When physics meets chemistry at the dynamic glass transition

Can the laws of physics be unified? One of the most puzzling challenges is to reconcile physics and chemistry, where molecular physics meets condensed-matter physics, resulting from the dynamic fluctuation and scaling effect of glassy matter at the glass transition temperature. The pioneer of condensed-matter physics, Nobel Prize-winning physicist Philip Warren Anderson referred to this gap as the deepest and most interesting unsolved problem in condensed-matter physics in 1995. In 2005, Science, in its 125th anniversary publication, highlighted that the question of ‘what is the nature of glassy state?’ was one of the greatest scientific conundrums for the next quarter century. However, the nature of the glassy state and its connection to the glass transition have not been fully understood owing to the interdisciplinary complexity of physics and chemistry, governed by physical laws at the condensed-matter and molecular scales, respectively. Therefore, the study of glass transition is essential to explore the working principles of the scaling effects and dynamic fluctuations in glassy matter and to further reconcile the interdisciplinary complexity of physics and chemistry. Initially, this paper proposes a thermodynamic order-to-disorder free-energy equation for microphase separation to formulate the dynamic equilibria and fluctuations, which originate from the interplay of the phase and microphase separations during glass transition. Then, the Adam-Gibbs domain model is employed to explore the cooperative dynamics and molecular entanglement in glassy matter. It relies on the concept of transition probability in pairing, where each domain contains e + 1 segments, in which approximately 3.718 segments cooperatively relax in a domain at the glass transition temperature. This model enables the theoretical modeling and validation of a previously unverified statement, suggesting that 50-100 individual monomers would relax synchronously at glass transition temperature. Finally, the constant free-volume fraction of 2.48% is phenomenologically obtained to achieve a condensed constant (C) of C= 0.12(1−γ) = 1.501 × 10⁻¹¹ J·mol⁻¹·K⁻¹, where γ represents the superposition factor of free volume and is characterised using the cumulative Poisson distribution function, at the condensed-matter scale, analogous to the Boltzmann constant (k _B) and gas constant (R).