Pierre J. Walker

Pierre J. Walker

PhD Student in Wang Group

Talks and presentations

Group Contribution and Machine Learning Approaches to Predict Abraham Solute Parameters, Solvation Free Energy, and Solvation Enthalpy

November 04, 2021

Poster, 2021 Annual Meeting of AIChE Computational Molecular Science and Engineering Forum, Online

Solvation free energy predictions play a key role in a variety of areas such as synthesis of organic molecules, optimization of purification processes, and pollutant level management. Having compiled a new and extensive solvation property database, we present a group contribution method (SoluteGC) and a machine learning model (SoluteML) to predict the Abraham solute parameters for solute compounds, as well as a machine learning model (DirectML) to predict solvation free energy and enthalpy for solvent-solute pairs. The proposed group contribution method uses atom-centered functional groups with corrections for ring and polycyclic strain and long-distance interaction whilst the machine learning models adopt a directed message passing neural network. The solute parameters predicted from SoluteGC and SoluteML are used to calculate solvation free energy and enthalpy via the linear free energy relationships [1,2]. The new data sets used to train the models contain 8366 solute parameters, 20253 solvation free energies and 6322 solvation enthalpies, larger than any current database. The three models are evaluated on the identical test sets using both random and substructure-based solute splits for solvation free energy and enthalpy predictions. The results show that, on average, the DirectML model is superior to the SoluteML and SoluteGC models for both solvation energy (mean absolute error on the random solute split: 0.41 kcal/mol cf. 0.48 kcal/mol and 0.63 kcal/mol, respectively) and enthalpy (mean absolute error on the random solute split: 0.47 kcal/mol cf. 0.50 kcal/mol and 0.64 kcal/mol, respectively) predictions. However, for certain solute and solvent substructures, this is not always the case. For this reason, when combined together, the three models can provide even more accurate predictions of solvation free energy and enthalpy. Nevertheless, DirectML can provide accuracy comparable to or even smaller than that of advanced quantum chemistry methods. SoluteML and SoluteGC also provide useful insights with regards to molecular structures and properties beyond solvation. Finally, we present our compiled open-source solvation energy and enthalpy databases and provide public access to our final prediction models through a simple web-based tool, conda package, and source code.

Introducing Students to Open-Source Partial Differential Equation Solver Codes in Python

November 04, 2021

Talk, 2021 Annual Meeting of AIChE Education Division, Online

Partial differential equations (PDE) are ubiquitous in many engineering fields and are one of the most complex mathematical topics that engineering students will encounter during their education. Despite the fact that numerical methods are often required for effective solution of PDE models for research and industrial applications, undergraduate students typically will have very limited exposure to relevant numerical methods and/or the use of PDE solver codes. This situation arises for a multitude of reasons such as the availability of space in the curriculum and/or access to suitable resources. Whilst addressing curriculum constraints is a challenging task, the availability of high quality resources suitable for teaching purposes can be well addressed. To that end, we believe that recent releases of multiple PDE solver codes native to the Python language offer exciting opportunities for educators and students. These solver codes are typically open-source in nature which makes them readily available. They are also easy to use as Python is a comparatively easier language for students to work with and are highly scalable, ofteni finding use in many research projects and publications. As a proof of concept, we have developed a short course (6 hours of contact time) using the solver code FiPy that we hope to integrate into the teaching of an advanced engineering mathematics course for 2nd year undergraduate students. With appropriate scaffolding, students were able to understand and solve a variety of problems including the Cahn-Hilliard equation. Student feedback indicated that they broadly found the course engaging and useful and that the visualization capabilities greatly facilitated their understanding of key concepts. All the course material is currently available on a public Github repository and we hope to implement additional exercises and use other solver codes in the future.

OpenSAFT: an extensible Julia implementation of SAFT‐type equations of state

July 07, 2021

Poster, ESAT 2021 - 31st European Symposium on Applied Thermodynamics, Online

The venerable Statistical Associating Fluid Theory (SAFT) equation of state has always had the reputation of being abstruse and impenetrable to the outside world—and to those working in the field, they are often stuck working with complicated legacy code. OpenSAFT.jl is a modern thermodynamics framework built in pure Julia for the full process of implementation and use of SAFT-type (or any free energy-based) models in an easy and intuitive way.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

July 07, 2021

Talk, ESAT 2021 - 31st European Symposium on Applied Thermodynamics, Online

A methodology for obtaining two-body interaction potentials from ab initio calculations is proposed for small species with interactions that are suitably described as isotropic. The corresponding force fields explicitly incorporate three-body interactions and quantum effects of fluids. The methodology provides one with a strategy to map the ab initio force field to effective Mie potentials. A density-dependent two-body approximation of the Axilrod-Teller three-body potential [1] and a temperature-dependent Feynman–Hibbs correction for an effective quantum potential [2] are used to enhance the accuracy of the Mie potentials. When the thermodynamic properties of systems characterized by these potentials are described with the SAFT-VR Mie equation of state, the reliance on thermophysical data to obtain model parameters is completely dispensed with, providing a wholly predictive platform.

