Extending Equations of State to Inhomogeneous Systems.
The paper to which I'll refer in this post is this one: FeOs: An Open-Source Framework for Equations of State and Classical Density Functional Theory Philipp Rehner, Gernot Bauer, and Joachim Gross Industrial & Engineering Chemistry Research 2023 62 (12), 5347-5357.
In the 1950's, Richard Feynman predicted an age of nanotechnology: There's plenty of room at the bottom.
It's here. In my day job, I often find myself contemplating nanoparticle formulations various therapeutics under development. The nanoparticle "genius" Robert Langer is on the scientific boards of hundreds of pharmaceutical companies, and I collaborate with some of them. (I do not know, and have never met, and will never meet, Robert Langer, although I have attended lectures at which he has spoken.)
For the record, the Moderna and BioNT/Pfizer mRNA vaccines are essentially dual fluid phase nanoparticles. There are many other examples of similar formulations, not all of which, not even perhaps, the majority of which, involve RNA.
Beyond their role in medicine nanoparticles, including solid phase nanoparticles can have many roles in many areas, including carbon capture for carbon utilization, an idea I support.
When my son graduated high school and was on his way to college, I asked, for my father's day present that he write a program in Mathematica to solve the Peng Robinson Equation of State. My idea was to encourage him to learn something about programming and Equations of State. I thought this would help him to prepare for college.
He blew me off as it happens, and although I was slightly disappointed at the time, my concern about "getting him ready" now seems laughable. In his first year Ph.D. graduate school he routinely works and programs with sophisticated software involving neural networks for machine learning applications, as he did when he was working on his Master's degree, and indeed as an undergraduate. His first scientific paper to be published in a peer reviewed journal, on which he will appear as coauthor, will involve as much, machine learning in atomic scale imaging.
I try to keep up on Equations of State, many of which are advanced well beyond the (still widely used) Peng Robinson equation of state.
I came across this paper, cited above today in my regular reading which refers to the class of situations (not all of which are nanoparticle based) for which inhomogeneous states apply, for example, fluidized bed systems which are widely used in all kinds of industries.
From the introductory paragraphs:
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...
Note that the authors have nobly made this software open sourced. They will get funded, but it's not about making money for them; it's about advancing the science and technology on which the survival of our planet very much depends, even as they have threatened the survival of our planet.
We live in the best of times and the worst of times.
Charles Dickens ain't got nothing on us.
For those among us who may be Christians, Happy Easter.
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