Determination of metastable zone width for combined anti-solvent/cooling crystallization

The metastable zone width (MSZW), induction time and primary nucleation kinetics have been measured and estimated for simultaneous anti-solvent and cooling crystallization of paracetamol in iso-propanol/water solution. ATR-FTIR spectroscopy and laser back-scattering are used to measure the solute concentration and primary nucleation event, respectively. Response surface analysis was applied to find the contribution of the crystallization mechanism on the MSZW and obtain a statistical model for quick estimation of the MSZW. Two theoretical approaches for the estimation of nucleation rate kinetic parameters from experimental data are presented. The methods are obtained by modifying the classical Nyvlt's correlation for simultaneous cooling/anti-solvent crystallizations. The nucleation order n for primary nucleation was deduced from the slope of a linear plot of log(MSZW) vs. log(cooling and anti-solvent rates). The induction time was also estimated by changing the classical methods for combined cooling and anti-solvent crystallization.     

Induction periods and mechanism and kinetics of nucleation of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles

Induction periods (t) and mechanism and kinetics of nucleation in barium tungstate crystallization from sodium tungstate melts in platinum crucibles were studied. A theoretical relation has been developed to express the dependence of t on the cooling rates (R_T) and the rate (R_c) of development of excess solute concentration. At any crystallization temperature the average rate-constant (k_n) for heterogeneous nucleation was related to R_c by (k_n/p)^1/(p+1) = 1/(tR_c^γ), where γ is a constant and p is the average number of particles in the critical nuclei. The critical temperature (T), critical supersaturation (S) and γ values were estimated.     

On the effect of impurities on the metastable zone width of phosphoric acid

The experimental data published in the literature on the metastable zone width, as determined by the maximum supercooling ΔT_max using the conventional polythermal method, of phosphoric acid aqueous solutions containing impurities were analyzed to understand an increase in ΔT_max/T₀ with an increase in saturation temperature T₀ of solute–solvent system and the effect of impurities on the metastable zone width. For the analysis the following relations were used: ln(ΔT_max/T₀)=Φ+βln R (K. Sangwal, Cryst. Res. Technol. 44, 2009, 231−247) and (T₀/ΔT_max)²=F(1−Zln R) (K. Sangwal, Cryst. Growth Des. 9, 2009, 942−950; J. Cryst. Growth 311, 2009, 4050−4061), where Φ, β, F and Z are constants. Analysis of the experimental data revealed that: (1) the parameters Φ and F strongly depend on saturation temperature T₀ and concentration c_i of impurities, but the constants β and Z are independent of T₀ and depend on c_i, (2) the dependence of the parameters Φ and F on T₀ follows an Arrhenius-type equation with activation energy E_sat, (3) the activation energy E_sat for diffusion of ions/molecules of phosphoric acid containing impurity ions is equal to the differential heat of adsorption Q_diff for these impurities, (4) the effectiveness of an impurity is directly connected with the values of their differential heat of adsorption Q_diff; the lower the values of Q_diff for an impurity, the lower is its effectiveness in promoting nucleation, (5) the activation energy E_sat is not related with its heat of dissolution ΔH_s and (6) the increase in ΔT_max/T₀ with an increase in T₀ for phosphoric acid is associated with the activation energy E_sat for diffusion of solute molecules in the solution such that E_sat<0.     

Kinetics of (R,S)- and (R)-mandelic acid in an unseeded cooling batch crystallizer

The objective of this work is to determine the nucleation and growth kinetics of (R,S)-mandelic acid ((R,S)-MA) and (R)-mandelic acid ((R)-MA) in aqueous solutions using an unseeded cooling crystallization process. To obtain the nucleation and growth kinetics, the solubility, metastable zone limits, and supersaturation were measured by in-situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and focused beam reflectance measurement (FBRM). The nucleation rate and growth rate parameters were determined by a nonlinear optimization algorithm. The effects of initial concentration and cooling rate on supersaturation and the nucleation rate are also discussed.     

Antisolvent crystallization of aqueous ammonium dihydrogen phosphate solutions by addition of acetone at different rates

Results of an investigation of in situ measurements of laser‐beam intensity I_s and I_m transmitted through aqueous ammonium dihydrogen phosphate (ADP) solutions saturated at 30 °C and water, respectively, and temperature T_s of solution and T_m of water during feeding of antisolvent acetone at different rates R_A, using an indigenously designed experimental setup, are presented and discussed. It was found that: (1) for the measurement of MSZW, defined as the maximum volume fraction of acetone content Δx_max in the solution, obtained from temperature measurements are more reliable than transmitted laser‐beam intensity measurements for solutions, (2) two minima ΔT_min1 and ΔT_min2 associated with endothermic reactions, separated by a maximum ΔT_max due to exothermic reactions appear in the plots of temperature difference ΔT = T_s−T_m against acetone feeding time t, and (3) in the ΔT(t) plots there are time intervals Δt of constant rates R_T of increase in ΔT of aqueous ADP solutions, and these values of R_T increase linearly with acetone feeding time rate R_A. The experimental data on the observed dependence of MSZW on antisolvent feeding rate R_A, the appearance of minima ΔT_min1 and ΔT_min2 and maximum ΔT_max and their dependence on R_A, and the relationship between R_T and R_A are discussed from consideration of processes of nucleation and growth of crystallites.     

