Joachim Gross

Phase behavior of hyperbranched polymer systems: experiments and application of the perturbed-chain polar SAFT equation of state.

Vapor-liquid equilibrium data for systems of hyperbranched polymer (HBP) and carbon dioxide are reported for temperatures of 285-455 K and pressures up to 13 MPa. The bubble-point pressures of (CO2 + hyperbranched polyester) and of (CO2 + hyperbranched polyglycerol + CH3OH) samples with fixed compositions were measured using a Cailletet apparatus. The system (CO2 + polyglycerol + CH3OH) also exhibits a liquid-liquid phase split characterized by lower critical solution temperatures. For this system cloud point curves and vapor-liquid-liquid bubble-point curves were also measured. Moreover, a thermodynamic model has been developed for HBP mixtures in the framework of the perturbed-chain polar statistical association fluid theory (PCP-SAFT) equation of state accounting for branching effects. There is no additional binary interaction parameter introduced along with the branching contributions to the model. Although the miscibility gap in the system (CO2 + polyglycerol + CH3OH) is not predicted by the model, PCP-SAFT including branching effects gives a good representation of the bubble-point curves of this system at temperatures lower than the lower solution temperature (LST).

Determining force field parameters using a physically based equation of state.

Force field parameters used in classical molecular simulations can be estimated from quantum mechanical calculations or spectroscopic measurements. This especially applies to bonded interactions such as bond-stretching, bond-bending, and torsional interactions. However, it is difficult and computational expensive to obtain accurate parameters describing the nonbonded van der Waals interactions from quantum mechanics. In many studies, these parameters are adjusted to reproduce experimental data, such as vapor-liquid equilibria (VLE) data. Adjusting these force field parameters to VLE data is currently a cumbersome and computationally expensive task. The reason is that the result of a calculation of the vapor-liquid equilibria depends on the van der Waals interactions of all atom types in the system, therefore requiring many time-consuming iterations. In this work, we use an analytical equation of state, the perturbed chain statistical associating fluid theory (PC-SAFT), to predict the results of molecular simulations for VLE. The analytical PC-SAFT equation of state is used to approximate the objective function f(p) as a function of the array of force field parameters p. The objective function is here for example defined as the deviations of vapor pressure, enthalpy of vaporization and liquid density data, with respect to experimental data. The parameters are optimized using the analytical PC-SAFT equation of state, which is orders of magnitude quicker to calculate than molecular simulation. The solution is an excellent approximation of the real objective function, so that the resulting method requires only very few molecular simulation runs to converge. The method is here illustrated by optimizing transferable Lennard-Jones parameters for the n-alkane series. Optimizing four force field parameters p = (ε(CH(2))(CH(2)), ε(CH(3))(CH(3)), σ(CH(2))(CH(2)), σ(CH(3))(CH(3))) we obtain excellent agreement of coexisting densities, vapor pressure and caloric properties within only 2 -3 molecular simulation runs.

Grand Canonical Monte Carlo Simulations Guided by an Analytic Equation of State—Transferable Anisotropic Mie Potentials for Ethers

In this study, we propose using an analytical equation of state for guiding molecular simulations in the grand canonical ensemble. Molecular simulations in the grand canonical ensemble deliver phase equilibrium properties with low statistical uncertainty. The entire phase envelope can be obtained when histograms of several simulations along the phase envelope are combined. In this study, we explore the use of an analytical equation of state for defining chemical potentials, temperatures, and intervals of molecule numbers for simulations in the grand canonical ensemble, such that the phase envelope is traced. We limit particle numbers to intervals and ensure even sampling of molecule numbers in each interval by applying a bias potential determined from transition-matrix sampling. The methodology is described for pure components and binary mixtures. We apply the simulation method to develop parameters of the transferable anisotropic Mie (TAMie) force field for ethers. We find that the partial charges optimized individually for diethyl ether and for dipropyl ether differ substantially from the partial charges optimized simultaneously to both substances. The concept of transferable partial charges is thus a significant assumption. For developing the (TAMie) force field, we constrained the partial charge to a range, where individually optimized partial charges were found.

The isotropic-nematic phase transition of tangent hard-sphere chain fluids--pure components.

An extension of Onsagers second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

Transferable Anisotropic United-Atom Force Field Based on the Mie Potential for Phase Equilibrium Calculations: n-Alkanes and n-Olefins.

