Configurational Entropy in Amorphous Solid Glass Formation

Povzetek

The Kauzmann paradox, the apparent vanishing of a supercooled liquid's configurational entropy at a finite
temperature above absolute zero, remains one of the central unresolved puzzles of glass physics, and its resolution
bears directly on whether an ideal glass transition underlies the kinetic glass transition observed experimentally. We
performed molecular dynamics simulations of a Kob-Andersen binary Lennard-Jones mixture (80:20 composition,
10,000 particles) cooled at four rates spanning three orders of magnitude, from 10^-3 to 10^-6 (reduced units), and
computed configurational entropy at each of 22 temperatures per cooling rate from the difference between total
entropy (via thermodynamic integration) and vibrational entropy (via the harmonic approximation about inherent
structures). Configurational entropy decreased monotonically on cooling for all four rates, from 1.98 k_B per particle
at the onset temperature T_o = 0.85 to a rate-dependent minimum near the simulation glass transition, with the
slowest cooling rate (10^-6) reaching a minimum configurational entropy of 0.31 k_B per particle at T = 0.40, 68%
lower than the fastest cooling rate's minimum of 0.52 k_B per particle at the same temperature. Extrapolating the
slowest-rate configurational entropy curve using the Adam-Gibbs functional form yielded an estimated Kauzmann
temperature of T_K = 0.30 +/- 0.02, approximately 25% below the simulation glass transition temperature T_g =
0.40 identified from the inflection point of the potential energy versus temperature curve. Structural relaxation times,
extracted from the self-intermediate scattering function, followed Adam-Gibbs scaling with configurational entropy
closely across all four cooling rates (R^2 = 0.94), with a fitted Adam-Gibbs constant of 0.62 +/- 0.05, and deviations
from Adam-Gibbs scaling exceeded 15% only below T = 0.42, close to T_g, where finite simulation timescales likely
prevented full equilibration. Cooling-rate dependence of the fragility parameter, computed from the temperature
dependence of relaxation time near T_g, ranged from m = 68 at the fastest cooling rate to m = 81 at the slowest,
indicating that apparent fragility measured in simulation is itself sensitive to the cooling protocol used to define T_g.
These results provide quantitative support for an Adam-Gibbs-consistent, entropy-controlled picture of structural
relaxation in this model glass former while underscoring that both the extrapolated Kauzmann temperature and the
fragility parameter extracted from finite-cooling-rate simulations remain protocol-dependent quantities requiring
careful reporting of cooling-rate metadata for meaningful cross-study comparison.