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Register a new userExtension of Classical Nucleation Theory for Uniformly Sheared Systems
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Nucleation is an out-of-equilibrium process, which can be strongly affected by the presence of external fields. In this letter, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow. The theory involves accounting for the anisotropy of the critical nucleus formation, and introduces a shear rate dependent effective temperature. This extended theory is used to analyze the results of extensive molecular dynamics simulations, which explore a broad range of shear rates and undercoolings. At fixed temperature, a maximum in the nucleation rate is observed, when the relaxation time of the system is comparable to the inverse shear rate. In contrast to previous studies, our approach does not require a modification of the thermodynamic description, as the effect of shear is mainly embodied into a modification of the kinetic prefactor and of the temperature.
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Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometime lack material-specific descriptions. Here we provide a comprehensive framework for constructing a continuum picture from an atomistic simulation of homogeneous nucleation. We use this framework to determine the shape of the equilibrium solid nucleus that forms inside bulk liquid for a Lennard-Jones potential. From this shape, we then extract the anisotropy of the solid-liquid interfacial free energy, by performing a reverse Wulff construction in the space of spherical harmonic expansions. We find that the shape of the nucleus is nearly spherical and that its anisotropy can be perfectly described using classical models.
We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume $V$ replaces the internal energy $U$ as a function of entropy $S$ in conventional statistical mechanics. In place of the effective temperature, the compactivity $X = partial V / partial S$ characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.
In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the curvature of the crystal nucleation free-energy barrier to sample and select optimal interparticle interactions for self-assembly into a desired structure. We apply this method to find interactions to target two simple crystal structures: a crystal with simple cubic symmetry and a two-dimensional plane with square symmetry embedded in a three-dimensional space. Finally, we discuss the potential and limits of our method and propose a general model by which a functionally infinite number of different interaction geometries may be constructed and to which our reverse self-assembly method could in principle be applied.
In standard nucleation theory, the nucleation process is characterized by computing $DeltaOmega(V)$, the reversible work required to form a cluster of volume $V$ of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly-spherical cluster of volume $V$ and a fluctuating surface area $A$, whereby the maximum of $DeltaOmega(V)$ is replaced by a saddle point in $DeltaOmega(V,A)$. Compared to the simpler theory based on volume only, the barrier height of $DeltaOmega(V,A)$ at the transition state is systematically larger by a few $k_BT$. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.
We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, <tau> = A*exp(beta*Gamma) (beta = 1/kT) [E. Jordao Neves and R.H. Schonmann, Commun. Math. Phys. 137, 209 (1991)]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a ``soft dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does NOT simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property.
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