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

187 results found

Antonio Estévez L, Colpas FJ, Müller EA, 2020, A simple thermodynamic model for the solubility of thermolabile solids in supercritical fluids, Chemical Engineering Science, 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, 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

Bernet T, Müller 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

© 2020 Author(s). Fundamental measure theory (FMT) is commonly considered within classical density functional theory (DFT) to describe inhomogeneous hard-sphere (HS) fluids. As opposed to the original FMT of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)], the dimensional interpolation FMT (DI-FMT) is a specific version of FMT which is well adapted to accurately describe the freezing of HSs and adsorption in extreme confinements by including tensorial weighted densities. The computation of these weighted densities is generally performed analytically for specific simple scenarios (e.g., planar, cylindrical, or spherical geometries), and this method is challenging to apply to pores of generic geometry. On the other hand, numerical approaches, using fast Fourier transform (FFT) techniques, can be adapted to deal with arbitrary 3D geometries. Computations with tensorial weights are, however, generally not considered with these approaches. In our current work, the FFT computation of weighted densities is detailed for tensorial quantities. We present a DI-FMT in general 3D computational space, for an arbitrary pore geometry, to obtain density profiles of pure HS fluids or mixtures. The other thermodynamic quantities, such as surface tension or excess adsorption, can then be determined by using the standard DFT framework. As an example of the implementation of the method, we present the results for the adsorption on a hard-wall model, representative of the solid structure of an anisotropic zeolite cavity.

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, Publisher: Department of Chemical Engineering, ISBN: 978-1-9160050-1-3


Theodorakis PE, Smith ER, Muller EA, 2019, Spreading of aqueous droplets with common and superspreading surfactants. A molecular dynamics study, COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, Vol: 581, ISSN: 0927-7757

Journal article

Muller E, Cárdenas H, 2019, Extension of the SAFT-VR-Mie equation of state for adsorption, Journal of Molecular Liquids, Vol: 294, Pages: 1-12, ISSN: 0167-7322

An empirical extension of the Statistical Associating Fluid Theory (SAFT-VR-Mie) is presented to take intoaccount the effect of confinement of fluids within cylindrical nanopores. The modification of the equationof state retains the bulk phase limit presented in the original formulation and adds a term corresponding tothe contribution to the Helmholtz energy of the confined fluid. The resulting expression employs the fluidfluid parameters obtained from fitting bulk fluid behaviour and adds two additional adjustable parametersreflecting the strength of the solid-fluid energy and the range of the surface attraction. The capability ofthe theoretical model is showcased by fitting adsorption isotherms of methane and n−nonane on activatedcarbons; ethane, n−hexane and benzene on MCM-41, and methane and carbon dioxide on carbon surrogatemodels of shale rocks; providing for an accurate correlation of the data with parameters that are temperatureindependent and robust. The physical nature of the underlying model allows it to be mapped to fluid-solidmolecular models which can then be resolved employing classical molecular simulation methods, providing foran avenue into probing not only the adsorption behaviour but also the transport and interfacial properties.

Journal article

Theodorakis PE, Smith ER, Craster RV, Müller EA, Matar OKet al., 2019, Molecular dynamics simulation of the super spreading of surfactant-laden droplets. A review, Fluids, Vol: 4, Pages: 1-23, ISSN: 2311-5521

Superspreading is the rapid and complete spreading of surfactant-laden droplets on hydrophobic substrates. This phenomenon has been studied for many decades by experiment, theory, and simulation, but it has been only recently that molecular-level simulation has provided significant insights into the underlying mechanisms of superspreading thanks to the development of accurate force-fields and the increase of computational capabilities. Here, we review the main advances in this area that have surfaced from Molecular Dynamics simulation of all-atom and coarse-grained models highlighting and contrasting the main results and discussing various elements of the proposed mechanisms for superspreading. We anticipate that this review will stimulate further research on the interpretation of experimental results and the design of surfactants for applications requiring efficient spreading, such as coating technology.

