Christopher Bertrand

Thermodynamics of Supercooled Water

We review the available experimental information on the thermodynamic properties of supercooled water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are also discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.

Peculiar thermodynamics of the second critical point in supercooled water.

On the basis of the principle of critical-point universality, we examine the peculiar thermodynamics of the liquid-liquid critical point in supercooled water. We show that the liquid-liquid criticality in water represents a special kind of critical behavior in fluids, intermediate between two limiting cases: the lattice gas, commonly used to model liquid-vapor transitions, and the lattice liquid, a weakly compressible liquid with an entropy-driven phase separation. While the ordering field in the lattice gas is associated with the chemical potential and the order parameter with the density, in the lattice liquid the ordering field is the temperature and the order parameter is the entropy. The behavior of supercooled water is much closer to lattice-liquid behavior than to lattice-gas behavior. Using new experimental data recently obtained by Mishima [J. Chem. Phys. 2010, 133, 144503], we have revised the parametric scaled equation of state, previously suggested by Fuentevilla and Anisimov [Phys. Rev. Lett. 2006, 97, 195702], and obtain a consistent description of the thermodynamic anomalies of supercooled water by adjusting linear backgrounds, one critical amplitude, and the critical pressure. We also show how the lattice-liquid description affects the finite-size scaling description of supercooled water in confined media.

Critical Behavior of the Dielectric Constant in Asymmetric Fluids

By applying a thermodynamic theory that incorporates the concept of complete scaling, we derive the asymptotic temperature dependence of the critical behavior of the dielectric constant above the critical temperature along the critical isochore and below the critical temperature along the coexistence curve. The amplitudes of the singular terms in the temperature expansions are related to the changes of the critical temperature and the critical chemical potential upon the introduction of an electric field. The results of the thermodynamic theory are then compared with the critical behavior implied by the classical Clausius-Mossotti approximation. The Clausius-Mossotti approximation fails to account for any singular temperature dependence of the dielectric constant above the critical temperature. Below the critical temperature it produces an apparent asymmetric critical behavior with singular terms similar to those implied by the thermodynamic theory, but with significantly different coefficients. We conclude that the Clausius-Mossotti approximation only can account for the observed asymptotic critical behavior of the dielectric constant when the dependence of the critical temperature on the electric field is negligibly small.

Dynamic signature of molecular association in methanol

Quasielastic neutron scattering measurements and molecular dynamics simulations were combined to investigate the collective dynamics of deuterated methanol, CD3OD. In the experimentally determined dynamic structure factor, a slow, non-Fickian mode was observed in addition to the standard density-fluctuation heat mode. The simulation results indicate that the slow dynamical process originates from the hydrogen bonding of methanol molecules. The qualitative behavior of this mode is similar to the previously observed α-relaxation in supercooled water [M. C. Bellissent-Funel et al., Phys. Rev. Lett. 85, 3644 (2000)] which also originates from the formation and dissolution of hydrogen-bonded associates (supramolecular clusters). In methanol, however, this mode is distinguishable well above the freezing transition. This finding indicates that an emergent slow mode is not unique to supercooled water, but may instead be a general feature of hydrogen-bonding liquids and associating molecular liquids.

Direct observation of critical adsorption on colloidal particles

Despite the fundamental role adsorbed solvent layers play in generating critical Casimir forces between colloidal particles, the structure of these layers has yet to be directly determined. Using small-angle neutron scattering, we have measured critical adsorption on the surface of small spherical silica particles suspended in a binary mixture of lutidine and water. The surface concentration profile and excess adsorption Γ were studied as functions of temperature at the critical concentration and three off-critical concentrations. We are able to differentiate three distinct contributions to the excess adsorption including the intrinsic shape of the concentration profile. The adsorption associated with the profile shape is found to increase monotonically with increasing 2,6-lutidine concentration and to decrease with increasing temperature, this later observation is consistent with expectations for curvature induced corrections to planar adsorption and leads to Γ∼(T-Tc)/Tc (-0.52), where Tc is the critical temperature. This scaling relation corresponds to a stronger divergence than found in the planar case, but a substantially weaker divergence than found previously.

Nanoscopic length scale dependence of hydrogen bonded molecular associates' dynamics in methanol

In a recent paper [C. E. Bertrand et al., J. Chem. Phys. 145, 014502 (2016)], we have shown that the collective dynamics of methanol shows a fast relaxation process related to the standard density-fluctuation heat mode and a slow non-Fickian mode originating from the hydrogen bonded molecular associates. Here we report on the length scale dependence of this slow relaxation process. Using quasielastic neutron scattering and molecular dynamics simulations, we show that the dynamics of the slow process is affected by the structuring of the associates, which is accessible through polarized neutron diffraction experiments. Using a series of partially deuterated samples, the dynamics of the associates is investigated and is found to have a similar time scale to the lifetime of hydrogen bonding in the system. Both the structural relaxation and the dynamics of the associates are thermally activated by the breaking of hydrogen bonding.

Molecular dynamics of a model dimerizing fluid

A model dimer forming fluid has been investigated by continuous molecular dynamics simulations. This study emphasizes the volume fraction and temperature dependence of the dynamic properties of the system, including the self and collective diffusion coefficients and the forward and reverse rate constants. The self and collective diffusion coefficients are found to be well described by a monomer fraction controlled interpolation formula. The forward rate constant (dimer formation) is found to be weakly temperature dependent and strongly volume fraction dependent. The opposite holds for the reverse rate constant. The dimer and monomer decay rates are not found to affect the intermediate scattering functions at the conditions studied.

Chapter 7:Thermodynamics of Fluids at Meso and Nano Scales

In contemporary process and product design, engineers often deal with systems or phenomena for which traditional thermodynamics may be insufficient, as in strongly fluctuating and nano-size systems, system with nano-scale heterogeneities, or mesoscopic dissipative structures. However, many such case...