Imperial College London

Professor Erich A. Muller

Faculty of EngineeringDepartment of Chemical Engineering

Professor of Thermodynamics



+44 (0)20 7594 1569e.muller Website




Mrs Raluca Reynolds +44 (0)20 7594 5557




409ACE ExtensionSouth Kensington Campus





Publication Type

207 results found

Hue KY, Lew JH, Myo Thant MM, Matar O, Luckham P, Muller Eet al., 2023, Molecular dynamics simulation of polyacrylamide adsorption on calcite, Molecules, Vol: 28, Pages: 1-17, ISSN: 1420-3049

In poorly consolidated carbonate rock reservoirs, solids production risk, which can lead to increased environmental waste, can be mitigated by injecting formation-strengthening chemicals. Classical atomistic molecular dynamics (MD) simulation is employed to model the interaction of polyacrylamide-based polymer additives with a calcite structure, which is the main component of carbonate formations. Amongst the possible calcite crystal planes employed as surrogates of reservoir rocks, the (1 0 4) plane is shown to be the most suitable surrogate for assessing the interactions with chemicals due to its stability and more realistic representation of carbonate structure. The molecular conformation and binding energies of pure polyacrylamide (PAM), hydrolysed polyacrylamide in neutral form (HPAM), hydrolysed polyacrylamide with 33% charge density (HPAM 33%) and sulfonated polyacrylamide with 33% charge density (SPAM 33%) are assessed to determine the adsorption characteristics onto calcite surfaces. An adsorption-free energy analysis, using an enhanced umbrella sampling method, is applied to evaluate the chemical adsorption performance. The interaction energy analysis shows that the polyacrylamide-based polymers display favourable interactions with the calcite structure. This is attributed to the electrostatic attraction between the amide and carboxyl functional groups with the calcite. Simulations confirm that HPAM33% has a lower free energy than other polymers, presumably due to the presence of the acrylate monomer in ionised form. The superior chemical adsorption performance of HPAM33% agrees with Atomic Force Microscopy experiments reported herein.

Journal article

Chaparro Maldonado G, Muller E, 2023, Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid, Journal of Chemical Physics, Vol: 158, ISSN: 0021-9606

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule–Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the “digital” equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model’s internal consistency is successfully assessed using Brown’s characteristic curves.

Journal article

Muller E, Tilloston M, Diamantonis NI, Buda C, Bolton LWet al., 2023, Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities, Physical Chemistry Chemical Physics, Vol: 25, Pages: 12607-12628, ISSN: 1463-9076

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

Journal article

, 2023, Chemical Engineering Research, Publisher: Department of Chemical Engineering, ISBN: 9781916005044

Reports of the 4th year research projects in the Department of Chemical Engineering at Imperial College London


Fayaz Torshizi M, Graham E, Adjiman C, Galindo A, Jackson G, Muller Eet al., 2023, SAFT-Υ force field for the simulation of molecular fluids 9: Coarse-grained models for polyaromatic hydrocarbons describing thermodynamic, interfacial, structural, and transport properties, Journal of Molecular Liquids, Vol: 369, ISSN: 0167-7322

Coarse-grained models of polyaromatic hydrocarbons parametrized by employing the SAFT- Mie approach are presented and assessed by comparison with experimental data and all-atom models in their ability to describe liquid densities, isothermal compressibilities, thermal expansivities, viscosities, and interfacial tensions. The structural behaviour characterized by the center of mass and angular radial distribution functions are also benchmarked. The SAFT- Mie force field models are shown to deliver quantitatively accurate predictions while promising significant speedups in the computational cost of performing molecular dynamics simulations.

Journal article

Mejia A, Cardenas H, Stephan S, Muller Eet al., 2023, The monotonicity behavior of density profiles at vapor-liquid interfaces of mixtures, Fluid Phase Equilibria, Vol: 564, Pages: 1-8, ISSN: 0378-3812

In their seminal monograph ’Molecular Theory of Capillarity’, Rowlinson and Widom describe different possible shapes of density profiles at the vapor-liquid interface of mixtures. They postulated that in some instances, density profiles could possibly be non-monotonic, exhibiting either a maximum and/ or a minimum. This contribution revisits this statement in the light of four decades of posterior research. We summarize the distinct morphologies at the vapor-liquid interface suggested in the literature recognizing that the condition of a single minimum in the profile has not yet been reported. Interfacial density profiles with a single maximum as well as fully monotonic density profiles have been observed and reported extensively. The case of a simultaneous maximum and minimum is more controversial, as it has only been predicted using theoretical approaches such as density gradient theory (DGT). This ambiguity is further investigated in this work using the example of the vapor-liquid interface of cyclohexane + butanol. Both DGT in combination with several distinct equations of state and molecular dynamics simulations are used. The results from the two methods are found to be contradictory: while the DGT results predict a maximum/minimum structure, the computer experiment results indicate only a single maximum in the density profiles. This work thereby emphasizes that results from DGT for highly non-ideal mixtures should not be taken for granted.

