Determination of nucleation kinetics of potassium tetraborate tetrahydrate

Abstract

In this study, the metastable zone width of potassium tetraborate tetrahydrate was determined for four different temperatures and cooling rates. The induction period of potassium tetraborate tetrahydrate in aqueous solution was examined according to polythermal method by using visual observation. The induction period, which changes inversely proportional to the nucleation rate has been used to determine the interfacial tension between the potassium tetraborate tetrahydrate and aqueous solution. By using interfacial tension, the nucleation parameters such as Gibbs free energy change for the formation of critical nucleus, ∆G*, free energy of formation, ∆G, radius of critical nucleus, r and number of molecules in the critical nucleus, i* has been calculated. The effect of Li + and Ca 2+ impurities on metastable zone width has been studied. The metastable zone width of aqueous solution of potassium tetraborate tetrahydrate decreases with increasing impurity concentrations. The equilibrium saturation concentration change is high in the presence of Ca 2+ ions while it is low in the presence of Li + ions.

Nucleation mechanism and kinetics from the analysis of polythermal crystallisation data: methyl stearate from kerosene solutions

“…At such a moment the solution concentration would hardly surpass the limit of metastability as a great amount of crystals would be formed leading to a rapid drop in supersaturation. [6,9,[13][14][15][16] . In this particular case, through a material balance, the rate of supersaturation change by cooling can be correlated to the nucleation rate as expressed through the following semi-empirical formula:…”

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

“…(6) and (7) with best-fit constants given in tables 1 and 2, respectively. Original data from: (a) Sahin et al [8], and (b) Kim and Mersmann [4]. Table 1 Values of constants (ΔT max ) 0 and α of Eq.…”

“…Therefore, metastable zone width is associated with the nucleation kinetics of a solute−solvent system. Nývlt's equation relating the maximum temperature difference ΔT max between saturation temperature and temperature of nucleation events with the cooling rate R is frequently used for the study of nucleation kinetics by the polythermal method [1][2][3]5,6,8]. The Nývlt equation is derived on the assumptions that: (1) nucleation rate J depends on concentration difference Δc or temperature difference ΔT relative to the saturation concentration c 2 ____________________ or temperature T 2 by empirical power-law relation with quantities like nucleation constant k 1 and nucleation order m [see Eq.…”

“…Due to these assumptions, the nucleation rate J has concentration-based units, such as kg⋅m The aim of the present paper is to propose a new self-consistent equation relating the ratio of supercooling ΔT max to initial saturation temperature T 0 of solution during cooling (hereafter referred to as maximum temperature ratio ΔT max /T 0 ) with cooling rate R, with newly defined nucleation constant K and nucleation order m. The new equation is derived using: (1) the dependence of nucleation rate J on dimensionless supersaturation ratio S by a power-law relation with constants K and m, and (2) the theory of regular solutions to describe the temperature dependence of solubility. The final expression is used to analyze the published experimental ΔT max (R) data on potassium tetraborate tetrahydrate [8], borax decahydrate [6], ammonium sulfate [2] and nitrotriazolone [4] from their aqueous solutions. The abbreviations used hereafter for potassium tetraborate tetrahydrate, borax decahydrate, ammonium sulfate, and nitrotriazolone are KTB, borax, ASF and NTO, respectively.…”

The Effect of EDTA on the Nucleation Kinetics and Mechanical Properties of KDP Crystal

“…The relationship between rate of nucleation (representing the number of nuclei formed per unit time per volume) and induction period can be expressed as [17] ( 1) where τ is the induction period of the solution at temperature T, v is the molar crystal volume, k is the Boltzmann constant and A is constant. S is the supersaturation ratio (S = C/C*).…”