A new predictive group‐contribution ideal‐heat‐capacity model, and its influence on second derivative properties calculated using a free‐energy equation of state

July 07, 2021

Poster, ESAT 2021 - 31st European Symposium on Applied Thermodynamics, Online

A statistical-thermodynamics-based group contribution (GC) method, commensurate with the GC methodology used in SAFT-𝛾 Mie, is proposed to model ideal heat capacities. The approach uses four vibrational temperatures per group as adjustable parameters. Parameter estimation is performed on a training set of 215 molecules; the use of dimensionless heat capacities (reduced relative to their classical limits) allows for a more-even distribution of relative errors across molecular weights in homologous series than seen with existing approaches. (Although here treated as adjustable, parameters may alternatively be obtained from ab initio methods or experimental infrared spectra, providing an approach to the prediction of ideal heat capacities of species, such as ions and radicals, that would otherwise be difficult to treat.) A tailored approach for halogenated groups allows many halogenated molecules to be modelled with few parameters. Parameters for small, single-group species agree well with experimental vibrational temperatures; those corresponding to groups used for larger species highlight effects such as anharmonicity and torsional modes. The proposed correlation consistently demonstrates higher accuracy than that of Joback and Reid [1].

Importance of the relative static permittivity in electrolytic SAFT-VR Mie equations of state

July 07, 2021

Talk, ESAT 2021 - 31st European Symposium on Applied Thermodynamics, Online

The influence and importance of the relative static permittivity (RSP) in electrolyte equations of state is examined in-depth for the case of aqueous sodium chloride. The SAFT-VR Mie equation of state is used to model the dispersive and associative interactions, whilst the Debye-Hückel (DH) or Mean-Spherical Approximation (MSA) terms, as well as the Born-solvation term, are used to account for the presence of ions within the mixture. The RSP is obtained from a variety of models, each differing in their dependencies; we consider constant, temperature dependent, temperature-volume dependent and temperature-volume-composition (of both the ions and solvent) dependent models. For a fair comparison between different combinations of electroÍstatic terms and RSP models, all ion-related parameters are obtained a priori. A novel combining rule is proposed to obtain the unlike parameters between solvents and ions; its reliability is examined for a variety of electrolyte systems. We also compare its performance relative to parameterised electrolyte models developed by Eriksen et al.[1] and Selam et al.[2].

The use and value of a student-led Wiki towards facilitating peer collaboration in Chemical Engineering

January 28, 2021

Talk, Advanced HE 2021 STEM Conference, Online

Wikis can facilitate an effective and increased online engagement between individuals who may be geographically distributed. In January 2020, a student-led Chemical Engineering Wiki was developed by two undergraduate students at Imperial College with progressive support from staff. Wiki pages were developed for ten second-year modules which by June 2020 had received over 10,000 views. 90% of the students who used the Wiki found it to be a valuable means of retrieving information, consolidating concepts and preparing for their examinations. These efforts will continue across all year groups in the new academic year and it is hoped that this will provide students additional opportunities for increased collaboration and peer scaffolding given the ongoing requirements for remote teaching and learning.

Students as partners in module design: The development and delivery of a computer-aided drawing course for chemical engineering undergraduate students

January 28, 2021

Talk, Advanced HE 2021 STEM Conference, Online

Teaching computer-aided design (CAD) software within the Chemical Engineering Department at Imperial College is somewhat limited by a condensed timetable and traditionally, students will produce 2D hand-drawn diagrams as part of their module requirements. With the move to remote teaching, students and staff collaborated on a series of online CAD training videos and exercises which were trialled for nine students before being rolled out to the entire third-year cohort. Initial feedback showed that the students found the CAD training to be helpful and relevant to not only the current module, but also to other design-based modules within their programme. This highlights the importance of staff-student collaborations and embedding the student voice to create more authentic learning experiences.

Modelling polymer blend demixing: complications and simplifications in the Gibbs energy of mixing function

November 04, 2020

Talk, 73rd Annual Meeting of the APS Division of Fluid Dynamics, Online

The Cahn-Hilliard equation, which can be used to model polymer blend morphology at a continuum scale, tracks the decrease of the Gibbs energy of the system through changes in the homogenous free energy, which is given the Gibbs energy of mixing, and the interfacial energy. In most problems, the Gibbs energy of mixing function is typically set as a simple quartic polynomial or in the case of polymer blends, the Flory-Huggins equation. In certain cases, such as for mineral solutions or alloys, more suitable free energy functions have been employed. However, more accurate and complex equations of state (EoS) applicable to polymer blends such as Statistical Associating Fluid Theory (SAFT) based EoS have yet to be explored within a phase-field setting. In this work, we explore how these advanced EoS can be integrated to model binary polymer blends, looking at both thermophysical properties and blend morphology. At the other end of the complexity spectrum, we also investigate the impact of various simplifications to the free energy function and the Cahn-Hilliard equation on the numerical solution.

The value of student-led projects towards facilitating independent learning in Engineering education

January 30, 2020

Talk, Advanced HE 2020 STEM Conference, Manchester, UK

Embedding and managing independent learning within Engineering curricula can be somewhat challenging. This work explores the value of student-led projects towards facilitating independent learning by examining the experiences of undergraduate Engineering students who have been involved in two small-scale projects. The first involves creating a student-led maker space to develop a working prototype of a 3D-printed separation column while the second focuses on the role of students as partners in module design. The results show that these student-led initiatives can provide rewarding independent learning situations that build leadership and resilience, encourage entrepreneurship, promote life-long learning and increase selfefficacy and motivation.