Journal article

Jimenez-Serratos G, Cardenas H, Muller E, 2019, Extension of the effective solid-fluid Steele potential for Mie force fields, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, Vol: 117, Pages: 3840-3851, ISSN: 0026-8976

Molecular simulation of fluid systems in the presence of surfaces require computationally expen-sive calculations due to the large number of solid–fluid pair interactions involved. Representingthe explicit solid as a continuous wall with an effective potential can significantly reduce thecomputational time and allows exploring larger temporal and spatial scales. Different ana-lytical expressions can be found in the literature depending on the structural characteristicsof the solid and the approximations adopted in the derivation. The well-known (10-4-3) Steelepotential is one such analytic expression that faithfully represents the effective solid–fluid inter-actions for homonuclear crystalline solids with hexagonal lattice symmetry. However, this andmost of the effective potentials found in the literature have been developed for fluids and solidsinteracting exclusively through Lennard-Jones potentials. In this work, we extend the Steelemodel to obtain the effective wall–fluid potentials for Mie force fields. We perform moleculardynamics simulations of coarse-grained fluids modelled via the SAFT force field approach inthe presence of explicit and implicit surfaces to compare structural and dynamic properties inboth representations. Also, we study the adsorption of ethane into slit-like pores with explicitand implicit surfaces via grand canonical Monte Carlo simulations. We explore the validityand the improvement in the simulation performance as well as the limitations of the proposedexpression.

Journal article

Muller E, Law J, Headen T, Jimenez Serratos M, Boek E, murgich Jet al., 2019, A catalogue of plausible molecular models for the molecular dynamics of asphaltenes and resins obtained from quantitative molecular representation, Energy and Fuels, Vol: 33, Pages: 9779-9795, ISSN: 0887-0624

Computer simulation studies aimed at elucidating the phase behavior of crude oils inevitably require atomistically-detailed models of representative molecules. For the lighter fractions of crudes, such molecules are readily available, as the chemical composition can be resolved experimentally. Heavier fractions pose a challenge, on one hand due to their polydispersity and on the other due to poor description of the morphology of the molecules involved. The Quantitative Molecular Representation (QMR) approach is used here to generate a catalogue of 100 plausible asphaltene and resin structures based on elemental analysis and 1H – 13C NMR spectroscopy experimental data. The computer-generated models are compared in the context of a review of previously proposed literature structures and categorized by employing their molecular weights, double bond equivalents (DBE) and hydrogen to carbon (H/C) ratios. Sample atomistic molecular dynamics simulations were carried out for two of the proposed asphaltene structures with contrasting morphologies, one island-type and one archipelago-type, at 7 wt% in either toluene or heptane. Both asphaltene models, which shared many characteristics in terms of average molecular weight, chemical composition and solubility parameters showed marked differences in their aggregation behavior. The example showcases the importance of considering diversity and polydispersity when considering molecular models of heavy fractions.

Journal article

Zheng L, Trusler JPM, Bresme F, Muller Eet al., 2019, Predicting the pressure dependence of the viscosity of 2,2,4-trimethylhexane using the SAFT coarse-grained force field, Fluid Phase Equilibria, Vol: 496, Pages: 1-6, ISSN: 0378-3812

This work is framed within AIChE's 10th Industrial Fluid Properties Simulation Challenge, with the aim of assessing the capability of molecular simulation methods and force fields to accurately predict the pressure dependence of the shear viscosity of 2,2,4-trimethylhexane at 293.15 K (20 °C) at pressures up to 1 GPa. In our entry for the challenge, we employ coarse-grained intermolecular models parametrized via a top-down technique where an accurate equation of state is used to link the experimentally-observed macroscopic volumetric properties of fluids to the force-field parameters. The state-of-the-art version of the statistical associating fluid theory (SAFT) for potentials of variable range as reformulated in the Mie incarnation is employed here. The potentials are used as predicted by the theory, with no fitting to viscosity data. Viscosities are calculated by molecular dynamics (MD) employing two independent methods; an equilibrium-based procedure based on the analysis of the pressure fluctuations through a Green-Kubo formulation and a non-equilibrium method where periodic perturbations of the boundary conditions are employed to simulate experimental shear stress conditions. There is an indication that, at higher pressures, the model predicts a solid phase (freezing) which we believe to be an artefact of the simplified molecular geometry used in the modelling. A comparison (made after disclosure of the experimental data) show that the model consistently underpredicts the viscosity by about 30%, but follows the pressure dependency accurately.

