Dynamical origin of thermodynamic properties: Analysis based on complex specific heat and complex entropy

We have been investigating molecular origin of anomalous prperties of water
by developing the quantumcorrected complex specific heat and entropy.
Thermodynamic picture of vitrification of water through complex specific heat and entropy: A Journey through ‘No Man’s Land’
We investigate thermodynamic properties of supercooled water across
the “no man’s land” onto the formation of amorphous ice. The calculations are
aided by very long computer simulations, often more than 50 μs long, with the
TIP4P/2005 model potential. Density fluctuations that arise from the proximity
to a putative liquidliquid (LL) transition at 228 K, cast a long shadow on
the properties of water, both above and below the LL transition. We carry out
the calculations of the quantum mechanical static and frequencydependent
specific heats by combining seminal works by Lebowitz, Percus, and Verlet
and Grest and Nagel with the harmonic approximation for the density of states.
The obtained values are in quantitative agreement with all available
experimental and numerical results of specific heats for both supercooled water
and ice. We calculate the entropy at all the state points by integrating
the specific heat. We find that the quantum correctedcontributions of
intermolecular vibrational entropy dominate the excess entropy of amorphous
phases over the crystal over a wide range of temperature. Interestingly,
the vibrational entropy lowers the Kauzmann temperature, TK, to 130 K,
just below the experimental glasstoliquid water transition temperature,
Tg, of 136 K and the calculated Tg of 135 K in our previous study.
A straightforward extrapolation of high temperature entropy from 250 K
to below however would give a much higher value of TK~190 K. The calculation
of Lindemann ratios places the melting of amorphous ice ~135 K. The amorphous
state exhibits an extremely short correlation length for the distance
dependence of orientational correlation.

Saito and Bagchi, J.Chem.Phys., (2019).
Frequency dependence of specific heat in supercooled liquid water and emergence of correlated
dynamics
Molecular origin of the wellknown specific heat anomaly in supercooled liquid water is investigated here
by using extensive computer simulations and theoretical analyses. A rather sharp increase in the values
of isobaric specific heat with lowering temperature and the weak temperature dependence of isochoric
specific heat in the same range are reproduced in simulations. We calculated the spatiotemporal
correlation among temperature fluctuations and examined the frequency dependent specific heat.
The latter shows a rapid growth in the low frequency regime as temperature is cooled below 270 K.
In order to understand the microscopic basis of this increase, we have performed a shellwise
decomposition of contributions of distant molecules to the temperature fluctuations in a central
molecule. This decomposition reveals the emergence, at low temperatures, of temporally slow, spatially
long ranged large temperature fluctuations. The temperature fluctuation time correlation function (TFCF)
can be fitted to a WilliamWatts stretched exponential form with the stretching parameter close to 0.6
at low temperatures, indicating highly nonexponential relaxation. Temperature dependence of the
relaxation time of the correlation function can be fitted to VogelFulcherTamermann (VFT) expression
which provides a quantitative measure of the fragility of the liquid. Interestingly, we find that
the rapid growth in the relaxation time of TFCF with lowering temperature undergoes a sharp crossover
from a markedly fragile state to a weakly fragile state around 220 K.

Saito, Ohmine, Bagchi, J.Chem.Phys., 138, 094503 (2013).