Generalised dissipative particle dynamics with energy conservation: density- and temperature-dependent potentials.

We present a generalised, energy-conserving dissipative particle dynamics (DPDE) method appropriate for the non-isothermal simulation of particle interaction force fields that are both density- and temperature-dependent. A detailed derivation is formulated in a bottom-up manner by considering the thermodynamics of small systems with the appropriate consideration of the fluctuations. Connected to the local volume is a local density and corresponding local pressure, which is determined from an equation-of-state based force field that depends also on a particle temperature. Compared to the original DPDE method, the formulation of the generalised DPDE method requires a change in the independent variable from the particle internal energy to the particle entropy. As part of the re-formulation, the terms dressed particle entropy and the corresponding dressed particle temperature are introduced, which depict the many-body contributions in the local volume. The generalised DPDE method has similarities to the energy form of the smoothed dissipative particle dynamics method, yet fundamental differences exist, which are described in the manuscript. The basic dynamic equations are presented along with practical considerations for implementing the generalised DPDE method, including a numerical integration scheme based on the Shardlow-like splitting algorithm. Demonstrations and validation tests are performed using analytical equation-of-states for the van der Waals and Lennard-Jones fluids. Particle probability distributions are analysed, where excellent agreement with theoretical estimates is demonstrated. As further validation of the generalised DPDE method, both equilibrium and non-equilibrium simulation scenarios are considered, including adiabatic flash heating response and vapour-liquid phase separation.

Logarithmic Exchange Kinetics in Monodisperse Copolymeric Micelles.

Experimental measurements of the relaxation kinetics of copolymeric surfactant exchange for micellar systems unexpectedly show a peculiar logarithmic decay. Several authors use polydispersity as an explanation for this behavior. However, in coarse-grained simulations that preserve microscopic details of the surfactants, we find evidence of the same logarithmic behavior. Since we use a strictly monodisperse distribution of chain lengths such a relaxation process cannot be attributed to polydispersity, but has to be caused by an inherent physical process characteristic of this type of system. This is supported by the fact that the decay is specifically logarithmic and not a power law with an exponent inherited from the particular polydispersity distribution of the sample. We suggest that the degeneracy of the energy states of the hydrophobic block in the core, which is broken on leaving the micelle, can qualitatively explain the broad distribution of energy barriers, which gives rise to the observed nonexponential relaxation.

Simulation Analysis of the Kinetic Exchange of Copolymer Surfactants in Micelles.

The exchange of surfactants in micelles involves several processes that are difficult to characterize experimentally. Microscopic simulations have the potential to reveal some of the key activities that occur when a surfactant spontaneously exits a micelle. In this work, we present a quantitative analysis of the kinetic exchange process over a large range of time. This study is based on a dynamic version of single-chain mean-field theory using a coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems. The kinetics described in our simulations involves three different regimes. After a fast initial rearrangement of the labeled chains, the system undergoes a logarithmic relaxation, which has been experimentally observed. Contrary to what has been reported in previous analyses, our simulations indicate that this regime is caused by the intrinsic physical behavior of the system and is not due only to the polydispersity of the samples. Finally, the terminal regime is characterized by an exponential decay. The exit rates predicted by our simulations are in good agreement with the values reported experimentally. In addition, we address the sequence of microscopic conformational changes undergone by the surfactants when leaving the micellar aggregates. We found a subtle variation in the radius of gyration of the hydrophobic block, which challenges the image of either a complete collapse or a full stretching commonly accepted in the current theoretical and experimental literature.

Mean-field coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems.

The microscopic modeling of surfactant systems is of the utmost importance in understanding the mechanisms related to the micellization process because it allows for prediction and comparison with experimental data of diverse equilibrium system properties. In this work, we present a coarse-grained model for Pluronics, a trademarked type of triblock copolymer, from simulations based on a single-chain mean-field theory (SCMF). This microscopic model is used to quantify the micellization process of these nonionic surfactants at 37 °C and has been shown to be able to quantitatively reproduce experimental data of the critical micelle concentration (CMC) along with other equilibrium properties. In particular, these results correctly capture the experimental behavior with respect to the lengths of the hydrophobic and hydrophilic moieties of the surfactants for low and medium hydrophobicities. However, for the more highly hydrophobic systems with low CMCs, a deviation is found which has been previously attributed to nonequilibrium effects in the experimental data (García Daza, F. A.; Mackie, A. D. Low Critical Micelle Concentration Discrepancy between Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 2027-2032).