Journal article

Seddon D, Müller EA, Cabral JT, 2022, Machine learning hybrid approach for the prediction of surface tension profiles of hydrocarbon surfactants in aqueous solution, Journal of Colloid and Interface Science, Vol: 625, Pages: 328-339, ISSN: 0021-9797

HYPOTHESIS: Predicting the surface tension (SFT)-log(c) profiles of hydrocarbon surfactants in aqueous solution is computationally non-trivial, and empirically challenging due to the diverse and complex architecture and interactions of surfactant molecules. Machine learning (ML), combining a data-based and knowledge-based approach, can provide a powerful means to relate molecular descriptors to SFT profiles. EXPERIMENTS: A dataset of SFT for 154 model hydrocarbon surfactants at 20-30 °C is fitted to the Szyszkowski equation to extract three characteristic parameters (Γmax,KL and critical micelle concentration (CMC)) which are correlated to a series of 2D and 3D molecular descriptors. Key (∼10) descriptors were selected by removing co-correlation, and employing a gradient-boosted regressor model to rank feature importance and carry out recursive feature elimination (RFE). The hyperparameters of each target-variable model were fine-tuned using a randomised cross-validated grid search, to improve predictive ability and reduce overfitting. FINDINGS: The ML models correlate favourably with test experimental data, with R2= 0.69-0.87, and the merits and limitations of the approach are discussed based on 'unseen' hydrocarbon surfactants. The incorporation of a knowledge-based framework provides an appropriate smoothing of the experimental data which simplifies the data-driven approach and enhances its generality. Open-source codes and a brief tutorial are provided.

Journal article

Muller E, fayaz-torshizi M, Xu W, Marshall B, Ravikovitch Pet al., 2022, Significant effect of rugosity on transport of hydrocarbon liquids in carbonaceous nanopores, Energy and Fuels, Vol: 36, ISSN: 0887-0624

We report the results of modelling the transport of n-octane and n-hexadecane andtheir mixtures through carbonaceous nanopores at high-pressure conditions. Pores aremodelled as smooth slit sheets with perturbations added as ridges and steps and aversion of the Statistical Associating Fluid Theory (SAFT-γ Mie) is used both as equation of state and as a coarse-grained force field to account for fluid-fluid and fluid-solidmolecular interactions. Molecular simulation allowed the description of transport diffusivities in terms of molecular flow, using boundary driven non-equilibrium moleculardynamics (BD-NEMD). Transport diffusivities are also independently calculated using equilibrium and external force non-equilibrium molecular dynamics (EF-NEMD)simulations, after accounting for the adsorption on the pores. We show consistency between the approaches for quantifying transport in terms of permeabilities (Darcy flows)and transport diffusivities. We find that smooth slit carbon pore models, which arecommonly employed in literature as surrogates for kerogen regions in shale, are an inadequate representation of ultra-confined natural pores. For slit pores, the flow patternsare characterized by a fully-mutualized plug-like flow and fast transport. However, byincorporating even a small amount of rugosity (roughness) to the solid walls, the diffusion coefficients decrease dramatically with surface roughness significantly affectingthe characteristic transport and velocity profiles inside the pores. In all cases, it is seenthat there are important cross-correlation effects, influencing the way components ofthe mixture flow together. Calculated self-diffusivities are orders of magnitude smallerthan the observed transport diffusivities for liquid mixtures. This work has a directimpact on the understanding and modelling of unconventional hydrocarbon recoveryand flow in organic shale rocks.

