arXiv subjects

Pierre J. Walker

Publications and source records attributed to Pierre J. Walker.

8 recordsLinked to original sources

arXiv2026

How Topology Shapes the Phase Behavior of Polyelectrolytes

We develop a topology-specific theory of polyelectrolyte coacervation using the random phase approximation and apply it to both simple and complex coacervation. Our results for stars and dendrimers show that more compact chain topologies display a greater propensity for liquid-liquid phase separation, as a function of both Bjerrum length and salt concentration. For mixtures of different topologies, we demonstrate that differences in polymer topology alone are sufficient to drive multiphase coacervation of polyelectrolytes, which we rationalize in terms of an effective $\chi$ parameter. Analysis of a simplified global phase diagram reveals that the propensity for such topology-driven phase separation is largest at a finite molecular weight. Overall, our results establish polymer topology as a powerful design lever for tuning the phase diagram of charged macromolecules independently of molecular weight, net charge, and monomer chemistry, since changes in topology enable fine-tuning of the effective charge density without altering these molecular characteristics.

cond-mat.soft↗

arXiv2026

Stockmayer Fluid with a Shifted Dipole: Bulk Behavior

Shifting the point dipole from the center of a Stockmayer particle is a simple geometric modification that has been explored previously, yet its implications for liquid structure, dielectric response, and phase behavior remain incompletely understood. Here, we combine molecular dynamics simulations with analytical theory to provide a unified physical interpretation of how dipole displacement reshapes microscopic correlations and propagates to macroscopic thermodynamic properties. We show that dipole shifting breaks the fore-aft symmetry of the local electrostatic field, producing only modest changes in radial packing but strong alterations in angular structure within the first solvation shell. Enhanced alignment near the dipole head is accompanied by frustrated orientational correlations near the tail, leading to broader angular distributions and a shift away from axial configurations at strong coupling. These structural asymmetries weaken cooperative ordering and result in a systematic reduction of the dielectric constant, despite locally stronger interactions. For large shifts, the dielectric response approaches the Debye limit, indicating effective suppression of dipole-dipole correlations. The same geometric frustration governs vapor-liquid equilibria: while increasing dipole strength raises the critical temperature, even modest shifts disrupt the highly polarized liquid states that emerge at strong coupling and can suppress ferroelectric-like ordering. Predictions from a reparameterized COFFEE theory capture these trends within its domain of validity, highlighting the direct connection between local orientational structure and macroscopic observables. Overall, this work demonstrates that dipole location, not only magnitude, provides a powerful control parameter in dipolar fluids and offers a clear framework for understanding geometric frustration in electrostatic liquids.

cond-mat.soft↗

arXiv2025

Stockmayer Fluid with a Shifted Dipole: Interfacial Behavior

We investigate the properties of the liquid-vapor interface in the shifted Stockmayer fluid using molecular dynamics simulations in the canonical ensemble. We study the role of the dipole moment strength and the degree of asymmmetry on equilibrium interfacial characteristics, including density profiles, polar order, nematic order, interfacial polarization, electric field, and electrostatic potential. In addition, we compute angular distribution functions across the interface to gain insight into how the dipole shift affects the molecular orientation. We find that the shift significantly effects angular distribution functions by altering the polar order while leaving the nematic order relatively unaffected, in comparison to the reference symmetric Stockmayer fluid. We find that these results are consistently explained using an image-dipole construction that has been previously applied to symmetric Stockmayer fluids but has never been extended to the shifted model. We find remarkable agreement between the simple theory and the simulations in the qualitative shape of the distribution functions for both the liquid and vapor phases in proximity to the interface. Unexpectedly, the spontaneous polarization at the interface, and therefore the generated electric field, changes sign as the dipole moment strength increases. This also leads to an inversion of the sign of the potential difference across the interface.

cond-mat.soft↗

arXiv2025

Mechanistic Modeling of Lipid Nanoparticle Formation for the Delivery of Nucleic Acid Therapeutics

Nucleic acids such as mRNA have emerged as a promising therapeutic modality with the capability of addressing a wide range of diseases. Lipid nanoparticles (LNPs) as a delivery platform for nucleic acids were used in the COVID-19 vaccines and have received much attention. While modern manufacturing processes which involve rapidly mixing an organic stream containing the lipids with an aqueous stream containing the nucleic acids are conceptually straightforward, detailed understanding of LNP formation and structure is still limited and scale-up can be challenging. Mathematical and computational methods are a promising avenue for deepening scientific understanding of the LNP formation process and facilitating improved process development and control. This article describes strategies for the mechanistic modeling of LNP formation, starting with strategies to estimate and predict important physicochemical properties of the various species such as diffusivities and solubilities. Subsequently, a framework is outlined for constructing mechanistic models of reactor- and particle-scale processes. Insights gained from the various models are mapped back to product quality attributes and process insights. Lastly, the use of the models to guide development of advanced process control and optimization strategies is discussed.

