Shift Between Two Types of Linear Viscoelastic Spectra in the Liquid-to-Solid Transition

We distinguish two rheological routes to the liquid-solid transition (LST) in soft materials by tracking the linear viscoelastic spectrum under small-amplitude oscillatory shear. Type I (dynamical arrest) shows the growth of a low-frequency elastic plateau without a reversal in the loss-tangent trend; Type II (percolation with criticality) features scale-free spectra at a well-defined time and a reversal in the loss-tangent trend. In synthetic hectorite suspensions spanning broad clay and salt concentrations, freshly prepared samples consistently follow Type II. After aging and pre-shear, the pathway becomes history-dependent: a map in composition-shear space reveals a boundary where high clay concentrations undergo Type I only, whereas lower clay concentrations evolve from Type I to Type II; increasing pre-shear rate shifts this boundary to higher clay content. A unified mechanism links these routes to aggregation kinetics: early particle-cluster growth yields peaked cluster-size distributions and Type I arrest; later depletion-enhanced cluster-cluster aggregation produces heavy-tailed distributions and Type II percolation. These results explain why "shear rejuvenation" does not restore the fresh state and provide a spectrum-based framework relevant to colloids and polymer systems undergoing physical or chemical gelation.