Journal article

Thiemann F, Schran C, Rowe P, Muller E, Michaelides Aet al., 2022, Water flow in single-wall nanotubes: Oxygen makes it slip, hydrogen makes it stick, ACS Nano, Vol: 16, Pages: 10775-10782, ISSN: 1936-0851

Experimental measurements have reported ultrafast and radius-dependent water transport in carbon nanotubes which are absent in boron nitride nanotubes. Despite considerable effort, the origin of this contrasting (and fascinating) behavior is not understood. Here, with the aid of machine learning-based molecular dynamics simulations that deliver first-principles accuracy, we investigate water transport in single-wall carbon and boron nitride nanotubes. Our simulations reveal a large, radius-dependent hydrodynamic slippage on both materials, with water experiencing indeed a ≈5 times lower friction on carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms across the two materials reveals that the fast water transport on carbon is governed by facile oxygen motion, whereas the higher friction on boron nitride arises from specific hydrogen–nitrogen interactions. This work not only delivers a clear reference of quantum mechanical accuracy for water flow in single-wall nanotubes but also provides detailed mechanistic insight into its radius and material dependence for future technological application.

Journal article

, 2022, Chemical Engineering Research: Reports of the 4th year research projects in the Department of Chemical Engineering at Imperial College London. Volume 4, Department of Chemical Engineering, ISBN: 978-1-9160050-3-7

This volume of Chemical Engineering Research collects the unedited research project reports written by 4th year undergraduates (Class of 2022) of the M.Eng. course on Chemical Engineering in the Department of Chemical Engineering at Imperial College London. The research project spans for one term (Autumn) during the last year of the career and has an emphasis on independence, ability to plan and pursue original project work for an extended period, to produce a high quality report, and to present the work to an audience using appropriate visual aids. Students are also expected to produce a literature survey and to place their work in the context of prior art. The papers presented showcase the diversity and depth of some of the research streams in the department, but obviously only touch on a small number of research groups and interests. For a full description of the research at the department, the reader is referred to the departmental website.


Fayaz-Torshizi M, Xu W, Vella J, Marshall B, Ravikovitch P, Muller Eet al., 2022, Use of boundary driven non-equilibrium molecular dynamics for determining transport diffusivities of multicomponent mixtures in nanoporous materials, The Journal of Physical Chemistry B: Biophysical Chemistry, Biomaterials, Liquids, and Soft Matter, Vol: 126, Pages: 1085-1100, ISSN: 1520-5207

The boundary-driven molecular modeling strategy to evaluate mass transport coefficients of fluids in nanoconfined media is revisited and expanded to multicomponent mixtures. The method requires setting up a simulation with bulk fluid reservoirs upstream and downstream of a porous media. A fluid flow is induced by applying an external force at the periodic boundary between the upstream and downstream reservoirs. The relationship between the resulting flow and the density gradient of the adsorbed fluid at the entrance/exit of the porous media provides for a direct path for the calculation of the transport diffusivities. It is shown how the transport diffusivities found this way relate to the collective, Onsager, and self-diffusion coefficients, typically used in other contexts to describe fluid transport in porous media. Examples are provided by calculating the diffusion coefficients of a Lennard-Jones (LJ) fluid and mixtures of differently sized LJ particles in slit pores, a realistic model of methane in carbon-based slit pores, and binary mixtures of methane with hypothetical counterparts having different attractions to the solid. The method is seen to be robust and particularly suited for the study of study of transport of dense fluids and liquids in nanoconfined media.

Journal article

Lew JH, Matar OK, Müller EA, Maung MTM, Luckham PFet al., 2022, Adsorption of hydrolysed polyacrylamide onto calcium carbonate, Polymers, Vol: 14, Pages: 405-405, ISSN: 2073-4360

Carbonate rock strengthening using chemical techniques is a strategy to prevent excessive fines migration during oil and gas production. We provide herein a study of the adsorption of three types of hydrolysed polyacrylamide (HPAM) of different molecular weight (F3330S, 11–13 MDa; F3530 S, 15–17 MDa; F3630S, 18–20 MDa) onto calcium carbonate (CaCO3) particles via spectrophotometry using a Shimadzu UV-2600 spectrometer. The results are compared to different adsorption isotherms and kinetic models. The Langmuir isotherm shows the highest correlation coefficient (R2 > 0.97) with equilibrium parameters (RL) ranging between 0 and 1 for all three HPAMs, suggesting a favorable monolayer adsorption of HPAM onto CaCO3. The adsorption follows pseudo-second order kinetics, indicating that the interaction of HPAM with CaCO3 is largely dependent on the adsorbate concentration. An adsorption plot reveals that the amount of HPAM adsorbed onto CaCO3 at equilibrium increases with higher polymer molecular weight; the equilibrium adsorbed values for F3330S, F3530S and F3630S are approximately 0.24 mg/m2, 0.31 mg/m2, and 0.43 mg/m2, respectively. Zeta potential analysis shows that CaCO3 has a zeta potential of +12.32 mV, which transitions into negative values upon introducing HPAM. The point of zero charge (PZC) is observed at HPAM dosage between 40 to 50 ppm, in which the pH here lies between 9–10.