Journal article

Kaimaki D-M, Haire B, Ryan H, Jiménez-Serratos G, Alloway RM, Little M, Morrison J, Salama I, Tillotson M, Smith BE, Moorhouse S, Totton TS, Hodges MG, Yeates SG, Quayle P, Clarke S, Muller EA, Durkan Cet al., 2019, Multiscale approach linking self-aggregation and surface interactions of synthesized foulants to fouling mitigation strategies, Energy & Fuels, Vol: 33, Pages: 7216-7224, ISSN: 0887-0624

Fouling of oil-exposed surfaces remains a crucial issue as a result of the continued importance of oil as the world’s primary energy source. The key perpetrators in crude oil fouling have been identified as asphaltenes, a poorly described mixture of diverse polyfunctional molecules that form part of the heaviest fractions of oil. Asphaltenes are responsible for a decrease in oil production and energy efficiency and an increase in the risk of environmental hazards. Hence, understanding and managing systems that are prone to fouling is of great value but constitutes a challenge as a result of their complexity. In an effort to reduce that complexity, a study of a synthesized foulant of archipelago structure is presented. A critical perspective on previously described solubility and aggregation mechanisms (e.g., critical nanoaggrerate concentration and critical clustering concentration) is offered because the characterized system favors a continuous distribution of n-mers instead. A battery of experimental and modeling techniques have been employed to link the bulk and interfacial behavior of a representative foulant monomer to effective fouling mitigation strategies. This systematic approach defines a new multiscale methodology in the investigation of fouling systems.

Journal article

Aasen A, Hammer M, Ervik Å, Muller E, Wilhelmsen Øet al., 2019, Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen and deuterium, Journal of Chemical Physics, Vol: 151, ISSN: 0021-9606

We present a perturbation theory that combines the use of a third-order Barker–Henderson expansion of theHelmholtz energy with Mie-potentials that include first (Mie-FH1) and second-order (Mie-FH2) Feynman–Hibbs corrections. The resulting equation of state (SAFT-VRQ Mie) is compared to molecular simulations,and is seen to reproduce the thermodynamic properties of generic Mie-FH1 and Mie-FH2 fluids accurately.SAFT-VRQ Mie is exploited to obtain optimal parameters for the potentials of neon, helium, deuterium,ortho-, para- and normal-hydrogen for the Mie-FH1 and Mie-FH2 formulations. For helium, hydrogen anddeuterium, the use of either the first or second-order corrections yields significantly higher accuracy in therepresentation of supercritical densities, heat capacities and speed of sounds when compared to classical Miefluids, although the Mie-FH2 is slightly more accurate than Mie-FH1 for supercritical properties. The MieFH1 potential is recommended for most of the fluids since it yields a more accurate representation of thepure-component phase equilibria and extrapolates better to low temperatures. Notwithstanding, for helium,where the quantum effects are largest, we find that none of the potentials give an accurate representation ofthe entire phase envelope, and its thermodynamic properties are represented accurately only at temperaturesabove 20 K. Overall, supercritical heat capacities are well represented, with some deviations from experimentsseen in the liquid phase region for helium and hydrogen.

Journal article

Joss L, Muller E, 2019, Machine learning for fluid property correlations: Classroom examples with MATLAB, Journal of Chemical Education, Vol: 96, Pages: 697-703, ISSN: 0021-9584

Recent advances in computer hardware and algorithms are spawning an explosive growth in the use of computer-based systems aimed at analyzing and ultimately correlating large amounts of experimental and synthetic data. As these machine learning tools become more widespread, it is becoming imperative that scientists and researchers become familiar with them, both in terms of understanding the tools and the current limitations of artificial intelligence, and more importantly being able to critically separate the hype from the real potential. This article presents a classroom exercise aimed at first-year science and engineering college students, where a task is set to produce a correlation to predict the normal boiling point of organic compounds from an unabridged data set of >6000 compounds. The exercise, which is fully documented in terms of the problem statement and the solution, guides the students to initially perform a linear correlation of the boiling point data with a plausible relevant variable (the molecular weight) and to further refine it using multivariate linear fitting employing a second descriptor (the acentric factor). Finally, the data are processed through an artificial neural network to eventually provide an engineering-quality correlation. The problem statements, data files for the development of the exercise, and solutions are provided within a MATLAB environment but are general in nature.