Chain architecture and micellization: a mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants.

Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.

Micellar morphological transformations for a series of linear diblock model surfactants.

The concentration induced shape transitions of linear model surfactants, H(x)T(y), on a lattice have been studied using Monte Carlo simulation. It has been found that a sphere to cylinder shape transition is generally found on shortening the hydrophilic part of the surfactant and anticipates an eventual phase transition. Asymmetric surfactants with longer heads than tails (x > y) prefer to form only spherical micelles independent of total surfactant concentration while asymmetric surfactants with longer tails than heads (x < y) form spherical micelles at lower concentration and undergo a shape transition to cylindrical micelles on increasing the total concentration. Finally, in the case of symmetric surfactants with x = y, only the shortest surfactants H1T1 and H2T2 undergo a sphere to cylinder shape transition on increasing surfactant concentration. Longer symmetric surfactants are always found to prefer to form spherical micelles.

Model shape transitions of micelles: spheres to cylinders and disks.

We present a microscopic analysis of shape transitions of micelles of model linear nonionic surfactants. In particular, symmetric H(4)T(4) and asymmetric H(3)T(6) surfactants have been chosen for the study. In a previous work, it has been observed that symmetric surfactants have a strong tendency to prefer spherical micelles over a wide range of chemical potentials, while asymmetric surfactants undergo shape transitions between a spherical micelle at low concentration to other forms, mainly finite cylindrical micelles. This study combines the application of a two-dimensional single-chain mean-field theory (SCMFT) with Monte Carlo (MC) simulations of exactly the same systems. On the one hand, the characteristics of the SCMFT make this method suitable for free energy calculations, especially for small surfactants, due to the incorporation of relevant microscopic details in the model. On the other hand, MC simulations permit us to obtain a complete picture of the statistical mechanical problem, for the purpose of validation of the mean-field calculations. Our results reveal that the spherical shape for the symmetric surfactant is stable over a large range of surfactant concentrations. However, the asymmetric surfactant undergoes a complex shape transition that we have followed by calculating the standard chemical potential as a function of the aggregation number. The results indicate that the system forms prolate spheroids prior to developing short capped cylinders that gradually grow in length, with some oscillations in the energy of formation. The most important result of our work is the evidence of a bifurcation where, together with the elongated objects, the system can develop oblate aggregates and finally a torus shape similar to a red blood cell.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 1: Theoretical Foundation and Algorithm.

An extension of the generalized energy-conserving dissipative particle dynamics method (GenDPDE) that allows mass transfer between mesoparticles via a diffusion process is presented. By considering the concept of the mesoparticles as property carriers, the complexity and flexibility of the GenDPDE framework were enhanced to allow for interparticle mass transfer under isoenergetic conditions, notated here as GenDPDE-M. In the formulation, diffusion is described via the theory of mesoscale irreversible processes based on linear relationships between the fluxes and thermodynamic forces, where their fluctuations are described by Langevin-like equations. The mass exchange between mesoparticles is such that the mass of the mesoparticle remains unchanged after the transfer process and requires additional considerations regarding the coupling with other system properties such as the particle internal energy. The proof-of-concept work presented in this article is the first part of a two-part article series. In Part 1, the development of the GenDPDE-M theoretical framework and the derivation of the algorithm are presented in detail. Part 2 of this article series is targeted for practitioners, where applications, demonstrations, and practical considerations for implementing the GenDPDE-M method are presented and discussed.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 2: Applications and Demonstrations.

We present the second part of a two-part paper series intended to address a gap in computational capability for coarse-grain particle modeling and simulation, namely, the simulation of phenomena in which diffusion via mass transfer is a contributing mechanism. In part 1, we presented a formulation of a dissipative particle dynamics method to simulate interparticle mass transfer, termed generalized energy-conserving dissipative particle dynamics with mass transfer (GenDPDE-M). In the GenDPDE-M method, the mass of each mesoparticle remains constant following the interparticle mass exchange. In part 2 of this series, further verification and demonstrations of the GenDPDE-M method are presented for mesoparticles with embedded binary mixtures using the ideal gas (IG) and van der Waals (vdW) equation-of-state (EoS). The targeted readership of part 2 is toward practitioners, where applications and practical considerations for implementing the GenDPDE-M method are presented and discussed, including a numerical discretisztion algorithm for the equations-of-motion. The GenDPDE-M method is verified by reproducing the particle distributions predicted by Monte Carlo simulations for the IG and vdW fluids, along with several demonstrations under both equilibrium and non-equilibrium conditions. GenDPDE-M can be generally applied to multi-component mixtures and to other fundamental EoS, such as the Lennard-Jones or Exponential-6 models, as well as to more advanced EoS models such as Statistical Associating Fluid Theory.