Journal article

Muller E, Fayaz-Torshizi M, 2022, Coarse-grained molecular simulation of polymers supported by the use of the SAFT-γ mie equation of state, Macromolecular Theory and Simulations, Vol: 31, Pages: 1-28, ISSN: 1022-1344

A framework to self-consistently combine a classical equation of state (EoS) and a molecular force field to model polymers and polymer mixtures is presented. The statistical associating fluid theory (SAFT-γ Mie) model is used to correlate the thermophysical properties of oligomers and generate robust and transferrable coarse-grained (CG) molecular parameters which can be used both in particle based molecular simulations and in EoS calculations. Examples are provided for polyethylene, polypropylene, polyisobutyleneatactic polystyrene, 1,4-cis-butadiene, polyisoprene, their blends and mixtures with low molecular weight solvents. Different types ofliquid-liquid phase behaviour are quantitatively captured both by the EoS and by direct molecular dynamics simulations. The use ofCG models following this top-down approach extends the time and length scales accessible to molecular simulation while retainingquantitative accuracy as compared to experimental results.

Journal article

Muller E, Schran C, Thiemann F, Rowe P, Marsalek O, Michaelides Aet al., 2021, Machine learning potentials for complex aqueous systems made simple, Proceedings of the National Academy of Sciences of USA, Vol: 38, Pages: 1-8, ISSN: 0027-8424

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning framework that enablesthe efficient development and validation of models for complex aqueous systems. Instead of trying to deliver a globally-optimal machinelearning potential, we propose to develop models applicable to specific thermodynamic state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with minimum human effort through a data-drivenactive learning protocol. Such models can afterwards be applied inexhaustive simulations to provide reliable answers for the scientificquestion at hand, or systematically explore the thermal performanceof ab initio methods. We showcase this methodology on a diverseset of aqueous systems comprising bulk water with different ionsin solution, water on a titanium dioxide surface, as well as waterconfined in nanotubes and between molybdenum disulfide sheets.Highlighting the accuracy of our approach with respect to the underlying ab initio reference, the resulting models are evaluated in detailwith an automated validation protocol that includes structural anddynamical properties and the precision of the force prediction of themodels. Finally, we demonstrate the capabilities of our approach forthe description of water on the rutile titanium dioxide (110) surface toanalyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicatedbut accurate extension of simulation time and length scales for complex systems.

Journal article

Muller E, Thiemann F, Rowe P, Zen A, Michaelides Aet al., 2021, Defect-dependent corrugation in graphene, ACS Nano Letters, Vol: 21, Pages: 8143-8150, ISSN: 1936-0851

Graphene’s intrinsically corrugated and wrinkled topology fundamentally influences its electronic, mechanical, and chemical properties. Experimental techniques allow the manipulation of pristine graphene and the controlled production of defects which allows one to control the atomic out-of-plane fluctuations and thus tune graphene’s properties. Here, we perform large scale machine learning-driven molecular dynamics simulations to understand the impact of defects on the structure of graphene. We find that defects cause significantly higher corrugation leading to a strongly wrinkled surface. The magnitude of this structural transformation strongly depends on the defect concentration and specific type of defect. Analyzing the atomic neighborhood of the defects reveals that the extent of these morphological changes depends on the preferred geometrical orientation and the interactions between defects. While our work highlights that defects can strongly affect graphene’s morphology, it also emphasizes the differences between distinct types by linking the global structure to the local environment of the defects.