Journal article

Wand CR, Fayaz-Torshizi M, Jimenez-Serratos G, Müller EA, Frenkel Det al., 2019, Solubilities of pyrene in organic solvents: Comparison between chemical potential calculations using a cavity-based method and direct coexistence simulations, The Journal of Chemical Thermodynamics, Vol: 131, Pages: 620-629, ISSN: 0021-9614

In this paper, we benchmark a cavity-based simulation method for calculating the relative solubility of large molecules in explicit solvents. The essence of the procedure is the accounting of the Gibbs energy change associated with an alchemical thermodynamic cycle where, in sequence, a cavity is created in a solvent, a solute is inserted in the cavity and the cavity is annihilated. The Gibbs energy change is equated to the excess chemical potential allowing the comparison of solubilities in different solvents. The results obtained using the cavity-based method are compared to direct large-scale molecular dynamics simulations performed using coarse-grained models for calculating the partition coefficient of pyrene between heptane and toluene. We demonstrate the applicability of this cavity-based technique under high pressure/temperature conditions.

Journal article

Jiménez-Serratos G, Totton TS, Jackson G, Muller EAet al., 2019, Aggregation behavior of model asphaltenes revealed from large-scale coarse-grained molecular simulations, Journal of Physical Chemistry B, Vol: 123, Pages: 2380-2396, ISSN: 1520-5207

Fully atomistic simulations of models of asphaltenes in simple solvents have allowed the study of trends in aggregation phenomena and the understanding of the role that molecular structure plays therein. However, the detail included at this scale of molecular modeling is at odds with the required spatial and temporal resolution needed to fully understand the asphaltene aggregation. The computational cost required to explore the relevant scales can be reduced by employing coarse-grained (CG) models, which consist of lumping a few atoms into a single segment that is characterised by effective interac- tions. In this work CG force fields developed via the SAFT-γ [Müller, E.A., Jackson, G. (2014) Annu. Rev. Chem. Biomolec. Eng., 5, 405–427] equation of state (EoS) provide a reliable pathway to link the molecular description with macroscopic thermophysical data. A recent modification of the SAFT-VR EoS [Müller, E.A. and Mejía, A. (2017) Langmuir, 33, 11518–11529], that allows parametrizing homonuclear rings, is selected as the starting point to propose CG models for polycyclic aromatic hydrocarbons (PAHs). The new aromatic-core parameters, along with others published for simpler organic molecules, are adopted for the construction of asphaltene models by combining different chemical moieties in a group-contribution fashion. We apply the procedure to two previously reported asphaltene models and perform Molecular Dynamics simulations to validate the coarse-grained representation against benchmark systems of 27 asphaltenes in pure solvent (toluene or heptane) described in a fully atomistic fashion. An excellent match between both levels of description is observed for cluster size, radii of gyration, and relative-shape-anisotropy-factor distributions. We exploit the advantages of the CG representation by simulating systems containing up to 2000 asphaltene molecules in explicit solvent investigating the effect of asphaltene concentration, so

Journal article

Cardenas H, Muller E, 2019, Molecular simulation of the adsorption and diffusion in cylindrical nanopores – effect of shape and fluid-solid interactions, Molecules, Vol: 24, ISSN: 1420-3049

We report on molecular simulations of model fluids composed of three tangentially bonded Lennard-Jones interaction sites with three distinct morphologies: a flexible “pearl-necklace” chain, a rigid “stiff” linear configuration, and an equilateral rigid triangular ring. The adsorption of these three models in cylindrical pores of diameters 1, 2, and 3 nm and with varying solid–fluid strength was determined by direct molecular dynamics simulations, where a sample pore was placed in contact with a bulk fluid. Adsorption isotherms of Type I, V, and H1 were obtained depending on the choice of pore size and solid–fluid strength. Additionally, the bulk-phase equilibria, the nematic order parameter of the adsorbed phase, and the self-diffusion coefficient in the direction of the pore axis were examined. It was found that both the molecular shape and the surface attractions play a decisive role in the shape of the adsorption isotherm. In general, the ring molecules showed a larger adsorption, while the fully flexible model showed the smallest adsorption. Morphology and surface strength were found to have a lesser effect on the diffusion of the molecules. An exceptional high adsorption and diffusion, suggesting an enhanced permeability, was observed for the linear stiff molecules in ultraconfinement, which was ascribed to a phase transition of the adsorbed fluid into a nematic liquid crystal.