Generalized Energy-Conserving Dissipative Particle Dynamics with Reactions.

We present an extension of the generalized energy-conserving dissipative particle dynamics method (J. Bonet Avalos, et al., Phys Chem Chem Phys, 2019, 21, 24891-24911) to include chemical reactivity, denoted GenDPDE-RX. GenDPDE-RX provides a means of simulating chemical reactivity at the micro- and mesoscales, while exploiting the attributes of density- and temperature-dependent many-body force fields, which include improved transferability and scalability compared to two-body pairwise models. The GenDPDE-RX formulation considers intra-particle reactivity via a coarse-grain reactor construct. Extent-of-reaction variables assigned to each coarse-grain particle monitor the temporal evolution of the prescribed reaction mechanisms and kinetics assumed to occur within the particle. Descriptions of the algorithm, equations of motion, and numerical discretization are presented, followed by verification of the GenDPDE-RX method through comparison with reaction kinetics theoretical model predictions. Demonstrations of the GenDPDE-RX method are performed using constant-volume adiabatic heating simulations of three different reaction models, including both reversible and irreversible reactions, as well as multistep reaction mechanisms. The selection of the demonstrations is intended to illustrate the flexibility and generality of the method but is inspired by real material systems that span from fluids to solids. Many-body force fields using analytical forms of the ideal gas, Lennard-Jones, and exponential-6 equations of state are used for demonstration, although application to other forms of equation of states is possible. Finally, the flexibility of the GenDPDE-RX framework is addressed with a brief discussion of other possible adaptations and extensions of the method.

Universal Scaling for the Exit Dynamics of Block Copolymers from Micelles at Short and Long Time Scales.

The correlation function for the exit of poloxamer copolymers from equilibrated micelles is found to show up to four regimes depending on the chain flexibility: an initial fast reorganization, a logarithmic intermediate regime, followed by an exponential intermediate regime, and a final exponential decay. The logarithmic intermediate regime has been observed experimentally and attributed to the polydispersity of the polymer samples. However, we present dynamic single-chain mean-field theory simulations with chains of variable flexibility which show the same logarithmic relaxation but with strictly monodisperse systems. In agreement with our previous studies, we propose that this logarithmic response arises from a degeneracy of energy states of the hydrophobic block in the micelle core. For this to occur, a sufficiently large number of degenerate conformational states are required, which depend on the polymer flexibility and therefore should not be present for rigid polymers. Experimental results for monodisperse polymeric samples claiming the absence of such a logarithmic response may also lack a sufficient number of hydrophobic blocks for the required number of configurational states for this type of response to be seen. The insight gained from analyzing the simulation results allows us to propose a modified Eyring equation capable of reproducing the observed dynamic behavior. On scaling experimental results from different sources and systems according to this equation, we find a unique master curve showing a universal nature of the intermediate regimes: the logarithmic regime together with the secondary exponential decay. The terminal exponential regime at long times proposed by the standard Halperin and Alexander model is beyond the range of the data analyzed in this article. The universality observed suggests an entropic origin of the short-time dynamic response of this class of systems rather than the polydispersity.

Generalized energy-conserving dissipative particle dynamics revisited: Insight from the thermodynamics of the mesoparticle leading to an alternative heat flow model.

Recently we introduced the generalized energy-conserving dissipative particle dynamics method (GenDPDE) [J. Bonet Avalos, M. Lísal, J. P. Larentzos, A. D. Mackie, and J. K. Brennan, Phys. Chem. Chem. Phys. 21, 24891 (2019)]PPCPFQ1463-907610.1039/C9CP04404C, which has been formulated for an emerging class of density- and temperature-dependent coarse-grain models. In the original work, GenDPDE was formulated to ensure a fundamental link is maintained with the underlying physical system at the higher resolution scale. In this paper, we revisit the formulation of the GenDPDE method, and rederive the particle thermodynamics to ensure consistency at the opposing scale extreme, i.e., between the local thermodynamics in the mesoscopic systems and the corresponding macroscopic properties. We demonstrate this consistency by introducing unambiguous, physically meaningful definitions of the heat and work, which lead to the formulation of an alternative heat flow model that is analogous to Fourier's law of heat conduction. We present further analysis of the internal, unresolved degrees-of-freedom of the mesoparticles by considering the thermodynamics of an individual mesoparticle within the GenDPDE framework. Several key outcomes of the analysis include: (i) demonstration that the choice of the independent variables alters the particle thermodynamic description; (ii) demonstration that the mesoscopic thermodynamic transformations introduce additional terms of the order of the size of the local fluctuations, which prevent an unambiguous definition of both the heat and work; (iii) an emphasis on the importance of the choice of the proper estimators of the thermodynamic properties that are embedded in the chosen thermodynamic description; and (iv) a clearly defined path for determining any thermodynamic quantity dressed by the fluctuations. The further insight provided by this deeper analysis is useful for both readers interested in the GenDPDE theoretical framework, as well as readers interested in the practical ramifications of the analysis, namely, the alternative heat flow model.

