Origin of the High Variability in Sol-Gel Phase Transitions: The Agar Gelation Model.

Sol-gel phase transitions are complex far-from-equilibrium processes characterized by limited reproducibility, whose origin remains poorly understood and rarely quantified. We investigated the thermally induced sol-gel transition of agar using turbidimetry. A phenomenological model was applied to extract key kinetic parameters (maximum absorbance, maximum rate, and characteristic times) from 96 independent replicates. Variability was quantified and compared with that of an enzymatic reaction exhibiting similar sigmoidal kinetics, allowing for separation of experimental, intrinsic, and nonergodic contributions. Agar gelation displays markedly higher variability. The total variability (CV ≈ 16%) exceeds both the experimental error (1-2%) and the nonergodic contribution (≈2%), demonstrating that it predominantly arises from intrinsic process dynamics. Variability increases sharply during early stages of gelation and then evolves more gradually, indicating that stochastic nucleation and network formation pathways drive divergent kinetic trajectories despite identical initial conditions. Variability in gelation is therefore not a measurement artifact but an intrinsic hallmark of the sol-gel transition. This inherent stochasticity limits the predictive power of deterministic models, particularly at meso- and microscopic scales, and should be considered a fundamental feature of gel-forming systems. Our approach provides a quantitative framework for characterizing variability in phase transitions and may be extended to more complex biological and soft matter systems.