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Register a new userNucleation of a stable solid from melt in the presence of multiple metastable intermediate phases: Wetting, Ostwald step rule and vanishing polymorphs
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In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can wet the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier since surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work we discuss a density functional theory (DFT) based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order parameter dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of Ostwald step rule and the well-known phenomenon of disappearing polymorphs that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics some of which may be explored via modern nanoscopic synthetic methods.
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We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rule, which predicts which phase will nucleate, must be modified probabilistically when the new phases are almost equally stable. Finally, we show that the nucleation rate of a phase depends, among other things, on the number of other phases accessible from it.
Biopolymer self-assembly pathways are central to biological activity, but are complicated by the ability of the monomeric subunits of biopolymers to adopt different conformational states. As a result, biopolymer nucleation often involves a two-step mechanism where the monomers first condense to form a metastable intermediate, and this then converts to a stable polymer by conformational rearrangement of its constituent monomers. While existing mathematical models neglect the dynamics by which intermediates convert to stable polymers, experiments and simulations show that these dynamics frequently occur on comparable timescales to condensation of intermediates and growth of mature polymers, and thus cannot be ignored. Moreover, nucleation intermediates are responsible for cell toxicity in pathologies such as Alzheimers, Parkinsons, and prion diseases. Due to the relationship between conformation and biological function, the slow conversion dynamics of these species will strongly affect their toxicity. In this study, we present a modified Oosawa model which explicitly accounts for simultaneous assembly and conversion. To describe the conversion dynamics, we propose an experimentally motivated initiation-propagation (IP) mechanism in which the stable phase arises locally within the intermediate, and then spreads through additional conversion events induced by nearest-neighbor interactions, analogous to one-dimensional Glauber dynamics. Our mathematical analysis shows that the competing timescales of assembly and conversion result in a nonequilibrium critical point, separating a regime where intermediates are kinetically unstable from one where conformationally mixed intermediates can accumulate. Our work provides the first general model of two-step biopolymer nucleation, which can be used to quantitatively predict the concentration and composition of biologically crucial intermediates.
Spatial distributions are presented that quantitatively capture how polymer properties (e.g., segment alignment, density, and potential energy) vary with distance from nascent polymer crystals (nuclei) in prototypical polyethylene melts. It is revealed that the spatial extent of nuclei and their interfaces is metric-dependent as is the extent to which nucleus interiors are solid-like. As distance from a nucleus increases, some properties, such as density, decay to melt-like behavior more rapidly than polymer segment alignment, indicating that a polymer nucleus resides in a nematic-like droplet. This nematic-like droplet region coincides with enhanced formation of ordered polymer segments that are not part of the nucleus. It is more favourable to find non-constituent ordered polymer segments near a nucleus than in the surrounding metastable melt, pointing to the possibility of one nucleus inducing the formation of other nuclei. These findings provide a conceptual bridge between polymer crystal nucleation under non-flow and flow conditions, and are used to rationalize previous results.
Resistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a super-cooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to ~377 meV at ~465 K and reaching zero at ~930 K, using a reference activation energy of 111 meV (3kBT/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at Tmelt ~ 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at ~ 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 {mu}V/K for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge.
One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motors fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.
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