293 results found
Kohns M, Lazarou G, Forte E, et al., 2020, Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulfuric and carbonic acid, Physical Chemistry Chemical Physics, Vol: 22, Pages: 15248-15269, ISSN: 1463-9076
The distribution of ionic species in electrolyte systems is important in many fields of science and engineering, ranging from the study of degradation mechanisms to the design of systems for electrochemical energy storage. Often, other phenomena closely related to the ionic speciation, such as ion pairing, clustering and hydrogen bonding, which are difficult to investigate experimentally, are also of interest. Here, we develop an accurate molecular approach, accounting for reactions as well as association and ion pairing, to deliver a predictive framework that helps validate experiment and guides future modelling of speciation phenomena of weak electrolytes. We extend the SAFT-VRE Mie equation of state [D. K. Eriksen et al., Mol. Phys., 2016, 114, 2724–2749] to study aqueous solutions of nitric, sulphuric and carbonic acid, considering complete and partially dissociated models. In order to incorporate the dissociation equilibria, correlations to experimental data for the relevant thermodynamic equilibrium constants of the dissociation reactions are taken from the literature and are imposed as a boundary condition in the calculations. The models for water, the hydronium ion, and carbon dioxide are treated as transferable and are taken from our previous work. Here we present new molecular models for nitric acid, and the nitrate, bisulfate, sulfate, and bicarbonate anions. The resulting framework is used to predict a range of phase behaviour and solution properties of the aqueous acids over wide ranges of concentration and temperature, including the degree of dissociation, as well as the activity coefficients of the ionic species, and the activity of water and osmotic coefficient, density, and vapour pressure of the solutions. The SAFT-VRE Mie models obtained in this manner provide a means of elucidating the mechanisms of association and ion pairing in the systems studied, complementing the experimental observations reported in the literature.
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.
Blas FJ, Galindo A, Jackson G, 2020, Thermodynamics 2019 Conference-Punta Umbria, Costa de la Luz, Huelva, Spain, 26-28 June 2019, MOLECULAR PHYSICS, Vol: 118, ISSN: 0026-8976
Morgado P, Colaco B, Santos V, et al., 2020, Modelling the thermodynamic properties and fluid-phase equilibria ofn-perfluoroalkanes and their binary mixtures with the SAFT-gamma Mie group contribution equation of state, MOLECULAR PHYSICS, Vol: 118, ISSN: 0026-8976
Di Lecce S, Lazarou G, Khalit SH, et al., 2020, Modelling and prediction of the thermophysical properties of aqueous mixtures of choline geranate and geranic acid (CAGE) using SAFT-gamma Mie (vol 9, pg 38017, 2019), RSC ADVANCES, Vol: 10, Pages: 19463-19465
Lee L, Graham E, Galindo A, et al., 2020, A comparative study of multi-objective optimization methodologies for molecular and process design, Computers and Chemical Engineering, Vol: 136, ISSN: 0098-1354
The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the suitability of different multi-objective optimization algorithm for the solution of such design problems. In this work, we present a systematic comparison of the performance of five mixed-integer non-linear programming (MINLP) multi-objective optimization algorithms on the selection of computer-aided molecular design (CAMD) and computer-aided molecular and process design (CAMPD) problems. The five methods are designed to address the discrete and nonlinear nature of the problem, with the aim of generating an accurate approximation of the Pareto front. They include: a weighted sum approach without global search phases (SWS), a weighted sum approach with simulated annealing (SA), a weighted sum approach with multi level single linkage (MLSL), the sandwich algorithm with MLSL and the non dominated sorting genetic algorithm-II (NSGA-II). The algorithms are compared systematically in two steps. The effectiveness of the global search methods is evaluated with SWS, WSSA and WSML. WSML is found to be most effective and a comparative analysis of WSML, SDML and NSGA-II is then undertaken. As a test set of these optimization techniques, two of CAMD and one CAMPD problems of varying dimensionality are formulated as case studies. The results show that the sandwich algorithm with MLSL provides the most efficient generation of a diverse set of Pareto points, leading to the construction of an approximate Pareto front close to exact Pareto front.
