Heterogeneous critical nucleation on a completely-wettable substrate

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely-wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free energy barrier of nucleation vanishes. In fact, there always exist a critical nucleus and a free energy barrier as the first-order pre-wetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. Recently, Sear [J.Chem.Phys {\bf 129}, 164510 (2008)] has shown by a direct numerical calculation of nucleation rate that the nucleus does not notice this change when it crosses the coexistence. In our work the morphology and the work of formation of critical nucleus on a completely-wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely-wettable substrate.Comment: 11pages, 9 figures, Journal of Chemical Physics to be publishe

Local structure of liquid carbon controls diamond nucleation

Diamonds melt at temperatures above 4000 K. There are no measurements of the steady-state rate of the reverse process: diamond nucleation from the melt, because experiments are difficult at these extreme temperatures and pressures. Using numerical simulations, we estimate the diamond nucleation rate and find that it increases by many orders of magnitude when the pressure is increased at constant supersaturation. The reason is that an increase in pressure changes the local coordination of carbon atoms from three-fold to four-fold. It turns out to be much easier to nucleate diamond in a four-fold coordinated liquid than in a liquid with three-fold coordination, because in the latter case the free-energy cost to create a diamond-liquid interface is higher. We speculate that this mechanism for nucleation control is relevant for crystallization in many network-forming liquids. On the basis of our calculations, we conclude that homogeneous diamond nucleation is likely in carbon-rich stars and unlikely in gaseous planets

PLACE-BASED CIVIC EDUCATION AND THE RURAL LEADERSHIP CRISIS IN NEBRASKA

The Great Plains is facing a pending leadership crisis as rural depopulation decreases the number of residents who are available to serve in civic and government positions. This problem is compounded by the loss of youth populations in rural areas. In this essay, we offer a cross-disciplinary analysis of avenues for addressing the rural leadership crisis. We bring together work from rural demography, education policy, and civic studies to argue that civic education in rural areas needs to be reformed specifically to train and retain rural youth for leadership positions. We use Nebraska as a case study as it has suffered from rural decline, especially from youth depopulation; it has adopted new civic education standards as of December 2012; and Nebraska school districts have local control over the implementation of curricula. We review two competing trends in civic education, global civics and place-based education, and reflect on the impact each of these has on preparing students for leadership. We conclude that place-based education has the most potential for preparing students for leadership positions and should be used in rural schools even if that requires schools to sacrifice global civics

Steady-state nucleation rate and flux of composite nucleus at saddle point

The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation for the growth of the composite nucleus, which consists of the core of the final stable phase surrounded by a wetting layer of the intermediate metastable phase nucleated from a metastable parent phase recently evaluated by the author [J. Chem. Phys. {\bf 134}, 164508 (2011)]. The Fokker-Planck equation is similar to that used in the theory of binary nucleation, but the non-diagonal elements exist in the reaction rate matrix. First, the general solution for the steady-state nucleation rate and the direction of nucleation flux is derived. Next, this information is then used to study the nucleation of composite nucleus at the saddle point. The dependence of steady-state nucleation rate as well as the direction of nucleation flux on the reaction rate in addition to the free-energy surface is studied using a model free-energy surface. The direction of nucleation current deviates from the steepest-descent direction of the free-energy surface. The results show the importance of two reaction rate constants: one from the metastable environment to the intermediate metastable phase and the other from the metastable intermediate phase to the stable new phase. On the other hand, the gradient of the potential $\Phi$ or the Kramers crossover function (the commitment or splitting probability) is relatively insensitive to reaction rates or free-energy surface.Comment: 12 pages, 6 figures, to be published in Journal of Chemical Physic

Self-Templated Nucleation in Peptide and Protein aggregation

Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar aggregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by the formation of disordered oligomeric assemblies. This process has received much attention because disordered oligomeric aggregates have been associated with neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Here we describe a self-templated nucleation mechanism that determines the transition between the initial condensation of polypeptide chains into disordered assemblies and their reordering into fibrillar structures. The results that we present show that at the molecular level this transition is due to the ability of polypeptide chains to reorder within oligomers into fibrillar assemblies whose surfaces act as templates that stabilise the disordered assemblies.Comment: 4 pages, 3 figure

Homogeneous Nucleation in Inhomogeneous Media I: Nucleation in a Temperature Gradient

We introduce a general formalism to analyze nucleation phenomena in inhomogeneous media which considers the influence of the metastable phase, which is treated as a heat bath in which clusters are embedded, in the dynamics of the nucleation process. A kinetic equation for the evolution of the probability density of the clusters, taking into account possible inhomogeneities in the bath, is derived using mesoscopic nonequilibrium thermodynamics. From it, we obtain the nucleation rate and analyze the role played by the metastable phase in the process. We discuss in particular condensation and polymer crystallization in a temperature gradient.Comment: 18 pages, 3 figures, accepted for publication in J. Chem. Phy

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.Comment: 9 pages, 8 figures, Journal of Chemical Physics to be publishe