Temperature control of protein crystal nucleation

The thermal variant of the classical nucleation‐growth‐separation principle is shown, both theoretically and experimentally, to be a reliable tool for studying protein crystal nucleation. The classical nucleation theory is used to elucidate the temperature dependence of crystal nucleus size. A one‐to‐one ratio of the number density of nuclei formed to crystals grown to visible size is achieved using the nucleation‐growth‐separation method. The experiments conducted in such a way show that new nuclei are prevented from appearing while avoiding any crystal loss due to dissolution. The same method is used to study experimentally the interval of growth temperatures where the number density of (nucleated) crystals is relatively insensitive to the growth temperature. It is argued that this temperature interval corresponds to the width of the so‐called metastable zone.     

Probabilistic approach to protein crystal nucleation

Simple probabilistic model for step‐wise growth of polymers is used for making some parallels with the nucleation of protein crystals. Although the considerations are made within 1D case, this approximation still shows some important peculiarities of protein crystal nucleation and growth. Thus, the present approach turns out to be useful for interpretation of some important experimental results regarding these processes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On slow protein crystal nucleation: cluster‐cluster aggregation on diffusional encounters

With a view to experimental results on protein crystal nucleation the effects of cluster coalescence are probed semi‐quantitatively. The steric association restriction, which stems from the patchy surface of the protein molecules, explains both experimentally measured low crystal nucleation rate and coalescence limitations for crystalline clusters of protein molecules. The conclusion is that due to its action, and the impact of rotational diffusion, the coalescence of critical (and/or supercritical) clusters should be rejected as a conceivable alternative for explaining the slow nucleation of protein crystals. Besides, the analysis of cluster‐cluster aggregation on diffusional encounters may be of more general interest; it may be helpful by considering the coalescence of structured bio‐nano‐particles. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetics and intimate mechanism of protein crystal nucleation

Experimental and theoretical investigations on protein crystal nucleation are reviewed. Various experimental applications of the classical principle, which requires separation of the nucleation and growth stages of the crystallization process, are described. Temperature control is used most frequently, hypergravity and concentration changes being auxiliary techniques. Nucleation time-lags are measured by imposing temperature evoked supersaturation gradients. Application perspectives are revealed. Nucleation rates are measured according to the classical principle mentioned above, and energy barriers for crystal nucleation and numbers of molecules constituting the critical nuclei are calculated. Surprisingly, although requiring unusually high supersaturation, protein crystal nucleation occurs much more slowly than that with small molecule substances. On this basis novel notions are suggested for the elementary mechanism of protein crystal bond formation. Due to the selection of the crystalline bonding patches a successful collision between protein molecules, resulting in the formation of a crystalline connection, requires not only sufficiently close approach of the species, but also their proper spatial orientation. Imposing a rigid steric constraint, the latter requirement postpones the crystal nucleus formation. Besides, it was shown that cluster coalescence is not a factor, hampering the protein crystal nucleation. The comparison of the model predictions with experimental results proved that nucleation kinetics is governed by kinetic (not by energetic) factors.     

Determination of nucleation parameters and the solid liquid interfacial energy of the KCl‐ethanol‐water system

The kinetic parameters of homogeneous nucleation of KCl in different ethanol‐water solvent mixtures were determined at 25°C from the experimental measurements of the width of the metastable zone at different cooling rates. The ethanol mass ratio in the ethanol water solvent mixture was varied from 0‐0.9 and the metastable zone width for each solvent mixture was measured under the cooling rates of 10, 20 and 30 K/h. The influence of ethanol ratio on the activity coefficient was calculated. It was found that increasing the ethanol ratio in the solvent mixture leads to an increase in the mean molal activity coefficient. The experimental results obtained showed that the increase in the ethanol ratio in the solvent widens the metastable zone for the crystallization of KCl. Also it has inferred from the calculations based on the classical nucleation theory that increasing of the ethanol ratio in the solvent mixture resulted in an increase of the nucleation rate order, increase of the critical size of nuclei and increase of the solid liquid interfacial energy. It has been found that the solid liquid interfacial energy can be good correlated with inversely proportionality to the solubility. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polyhedral stability ‐ on the growth of flat crystal faces on small molecule and protein crystals

The old standing problem of face morphology is discussed. A special emphasis is put on the macroscopically flat faces, appearing on small molecule crystals mostly during calm growth, under low supersaturations. As distinct, protein crystals are growing with macroscopically flat faces even under surprisingly high supersaturations. Explanations of these facts are suggested by considering the surface micro‐profile of crystal faces which growth is driven by screw dislocations. It is shown that, due to kinetic reasons, the tips of the growth hillocks and the valley between them have to be levelled to some extent (at least on a quasi‐atomic scale) under low enough supersaturations. The amplitude of the surface roughness has to be suppressed also due to the surface energy gain, especially under quasi‐equilibrium. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions; Part 3: Model of the crystallization process

A model of spontaneous crystallization process was proposed. The model describes kinetics of the crystallization process after the end of the induction period. To test the model the published earlier data on crystallization and aggregation kinetics of potassium chloride at its spontaneous crystallization from supersaturated aqueous and aqueous‐ethanol solutions were used. It was found excellent coincidence of the experimental and theoretical data on concentration of the salt and the total number of crystals in solution at crystallization. Somewhat change for the worse was at the theoretical calculations of crystal size distribution at the end of the crystallization process. It indicated that the ways of calculation of size of crystals and their weight fraction in deposit were very approximate. The model allows predicting with satisfactory accuracy kinetics of crystallization using such general parameters of potassium chloride as the specific surface energy and the height of the nucleus‐bridges between crystals at coalescence. It needs further test of the model for other salts. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unidirectional growth of α‐NiSO4·6H2O crystal by Sankaranarayanan–Ramasamy (SR) method

Large cylindrical [001] direction α‐nickel sulphate hexahydrate crystal with 20 mm diameter and 140 mm length was grown from an aqueous solution by uniaxially solution‐crystallization method of Sankaranarayanan–Ramasamy (SR). The grown crystal was examined by X‐ray diffraction, UV‐Vis‐NIR spectroscopy and TGA/DTA analysis methods.     

An effective growth method to improve the homogeneity of relaxor ferroelectric single crystal Pb(In1/2Nb1/2)O3‐ Pb(Mg1/3Nb2/3)O3‐PbTiO3

Compositional segregation usually has negative effects on the growth of solid solution ferroelectric single crystals of Pb(In_1/2Nb_1/2)O₃‐Pb(Mg_1/3Nb_2/3)O₃‐PbTiO₃ (abbr. PIN‐PMN‐PT or PIMNT). A modified Bridgman method was adopted in this work to control the segregation and improve the compositional homogeneity significantly. The characteristic of this work is to use multiround growths and gradient composition raw materials in order to keep the PbTiO₃ concentration constant during the crystal growth. As an example, the two‐round growth of ternary PIN‐PMN‐PT single crystal is conducted in the same Pt crucible with gradient raw materials, where the first‐round boule was used as the seed crystal for the second‐round growth. Our results show that the as‐grown (Ф80 mm × 270 mm) PIN‐PMN‐PT crystals exhibit higher phase transition temperatures (T_c∼180 °C, T_r/t∼110 °C) and larger coercive field (E_c∼5–5.5 kV/cm), which are much better than the performances of Pb(Mg_1/3Nb_2/3)O₃‐PbTiO₃ crystals, and similar dielectric and piezoelectric performances (ε∼5000, tanδ∼1.25%, d₃₃∼1500 pC/N, k_t∼60%). And about 85 percent of the crystal boule grown by the two‐round growth technique could maintain its compositions around the morphotropic phase boundary.