Journal article

, 2019, Chemical Engineering Research: Reports of the 4th year research projects in the Department of Chemical Engineering at Imperial College London, London, Publisher: Department of Chemical Engineering, Imperial College London, ISBN: 9781916005006

This book is a compilation of manuscripts created as part of a teaching assignment on the 4th year’s Chemical Engineering CE4-01-1 course.


Shahruddin S, Jimenez-Serratos G, Britovsek G, Matar O, Muller Eet al., 2019, Fluid-solid phase transition of n-alkane mixtures: Coarse-grained molecular dynamics simulations and diffusion-ordered spectroscopy nuclear magnetic resonance, Scientific Reports, Vol: 9, ISSN: 2045-2322

Wax appearance temperature (WAT), defined as the temperature at which the first solid paraffin crystal appears in a crude oil, is one of the key flow assurance indicators in the oil industry. Although there are several commonly-used experimental techniques to determine WAT, none provides unambiguous molecular-level information to characterize the phase transition between the homogeneous fluid and the underlying solid phase. Molecular Dynamics (MD) simulations employing the statistical associating fluid theory (SAFT) force field are used to interrogate the incipient solidification states of models for long-chain alkanes cooled from a melt to an arrested state. We monitor the phase change of pure long chain n-alkanes: tetracosane (C24H50) and triacontane (C30H62), and an 8-component surrogate n-alkane mixture (C12-C33) built upon the compositional information of a waxy crude. Comparison to Diffusion Ordered Spectroscopy Nuclear Magnetic Resonance (DOSY NMR) results allows the assessment of the limitations of the coarse-grained models proposed. We show that upon approach to freezing, the heavier components restrict their motion first while the lighter ones retain their mobility and help fluidize the mixture. We further demonstrate that upon sub-cooling of long n-alkane fluids and mixtures, a discontinuity arises in the slope of the self-diffusion coefficient with decreasing temperature, which can be employed as a marker for the appearance of an arrested state commensurate with conventional WAT measurements.

Journal article

Jaeger F, Matar OK, Müller EA, 2019, Transport properties of water confined in a graphene nanochannel

Equilibrium molecular dynamics simulations are used to investigate the effectof phase transitions on the transport properties of highly-confined waterbetween parallel graphene sheets. An abrupt reduction by several orders ofmagnitude in the mobility of water is observed in strong confinement, asindicated by reduced diffusivity and increased shear viscosity values. The bulkviscosity, which is related to the resistance to expansion and compression of asubstance, is also calculated, showing an enhancement compared to the bulkvalue for all levels of confinement. An investigation into the phase behaviourof confined water reveals a transition from a liquid monolayer to a rhombicfrozen monolayer at nanochannel heights between 6.8-7.8 \r{A}; for largerseparations, multilayer liquid water is recovered. It is shown how this phasetransition is at the root of the impeded transport.

Working paper

Herdes Moreno C, Ervik A, Mejia A, Muller EAet al., 2018, Prediction of the water/oil interfacial tension from molecular simulations using the coarse-grained SAFT-γ Mie force field, Fluid Phase Equilibria, Vol: 476, Pages: 9-15, ISSN: 0378-3812

