Thermodynamic equations of state (EoS) are fundamental tools in thermal and chemical engineering (1?3) They enable calculating properties of multicomponent systems as a function of experimentally accessible quantities such as temperature, pressure, and composition. Equations of state differ in the breadth of their applicability and complexity, and depending on the field of application, there are requirements on functionality, robustness, precision, and computational speed. A milestone in the description of fluid phases was provided by van der Waals’ equation of state, (4) which is based on a (coarse) molecular model and first led to description of vapor/liquid coexistence. Prominent modifications of the model by van der Waals that preserve the cubic volume-dependence are Redlich–Kwong, (5) Soave–Redlich–Kwong, (6) and Peng–Robinson. (7) Due to their fast evaluation times, cubic EoS are still widely used in technical applications. However, they lack a physical basis when describing nonspherical, polar, or hydrogen-bonding substances and mixtures. Modern EoS are developed based on a molecular model, i.e., a description of (pairwise) intra- and intermolecular interactions. Although theories for fluids with simple spherical intermolecular interactions were developed in the 1970s, (8) the field made a leap with a development of M.S. Wertheim, who derived a description for highly directional interactions. (9?12) Wertheim’s theory led to the statistical associating fluid theory (SAFT), (13) which regards molecules as chains of spherical segments (thus accounting for the nonspherical shape of real molecules due to covalent bonds) and allows for short-ranged attractive (hydrogen) bonds. The success of SAFT led to the development of a plethora of derived models, of which the most used ones are PC-SAFT, (14?17) SAFT-VR-Mie, (18) and soft-SAFT. (19,20) A combination of a cubic equation of state with the association contribution from TPT1 was published as cubic + association (CPA). (21?23) Finally, TPT1 and SAFT can resolve individual segments on a molecule, leading to the development of heterosegmented EoS likeSAFT-?-Mie (24) and gc-PC-SAFT. (25)

Cubic and SAFT-type EoS aim to describe fluids based on a few either macroscopic (cubic) or microscopic (SAFT) properties. The small number of parameters ensures a robust extrapolation to state points for which no experimental data is available and the molecular model underlying these EoS ensure a meaningful description of mixtures with few binary interaction parameters or even predictions of mixture properties. However, experimental data is abundant for some fluids, and reference equations of state that use a large number of adjustable parameters to represent the experimental data of those substances have been developed. Reference EoS were published for pure components like water, (26) CO2, (27) and nitrogen, (28) but also for mixtures like natural gas or related systems. (29)
While EoS are used to compute properties of homogeneous fluid phases and to model phase equilibria and phase stability, they cannot model properties of microscopically inhomogeneous systems like fluids at interfaces or in porous media. Being able to model these phenomena is essential for dynamic processes such as droplet coalescence or formation of micelles or engineering applications such as adsorption. Classical density functional theory (30) (DFT) is a framework that extends fluid theories (i.e., equations of state based on a molecular model) to inhomogeneous systems. In DFT, the system is described by the grand potential, which can be expressed as a functional of the (partial) density profiles. Despite the fact that DFT is a formalism that has been used and studied in research for decades, it is not a commonly used method in industry as of today, although it can be used to predict properties that are difficult or expensive to measure, such as surface tensions of mixtures, (31) contact angles, (32) and adsorption isotherms. (33,34) In addition, it can provide insights into phenomena that are experimentally difficult to assess, such as the accumulation of light-boiling or amphiphilic molecules at interfaces. (35)

Within the last years, multiple open-source packages in the field of thermodynamics and equations of state were published, each with its own focus. CoolProp (36) and thermo (37) provide databases, correlations for properties such as vapor pressures and activity coefficients, and equations of state. Thermopack (38,39) (written in Fortran) focuses on equations of state with an emphasis on robust algorithms for phase equilibria and critical points, including multiphase flashes to be used within computational fluid dynamics simulations. phasepy (40,41) provides Python implementations of equations of state and algorithms for phase equilibria, including square gradient theory which can be used to describe density profiles across vapor liquid interfaces. teqp (42) (written in C++) and Clapeyron.jl (43) (written in Julia)─similar to FeOs─both utilize automatic differentiation, which circumvents the need to implement analytic derivatives of the Helmholtz energy. All of these projects have a common feature: they provide an interface to a dynamic, high-level programming language. Clapeyron.jl is implemented in the Julia programming language, while the others are either fully implemented in Python (phasepy, thermo) or provide Python bindings (CoolProp, Thermopack, teqp). Clearly, for a modern toolkit, this is a necessity as it enables access to a broader range of users and allows using tools such as Jupyter notebooks that make research more transparent and reproducible.

A recent survey of the Working Party of Thermodynamics and Transport Properties of the European Federation of Chemical Engineering summarizes the most important gaps and concerns raised by industry in the field of applied thermodynamics and outlines specific requirements for model frameworks. (44) In a subsequent publication, the authors outline the “main directions that [they] believe the applied thermodynamics community should adopt in the coming decade”: (3)

There is a need for methods to assess the properties of fluids under confinement, at interfaces, and in the presence of external fields.
Users must be able to parametrize the model and assess its uncertainties and range of applicability

In the same vein, access to these models and parameters has to be transparent, ideally in a standardized form and including the data used for the parametrization.

