Here we develop an elasticity-based theory of crystallization in glasses that incorporates structural heterogeneity, fictive temperature, and polymorph-mediated pathways. In a glass, structural degrees of freedom are effectively frozen, so that the fictive temperature Tf remains higher than the ambient temperature T, rendering the system intrinsically out of equilibrium. A central result is that the crystal-glass interfacial penalty is renormalized in fragile systems by soft, liquid-like regions, leading to a subquadratic mismatch energy scaling as ΣR3/2 rather than the classical R2 form. Applying this framework to ethanol, we show that nucleation proceeds preferentially via a two-step route through a plastic crystalline polymorph. The associated barriers are dramatically reduced: the glass-to-plastic step exhibits barriers of only ∼5 kBT, compared to ∼102 kBT for the direct glass-to-crystal transition. This large separation explains the dominance of the Ostwald pathway and the emergence of a pronounced time-temperature-transformation (TTT) nose. In contrast, silica retains the classical R2 scaling due to its rigid network, leading to very large barriers and suppressed bulk nucleation.
Helical segments in polymer chains are often transient, finite, and dynamically evolving, yet their origin and stability remain incompletely understood. Here, we develop a minimal coarse-grained statistical-mechanical theory that explains how such "living helices" emerge in fluctuating polymer systems. Using a three-state model with cooperative interactions, we show that helix formation proceeds through a multistep nucleation mechanism. An initial constrained pre-nucleus forms first, followed by cooperative stabilization that promotes the growth of finite helical segments. The resulting free-energy landscape naturally favors marginally stable helices whose size is determined by a competition between cooperative gains and nonlinear penalties arising from stiffness, torsional strain, and solvent fluctuations. By formulating the dynamics as a stochastic process in segment size, we derive analytical expressions for both formation times and lifetimes within a mean first-passage framework. For representative parameters relevant to flexible polymers and peptide segments, the theory predicts characteristic timescales in the nanosecond to sub-microsecond range. These results provide a unified physical picture of "living helices" as finite, mobile, and fluctuating excitations and identify cooperativity and fluctuations as the key determinants of transient secondary structure in polymeric systems.
Biman Bagchi· Journal of Chemical Physics· 0 citations