Papadopoulos A, Shavalieva G, Papadokonstantakis S, et al., 2020, An approach for simultaneous computer-aided molecular design with holistic sustainability assessment: Application to phase-change CO2 capture solvents, COMPUTERS & CHEMICAL ENGINEERING, Vol: 135, ISSN: 0098-1354
Bowskill DHH, Tropp UE, Gopinath S, et al., 2020, Beyond a heuristic analysis: integration of process and working-fluid design for organic Rankine cycles, MOLECULAR SYSTEMS DESIGN & ENGINEERING, Vol: 5, Pages: 493-510, ISSN: 2058-9689
Jonuzaj S, Watson OL, Ottoboni S, et al., 2020, Computer-aided Solvent Mixture Design for the Crystallisation and Isolation of Mefenamic Acid, Computer Aided Chemical Engineering, Pages: 649-654
© 2020 Elsevier B.V. We present a systematic computer-aided methodology for the integrated design of solvent blends used in the purification (i.e., crystallisation and isolation) of pharmaceutical compounds. In particular, we investigate the design of optimal solvent mixtures for combined cooling and antisolvent crystallisation, taking into account interlinked design decisions across both crystallisation and isolation (washing) stages. Within the proposed approach, the optimal solvents, antisolvents, the best mixture composition and the optimal process temperatures are determined simultaneously. Furthermore, comprehensive design specifications for both crystallisation and isolation units, such as the miscibility of crystallisation and wash solvents, their environmental impact, and health and safety metrics, are investigated. The design method is applied to identifying potential high-performance solvent blends for the purification of mefenamic acid, while removing an impurity, chlorobenzoic acid, from the system.
Ravipati S, Galindo A, Jackson G, et al., 2019, An investigation of free-energy-averaged (coarse-grained) potentials for fluid adsorption on heterogeneous solid surfaces, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, Vol: 21, Pages: 25558-25568, ISSN: 1463-9076
Hall CK, Kofke DA, Galindo A, et al., 2019, Peter Cummings - a pillar in the field of statistical mechanics and molecular simulation FOREWORD, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, Vol: 117, Pages: 3479-3483, ISSN: 0026-8976
Di Lecce S, Galindo A, Khalit SH, et al., 2019, Modelling and prediction of the thermophysical properties of aqueous mixtures of Choline Geranate and Geranic acid (CAGE) using SAFT-g Mie, RSC Advances: an international journal to further the chemical sciences, Vol: 9, Pages: 38017-38031, ISSN: 2046-2069
Deep eutectic solvents and room temperature ionic liquids are increasingly recognised as appro-priate materials for use as active pharmaceutical ingredients and formulation additives. Aque-ous mixtures of choline and geranate (CAGE), in particular, have been shown to offer promisingbiomedical properties but the understanding of the thermophysical behaviour of these mixturesremains limited. Here, we develop interaction potentials for use in the SAFT–γgroup–contributionapproach, to study the thermodynamic properties and phase behaviour of aqueous mixtures ofcholine geranate and geranic acid. The determination of the interaction parameters betweenchemical functional groups is carried out in a successive fashion, characterising each group basedon those previously developed. The parameters of the groups relevant to geranic acid are esti-mated using experimental phase–equilibrium data such as vapour pressure and saturated–liquiddensity of simple pure components (n–alkenes, branched alkenes and carboxylic acids) and thephase equilibrium data of mixtures (aqueous solutions of branched alkenes and of carboxylicacids). Geranate is represented by further incorporating the anionic carboxylate group, COO−,which is characterised using aqueous solution data of sodium carboxylate salts, assuming fulldissociation of the salt in water. Choline is described by incorporating the cationic quaternaryammonium group, N+, using data on choline choride solutions. The osmotic pressure of aque-ous mixtures of CAGE at several concentrations is predicted and compared to experimental dataobtained as part of our work to assess the accuracy of the modelling platform. The SAFT–γMieapproach is shown to be predictive, providing a good description of the measured data for a widerange of mixtures and properties. Furthermore, the new group interaction parameters neededto represent CAGE extend the set of functional group
Bowron DT, Fernandez-Alonso F, Jackson G, 2019, A tribute to Alan Soper - foreword by the editors FOREWORD, MOLECULAR PHYSICS, Vol: 117, Pages: 3195-3196, ISSN: 0026-8976
Febra SA, Aasen A, Adjiman CS, et al., 2019, Intramolecular bonding in a statistical associating fluid theory of ring aggregates, MOLECULAR PHYSICS, ISSN: 0026-8976
Campos-Villalobos G, Ravipati S, Haslam AJ, et al., 2019, Modelling adsorption using an augmented two-dimensional statistical associating fluid theory: 2D-SAFT-VR Mie, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, Vol: 117, Pages: 3770-3782, ISSN: 0026-8976
We present an extension of the SAFT-VR Mie approach to model adsorption of molecular fluids based on a two-dimensional (2D) approximation to describe the adsorbed fluid. Analytical results are provided for the first- and second-order perturbation terms of the free energy for the 2D system. The adsorption model is based on the assumption that the particle pair interactions in the adsorbed and bulk phases are described with the same Mie potential exponents λa and λr, in contrast with the square-well version of the 2D-SAFT-VR approach in which it is considered necessary to modify the attractive ranges of the SW interactions. This important difference between the two approaches leads to a reduction in the number of molecular parameters to be determined. In order to demonstrate the performance of the 2D-SAFT-VR Mie approach, we present results for the the modelling of carbon dioxide (CO2) and methane (CH4) adsorbed onto dry coal.