cond-mat.soft↗

arXiv2023

Confronting the thermodynamics knowledge gap: A short course on computational thermodynamics in Julia

Computational elements in thermodynamics have become increasingly important in contemporary chemical-engineering research and practice. However, traditional thermodynamics instruction provides little exposure to computational thermodynamics, leaving students ill-equipped to engage with the state-of-the-art deployed in industry and academia. The recent rise of easy-to-use open-source thermodynamic codes presents an opportunity for educators to help bridge this gap. In this work, we present a short course that was developed and rolled-out using the Clapeyron.jl package, the material of which is all openly available on GitHub. The course can serve as a foundation for others to similarly integrate computational material in thermodynamics education. The course is structured into three sections. Section one serves as a refresher and covers core material in numerical methods and thermodynamics. Section two introduces a range of thermodynamic models such as activity-coefficient models and cubic equations of state, outlining their implementation. In section three the focus is moved to deployment, guiding students on how to implement computational-thermodynamics methods covering volume solvers, saturation solvers, chemical-stability analysis and flash problems. In a pilot study conducted with both undergraduate and graduate students, participants found the material engaging and highly relevant to their chemical-engineering education.

physics.ed-ph↗

arXiv2023

Confidence Interval and Uncertainty Propagation Analysis of SAFT-type Equations of State

Thermodynamic models and, in particular, SAFT-type equations are vital in characterizing complex systems. This paper presents a framework for sampling parameter distributions in PC-SAFT and SAFT-VR Mie equations of state to understand parameter confidence intervals and correlations. We identify conserved quantities contributing to significant correlations. Comparing the equations of state, we find that additional parameters introduced in the SAFT-VR Mie equation increase relative uncertainties (1\%-2\% to 3\%-4\%) and introduce more correlations. When incorporating association through additional parameters, relative uncertainties increase, but correlations slightly decrease. We investigate how uncertainties propagate to derived properties and observe small uncertainties for that data with which the parameters were regressed, especially for saturated-liquid volumes. However, extrapolating to saturated-vapour volumes yields larger uncertainties due to the larger isothermal compressibility. Near the critical point, uncertainties in saturated volumes diverge due to increased sensitivity of the isothermal compressibility to parameter uncertainties. This effect significantly impacts bulk properties, particularly isobaric heat capacity, where uncertainties near the critical point become extremely large, even when these uncertainties are small. We emphasize that even small uncertainties near the critical point lead to divergences in predicted properties.

physics.chem-ph↗

arXiv2022

Clapeyron.jl: An extensible, open-source fluid-thermodynamics toolkit

Thermodynamic models are often vital when characterising complex systems, particularly natural gas, electrolyte, polymer, pharmaceutical and biological systems. However, their implementations have historically been abstruse and cumbersome, and as such, the only options available were black-box commercial tools. In this article, we present Clapeyron.jl: a pioneering attempt at an open-source fluid-thermodynamics toolkit to build and make use of thermodynamic models. This toolkit is built in Julia, a modern language for scientific computing known for its ease of use, extensibility, and first-class support for differentiable programming. We currently support more models than any package available, including standard cubic (SRK, PR, PSRK, etc.), activity-coefficient (NRTL, UNIFAC, etc.), COSMO-based, and the venerable SAFT equations. The property-estimation methods supported are extensive, including bulk, VLE, LLE, VLLE and critical properties. With Clapeyron.jl, researchers and enthusiasts alike will be able to focus on the application and worry less about the implementation.

physics.comp-ph↗

arXiv2020

Introducing students to research codes: A short course on solving partial differential equations in Python

Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease with which a problem can be implemented and solved using these codes reduce the barrier to entry for users. We demonstrate how one of these codes,FiPy, can be introduced to students through a short course using progression as the guiding philosophy. Four exercises of increasing complexity were developed. Basic concepts from more advanced numerical methods courses are also introduced at appropriate points. To further engage students, we demonstrate how an open research problem can be readily implemented and also incorporate the use of ParaView to post-process their results. Student engagement and learning outcomes were evaluated through a pre and post-course survey and a focus group discussion. Students broadly found the course to be engaging and useful with the ability to easily visualise the solution to PDEs being greatly valued. Due to the introductory nature of the course, due care in terms of set-up and the design of learning activities during the course is essential. This course, if integrated with appropriate level of support, can encourage students to use the provided codes and improve their understanding of concepts used in numerical analysis and PDEs.

physics.ed-ph↗