Journal article

Mejía A, Cartes M, Chaparro G, Feria E, Blas FJ, Míguez JM, Algaba J, Müller EAet al., 2021, Phase equilibria and interfacial properties of selected methane + n-alkane binary mixtures, Journal of Molecular Liquids, Vol: 341, Pages: 1-13, ISSN: 0167-7322

Experimental determination, theoretical modeling, and molecular simulation have been combined to describe the bulk phase equilibria (i.e., pressure, liquid, and vapor saturated mass densities) and interfacial properties (i.e., interfacial concentration, adsorption, and interfacial tension) for methane + n-decane, n-dodecane, n-tetradecane and n-hexadecane binary mixtures at 344.15 K and in a pressure range between 0.1 and 30 MPa. Experimental determinations are carried out using a combined apparatus that includes a high-pressure vibrating tube densimeter and a high-pressure pendant drop tensiometer. The theoretical approach is based on the van der Waals gradient theory coupled to the Statistical Associating Fluid Theory of Variable Range employing a Mie potential (SAFT-VR-Mie) equation of state, where the fluids are described as Coarse Grained (CG) atoms. Molecular dynamics simulation for the same systems based on the CG Mie potential are reported. The three approaches are able to indepen independently predict phase equilibrium and interfacial properties, showing a very good agreement amongst themselves. For the systems and conditions studied here, the vapor mass density increases; the liquid mass density and interfacial tensions decrease as the pressure increases, and with a fixed temperature and pressure, the liquid mass density and interfacial tensions increase as the n-alkane molecular chain length increases. It is observed that methane is adsorbed along the interfacial region, whereas the n-alkanes (n-decane, n-dodecane, n-tetradecane, n-hexadecane) do not exhibit surface activity. The relative Gibbs adsorption of methane increases significantly with pressure until it reaches a maximum denoting the adsorption saturation limit. It is also observed that the adsorption of methane only slightly increases with the chain length of the n-alkane.

Journal article

Muller E, Fayaz Torshizi M, 2021, Coarse-grained molecular dynamics study of the self- assembly of polyphilic bolaamphiphiles using the SAFT- γ mie force field, Molecular Systems Design & Engineering, Vol: 6, Pages: 594-608, ISSN: 2058-9689

A methodology is outlined to parametrize coarse grained molecular models for the molecular dynamics simulation of liquid crystalline bolaamphiphiles (BAs). We employ a top down approach based on the use of the Statistical Associating Fluid Theory (SAFT) that provides a robust and transferable set of building blocks from the fitting of thermophysical properties of smaller molecules. The model is employed to characterise symmetric and asymmetric swallow-tailed BAs and to compare them with an isomeric T-shaped BA. Branching of the side chain of the BAs, leading to the swallow-tailed geometry generates a richness in the number and morphology of liquid crystal mesophases. The simulations elucidate some of the intriguing results observed in experiments.

Journal article

Mejia A, Muller E, Chaparro Maldonado G, 2021, SGTPy: A Python code for calculating the interfacial properties of fluids based on the Square Gradient Theory using the SAFT-VR Mie equation of state, Journal of Chemical Information and Modeling, Vol: 61, Pages: 1244-1250, ISSN: 1549-9596

In this work, we showcase SGTPy, a Python open-source code developed to calculate interfacial properties (interfacial concentration profiles and interfacial or surface tension) for pure fluids and fluid mixtures. SGTPy employs the Square Gradient Theory (SGT) coupled to the Statistical Associating Fluid Theory of Variable Range employing a Mie potential (SAFT-VR-Mie). SGTPy uses standard Python numerical packages (i.e., NumPy, SciPy) and can be used under Jupyter notebooks. Its features are the calculation of phase stability, phase equilibria, interfacial properties, and the optimization of the SGT and SAFT parameters for vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria for pure fluids and multicomponent mixtures. Phase equilibrium calculations include two-phase and multiphase flash, bubble and dew points, and the tangent plane distance. For the computation of interfacial properties, SGTPy incorporates several options to solve the interfacial concentration, such as the path technique, an auxiliary time function, and orthogonal collocation. Additionally, the SGTPy code allows the inclusion of subroutines from other languages (e.g., Fortran, and C++) through Cython and f2py Python tools, which opens the possibility for future extensions or recycling tested and optimized subroutines from other codes. Supporting Information includes a review of the theoretical expressions required to couple SAFT-VR-Mie equation of state with the SGT. The use and capabilities of SGTPy are illustrated through step by step examples written on Jupyter notebooks for the cases of pure fluids and binary and ternary mixtures in bi- and three- phasic equilibria. The SGTPy code can be downloaded from

Journal article

, 2021, Chemical Engineering Research, Publisher: Department of Chemical Engineering, ISBN: 978-1-9160050-2-0

Reports of the 4th year research projects in the Department of Chemical Engineering at Imperial College London.


