A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action

Entropically driven melting of Cu-based 1D coordination polymers

We investigated the melting behavior of four CPs with one-dimensional structures from a thermodynamic point-of-view. The difference in melting points depending on the crystal structures is observed. The interactions within the crystals were analyzed using DFT calculations. These analyses suggest that entropic terms dominate the melting points.

On the Potential of Gallium- and Indium-Based Liquid Metal Membranes for Hydrogen Separation

The concept of liquid metal membranes for hydrogen separation, based on gallium or indium, was recently introduced as an alternative to conventional palladium-based membranes. The potential of this class of gas separation materials was mainly attributed to the promise of higher hydrogen diffusivity. The postulated improvements are only beneficial to the flux if diffusion through the membrane is the rate-determining step in the permeation sequence. Whilst this is a valid assumption for hydrogen transport through palladium-based membranes, the relatively low adsorption energy of hydrogen on both liquid metals suggests that other phenomena may be relevant. In the current study, a microkinetic modeling approach is used to enable simulations based on a five-step permeation mechanism. The calculation results show that for the liquid metal membranes, the flux is limited by the dissociative adsorption over a large temperature range, and that the membrane flux is expected to be orders of magnitude lower compared to the membrane flux through pure palladium membranes. Even when accounting for the lower cost of the liquid metals compared to palladium, the latter still outperforms both gallium and indium in all realistic scenarios, in part due to the practical difficulties associated with making liquid metal thin films.

Structural Dynamics of C2F4I2 in Cyclohexane Studied via Time-Resolved X-ray Liquidography

The halogen elimination of 1,2-diiodoethane (C2H4I2) and 1,2-diiodotetrafluoroethane (C2F4I2) serves as a model reaction for investigating the influence of fluorination on reaction dynamics and solute-solvent interactions in solution-phase reactions. While the kinetics and reaction pathways of the halogen elimination reaction of C2H4I2 were reported to vary substantially depending on the solvent, the solvent effects on the photodissociation of C2F4I2 remain to be explored, as its reaction dynamics have only been studied in methanol. Here, to investigate the solvent dependence, we conducted a time-resolved X-ray liquidography (TRXL) experiment on C2F4I2 in cyclohexane. The data revealed that (ⅰ) the solvent dependence of the photoreaction of C2F4I2 is not as strong as that observed for C2H4I2, and (ⅱ) the nongeminate recombination leading to the formation of I2 is slower in cyclohexane than in methanol. We also show that the molecular structures of the relevant species determined from the structural analysis of TRXL data provide an excellent benchmark for DFT calculations, especially for investigating the relevance of exchange-correlation functionals used for the structural optimization of haloalkanes. This study demonstrates that TRXL is a powerful technique to study solvent dependence in the solution phase.

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot's heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr²ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr²ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck's quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine's inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot's calorique, or the non-sensible heat later described by Clausius as 'work-heat', exclusively to negative Gibbs energy (-G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth's climates.

Is water one liquid or two?

The idea that water is a mixture of two distinct states is analyzed in some detail. It is shown that the known compressibility of water is in fact sufficiently small that for a volume of water of size 1 nm³, the density fluctuations are of order 4% of the average density. This is much smaller than the ≈25% density fluctuations that would be required for significant regions of high and low density water to occur on this volume scale. It is also pointed out that the density fluctuations in water are, if anything, smaller than those that occur in other common liquids which do not have the anomalous properties of water. It is shown that if the distribution of density fluctuations is unimodal, the system is in the one-phase region, and if bimodal, it is in the two-phase region. None of the liquid or amorphous phases of water explored in this work give any sign of being in the two-phase region. Existing neutron and X-ray scattering data on water in the amorphous phases, and in the stable liquid phases as a function pressure and temperature, are subject to a new set of empirical potential structure refinement simulations. These simulations are interrogated for their configurational entropy, using a spherical harmonic reconstruction of the full orientational pair correlation function. It is shown that the excess pair entropy derived from this function, plus the known perfect gas contributions, give a reasonable account of the total entropy of water, within the likely errors. This estimated entropy follows the expected declining trend with decreasing temperature. Evidence that higher density water will have higher entropy than lower density water emerges, in accordance with what is expected from the negative thermal expansion coefficient of water at low temperatures. However, this entropy increase is not large and goes through a maximum before declining at yet higher densities and pressures, in a manner reminiscent of what has been previously observed in the diffusion coefficient as a function of pressure. There is no evidence that ambient water can be regarded as patches of high density, high entropy and low density, low entropy liquid, as some have claimed, since high density water has a similar entropy to low density water. There is some evidence that the distinction between these two states will become more pronounced as the temperature is lowered. Extensive discussion of the use of order parameters to describe water structure is given, and it is pointed out that these indices generally cannot be used to infer two-state behavior.