Estimation of activation parameters for diffusion-controlled crystallization of barium tungstate from sodium tungstate melts by differential thermal analysis

The proximity (d₁₂) between a diffusing species and its host crystal necessary for a successful diffusion for diffusion-controlled crystallization of barium tungstate from sodium tungstate melts in platinum crucibles was estimated. These distances increased with increased cooling rates (R_T) and crystallization temperatures (T₀). Energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) were evaluated using an ordinary Arrhenius equation k_D1 = k₀e^−E/RT, where k_D1 was the diffusion rate-constant. These parameters were virtually unaffected by the changes in T₀ and R_T.     

A new criterion for the glass-forming ability of liquids

Based on theoretical calculations using the fragility concept and the nucleation theory for a model glass-forming system, we propose a dimensionless criterion, ?, expressed by T_rg(ΔT_x/T_g)^a, with T_rg, the reduced glass-transition temperature, ΔT_x, the width of the supercooled liquid region when heating a glass, T_g, the glass transition temperature, and a, the exponent. The application of this simple criterion to various glasses, including network, metallic, and molecular glasses (except pure water), indicates an excellent correlation between the critical cooling rate R_c and ? in a Log R_c-? single master plot with a = 0.143.     

Nucleation kinetics of paracetamol–ethanol solutions from metastable zone widths

A study of the nucleation kinetics for a cooling crystallisation of paracetamol–ethanol solutions in a batch reactor is described in this paper. Metastable zone width (MSZW) experiments were conducted in order to estimate the nucleation kinetics of the system. Measured MSZWs can be affected by numerous process parameters, such as cooling rate, concentration, agitation rate, and working volume. Two theoretical approaches were employed to estimate the nucleation kinetics, the classical mass based approach of Nývlt, and a more recent approach by Kubota, which also considers number density. Both approaches were found to produce similar estimates for the nucleation rates of the paracetamol–ethanol solutions as a function of supersaturation for an assumed nucleus size of 10 μm. The theory of Kubota was found to predict satisfactory estimates for the induction time of the nucleation process from MSZW data. The induction time was observed to be independent of the solution temperature as suggested by Kubota’s theory. This is a novel finding and serves to validate the induction time theory of Kubota. In this investigation, MSZWs were observed to decrease with increased levels of agitation and found to be independent of working volume.     

Differential Thermal Analysis Studies on the Crystallization of Strontium Tungstate from Sodium Tungstate Melts Thermodynamic and Kinetic Parameters

From the estimated diffusion rate-constants (k_D1) of strontium tungstate crystal growth from sodium tungstate melts in platinum crucibles, energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) for the process were estimated using an ordinary Arrhenius equation k_Dl = k₀e^−E/RT. These thermodynamic parameters were virtually unaffected by the changes in crystallization temperatures (T₀) and cooling rates (R)_T. The distance (r₁₂), between a diffusing species and its host necesary for a successful diffusion, increased with T₀ and T_T but there was no direct correlation.     

A study of the primary crystallization of a mixed anion silicate glass

This paper presents the results of a study of the primary crystallization of a multicomponent mixed anion silicate glass. The primary phase, leucite, and the secondary phase, diopside, were formed by surface crystallization, while the secondary phase, phlogopite, was formed by volume crystallization. The influence of the particle size of glass powder samples in the range 0-1 mm on the temperature of the DTA crystallization peak, T_p, the height of the peak, (δT)_p, and the parameter /(ΔT)_p was studied. The behaviors of the parameters (δT)_p and /(ΔT)_p depend only on the change in the surface-to-volume nuclei ratio, as is the case with polymorphic crystallization. However, the particle size ranges in which the surface, volume and mixed crystallization mechanism dominate are considerably narrower for this glass. The influence of the duration of a pre-DTA heat treatment on the parameters T_p, (δT)_p, and ΔT_p for fixed temperatures in the range T = 550-750 °C was investigated. The T_p of the samples thermally treated for different times, at fixed temperatures, decreased up to t = 5 h and then increased to a value close to that of an as-quenched sample, after which the value remained constant. The curves of (δT)_p, and ΔT_p as a function of time for fixed temperatures show a maximum. The influence of the temperature of the pre-DTA heat treatment on the parameters T_p, (δT)_p, and ΔT_p for fixed times of t = 1−5 h was also investigated. On increasing the pre-DTA heat treatment time, the curves changed significantly. The curves for 3 and 5 h in the temperature range 580-660 °C were similar to the nucleation curve, which indicated that the volume nucleation process proceeded in this temperature range. The behavior of these parameters, as a result of the simultaneous action of different nucleation mechanisms and crystal growth differ from those previously reported for the case of polymorphic crystallization.     