A new transferable force field parametrization for n-alkanes and n-olefins is proposed in this work. A united-atom approach is taken, where hydrogen atoms are lumped with neighboring atoms to single interaction sites. A comprehensive study is conducted for alkanes, optimizing van der Waals force field parameters in 6 dimensions. A Mie n-6 potential is considered for the van der Waals interaction, where for n-alkanes we simultaneously optimize the energy parameters ϵCH3 and ϵCH2 as well as the size parameters σCH3 and σCH2 of the CH3(sp(3)) and CH2(sp(3)) groups. Further, the repulsive exponent n of the Mie n-6 potential is varied. Moreover, we investigate the bond length toward the terminal CH3 group as a degree of freedom. According to the AUA (anisotropic united-atom) force field, the bond length between the terminal CH3 group and the neighboring interaction site should be increased by Δl compared with the carbon-carbon distance in order to better account for the hydrogen atoms. The parameter Δl is considered as a degree of freedom. The intramolecular force field parametrization is taken from existing force fields. A single objective function for the optimization is defined as squared relative deviations in vapor pressure and in liquid density of propane, n-butane, n-hexane, and n-octane. A similar study is also done for olefins, where the objective function includes 1-butene, 1-hexene, 1-octene, cis-2-pentene, and trans-2-pentene. Molecular simulations are performed in the grand canonical ensemble with transition-matrix sampling where the phase equilibrium properties are obtained with the histogram reweighting technique. The 6-dimensional optimization of strongly correlated parameters is possible, because the analytic PC-SAFT equation of state is used to locally correlate simulation results. The procedure is iterative but leads to very efficient convergence. An implementation is proposed, where the converged result is not affected (disturbed) by the analytic equation of state. The resulting transferable anisotropic Mie-potential (TAMie) force field shows average relative deviations in vapor pressure of 1.1% and in liquid density of 0.9% for alkanes, and 2% and 1.5% for olefins, respectively, in a wide range of (reduced) temperature, Tr = 0.55-0.97. For substances that were not members of the objective function, the TAMie force field enables predictions of phase equilibrium properties with good accuracy.

Computer-aided Molecular Design of ORC Working Fluids using PC-SAFT

Abstract Organic Rankine Cycles (ORCs) are used for the transformation of low-temperature heat to power. The key design variables are the process settings and the working fluid. This paper presents a holistic method for the computer-aided molecular design (CAMD) of ORC working fluids. The basis for the design is a novel approach allowing for the simultaneous optimization of the working fluid and the process by exploiting the molecular picture underlying PC-SAFT. The simultaneous design yields a target for a hypothetical working fluid and optimal process settings from one optimization problem. The hypothetical target fluid forms the basis for the CAMD method. For this purpose, a group contribution (GC) method is developed for the prediction of PC-SAFT pure component parameters. Thereby, a holistic design of novel working fluids and optimal processes is achieved.

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility.

Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].

An equation of state for the isotropic phase of linear, partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.

Acceleration of Monte-Carlo molecular simulations on hybrid computing architectures

Markov-Chain Monte-Carlo (MCMC) methods are an important class of simulation techniques, which execute a sequence of simulation steps, where each new step depends on the previous ones. Due to this fundamental dependency, MCMC methods are inherently hard to parallelize on any architecture. The upcoming generations of hybrid CPU/GPGPU architectures with their multi-core CPUs and tightly coupled many-core GPGPUs provide new acceleration opportunities especially for MCMC methods, if the new degrees of freedom are exploited correctly. In this paper, the outcomes of an interdisciplinary collaboration are presented, which focused on the parallel mapping of a MCMC molecular simulation from thermodynamics to hybrid CPU/GPGPU computing systems. While the mapping is designed for upcoming hybrid architectures, the implementation of this approach on an NVIDIA Tesla system already leads to a substantial speedup of more than 87× despite the additional communication overheads.

A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid

The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into reference and perturbation parts. The first four perturbation terms are evaluated for various densities and temperatures (in the ranges ρ*=0-1.5 and T*=0.5-12) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several approximate theoretical methods for describing perturbation terms or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a careful comparison between the BH and WCA formalisms, and (2) a systematic examination of the effect of higher-order perturbation terms on calculated thermodynamic properties of fluids. Properties included in the comparison are supercritical thermodynamic properties (pressure, internal energy, and chemical potential), vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher-order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. We find no reason to prefer the WCA formalism over the BH formalism.