Effect of cooling rate on the critical undercooling for crystallization

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

“…Although widely used, the Nyvlt approach has received some criticism mainly due to its semi-empirical nature, as the two nucleation parameters used lack any direct physical significance and also the growth of the generated nuclei to detectable size is neglected [1,5] .…”

“…More recently, the approach [1,2] has led to alternative expressions that overcome some of the drawbacks of the previous approaches [5,6,[8][9][10] . These expressions do not contain empirical parameters and allow -rulled crystallisation to be distinguished from that mediated by , because while, in the former case the critical undercooling depends on both the nucleation and the growth rate of the crystallites, in the latter case, it is only controlled by the growth rate of the instantaneously nucleated crystallites provided their concentration is independently known.…”

“…The analytical performing of the integral in the equation [1,17] allows obtaining the dependence of the relative critical undercooling on the cooling rate at the early stage of the crystallisation when meets the inequalities [1] :…”

“…In particular, the problem of the effect that the cooling rate has on the metastable zone width ( ) has recently been dealt with in a comprehensive theoretical study [1,2] . A detailed understanding of crystallisation phenomena is not only required to help design chemical separation and purification processes, but also to prevent the appearance of crystals when they are not desired.…”

“…Recently, employing the classical nucleation theory, Sangwal [5,9,10] obtained a ( ) formula which provides physical insight into the parameters associated with it and which reveals linearity between ( ) and ln . More recently Kashchiev, Borissova, Hammond and Roberts ( ) developed an analytical approach [1,2] , based on that of Kolmogorov-Johnson-Mehl-Avrami ( ), which led to ( ) expressions derived from the initial temporal evolution of either the fraction ( ) of crystallised volume or the number ( ) of nucleated crystallites. The expressions derived, when applied to experimental data, not only allow the determination of key parameters associated with both the nucleation and the growth processes, but also make it possible to gain an insight into the nucleation mechanism by differentiating between instantaneous nucleation ( ) and progressive nucleation ( ).…”