A resolution for the enigma of a liquid’s configurational entropy-molecular kinetics relation

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Abstract
The literature data on the entropy and heat capacity of 33 glass-forming liquids have been used to examine the validity of the Adam–Gibbs relation between a liquid’s configurational entropy, Sconf, and its molecular kinetics. The critical entropy, sc*, of kB ln 2 (=0.956×10−23 J molecule−1 K−1) in the equation is less than even the residual entropy per molecule in a glass at 0 K, and this creates difficulties in determining the size of the cooperatively rearranging region, z*, in the liquid. It is argued that, z*=[1−(T0/T)]−1, and the temperature-invariant energy term, Δμ, is equal to RB, which has been determined from the knowledge of the Vogel–Fulcher–Tamman parameters B and T0, with R being the gas constant, and on the basis of the argument that the preexponential term of this equation is identical to that of the Adam–Gibbs relation. As the lattice modes in a glass are lower in frequency and more anharmonic than in its crystal, its vibrational entropy, Svib, would be higher than that of the crystal phase. Therefore, Sconf of a glass (and liquid) is significantly less than the difference between the entropy of the glass (and liquid) and the entropy of its completely ordered crystal phase. Both quantities, Svib and Sconf, have been estimated without reference to the vibrational spectra. The conclusions can be tested by determining z* and Δμ from measurements of the dielectric spectra of a liquid confined to nanometer-size pores. This is elaborated by a calculation for 3-bromopentane.