Antonio Estévez L, Colpas FJ, Müller EA, 2020, A simple thermodynamic model for the solubility of thermolabile solids in supercritical fluids, Chemical Engineering Science, Vol: 232, Pages: 1-10, ISSN: 0009-2509

An equation-of-state (EoS) scheme to correlate the solubility of solids in supercritical fluids is presented. The solute fugacity coefficient is obtained using the pure-solvent compressibility factor, and empirical solute-to-solvent parameter ratios of cohesion factors and covolumes. The proposed method is simpler than EoS conventional calculations since no iteration is required. We retain the link to classical cubic EoS and mixing rules and showcase the application employing both the Redlich-Kwong and Peng-Robinson EoS. The method uses two adjustable parameters, which are computed from experimental data for several binary systems and used to predict solubilities. The results have been favorably compared to those computed by other methods. The advantage of EoS-based models over empirical ones has been emphasized for cases where the solubilities are extrapolated beyond the range of experimental data. The proposal is advantageous for correlating solubility of thermolabile solids in supercritical fluids since no critical properties of the solute are required.

Journal article

Thiemann F, Rowe P, Muller E, Michaelides Aet al., 2020, A machine learning potential for hexagonal boron nitride applied to thermally and mechanically induced rippling, The Journal of Physical Chemistry C: Energy Conversion and Storage, Optical and Electronic Devices, Interfaces, Nanomaterials, and Hard Matter, Vol: 124, Pages: 22278-22290, ISSN: 1932-7447

We introduce an interatomic potential for hexagonal boron nitride (hBN) based on the Gaussian approximation potential (GAP) machine learning methodology. The potential is based on a training set of configurations collected from density functional theory (DFT) simulations and is capable of treating bulk and multilayer hBN as well as nanotubes of arbitrary chirality. The developed force field faithfully reproduces the potential energy surface predicted by DFT while improving the efficiency by several orders of magnitude. We test our potential by comparing formation energies, geometrical properties, phonon dispersion spectra, and mechanical properties with respect to benchmark DFT calculations and experiments. In addition, we use our model and a recently developed graphene-GAP to analyze and compare thermally and mechanically induced rippling in large scale two-dimensional (2D) hBN and graphene. Both materials show almost identical scaling behavior with an exponent of η ≈ 0.85 for the height fluctuations agreeing well with the theory of flexible membranes. On the basis of its lower resistance to bending, however, hBN experiences slightly larger out-of-plane deviations both at zero and finite applied external strain. Upon compression, a phase transition from incoherent ripple motion to soliton-ripples is observed for both materials. Our potential is freely available online at [].

Journal article

Zhu K, Muller E, 2020, Generating a machine-learned equation of state for fluid properties, The Journal of Physical Chemistry B: Biophysical Chemistry, Biomaterials, Liquids, and Soft Matter, Vol: 124, Pages: 8628-8639, ISSN: 1520-5207

Equations of state (EoS) for fluids have been a staple of engineering design and practice for over a century. Available EoS are based on the fitting of a closed-form analytical expression to suitable experimental data. The mathematical structure and the underlying physical model significantly restrain the applicability and accuracy of the resulting EoS. This contribution explores the issues surrounding the substitution of machine-learned models for analytical EoS. In particular, we describe, as a proof of concept, the effectiveness of a machine-learned model to replicate the statistical associating fluid theory (SAFT-VR Mie) EoS for pure fluids. To quantify the effectiveness of machine-learning techniques, a large set of pseudodata is obtained from the EoS and used to train the machine-learning models. We employ artificial neural networks and Gaussian process regression to correlate and predict thermodynamic properties such as critical pressure and temperature, vapor pressures, and densities of pure model fluids; these are performed on the basis of molecular descriptors. The comparisons between the machine-learned EoS and the surrogate data set suggest that the proposed approach shows promise as a viable technique for the correlation and prediction of thermophysical properties of fluids.

