals, formed at high SCaCO3, possess higher surface free energy (therefore higher apparent solubility) than their rhombohedral counterparts. This sequence of dissolution and recrystallization demonstrates that the ORS does not only drive the crystal towards its thermodynamically most stable polymorph but also towards its most stable crystal habit.

Synchrotron and Raman Study of the Rotator Phases and Polymorphism in Tricosane Paraffin.

A detailed study of the phase behavior of n-paraffin C23H48 has been performed by means of real-time variable-temperature experiments with synchrotron radiation. Two detectors were employed for simultaneous analysis of the small-angle (SAXS) and wide-angle X-ray-scattering (WAXS) regions. This paraffin presents a very interesting phase behavior, involving two crystal polymorphs, three rotator phases and the liquid state. The Ostwald rule of stages is invoked to find similarities of the rotator phases with the eventual transient mesomorphic structure in the multistage model of polymer crystallization. That study is complemented by variable-temperature Raman experiments covering frequencies down to 150 cm−1. It was found that the low-frequency region is the most informative regarding the phase transitions, and specifically the intensity of the first overtone. From these analyses, several parameters are evaluated as function of temperature.

Multiscale Experimental Study and Modeling of l-Glutamic acid Crystallization: Emphasis on a Kinetic Explanation of the Ostwald Rule of Stages

This work presents an experimental and a numerical study to highlight a kinetic explanation to of the Ostwald rule of stages (ORS). To demonstrate this explanation, L-glutamic acid (LGlu) (a monotropic system with two polymorphs) were crystallized in three different scales: Liter scale in a 2L stirred crystallizer, milliliter scale in a 4ml stagnant cell and microliter scale in microfluidic channels. Cooling crystallization experiments were performed in water at different temperature and supersaturation conditions. The LGlu polymorphic system was found to follow the ORS at low temperature (between 5°C and 30°C). However, in similar operating conditions, the stable polymorph crystallized preferentially or exclusively in the stagnant cell and in microfluidics. To explain the ORS in the stirred crystallizer at low temperature, a model based on the kinetic equation was used. By taking into account the Gibbs Thomson effect (Solubility variation with size), the simulations in the nanoscopic scale showed the dissolution of the slow-growing stable phase nuclei in favor of the fast-growing metastable phase nuclei. Consequently, the numerical results showed that the Gibbs Thomson effect is a key factor in polymorph competition and that considering this effect, in certain kinetic and equilibrium conditions, could allow explaining and simulating the ORS.

Fabrication of composite particles by liquid–liquid interfacial crystallization using an ultrasonic spray nozzle

The purpose of this study was to produce composite particles, consisting of core starch particles coated with glycine, by liquid–liquid interfacial crystallization with an ultrasonic spray nozzle and to investigate the effect of operating conditions on glycine particle morphology. We confirmed that ultrasonic irradiation could improve the coating efficiency of the core starch particles during the crystallization process. We also investigated the transformation between different polymorphs of glycine crystals that covered the starch surface. The coating efficiency of the fine glycine crystals on the starch particles was improved by using an ultrasonic spray nozzle rather than anti-solvent crystallization without an ultrasonic spray nozzle. The glycine crystals on the surface of starch particles transformed from unstable to stable forms according to the solution-mediated mechanism and Ostwald rule of stages. The interaction between the core particles and guest particles was found to be a key factor in producing the composite particles. The results indicate that this crystallization process using the ultrasonic spray nozzle is promising for efficiently producing composite particles.

Alternating metastable/stable pattern in the mercuric iodide crystal formation outside the Ostwald Rule of Stages.

We report a reaction-diffusion system in which two initially separated electrolytes, mercuric chloride (outer) and potassium iodide (inner), interact in a solid hydrogel media to produce a propagating front of mercuric iodide precipitate. The precipitation process is accompanied by a polymorphic transformation of the kinetically favored (unstable) orange, (metastable) yellow, and (thermodynamically stable) red polymorphs of HgI2. The sequence of crystal transformation is confirmed to agree with the Ostwald Rule of Stages. However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A theoretical model based on reaction diffusion coupled to a special nucleation and growth mechanism is proposed. Its numerical solution is shown to reproduce the experimental results.

Controlling Crystal Polymorphism in Organic-Free Synthesis of Na-Zeolites

Controlling polymorphism is critical in areas such as pharmaceuticals, biomineralization, and catalysis. Notably, the formation of unwanted polymorphs is a ubiquitous problem in zeolite synthesis. In this study, we propose a new platform for controlling polymorphism in organic-free Na-zeolite synthesis that enables crystal composition and properties to be tailored without sacrificing crystal phase purity. Through systematic adjustment of multiple synthesis parameters, we identified ternary (kinetic) phase diagrams at specific compositions (i.e., Si, Al, and NaOH mole fractions) using colloidal silica and sodium aluminate. Our studies identify multiple stages of zeolite phase transformations involving the framework types FAU, LTA, EMT, GIS, SOD, ANA, CAN, and JBW. We report an initial amorphous-to-crystalline transition of core-shell particles (silica core and alumina shell) to low-density framework types and their subsequent transformation to more dense structures with increasing temperature and/or time. We show that reduced water content facilitates the formation of structures such as EMT that are challenging to synthesize in organic-free media and reduces the synthesis temperature required to achieve higher-density framework types. A hypothesis is proposed for the sequence of phase transformations that is consistent with the Ostwald rule of stages, wherein metastable structures dissolve and recrystallize into more thermodynamically stable structures. The ternary diagrams developed here are a broadly applicable platform for rational design that offers an alternative to time- and cost-intensive methods of ad hoc parameter selection without a priori knowledge of crystal phase behavior.