Skutnik RA, Lehmann L, Puschel-Schlotthauer S, et al., 2019, The formation of biaxial nematic phases in binary mixtures ofthermotropic liquid-crystals composed of uniaxial molecules, Molecular Physics, Vol: 117, Pages: 2830-2845, ISSN: 0026-8976
Monte Carlo simulations in the isothermal-isobaric ensemble are used to investigate the formation of an ordered, biaxial nematic phase in a binary mixture of thermotropic liquid crystals. The orientational dependence of the interaction between molecules of each pure component is the same as in the well-known Maier-Saupe model; each pure component of the mixture is therefore capable of forming a uniaxial nematic phase. For the interaction between molecules of different components, we use the same Maier-Saupe model but change the sign of the coupling constant. As a consequence a T-shaped arrangement of these molecules is energetically favoured. The formation of the biaxial phase occurs in two steps. At higher temperatures T, one of the components forms a uniaxial nematic phase whereas the other is in a quasi two-dimensional restricted isotropic liquid state. We develop a simple theoretical model to understand the high degree of (ostensible) nematic order in the latter. At lower T, the second component becomes nematic and then the entire mixture of the two compounds has biaxial symmetry. The biaxial nematic phase does not demix into domains rich in molecules of one or the other species.
Jiménez-Serratos G, Totton TS, Jackson G, et 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
Watson OL, Galindo A, Jackson G, et al., 2019, Computer-aided Design of Solvent Blends for the Cooling and Anti-solvent Crystallisation of Ibuprofen, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 949-954, ISBN: 978-0-12-819939-8
Lee YS, Graham E, Jackson G, et al., 2019, A comparison of the performance of multi-objective optimization methodologies for solvent design, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 37-42, ISBN: 978-0-12-819939-8
Kazepidis P, Papadopoulos AI, Seferlis P, et al., 2019, Optimal design of post combustion CO2 capture processes based on phase-change solvents, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 463-468, ISBN: 978-0-12-819939-8
Galindo A, Rahman S, Lobanova O, et 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.
Avendano C, Jackson G, Wensink HH, 2018, Nanorings in planar confinement: the role of repulsive surfaces on the formation of lacuna smectics, Molecular Physics, Vol: 116, Pages: 2901-2910, ISSN: 0026-8976
We study the structure and liquid-crystalline phase behaviour of a model of nonconvexcircular soft-repulsive nanorings con ned in a planar slit geometry usingmolecular-dynamics simulation. The separation distance between the structurelessparallel soft-repulsive walls is large enough to allow for the formation of a distinctbulk phase in the central region of the box which is in coexistence with the adsorbeduid thus allowing the analysis of single wall e ects. As the concentrationof the particles is increased, the uid adsorbs (wets) onto the planar surfaces leadingto the formation of well-de ned smectic-A layers with a spacing proportional tothe diameter of the rings. An analysis of the nematic order parameter at distancesperpendicular to the surface reveals that the particles in each layer exhibit antinematicbehaviour and planar (edge-on) anchoring relative to the short symmetryaxis of the rings. This behaviour is in stark contrast to the behaviour observed inconvex disc-like particles that have the tendency to form nematic (discotic) structureswith hometropic (face-on) anchoring. The smectic phases formed by nanoringsin the bulk and under con nement are characterized by the formation of low-densitylayered liquid-crystalline states with large voids, referred to here as lacuna smecticphases. In contrast to what is typically found for con ned liquid-crystalline systemsinvolving convex particles, no apparent biaxiality is found for the nanorings in planarcon nement. We argue that formation of the low-density lacuna smectic layers withplanar anchoring is a consequence of the non-convex shape of the circular rings thatallow for interpenetration between the particles as observed for nanorings underbulk conditions [Avenda~no et al., Proc. Natl. Acad. Sci. U. S. A. 113, 9699 (2016);H. H. Wensink and C. Avenda~no, Phys. Rev. E 94 062704 (2016)].