Journal article

Cardenas H, Muller E, 2020, How does the shape and surface energy of pores affect the adsorption of nanoconfined fluids?, AIChE Journal, Vol: 67, Pages: 1-11, ISSN: 0001-1541

We report a systematic molecular simulation study of the behavior of Lennard‐Jones fluids inside nanopores of diverse shapes, focusing on the effect that the pore geometry and the local energetic environment have on the adsorption isotherms. Infinitely long pores with polygon (triangle, square, pentagon, hexagon, octagon, decagon and circle) cross sections are considered. Three different pore sizes commensurate with the molecular diameters along with three different values of fluid‐solid energy interactions are chosen to perform Grand Canonical Monte Carlo simulations at a subcritical temperature. Overall, the effect of nanoconfinement on the adsorption of fluids is seen to be a delicate balance between the geometric packing restrictions imposed by the hard cores of the molecules and the surfaces, the excess adsorption induced by the presence (or absence) of energetically favored “hot spots” and the overall ratio of surface/bulk fluid volume present in the pore.

Journal article

Bhatia N, Müller EA, Matar O, 2020, A GPU accelerated Lennard-Jones system for immersive molecular dynamics simulations in virtual reality, International Conference on Human-Computer Interaction, Publisher: Springer International Publishing, Pages: 19-34, ISSN: 0302-9743

Interactive tools and immersive technologies make teaching more engaging and complex concepts easier to comprehend are designed to benefit training and education. Molecular Dynamics (MD) simulations numerically solve Newton’s equations of motion for a given set of particles (atoms or molecules). Improvements in computational power and advances in virtual reality (VR) technologies and immersive platforms may in principle allow the visualization of the dynamics of molecular systems allowing the observer to experience first-hand elusive physical concepts such as vapour-liquid transitions, nucleation, solidification, diffusion, etc. Typical MD implementations involve a relatively large number of particles N = O( 104 ) and the force models imply a pairwise calculation which scales, in case of a Lennard-Jones system, to the order of O( N2 ) leading to a very large number of integration steps. Hence, modelling such a computational system over CPU along with a GPU intensive virtual reality rendering often limits the system size and also leads to a lower graphical refresh rate. In the model presented in this paper, we have leveraged GPU for both data-parallel MD computation and VR rendering thereby building a robust, fast, accurate and immersive simulation medium. We have generated state-points with respect to the data of real substances such as CO 2 . In this system the phases of matter viz. solid liquid and gas, and their emergent phase transition can be interactively experienced using an intuitive control panel.

Conference paper

Bernet T, Mueller EA, Jackson G, 2020, A tensorial fundamental measure density functional theory for the description of adsorption in substrates of arbitrary three-dimensional geometry, JOURNAL OF CHEMICAL PHYSICS, Vol: 152, ISSN: 0021-9606

Journal article

Zheng L, Rucker M, Bultreys T, Georgiadis A, Mooijer M, Bresme F, Trusler J, Muller Eet al., 2020, Surrogate models for studying the wettability of nanoscale natural rough surfaces using molecular dynamics, Energies, Vol: 13, ISSN: 1996-1073

A molecular modeling methodology is presented to analyze the wetting behavior of natural surfaces exhibiting roughness at the nanoscale. Using atomic force microscopy, the surface topology of a Ketton carbonate is measured with a nanometer resolution, and a mapped model is constructed with the aid of coarse-grained beads. A surrogate model is presented in which surfaces are represented by two-dimensional sinusoidal functions defined by both an amplitude and a wavelength. The wetting of the reconstructed surface by a fluid, obtained through equilibrium molecular dynamics simulations, is compared to that observed by the different realizations of the surrogate model. A least-squares fitting method is implemented to identify the apparent static contact angle, and the droplet curvature, relative to the effective plane of the solid surface. The apparent contact angle and curvature of the droplet are then used as wetting metrics. The nanoscale contact angle is seen to vary significantly with the surface roughness. In the particular case studied, a variation of over 65° is observed between the contact angle on a flat surface and on a highly spiked (Cassie–Baxter) limit. This work proposes a strategy for systematically studying the influence of nanoscale topography and, eventually, chemical heterogeneity on the wettability of surfaces.

