Miguel A. Durán-Olivencia, Fermín Otálora
In this work a phenomenological Stochastic Differential Equation (SDE) is proposed for modelling the time-evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a SDE constitutes the basis for the calculation of the (nucleation) induction time under the Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson's rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous or heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature but agreement is not so good for induction time statistics. Stochastic simulations truncated to the maximum waiting time of the experiments confirm that this fact is due to the time constraints imposed by experiments. Correcting for this effect, the experimental and predicted curves fit remarkably well. Thus, the proposed model seems to be a versatile tool to predict cluster size distributions, nucleation rates, (nucleation) induction time and induction time statistics for a wide range of conditions (e.g. time-dependent temperature, supersaturation, pH, etc.) where Classical Nucleation Theory (CNT) is of limited applicability.
View original:
http://arxiv.org/abs/1209.2648
No comments:
Post a Comment