Differential thermal analysis studies on the crystallization of strontium tungstate melts. Variation of rate constants with crystallization temperatures and cooling rates

Kinetics of strontium tungstate crystallization from sodium tungstate melts were studied in platinum crucibles (by DTA) by continuous cooling from initial crystallization temperatures T₀ = 800° to 1000° to below the eutectic temperature at cooling rates R_T = 0.67° to 3.3° min⁻¹. Heterogeneous nuclei first formed slowly onto metal platinate particles within the solution during induction periods (t ); the main crystal growth then started after the development of some exces solute concentration (ΔC ) at the induction temperature (T ). The actual growth after t was diffusion rate-controlled. The diffusion rate-constants (k_Dt) for growth after the induction periods along the major axis were estimated; the increased with T₀ and R_T. These values were higher than those for diffusion-controlled crystal growth of strontium tungstate from sodium tungstate melts in alumina crucibles but much smaller than the real diffusion rate-constants (k_Dl)_real.     

Preparation,crystal structure,spectrographic characterization,thermal and third order nonlinear optical properties of benzyltriethylamine bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickel(III)

The preparation and crystal structure of a novel nonlinear optical organometallic crystal, benzyltriethylamine bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickel(III) (BTEANDT), are described. The crystal was characterized by elemental analyses, infrared and X-ray powder diffraction spectroscopy, thermal analysis and optical absorption. The third order nonlinear optical properties of crystal were investigated by using the Z-scan technique at 1064 nm with 20 ps. A self-focusing effect and a saturable absorption were observed. The nonlinear refraction coefficient (n₂) and the nonlinear absorption coefficient (β) have been found to be 7.311×10⁻¹⁸ m²/W and −6.064×10⁻¹¹ m/W when the on-axis irradiance at focus (I₀) is 3.025 GW/cm². The relationship between β and I₀ was studied, which has revealed that the former is proportional to the latter. The result has been explained with the theory of absorption cross-section.     

Barrier to crystal nucleation in anorthite

The kinetics of crystal nucleation in anorthite (CaAl₂Si₂O₈) have been determined over the range of undercooling between 475 and 600°C. The plot of In(I_vη) versus (ΔT_|staggered|r²T_|staggered|r³)^?1 is a straight line of negative slope over the temperature range investigated. The slope of this relation indicates a free energy barrier to crystal nucleation of about 82 kT1 (where $\text{T1 = 0.8T}{}_{\mathrm{E}}$). The intercept at (ΔT_|staggered|r²T_staggered|r³)^?1 = 0 is approximately 10²⁷ cm^?3 s^?1P. Samples of anorthite glass were also analyzed by differential thermal analysis, with the temperature of maximum crystallization rate being determined as a function of heating rate. From this variation, a nucleation barrier of about 80 kT1 was estimated. The combined results are in good agreement with predictions of the classical theory of homogeneous nucleation.     

Effect of impurities on the metastable zone width of solute–solvent systems

The novel approach to interpret the metastable zone width obtained by the polythermal method using the classical theory of three-dimensional nucleation proposed recently [K. Sangwal, Cryst. Growth Des. 9 (2009) 942] is extended to describe the metastable zone width of solute–solvent systems in the presence of impurities. It is considered that impurity particles present in the solution can change the nucleation rate J by affecting both the kinetic factor A and the term B related with the solute–solvent interfacial energy γ. An expression relating metastable zone width, as defined by the maximum supercooling ΔT_max of a solution saturated at temperature T₀, with cooling rate R is proposed in the form: (T₀/ΔT_max)²=F(1−Z ln R), where F and Z are constants. The above relation can also be applied to describe the experimental data on maximum supercooling ΔT_max obtained at a given constant R as a function of impurity concentration c_i by the polythermal method and on maximum supersaturation σ_max as a function of impurity concentration c_i by the isothermal method. Experimental data on ΔT_max obtained as a function of cooling rate R for solutions containing various concentrations c_i of different impurities and as a function of concentration c_i of impurities at constant R by the polythermal method and on σ_max as a function of impurity concentration c_i by the isothermal method are analyzed satisfactorily using the above approach. The experimental data are also analyzed using the expression of the self-consistent Nývlt-like approach [K. Sangwal, Cryst. Res. Technol. 44 (2009) 231]: ln(ΔT_max/T₀)=Φ+β ln R, where Φ and β are constants. It was found that the trends of the dependences of Φ and β on impurity concentration c_i are similar to those observed in the trends of the dependences of constants F and Z on c_i predicted by the approach based on the classical nucleation theory.     