Anisotropic united-atoms (AUA) potential for alcohols.

An anisotropic united-atom (AUA4) intermolecular potential has been derived for the family of alkanols by first optimizing a set of charges to reproduce the electrostatic potential of the isolated molecules of methanol and ethanol and then by adjusting the parameters of the OH group to fit selected equilibrium properties. In particular, the proposed potential includes additional extra-atomic charges in order to improve the matching to the electrostatic field. Gibbs ensemble Monte Carlo simulations were performed to determine the phase equilibria, while the critical region was explored by means of grand canonical Monte Carlo simulations combined with histogram reweighting techniques. In order to increase the transferability of the model, only the parameters of the Lennard-Jones OH group have been fitted, the parameters of the other AUA groups are taken from previous works. Nevertheless, a good level of agreement was obtained for all compounds considered in this work. In particular, excellent results were obtained for the Henry constants calculation of different gases in alkanols.

An anisotropic united atoms (AUA) potential for thiophenes.

The optimization of the parameters of the Lennard-Jones (LJ) 12-6 potential of the sulfur atom in thiophene has allowed the AUA 4 potential to be successfully extended to alkyl and polythiophenes. Monte Carlo Gibbs ensemble and grand canonical simulations combined with histogram reweighting techniques have been performed to investigate the resulting phase equilibrium and the critical region of different molecules of this family in order to test the proposed potential. Excellent agreement with experimental densities, enthalpies of vaporization, and saturation pressures has been obtained in most of the cases. In particular, the critical point of our model for thiophene has been located with a statistical precision of less than 0.1% and is within 1% of the experimental value. The calculation of the critical points has been made through a recently implemented methodology based on the calculation of a fourth order cumulant (Binder parameter) combined with the use of finite size scaling methods, allowing the critical points to be located in a straightforward and accurate way.

Physical Absorption of Green House Gases in Amines: The Influence of Functionality, Structure, and Cross-Interactions.

Monte Carlo simulations were performed in the isothermal-isobaric ensemble (NPT) to calculate the Henry constants of methane (CH4), nitrous oxide (N2O), and carbon dioxide (CO2) in pure H2O, amines, and alkanolamines using the classical Lorentz-Berthelot combining rules (L-B). The Henry constants of N2O and CO2 in water are highly overestimated and motivated us to propose a new set of unlike interactions. Contrarily, the Henry constant of N2O in MEA is underestimated by around 40%, and again, a new reoptimized cross unlike parameter is able to reproduce the constant to within 10%. An analysis is given of the relationship between the physical absorption of these gases and the chemical structure or functionality of 12 molecules including amines and alkanolamines using the anisotropic united atom intermolecular potential (AUA4). Finally, the solubility of N2O in an aqueous solution of monoethanolamine (MEA) at 30% (wt) was also studied. A Henry constant within 7% of the experimental value was found by using the reoptimized parameters along with L-B to account for the MEA + H2O unlike interactions. This very good agreement without additional adjustments for the MEA + H2O system may be attributed to the good excess properties predictions found in previous works for the binary mixture (MEA + H2O). However, further work, including additional alkanolamines in aqueous solutions at several concentrations, is required to verify this particular point.

Optimized intermolecular potential for aromatic hydrocarbons based on anisotropic united atoms. III. Polyaromatic and naphthenoaromatic hydrocarbons.