Sarkisov L, Sweatman MB, Jackson G, 2018, Thermodynamics 2017 Conference Edinburgh, Scotland, 5-8 September 2017, Molecular Physics, Vol: 116, Pages: 1909-1914, ISSN: 0026-8976
Wu L, Malijevsky A, Avendano C, et al., 2018, Demixing, surface nematization, and competing adsorption in binarymixtures of hard rods and hard spheres under confinement, Journal of Chemical Physics, Vol: 148, ISSN: 0021-9606
A molecular simulation study of binary mixtures of hard spherocylinders (HSCs) and hard spheres (HSs)confined between two structureless hard walls is presented. The principal aim of the work is to understandthe effect of the presence of hard spheres on the entropically-driven surface nematization of the hard rod-likeparticles at the walls. The mixtures are studied using a constant normal-pressure Monte Carlo algorithm.The surface adsorption at different compositions of hard spheres is examined in detail. At moderate hard-sphere concentrations preferential adsorption of the spheres at the wall is found. However, at moderate tohigh pressure (density), we observe a crossover in the adsorption behaviour with nematic layers of the rodsforming at the walls leading to a local demixing of the system. The presence of the spherical particles is seento destabilize the surface nematization of the rods, and the degree of demixing increases on increasing the HSconcentration.
Carbon capture and storage (CCS) is broadly recognised as having the potential to play a key role in meeting climate change targets, delivering low carbon heat and power, decarbonising industry and, more recently, its ability to facilitate the net removal of CO2 from the atmosphere. However, despite this broad consensus and its technical maturity, CCS has not yet been deployed on a scale commensurate with the ambitions articulated a decade ago. Thus, in this paper we review the current state-of-the-art of CO2 capture, transport, utilisation and storage from a multi-scale perspective, moving from the global to molecular scales. In light of the COP21 commitments to limit warming to less than 2 °C, we extend the remit of this study to include the key negative emissions technologies (NETs) of bioenergy with CCS (BECCS), and direct air capture (DAC). Cognisant of the non-technical barriers to deploying CCS, we reflect on recent experience from the UK's CCS commercialisation programme and consider the commercial and political barriers to the large-scale deployment of CCS. In all areas, we focus on identifying and clearly articulating the key research challenges that could usefully be addressed in the coming decade.
Jackson G, dufal S, Lafitte T, et al., 2018, Corrigendum: The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids, Molecular Physics, Vol: 116, Pages: 283-285, ISSN: 0026-8976
Jackson G, 2017, Announcement of the winner of the Longuet–Higgins Early Career Researcher Prize 2016, Molecular Physics, Vol: 115, Pages: 2903-2904, ISSN: 0026-8976
brumby PE, wensink HH, haslam AJ, et al., 2017, Structure and interfacial tension of a hard-rod fluid in planar confinement., Langmuir, Vol: 33, Pages: 11754-11770, ISSN: 0743-7463
The structural properties and interfacial tension of a fluid of hard-spherocylinder rod-like particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a non-monotonic trend as a function of bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario can be confirmed from our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which may serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from a second-virial density functional theory, which are in good qualitative agreement with the simulation results.
Zhao B, Lindeboom T, Benner S, et al., 2017, Predicting the Fluid-Phase Behavior of Aqueous Solutions of ELP (VPGVG) Sequences Using SAFT-VR., Langmuir, Vol: 33, Pages: 11733-11745, ISSN: 0743-7463
The statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to predict the fluid phase behavior of elastin-like polypeptide (ELP) sequences in aqueous solution with special focus on the loci of lower critical solution temperatures (LCSTs). A SAFT-VR model for these solutions is developed following a coarse-graining approach combining information from atomistic simulations and from previous SAFT models for previously reported relevant systems. Constant-pressure temperature-composition phase diagrams are determined for solutions of (VPGVG)n sequences + water with n = 1 to 300. The SAFT-VR equation of state lends itself to the straightforward calculation of phase boundaries so that complete fluid-phase equilibria can be calculated efficiently. A broad range of thermodynamic conditions of temperature and pressure are considered, and regions of vapor-liquid and liquid-liquid coexistence, including LCSTs, are found. The calculated phase boundaries at low concentrations match those measured experimentally. The temperature-composition phase diagrams of the aqueous ELP solutions at low pressure (0.1 MPa) are similar to those of types V and VI phase behavior in the classification of Scott and van Konynenburg. An analysis of the high-pressure phase behavior confirms, however, that a closed-loop liquid-liquid immiscibility region, separate from the gas-liquid envelope, is present for aqueous solutions of (VPGVG)30; such a phase diagram is typical of type VI phase behavior. ELPs with shorter lengths exhibit both liquid-liquid and gas-liquid regions, both of which become less extensive as the chain length of the ELP is decreased. The strength of the hydrogen-bonding interaction is also found to affect the phase diagram of the (VPGVG)30 system in that the liquid-liquid and gas-liquid regions expand as the hydrogen-bonding strength is decreased and shrink as it is increased. The LCSTs of the mixtures are seen to decrease as the ELP chain length is in
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