Journal article

alonso G, chaparro G, cartes M, Muller E, Mejia Aet al., 2020, Probing the interfacial behavior of Type IIIa binary mixtures along the three-phase line employing molecular thermodynamics, Molecules, Vol: 25, ISSN: 1420-3049

Interfacial properties such as interfacial profiles, surface activity, wetting transitions, and interfacial tensions along the three-phase line are described for a Type IIIa binary mixture. The methodological approach combines the square gradient theory coupled to the statistical associating fluid theory for Mie potentials of variable range, and coarse-grained molecular dynamics simulations using the same underlying potential. The water + n-hexane mixture at three-phase equilibrium is chosen as a benchmark test case. The results show that the use of the same molecular representation for both the theory and the simulations provides a complementary picture of the aforementioned mixture, with an excellent agreement between the molecular models and the available experimental data. Interfacial tension calculations are extended to temperatures where experimental data are not available. From these extrapolations, it is possible to infer a first order wetting transition at 347.2 K, where hexane starts to completely wet the water/vapor interface. Similarly, the upper critical end point is estimated at 486.3 K. Both results show a very good agreement to the available experimental information. The concentration profiles confirm the wetting behavior of n-hexane along with a strong positive surface activity that increases with temperature, contrasting the weak positive surface activity of water that decreases with temperature.

Journal article

Muller E, Trusler J, Bresme F, Zheng Let al., 2020, Employing SAFT coarse grained force fields for the molecular simulation of thermophysical and transport properties of CO2 – n-alkane mixtures, Journal of Chemical and Engineering Data, Vol: 65, Pages: 1159-1171, ISSN: 0021-9568

We report an assessment of the predictive and correlative capability of the SAFT coarse-grained force field as applied to mixtures of CO2 with n-decane and n-hexadecane. We obtain the pure and cross-interaction parameters by matching simulations to experimental phase equilibrium behavior and transfer these parameters to predict shear viscosities. We apply both equilibrium (based on the Green–Kubo formulation) and nonequilibrium (based on the application of an external force to generate an explicit velocity field) algorithms. Single- and two-site models are explored for CO2, and while for volumetric properties both models provide good results, only the model that aligns with the molecular shape is found to be robust when describing highly asymmetric binary mixtures over wide ranges of temperature and pressure. While the models provide good quantitative predictions of viscosity, deviations among the algorithms and with experimental data are encountered for binary mixtures involving longer chain fluids, and in particular at high-pressure and low-temperature states.

Journal article

Aasen A, Hammer M, Müller EA, Wilhelmsen Øet al., 2020, Equation of state and force fields for Feynman-Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium., Journal of Chemical Physics, Vol: 152, Pages: 074507-1-074507-18, ISSN: 0021-9606

We extend the statistical associating fluid theory of quantum corrected Mie potentials (SAFT-VRQ Mie), previously developed for pure fluids [Aasen et al., J. Chem. Phys. 151, 064508 (2019)], to fluid mixtures. In this model, particles interact via Mie potentials with Feynman-Hibbs quantum corrections of first order (Mie-FH1) or second order (Mie-FH2). This is done using a third-order Barker-Henderson expansion of the Helmholtz energy from a non-additive hard-sphere reference system. We survey existing experimental measurements and ab initio calculations of thermodynamic properties of mixtures of neon, helium, deuterium, and hydrogen and use them to optimize the Mie-FH1 and Mie-FH2 force fields for binary interactions. Simulations employing the optimized force fields are shown to follow the experimental results closely over the entire phase envelopes. SAFT-VRQ Mie reproduces results from simulations employing these force fields, with the exception of near-critical states for mixtures containing helium. This breakdown is explained in terms of the extremely low dispersive energy of helium and the challenges inherent in current implementations of the Barker-Henderson expansion for mixtures. The interaction parameters of two cubic equations of state (Soave-Redlich-Kwong and Peng-Robinson) are also fitted to experiments and used as performance benchmarks. There are large gaps in the ranges and properties that have been experimentally measured for these systems, making the force fields presented especially useful.

Journal article

, 2020, Chemical Engineering Research: Reports of the 4th year research projects in the Department of Chemical Engineering at Imperial College London. Volume 2, London, UK, Publisher: Department of Chemical Engineering, Imperial College London, ISBN: 9781916005013

This volume of Chemical Engineering Research collects the unedited research project reportswritten by 4th year undergraduates (Class of 2020) of the M.Eng. course on ChemicalEngineering in the Department of Chemical Engineering at Imperial College London. Theresearch project spans for one term (Autumn) during the last year of the career and has anemphasis on independence, ability to plan and pursue original project work for an extendedperiod, to produce a high quality report, and to present the work to an audience usingappropriate visual aids. Students are also expected to produce a literature survey and to placetheir work in the context of prior art. The papers presented showcase the diversity and depth ofsome of the research streams in the department, but obviously only touch on a small numberof research groups and interests. For a full description of the research at the department, thereader is referred to the departmental website


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