Thermodynamic properties of strontium tungstate crystal growth from sodium tungstate melts

Energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) of the ordinary Arrhenius equation k_Dl = k₀e–E/RT were estimated for diffusion-controlled crystal growth of SrWO₄ from Na₂WO₄ melts. E increased slightly with increased cooling rates (R_T). k₀ was parallel to k_Dl and increased with increasing R_T. ΔH_a, ΔS_a, and ΔG_a did not change with the changes in R_T and crystallization temperature (T₀). The distance (d₁₂), between a diffusing particle and its host necessary for a successful diffusion, was estimated. Such distances slightly increased with T₀ and R_T.     

Nucleation kinetics of selenium (+4) precipitation from an acidic copper sulphate solution

The removal of selenium from copper sulphate solution prior to the electrowinning of copper is desirable in order to minimise contamination of the copper cathodes by selenium and other impurities. The selenium removal is effected by a precipitation process that takes place under high supersaturation conditions, which favour nucleation over any other particle formation processes. There is currently no fundamental information on the nucleation kinetics of this important process. In this study, the nucleation kinetics of selenium (+4) precipitation from an acidic copper sulphate solution was determined using the classical nucleation theory (CNT). Experiments were carried out by varying the levels of supersaturation from 8.66×10¹⁵ to 4.33×10¹⁷ at a temperature of 95 °C under atmospheric pressure. The nucleation rates for four different levels of supersaturation, the nucleation work and the nucleus size were determined. The kinetic constant A was found to be 3.92×10²⁷ m⁻³ s⁻¹, which shows that the nucleation process takes place through a homogeneous mechanism. The associated thermodynamic parameter (B) was determined to be 8.98×10⁰⁴.     

Electrical properties of TiO2 thin films

The electrical properties of n-type titanium dioxide thin films deposited by magnetron-sputtering method have been investigated by temperature-dependent conductivity. We observed that the temperature dependence of the electrical conductivity of titanium dioxide films exhibits a crossover from T^?1/4 to T^?1/2 dependence in the temperature range between 80 and 110 K. Characteristic parameters describing conductivity, such as the characteristic temperature (T₀), hopping distance (R_hop), average hopping energy (Δ_hop), Coulomb gap (Δ_C), localization length (ξ) and density of states (N(E_F)), were determined, and their values were discussed within the models describing conductivity in TiO₂ thin films.     

The Precipitation of Sparingly-Soluble Alkaline-Earth Metal and Lead Salts with Slow Development of Supersaturation (Slow Anion and Hydroxyl Ion Addition): Kinetics of Nucleation and Induction Periods

Barium and lead sulphate and chromate precipitations were studied at 20° to 95°C at precipitation rates varying from 10⁻³ to 10⁻⁷ ion l⁻¹ sec⁻¹: the supersaturation was developed by slow direct addition of anion to metal nitrate solution and by neutralisation of equivalent metal salt in excess acid solution. Slow heterogeneous nucleation occurred onto particles dispersed within the aqueous solution. The nucleation rate at any time was Where k_n is the rate constant for heterogeneous nucleation, N_∞ is the maximum number of potential nuclei, n_t is the number of nuclei after time t, I. P_t is the ionic product (C_mt)(C_mt) and 2π is the number of metal salt ions in the critical nucleus, generally eight. Crystal growth started after induction periods (t̄) at times just after the times for maximum rate of formation of nuclei. The induction periods (t̄) for precipitations from solutions of initial cation concentration ^cM₀ varied with precipitation rate (R) according to the relation, where γ = π/(π + 1) and k₁ (the unit reciprocal induction period) = . Nucleation rate constants for different precipitations were estimated from the k₁ values and are tabulated. For slow precipitations by direct anion addition, the rate constants were lower for precipitation from solution of the salt of greater solubility. The rate constants for slow precipitation of metal chromates from acid solution were far lower than those for slow precipitation by direct chromate addition. Rate constants decreased somewhat with rise in precipitation temperature.     

A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

Using a power‐law relation between three‐dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt‐like equation of metastable zone width of solution relating maximum supercooling ΔT_max with cooling rate R is proposed in the form: ln(ΔT_max/T₀) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔH_s/R_GT_lim) + (1/m)ln(f/KT₀) and slope β = 1/m. Here T₀ is the initial saturation temperature of solution in a cooling experiment, ΔH_s is the heat of dissolution, R_G is the gas constant, T_lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T₀ is essentially determined by the constant m and the factor f. The value of the factor f for a solute–solvent system at initial saturation temperature T₀ is determined by solute concentration c₀. Analysis of the experiment data for four different solute‐water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature‐independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T₀, following an Arrhenius‐type equation with an activation energy E_sat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E_sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E_sat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)