Unusual Shapes of C60 Crystals Formed at Liquid–Liquid Interfaces

Abstract We have found some unusually shaped C60 crystals which formed at liquid–liquid interfaces when m-xylene and ethanol were used as good and poor solvents, respectively. The crystals coexisted with large amounts of needle-like or whisker-like crystals which likely form at the initial stage of mixing the two solvents, probably indicating that this system follows Ostwald rule of stages like well-studied isoxazolone dye which has two polymorphs, i.e., the least stable needle-like one with a small size and the most stable rhombic crystal with a large size.

Systematic Thermodynamics of Hydration (and of Solvation) of Inorganic Solids

The thermodynamics of the formation of solid and liquid inorganic hydrates and ammoniates is examined. In earlier studies, average values of the Gibbs energy of reaction, Delta(r)G, assuming a constant additivity per mole of bound water, have been obtained and have suggested that hydration is always marginally thermodynamically favorable. More detailed consideration now demonstrates that the mean value of Delta(r)G per mole of water, from anhydrous parent to hydrate within a sequence, increases consistently toward zero, becoming progressively less favorable as the degree of hydration, n, increases, and broadly independent of any structural features of the materials. Furthermore, the consistent behavior suggests that missing intermediate hydrates in hydrate sequences are likely to be thermodynamically stable, even if difficult to prepare, isolate, or measure.The behavior of ammoniates is similar but less regular, the irregularity being ascribed to a wider range of interactions within the solid ammoniates than in the hydrates. The "Ostwald Rule of Stages" suggests that the first precipitate from a supersaturated solution is usually a metastable phase, having an intermediate value of the Gibbs energy between that of the anhydrous parent and of the thermodynamically stable phase, then progressing to the stable phase with the lowest Gibbs energy, implying kinetic rather than thermodynamic control of the sequence of precipitation. The implications for hydrate formation are briefly considered.

Theoretical Evidence for a Dense Fluid Precursor to Crystallization

We present classical density functional theory calculations of the free-energy landscape for fluids below their triple point as a function of density and crystallinity. We find that, both for a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.

The Ostwald Rule of Stages

AbstractCrystallization from solutions often starts in such a way that thermodynamically unstable phases appear first followed by recrystallization to thermodynamically stable phases. This empirical observation, called as Ostwald's rule of stages, is explamed here on the basis of structure changes of solutions. Experiments supporting this explanation have been carried out with aqueous solutions of citric acid, sodium hydrogen phosphate and ferrous sulphate, respectively.

A kinetic study of precipitation from supersaturated calcium phosphate solutions

The formation of three different crystalline calcium phosphates (DCPD, OCP, HAP) and an amorphous calcium phosphate was studied as a function of pH and supersaturation. Under the experimental conditions the formation of HAP is always found to be preceded by one or more precursors in a sequence that is in agreement with the Ostwald rule of stages. Homogeneous formation of HAP at low concentrations is never observed. A semiquantitative analysis of growth curves and of relaxation times at pH 6.7 and 26°C reveals the growth of OCP to be described best by a mononuclear growth model with fourth-order dependence on the relative supersaturation. The heterogeneous formation of HAP on OCP surfaces is noted to shift to lower α values (reaction extent) with increasing initial supersaturation. It can be described by a polynuclear growth model.

Precipitation from supersaturated aluminate solutions. II. Role of temperature

The effect of temperature on the precipitation of aluminum hydroxide from dilute potassium aluminate solutions ( C Al(OH) 4 = 4 × 10 −3 M) was studied in acid titration and pH-stat experiments. The precipitation sequence is largely dictated by the supersaturation (II) and follows the Ostwald rule of stages: amorphous → pseudoboehmite → bayerite → gibbsite. The precipitation boundaries, -log a Al(OH) 4 − a OH − , of the amorphous phase (−1.9) and pseudoboehmite (−1.2) evaluated by interpretations of relaxation time curves are temperature insensitive. The interpretation of relaxation curves in the supersaturation region where pure bayerite forms is based on a surface nucleation mechanism and allows estimates of the free energy of formation of the critical nucleus (∼20 kJ/mole), interfacial tension and two activation energies (−30 kJ/mole, +95 kJ/mole). The preferred formation of pseudoboehmite at high pOH is shown to be the result of a lower interfacial energy and the retarding effect it exerts at all temperatures on the competing growth of bayerite crystals. The growth rate of bayerite is shown to be proportional to the available surface and the square of the supersaturation and is characterized by an activation energy of about 60–80 kJ/mole.

The ostwald rule of stages in precipitation from highly supersaturated solutions: a model and its application to the formation of the nonstoichiometric amorphous calcium phosphate precursor phase

A model is presented which describes the factors influencing the nature of nonstoichiometric amorphous precursor phases precipitating in highly supersaturated solutions. The model is applied to amorphous calcium phosphate and explains the variable stoichiometry of this solid. The relation between amorphous calcium phosphate and the precursor phases in the precipitation of strontium phosphates is also shown.