Finally, there is increasing demand for ongoing education, training, and collaboration.

FeOs is well suited to address these important topics. The implementation of DFT in FeOs is designed with respect to the modeling of industrially relevant problems. It provides ad hoc functionalities to describe confined media and interfaces or to specify external potentials. Furthermore, FeOs provides utilities to optimize model parameters within a couple of lines of code. All of this is possible from within Jupyter notebooks without sacrificing performance. With the simple installation and availability on all major platforms, results can easily be shared and reproduced.

FeOs is developed with two use-cases in mind. First, it provides implementations for equations of state and Helmholtz energy functionals for DFT together with algorithms for critical point and phase equilibrium calculations as well as solvers for density profiles in multiple dimensions and coordinate systems. It can therefore be used as a toolkit to compute thermodynamic properties of homogeneous and inhomogeneous systems. And second, it provides interfaces and data types that can be used to extend the code, e.g., to implement new models and algorithms...

When I joined DU in 2002, I believed that solar and wind were important tools for addressing climate change. I was supportive of money spent on the infrastructure and research devoted to this theory. Of course, when I joined DU in November of 2002, the concentration of the dangerous fossil fuel waste carbon dioxide in the planetary atmosphere was 372.68 ppm. For the last week for which Mauna Loa data has been posted as of this writing, the week beginning July 3, 2022, that measurement was 419.73. I trust - hopefully not naively - that people can add and subtract. The first derivative, the rate of change of CO2 concentrations as measured by 12 month running averages of weekly Mauna Loa CO2 Observatory data, in November 2002 in the week I joined DU, was 1.66 ppm/year. Given the last data point as of this writing, it has reached 2.45 ppm/year.

Let's do something very, very, very crude, just as an illustration with the understanding that it is unsophisticated but may be illustrative:

As of this writing, I have been a member of DU for 19 years and 240 days, which works out in decimal years to 19.658 years. This means the second derivative, the rate of change of the rate of change is 0.04 ppm/yr^2 for my tenure here. (A disturbing fact is that the second derivative for seven years of similar data running from April of 1993 to April of 2000 showed a second derivative of 0.03 ppm/yr^2; the third derivative is also positive, but I'll ignore that for now.) If these trends continue, this suggests that “by 2050,” 28 years from now, using the language that bourgeois assholes in organizations like Greenpeace use to suggest the outbreak of a “renewable energy” nirvana, the rate of change, the first derivative, will be on the order of 3.6 ppm/year. Using very simple calculus, integrating the observed second derivative twice, using the boundary conditions – the current data - to determine the integration constants, one obtains a quadratic equation (0.04)t^2+(2.45)t+ 419.71 = c where t is the number of years after 2022 and c is the concentration at the year in question...

...This admittedly crude "model" roughly suggests that the concentration of dangerous fossil fuel waste, carbon dioxide concentrations, given the trend, will be around 520 ppm “by 2050,” in 28 years, passing, by solving the resultant quadratic equation, somewhere around 500 ppm around 2046, just 24 years from now.

Barrier organs such as the lung are directly affected by exposure to environmental challenges. Accordingly, more than 20 environmental and occupational agents are lung carcinogens2, and exposure to these are of particular relevance in understanding lung cancer in the never-smoking population. Lung cancer in never-smokers (LCINS) is the eighth most common cause of cancer death in the UK and has distinct clinical and molecular characteristics compared with lung cancer in smokers3. LCINS frequently harbour adenocarcinomas with oncogenic EGFR mutations and are more commonly observed in female individuals and in individuals with East Asian ancestry compared with patients with Western ancestry4. Several factors have been proposed to explain the observed sex and geographical disparities of lung cancer driven by EGFR mutations, including germline genetics5, ethnicity, radon exposure, occupational carcinogen exposure and air pollution6.

Air pollution accounts for 7?million deaths per year, with 99% of people living in areas that exceed World Health Organization guidelines (less than 5??g?m–3 annually)7. Particulate matter (PM) is a key constituent of air pollution and is classified by aerodynamic size. Fine particles ?2.5??m (PM2.5) are able to travel deep into the lung and are linked to multiple adverse health effects, including heart disease and lung cancer7...

Traditionally, it is thought that carcinogens cause tumours by directly inducing DNA damage. However, recent data suggest that many carcinogens do not cause a detectable DNA mutational signature in tumours following exposure8,9. Genetic analyses of oesophageal cancer showed that mutational signatures do not fully explain the varied geographical incidence of this cancer10, and efforts that have profiled tumour genomes in LCINS failed to detect a dominant carcinogenic signal of mutations deriving from exogenous sources11,12,13.