This work reports the award-winning entry for the Ninth Industrial Fluid Properties Simulation Challenge. This worldwide competition was set with the aim of assessing the capability of molecular simulation methods and force fields to accurately predict the interfacial tension of oil + water mixtures at high temperatures and pressures. The challenge focused on predicting the liquid-liquid interfacial tension of binary mixtures of dodecane + water, toluene + water and a 50:50 (wt%) mixture of dodecane:toluene + water at 1.825 MPa (250 psig) and temperatures from 110 to 170 °C. In our entry for the challenge, we employed coarse-grained intermolecular models parametrized via a top-down technique in which an accurate equation of state is used to link experimentally observed macroscopic properties of fluids with the force-field parameters. The state-of-the-art version of the statistical associating fluid theory (SAFT) for potentials of variable range as reformulated in terms of the Mie potential is employed here. Interfacial tensions are calculated through a direct method, where an elongated simulation cell is sampled through molecular dynamics in the isobaric-isothermal constant area ensemble (NPzzAT). The coarse-grained nature of the force field allows for the accelerated calculation of relatively large systems. The binary interaction parameters that describe the cross-interactions have been obtained in previous works by fitting to interfacial tensions of the constituent binaries at lower pressures and temperatures; these are taken as constant for all conditions and mixtures studied. After disclosure of the challenge results, we observe that the interfacial properties of the mixtures are described with an error of less than 5 mN/m over the whole range of conditions, demonstrating the accuracy and transferability of the top-down SAFT-γ Mie force field approach.

Journal article

cumicheo C, cartes M, Muller EA, Mejia Aet al., 2018, Experimental measurements and theoretical modeling of high-pressure mass densities and interfacial tensions of carbon dioxide + n-heptane + toluene and its carbon dioxide binary systems, Fuel, Vol: 228, Pages: 92-102, ISSN: 0016-2361

Experimental determination and theoretical predictions of the isothermal (344.15 K) mass densities and interfacial tensions for the system carbon dioxide (CO2) with heptol (n-heptane + toluene) mixtures varying liquid volume fraction compositions of toluene (0, 25, 50, 75, 100 % v/v) and over the pressure range 0.1 to 8 MPa are reported. Measurements are carried out on a high-pressure device that includes a vibrating tube densimeter and a pendant drop tensiometer. Theoretical modeling of mass densities phase equilibria and interfacial properties (i.e., interfacial tension and interfacial concentration profiles) are performed by employing the Square Gradient Theory using an extension of the Statistical Associating Fluid Theory equation of state that accounts for ring fluids. The experimental bulk phase equilibrium densities and interfacial tensions obtained are in very good agreement with the theoretical predictions. Although there are no previous experimental data of these mixtures at the conditions explored herein, the results follow the same trends observed from experimental data at other conditions. The combination of experimental and modeling approaches provides a route to simultaneously predict phase equilibrium and interfacial properties within acceptable statistical deviations. For the systems and conditions studied here, we observe that the phase equilibrium of the mixtures display zeotropic vapor-liquid equilibria with positive deviations from ideal behavior. The mass bulk densities behave ordinarily whereas the interfacial tensions decrease as the pressure or liquid mole fraction of CO2 increases and/or the ratio toluene/heptane decreases. The interfacial concentration along the interfacial region exhibits a remarkable high excess adsorption of CO2, which increases with pressure and it is larger in n-heptane than in toluene. Toluene does not exhibit any special ads

Journal article

Galindo A, Rahman S, Lobanova O, Jimenez-Serratos G, Braga C, Raptis V, Muller E, Jackson G, Avendano Cet al., 2018, SAFT‑γ force field for the simulation of molecular fluids. 5. Hetero Group coarse-grained models of linear alkanes and the importance of intramolecular interactions, Journal of Physical Chemistry B, Vol: 122, Pages: 9161-9177, ISSN: 1520-5207

The SAFT-γ Mie group-contribution equation of state [Papaioannou J. Chem. Phys. 2014, 140, 054107] is used to develop a transferable coarse-grained (CG) force-field suitable for the molecular simulation of linear alkanes. A heterogroup model is fashioned at the resolution of three carbon atoms per bead in which different Mie (generalized Lennard-Jones) interactions are used to characterize the terminal (CH3–CH2–CH2−) and middle (−CH2–CH2–CH2−) beads. The force field is developed by combining the SAFT-γ CG top-down approach [Avendaño J. Phys. Chem. B 2011, 115, 11154], using experimental phase-equilibrium data for n-alkanes ranging from n-nonane to n-pentadecane to parametrize the intermolecular (nonbonded) bead–bead interactions, with a bottom-up approach relying on simulations based on the higher resolution TraPPE united-atom (UA) model [Martin; , Siepmann J. Phys. Chem. B 1998, 102, 2569] to establish the intramolecular (bonded) interactions. The transferability of the SAFT-γ CG model is assessed from a detailed examination of the properties of linear alkanes ranging from n-hexane (n-C6H14) to n-octadecane (n-C18H38), including an additional evaluation of the reliability of the description for longer chains such as n-hexacontane (n-C60H122) and a prototypical linear polyethylene of moderate molecular weight (n-C900H1802). A variety of structural, thermodynamic, and transport properties are examined, including the pair distribution functions, vapor–liquid equilibria, interfacial tension, viscosity, and diffusivity. Particular focus is placed on the impact of incorporating intramolecular interactions on the accuracy, transferability, and representability of the CG model. The novel SAFT-γ CG force field is shown to provide a reliable description of the thermophysical properties of the n-alkanes, in most cases at a level comparable to the that obtained with higher resolution models.

