Fig. 3: Kinetics of LDL aggregation at high temperatures.

a I(q) profiles collected at a sample temperature of T = 85 °C as a function of isothermal waiting time, t_w as indicated by the colour bar. The error bars indicate the standard deviation. The dashed line represents ~q⁻⁴. b The correlation length (\(\zeta=\frac{2\pi }{{q}_{{{{{{{{\rm{peak}}}}}}}}}}\)) estimated from the scattering profiles as a function of t_w for sample temperatures T ≥ 75 °C. The error bars are obtained from the error in q_peak estimation (see Supplementary Note 7). The kinetics of LDL aggregation shows two growth regimes: stage-I - exponential growth phase, and stage-II - power-law growth phase. The solid lines are sigmoidal fits of log₁₀(ζ) vs log₁₀(t_w) using Eq. (5). The light-coloured shaded area around the solid sigmoidal fit lines represents the 95% confidence band. The green dashed lines in stage-II are power-law fits (\(\zeta \sim {t}_{{{{{{{{\rm{w}}}}}}}}}^{\mu }\)). c The correlation length as a function of normalised t_w with respect to \({t}_{1/2}^{{{{{{{{\rm{LDL}}}}}}}}}\). For convenience, double x and y scales are given in b, c. The temperature dependence of \({t}_{1/2}^{{{{{{{{\rm{LDL}}}}}}}}}\) is shown in an Arrhenius plot in the inset of c. The error bar in \({t}_{1/2}^{{{{{{{{\rm{LDL}}}}}}}}}\) indicate the parameter uncertainty obtained from the fits using least-squares minimisation. The green line represents an Arrhenius fit with an activation energy of 410 ± 20 kJ/mol (≈98 kcal/mol or ≈4.2 eV). The horizontal dashed line in b, c indicates the boundary between stage-I and stage-II. Source data are provided as a Source Data file.