Fig. 4: Root mean squared displacement for the molecules participating in the \({\beta }_{{\rm{JG}}}\) process at \({\tau }_{{\beta }_{{\rm{JG}}}}^{{\rm{DS}}}\).

a Characteristic center-of-mass root-mean-squared displacement at \({\tau }_{{\beta }_{{\rm{JG}}}}^{{\rm{DS}}}\) for the molecules participating in the β_JG-relaxation rescaled to the corresponding inter-molecular distance (center-of-mass to center-of-mass). Red circles: 1-propanol; blue circles: 5M2H; green circles: OTP. The gray area shows the range of typical values for the Lindemann criterion in crystals (see ref. ²⁰ and references therein) expressed in terms of root-mean-squared displacement. b T_g-rescaled inverse T-dependence of the α-relaxation and β_JG-relaxation times (τ) measured by dielectric spectroscopy and/or depolarized dynamic light-scattering for 5M2H (blue diamonds,¹²), 1-propanol (red left-pointing triangles and squares,³⁶; red circles, this work) and OTP (green squares,⁴³; green circles,¹; green diamonds, this work). To facilitate the comparison the relaxation times have been scaled to the value of the corresponding \({\tau }_{{\beta }_{{\rm{JG}}}}^{{\rm{DS}}}\) at T_g. All errorbars shown in panels a and b correspond to ±1 SD.