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

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, S-conf, and its molecular kinetics. The critical entropy, s(c)*, of k(B) ln 2 (=0.956x10(-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-(T-0/T)](-1), and the temperature-invariant energy term, Delta mu, is equal to RB, which has been determined from the knowledge of the Vogel-Fulcher-Tamman parameters B and T-0, 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, S-vib, would be higher than that of the crystal phase. Therefore, S-conf 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, S-vib and S-conf, have been estimated without reference to the vibrational spectra. The conclusions can be tested by determining z* and Delta mu from measurements of the dielectric spectra of a liquid confined to nanometer-size pores. This is elaborated by a calculation for 3-bromopentane. (C) 2000 American Institute of Physics. [S0021-9606(00)50620-5].