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

214 results found

Chaparro G, Muller E, 2024, Simulation and data-driven modeling of the transport properties of the Mie fluid, The Journal of Physical Chemistry B: Biophysical Chemistry, Biomaterials, Liquids, and Soft Matter, Vol: 128, Pages: 551-566, ISSN: 1520-5207

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

Journal article

Muller E, Mejia A, chaparro G, cartes Met al., 2024, Assessment and modeling of the isobaric vapor-liquid-liquid equilibrium for water + cyclopentyl methyl ether + alcohol (ethanol or propan-1-ol) ternary mixtures, Journal of Molecular Liquids, ISSN: 0167-7322

Journal article

Xu W, Fayaz-Torshizi M, Muller E, 2024, Effect of surface roughness and morphology on the adsorption and transport of CH4/CO2 mixtures in nanoporous carbons, Journal of Co2 Utilization, Vol: 79, ISSN: 2212-9820

We report here molecular simulations of the adsorption and transport behaviour of CH4/CO2 mixtures in two types of non-ideal carbon nanopores. One model decorates an otherwise slit pore with surface imperfections which disrupt the smooth walls; a second model considers a disordered media, formed of randomly arranged coronene flakes, resulting in significant tortuosity. Boundary-Driven Non-Equilibrium Molecular Dynamics (BD-NEMD) and External Force Non-Equilibrium Molecular Dynamics (EF-NEMD) are used to study adsorption and transport properties in both types of pores with varying degrees of rugosity and tortuosity. Intermolecular interactions and bulk fluid properties are described by the statistical associating fluid theory (SAFT) coarse-grained Mie potential and equation of state respectively. Strong CO2 adsorption and fast CH4 transport are observed in smooth slit pores. Small instances of surface rugosity change the dynamics significantly, reducing the transport diffusivity by over an order of magnitude. The fast plug-like flow reported in slit pores dissipates with increasing rugosity, indicating a fundamental change in the flow pattern. Furthermore, rugose pores exhibit a lower capacity for CO2 adsorption, suggesting the performance of CO2 -enhanced oil recovery may be overestimated by the smooth pore models. A pore characteristic factor is shown to be appropriate to correlate the transport diffusivities in nano-pores.

Journal article

Horsch MT, Chiacchiera S, Guevara Carrión G, Kohns M, Müller EA, Šarić D, Stephan S, Todorov IT, Vrabec J, Schembera Bet al., 2023, Epistemic Metadata for Computational Engineering Information Systems, Pages: 302-317, ISSN: 0922-6389

Digitalization is a priority for innovation in the engineering sciences. The digital transformation requires making the knowledge claims from scientific research data machine-actionable, so that they can be integrated and analysed with minimal human intervention. Up until now, the depth of digitalization is often too shallow, with annotations that are only of use to a human reader. In addition, digital infrastructures and their metadata standards are tedious to use: They demand too much effort from researchers, much of which goes into metadata that contribute nothing to an improved reuse of knowledge. These shortcomings are related. Data documentation and annotation are complicated and of little use whenever the metadata that make knowledge reusable are not prioritized. Addressing this gap, we discuss metadata standardization efforts targeted at documenting the knowledge status of data; we refer to such an annotation as epistemic metadata. We propose a schema for epistemic metadata, with a focus on knowledge and reproducibility claims, that is designed to be user-friendly and flexible enough to apply to a spectrum of circumstances and validity assessments. These developments are implemented as part of the PIMS-II ontology. They were conducted in line with requirements procured through a case study on papers and claims from molecular modelling and simulation.

Conference paper

Lew JH, Luckham PF, Matar OK, Müller EA, Santos AS, Maung Maung MTet al., 2023, Consolidation of Calcium Carbonate Using Polyacrylamides with Different Chemistries, Powders, Vol: 3, Pages: 1-16

<jats:p>In this work, the consolidation of calcium carbonate (CaCO3) by polyacrylamide (PAM) of different molecular weights, charge densities, and functional groups was investigated via oscillatory rheology and unconfined compressive strength (UCS) analysis. Oscillatory rheology showed that the storage modulus G′ was approximately 10 times higher than the loss modulus G″, indicating a highly elastic CaCO3 sample upon consolidation via PAM. Both oscillatory rheology and UCS analysis exhibited similar trends, wherein the mechanical values (G′, G″, and UCS) first increased with increasing polymer dosage, until they reached a peak value (typically at 3 mgpol/gCaCO3), followed by a decrease in the mechanical values. This indicates that there is an optimum polymer dosage for the different PAM-CaCO3 colloidal systems, and that exceeding this value induces the re-stabilisation of the colloidal system, leading to a decreased degree of consolidation. Regarding the effect of the PAM molecular weight, the peak G′ and UCS values of CaCO3 consolidated by hydrolysed PAM (HPAM) of different molecular weights are very similar. This is likely due to the contour length of the HPAMs being either almost the same or longer than the average distance between two CaCO3 particles. The effect of the PAM charge density revealed that the peak G′ and UCS values decreased as the charge density of the PAM increased, while the optimum PAM dosage increased with decreasing PAM charge density. The higher likelihood of lower-charge PAM bridging between the particles contributes to higher elastic energy and mechanical strength. Finally, regarding the PAM functional group, CaCO3 consolidated by sulfonated polyacrylamide (SPAM) typically offers lower mechanical strength than that consolidated with HPAM. The bulky sulfonate side groups of SPAM interfere with the surface packing, reducing the number of polymers able to adsorb onto the surface and, eventually, reduci