Journal article

Herdes C, Petit C, Mejia A, Muller EAet al., 2018, Combined experimental, theoretical and molecular simulation approach for the description of the fluid phase behavior of hydrocarbon mixtures within shale rocks, Energy and Fuels, Vol: 32, Pages: 5750-5762, ISSN: 0887-0624

An experimental, theoretical and molecular simulation consolidated framework for the efficient characterization of the adsorption and fluid phase behaviorof multicomponent hydrocarbon mixtures within tight shale rocks is presented.Fluid molecules are described by means of a top-down coarse-grained modelwheresimple Mie intermolecular potentials areparametrizedby means of the statisticalassociatingfluid theory (SAFT). A four component (methane, pentane, decane, naphthalene) mixture is used a surrogate model with a composition representative of commonly encountered shale oils. Shales are modelledas a hierarchical network of nanoporous slits in contact with a mesoporous region. The rock model is informed by the characterization of four distinctand representative shale core samples through nitrogen adsorption, thermogravimetric analysis and contact angle measurements. Experimental results suggest the consideration of two types of pore surfaces; a carbonaceous wall representing the kerogen regions of a shale rock and an oxygenated wall representing the clay-based porosity.Molecular dynamics (MD)simulations are performed at constant overall compositionsat a temperature of 398.15 K(257 °F) and explorepressures from6.9 MPa up to 68.95 MPa (1000to 10000 psi).Simulationsrevealthat it is the organic nanopores of 1 nm and 2 nm that preferentially adsorb the heavier components, while the oxygenated counterparts show little selectivitybetween the adsorbed and free fluid.Upon desorption, this trend is intensified, as the gas phase in equilibrium with a carbon nanopore becomes increasing leaner (richerin light components)and almost completely depleted of the heavy components which remain trapped in the nanopores and surfaces of the mesopores.Oxygenated pores do not contribute tothis unusualbehavior, even for the very tight pores considered. The results presentedelucidate

Journal article

Jaeger F, Matar OK, Muller EA, 2018, Bulk viscosity of molecular fluids, Journal of Chemical Physics, Vol: 148, ISSN: 0021-9606

The bulk viscosity of molecular models of gases and liquids is determined by molecular simulations as acombination of a dilute gas contribution, arising due to the relaxation of internal degrees of freedom, and aconfigurational contribution, due to the presence of intermolecular interactions. The dilute gas contributionis evaluated using experimental data for the relaxation times of vibrational and rotational degrees of freedom.The configurational part is calculated using Green-Kubo relations for the fluctuations of the pressure tensorobtained from equilibrium microcanonical molecular dynamics simulations. As a benchmark, the Lennard-Jones fluid is studied. Both atomistic and coarse-grained force fields for water, CO2and n-decane areconsidered and tested for their accuracy. Comparison to experimental data, where present, demonstratesthat the tested models show various degrees of success in predicting bulk viscosity values, although atomisticforce fields in general seem to perform more consistently than the corresponding coarse-grained counterparts.The dilute gas contribution to the bulk viscosity is seen to be significant only in the cases when intramolecularrelaxation times are in theμs range, and for low vibrational wave numbers (<1000 cm−1); This explainsthe abnormally high values of bulk viscosity reported for CO2. In all other cases studied, the dilute gascontribution is negligible, and the configurational contribution dominates the overall behaviour. In particular,the configurational term is responsible for the enhancement of the bulk viscosity near the critical point.

Journal article

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