We propose that air pollutants might promote inflammatory changes in the lung tissue microenvironment that permit pre-existing mutated clones to expand, consistent with the two-stage carcinogenesis model of initiation and promotion1. To address this hypothesis, we combined epidemiological evidence with functional preclinical models and clinical cohorts to decipher potential mechanisms of air-pollution-induced lung tumour promotion and actionable targets for molecular cancer prevention (Extended Data Fig. 1a).

The model of tumour initiation and promotion is contingent on histologically normal tissue cells harbouring oncogenic driver mutations1. In 15 reported studies involving deep sequencing of human histologically normal tissues from different anatomical sites (n?=?9,380 samples from 380 patients), an oncogenic EGFRL858R mutation was only reported in a single clone from a skin microbiopsy, which indicated that these mutations are rare (Supplementary Table 6). Using digital droplet PCR (ddPCR) and duplex sequencing (Duplex-seq), we sought for evidence of EGFR-driver mutations in non-cancerous lung tissue from patients with lung cancer or with cancers of other organs and from individuals with no evidence of cancer (Extended Data Figs. 7 and 8a and Supplementary Table 7).

Researchers have detected increased emissions for five ozone-depleting chlorofluorocarbons.

The Montreal Protocol, which banned most uses of ozone-destroying chemicals known as chlorofluorocarbons (CFCs) and called for their global phase-out by 2010, has been a great success story: Earth’s ozone layer is projected to recover by the 2060s.

So atmospheric chemists were surprised to see a troubling signal in recent data. They found that the levels of five CFCs rose rapidly in the atmosphere from 2010 to 2020. Their results are published today in Nature Geoscience1.

“This shouldn’t be happening,” says Martin Vollmer, an atmospheric chemist at the Swiss Federal Laboratories for Materials Science and Technology in Dübendorf who helped to analyse data from an international network of CFC monitors. “We expect the opposite trend, we expect them to slowly go down.”

At current levels, these CFCs do not pose much threat to the ozone layer’s healing, said Luke Western, a chemist at the University of Bristol, UK, at an online press conference on 30 March. CFCs, once used as refrigerants and aerosols, can persist in the atmosphere for hundreds of years. Given that they are potent greenhouse gases, eliminating emissions of these CFCs will also have a positive impact on Earth’s climate. The collective annual warming effect of these five chemicals on the planet is equivalent to the emissions produced by a small country like Switzerland.

It’s highly likely that manufacturing plants are accidently releasing three of the chemicals — CFC-113a, CFC-114a and CFC-115 — while producing replacements for CFCs. When CFCs were phased out, hydrofluorocarbons (HFCs) were brought in as substitutes. But CFCs can crop up as unintended by-products during HFC manufacture. This accidental production is discouraged by the Montreal Protocol, but not prohibited by it.

“A lot of this probably boils down to the factory level,” Vollmer says, pointing out that HFC production is on the rise. “A factory can be run relatively clean or relatively dirty...”

The Department of Energy released Pathways to Commercial Liftoff: Advanced Nuclear earlier this month. It is one of the first in a series of reports on clean energy technologies and the private and public investments needed to overcome hurdles to full-scale deployment. The report makes a clear case for investment in nuclear power and challenges potential investors and operators to move beyond the current “wait and see” stalemate and generate “a committed orderbook . . . for 5–10 deployments of at least one reactor design by 2025.”

Define “liftoff”: According to the Advanced Nuclear report, “‘liftoff’ refers to the economic and technical state at which the industry becomes self-sustaining in service of meeting U.S. decarbonization goals.”

The DOE says its Liftoff reports are “developed through extensive stakeholder engagement and a combination of system-level modeling and project-level financial modeling. . . . They do not reflect DOE official policy or strategic plans; they are a resource intended to inform decision-making across industry, investors, and the broader stakeholder community.”

Before we get into the details a few more definitions are needed. Useful (if overused) terms like “small modular reactor” and “advanced reactor” have been tailored to fit dozens of designs that may not have much in common. In this report, advanced reactors include “a range of proven and innovative technologies” in two categories: Gen III+ and Gen IV. Gen III+ designs are water cooled and fueled with low-enriched uranium, while Gen IV designs use “novel” fuels and coolants. Both Gen III+ and Gen IV reactors may be categorized as “large reactors (~1 GW), small modular reactors (~50–300 MW), and microreactors (50 MW or less).”

First steps for nuclear: Advanced nuclear developers must have “a committed orderbook, e.g., signed contracts, for 5–10 deployments of at least one reactor design by 2025 . . . to catalyze commercial liftoff in the U.S.” The report ventures to say that “given expressed U.S. utility risk tolerances, it is likely that the first design to reach a critical mass of orders may be a Gen III+ SMR, which could be followed in parallel or sequence by Gen IV reactors.”

The next step? Delivering those plants “on time and on budget (i.e., ±20%) will be essential for generating sustained demand and commercial momentum,” the report states. “While the estimated first of a kind (FOAK) cost of a well-executed nuclear construction project is ~$6,200 per kW, recent nuclear construction projects in the U.S. have had overnight capital costs over $10,000 per kW.”...