Journal article

Lew JH, Matar O, Muller E, Luckham P, Santos A, Thant MMTet al., 2023, Atomic Force Microscopy of hydrolysed polyacrylamide adsorption onto calcium carbonate, Polymers, Vol: 15, ISSN: 2073-4360

In this work, the interaction of hydrolysed polyacrylamide (HPAM) of two molecular weights (F3330, 11–13 MDa; F3530, 15–17 MDa) with calcium carbonate (CaCO3) was studied via atomic force microscopy (AFM). In the absence of polymers at 1.7 mM and 1 M NaCl, good agreement with DLVO theory was observed. At 1.7 mM NaCl, repulsive interaction during approach at approximately 20 nm and attractive adhesion of approximately 400 pN during retraction was measured, whilst, at 1 M NaCl, no repulsion during approach was found. Still, a significantly larger adhesion of approximately 1400 pN during retraction was observed. In the presence of polymers, results indicated that F3330 displayed higher average adhesion (450–625 pN) and interaction energy (43–145 aJ) with CaCO3 than F3530’s average adhesion (85–88 pN) and interaction energy (8.4–11 aJ). On the other hand, F3530 exerted a longer steric repulsion distance (70–100 nm) than F3330 (30–70 nm). This was likely due to the lower molecular weight. F3330 adopted a flatter configuration on the calcite surface, creating more anchor points with the surface in the form of train segments. The adhesion and interaction energy of both HPAM with CaCO3 can be decreased by increasing the salt concentration. At 3% NaCl, the average adhesion and interaction energy of F3330 was 72–120 pN and 5.6–17 aJ, respectively, while the average adhesion and interaction energy of F3530 was 11.4–48 pN and 0.3–2.98 aJ, respectively. The reduction of adhesion and interaction energy was likely due to the screening of the COO− charged group of HPAM by salt cations, leading to a reduction of electrostatic attraction between the negatively charged HPAM and the positively charged CaCO3.

Journal article

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

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

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

Pajak E, Aldren C, 2023, Digital twins to address flowsheeting limitations, Chemical Engineering Research, Editors: Muller, Publisher: Department of Chemical Engineering, Imperial College London, Pages: 305-314, ISBN: 9781916005044

As a rapidly growing field, the flowsheeting industry’s fundamental importance to process design is illustrated by its lucrative nature. Flowsheeting software, as with any assumption-based engineering modelling, faces limitations. Digital twins offer potential advancements that could address the limitations of flowsheeting, such as poor modelling accuracy, limited customisation, accumulation of errors, and poor cost estimation. Whilst research has explored unit operation digital twins, there has not been an endeavour to apply them specifically to the limitations of flowsheeting. Therefore, this project aimed to explore the use of digital twins of unit operations to specifically address flowsheeting limitations. In line with achieving this aim, a pump, heat exchanger, and reactor were selected, coded in Python, and subsequently embedded in the open-source flowsheeting software, DWSIM. Data for the digital twins were either sourced from manufacturers or generated in ASPEN, before processing through methods such as neural networks or polynomial regression. The key findings included: the pump library demonstrating a more accurate cost estimation compared to traditional models; the grey box reactor digital twin addressing assumptions of idealised models, improving accuracy; and the heat exchanger’s preliminary success in its application to multiple fluid cases, showing potential to reduce the data required by digital twins. It was concluded that with consideration of the limitations around data availability, paired with further engineering theory implementation, unit operation digital twins have the potential to offer improvements to flowsheeting. Looking at the applications of this potential, from a manufacturer's perspective, digital twins of their equipment could offer compatibility validation and real system performance predictions which would improve customer confidence and, in turn, equipment sales.

Book chapter

, 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 &gt; 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

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

Request URL: Request URI: /respub/WEB-INF/jsp/search-html.jsp Query String: respub-action=search.html&id=00328642&limit=30&person=true