In this third article of the series, a new anisotropic united atoms (AUA) intermolecular potential parameter set has been proposed for the carbon force centers connecting the aromatic rings of polyaromatic hydrocarbons to predict thermodynamic properties using both the Gibbs ensemble and NPT Monte Carlo simulations. The model uses the same parameters as previous AUA models used for the aromatic CH force centers. The optimization procedure is based on the minimization of a dimensionless error criterion incorporating various thermodynamic data of naphthalene at 400 and 550 K. The new model has been evaluated on a series of polyaromatic and naphthenoaromatic hydrocarbons over a wide range of temperatures up to near-critical conditions. Vaporization enthalpy, liquid density, and normal boiling temperature are reproduced with good accuracy. The new potential parameters have also been tested successfully on toluene, 1,3,5-trimethylbenzene, styrene, m-xylene, n-hexylbenzene, and n-dodecylbenzene to demonstrate their transferability to alkylbenzenes.

Low Critical Micelle Concentration Discrepancy between Theory and Experiment.

Experimental measurements for a variety of surfactants unexpectedly show that the critical micelle concentration (CMC) becomes constant with respect to increasing the size of the hydrophobic tail. This observation disagrees with theoretical models where it is expected to continue to decrease exponentially. Because of the lack of a satisfactory explanation for such a discrepancy from theory, we have studied these systems using a coarse-grained model within the single-chain mean field (SCMF) theory combined with relevant micellar kinetic effects. In particular, a microscopic model for poly(ethylene oxide) alkyl ether was applied to describe a series of nonionic gemini surfactants. When kinetic effects are used to correct the equilibrium CMC values from the SCMF scheme together with the loss of surfactants due to adsorption on the experimental recipient, it is possible to reproduce the correct order of magnitude of the experimental CMC results. Hence it appears that the experimental values disagree with the theoretical predictions because they are not true equilibrium values due to the fact that the time scales for these low CMC values become astronomically large.

A Transferable Force Field for Primary, Secondary, and Tertiary Alkanolamines.

Due to the importance of alkanolamines as solvents in several industrial processes and the absence of a dedicated transferable force field for them, we have developed an anisotropic united-atom (AUA4) force field for primary, secondary, and tertiary alkanolamines. In addition to correctly reproducing the experimental densities, additional properties for six different molecules have been verified at different temperatures including vaporization enthalpies, vapor pressures, normal boiling points, critical temperatures, and critical densities. A qualitative analysis of the radial distribution function of pure monoethanolamine has also been carried out. Furthermore, the viscosity coefficients were also calculated as a function of temperature and found to be in good agreement with experimental data. Finally, and perhaps most strikingly, the prediction of the excess enthalpies of alkanolamines in aqueous solutions has been found to be in excellent qualitative agreement with experimental data.

Transferable force field for equilibrium and transport properties in linear and branched monofunctional and multifunctional amines. II. Secondary and tertiary amines.

Following the same philosophy of our previous force field for primary amines (J. Phys. Chem. B2011, 115, 14617), we present an extension for secondary and tertiary amines using the anisotropic united atom (AUA4) approach. The force field is developed to predict the phase equilibrium and transport properties of secondary and tertiary amines. The transferability was studied for an important set of molecules including as secondary amines dimethylamine, diethylamine, di-n-propylamine, di-iso-propylamine, and di-iso-butylamine. We have also tested diethylenetriamine, a multifunctional molecule which includes two primary and one secondary amino groups. For tertiary amines, we have included simulations for trimethylamine, triethylamine, tri-n-propylamine, and methyldiethylamine. Monte Carlo simulations in the Gibbs ensemble were carried out to study thermodynamic properties such as equilibrium densities, vaporization enthalpies, and vapor pressures. Critical coordinates (critical density and critical temperature) and normal boiling points were also calculated. The shear viscosity coefficients were studied for dimethyl, diethyl, di-n-propyl, trimethyl, triethyl, and tri-n-propylamine at different temperatures using molecular dynamics in the isothermal isobaric ensemble. Our results show a very good agreement with experimental values for all the studied molecules for both thermodynamic and transport properties, demonstrating the transferability of our force field.

Accurate critical micelle concentrations from a microscopic surfactant model.

A single chain mean field theory is used to quantitatively describe the micellization process of the nonionic polyethylene oxide alkyl ether, C(n)E(m) class of surfactants at 25 °C. An explicit but simple microscopic model with only three interaction parameters is shown to be able to reproduce with high accuracy the critical micelle concentrations of a wide range of head and tail surfactant lengths. In addition, the aggregation number of the micelles is studied, the effect of the number of the hydrophobic and hydrophilic segments on CMC and aggregation number of the micelles are discussed and volume fraction profiles are given.