Non classical nucleation theoriesa new stochastic paradigm

Resumen

is work has been concerned on improving our basic understanding of nucleation, an ubiquitous process which plays a prominent role inmany areas of science. e current work was precisely focused on nucleation of a dense phase from a low-concentration (so-called weak) solution. e new phase can be either a disordered, liquid-like droplet or an ordered crystalline phase. e rst part of our research (section ì.Õ) was devoted to constructing phenomenological models with the aim of studying the characteristic randomness of the process. is simple methodology allowed us to respond the rst couple of questions stated in chapter ó. By using a simple SDE, we found a practical way of reproducing the experimental nucleation rates and induction time statistics. While this method is very useful for practical purposes, it cannot be used to give answer to profound theoretical questions which require a more general framework. e second part of this study (sections ì.ó-ì.¦) was intended to explore and apply a more general approach recently derived. What makes this formalism so attractive is the ability of simultaneously describing both the stochastic dynamics and the nucleation paths. When a single order parameter was considered we recovered a slightly modied CNT.We further improved this new CNT by modifying the original capillary approximation to consider clusters with nite interfacial width. e results were in good agreement with CNT predictions when the classical capillary model is imposed. However, large deviations were obtained aŸer considering its extended version due to the free-energy contribution associated with the nite interface. is theory was also extended to conned geometries and we thus responded another question stated in chapter ó.ere exists a minimum volume for nucleation to proceed. It was also shown that the nucleation rate can be enhanced when the volume is close enough to the minimum volume. Moreover, the dynamical approach to nucleation allows a multiparameter description of clusters.is removes the necessity of using the capillary approximation. In our study we introduced a natural two-variable extension of the capillary model to consider the inner density of clusters as the second independent variable. en, the most likely paths were computed for several supersaturation ratios. ese paths showed a non-classical behaviour passing through three phases. is constitutes the answer to the last question stated in chapter ó. at is, the nucleating system will pass through intermediate metastable states to go from the initial to the nal state. e two-parameter extension we developed also showed considerable deviations from CNT predictions for nucleation rates. ese cannot be only associated with the rudimentary free-energy calculations made in CNT, but also with the metric which is much more complex than the classical attachment rate. e results we collected in this thesis show the complexity of analytically describing nucleation, a purely stochastic processes simultaneously involving both thermodynamics and kinetics. While a comprehensive description has been already developed based on žuctuating hydrodynamics, the specic study of dišerent models for clusters gives rise to numerous di›culties and new mathematical problems. Even when it could seem trivial to apply this formalism, it involved hard problems which unfortunately did not have a trivial solution. Here we have explored both one- and two-variable parametrizations. While the rst case solved several questions which did not require a major detail in modelling clusters, only the second is capable of illustrating the full complexity of nucleation, including strong noise ešects and a continuum of possible nucleation pathways. Both the one-dimensional and the two-dimensionalmodels showed large deviations from CNT predictions. at is why, our main practical conclusion is that these dišerences could not be attributed to errors in the calculation of the free energy barrier but, rather, are a direct result of the more complex dynamics. For this reason, we believe that nucleation can only be properly understood when both thermodynamics and dynamics are incorporated in a self-consistent manner.