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Molecular-based equations of state for describing the thermodynamics of chain molecules are often based on mean-field like arguments that reduce the problem of describing the interactions between chains to a simpler one involving only nonbonded monomers. While for dense liquids such arguments are known to work well, at low density they are typically less appropriate due to an incomplete description of the effect of chain connectivity on the local environment of the chains' monomer segments. To address this issue, we develop three semi-empirical approaches that significantly improve the thermodynamic description of chain molecules at low density. The approaches are developed for chain molecules with repulsive intermolecular forces; therefore, they could be used as reference models for developing equations of the state of real fluids based on perturbation theory. All three approaches are extensions of Wertheim's first-order thermodynamic perturbation theory (TPT1) for polymerization. The first model, referred to as TPT1-v, incorporates a second-virial correction that is scaled to zero at liquid-like densities. The second model, referred to as TPT1-y, introduces a Helmholtz-energy contribution to account for correlations between next-nearest-neighbor segments within chain molecules. The third approach, called TPT-E, directly modifies TPT1 without utilizing an additional Helmholtz energy contribution. By employing TPT1 at the core of these approaches, we ensure an accurate description of mixtures and enable a seamless extension from chains of tangentially bonded hard-sphere segments of equal size to hetero-segmented chains, fused chains, and chains of soft repulsive segments (which are influenced by temperature). The low-density corrections implemented in TPT1 are designed to preserve these good characteristics, as confirmed through comparisons with novel molecular simulation results for the pressure of various chain fluids. TPT1-v exhibits excellent transferability across different chain types, but it relies on knowing the second virial coefficient of the chain molecules, which is non-trivial to obtain and determined here using Monte Carlo simulation. The TPT1-y model, on the other hand, achieves comparable accuracy to TPT1-v while being fully predictive, requiring no input besides the geometry of the chain molecules. [ABSTRACT FROM AUTHOR]

This study extends entropy scaling to inhomogeneous fluids by using the classical density functional theory together with a new viscosity reference that takes into account the influence of solid–fluid interactions on the fluid viscosity. The density functional theory uses a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory; the local residual entropy per particle is determined from the temperature derivative of the Helmholtz energy functional in combination with an appropriate weighted density profile. The weighted density calculation requires a single transferable parameter, which is adjusted to a reference molecular dynamics simulation. In particular, local viscosity values for fluids under nanoconfinement near solid–fluid interfaces are predicted using the same entropy scaling parameters as for homogeneous fluids. We validate the model by comparing viscosity and velocity profiles with results from non-equilibrium molecular dynamics simulations of a Couette flow in a slit pore. Good agreement is found between the entropy scaling model and the non-equilibrium molecular dynamics results for both the viscosity and velocity profiles of the Lennard–Jones truncated and shifted fluid. The proposed model extrapolates well to systems with different temperatures, fluid densities, and shear forces as well as to systems with different wetting behaviors. These results demonstrate that entropy scaling can be generalized to inhomogeneous fluids using an appropriate combination of residual entropy profile and viscosity reference. [ABSTRACT FROM AUTHOR]

The curvature dependence of interfacial properties has been discussed extensively over the last decades. After Tolman published his work on the effect of droplet size on surface tension, where he introduced the interfacial property now known as Tolman length, several studies were performed with varying results. In recent years, however, some consensus has been reached about the sign and magnitude of the Tolman length of simple model fluids. In thiswork, we re-examine Tolman's equation and how it relates the Tolman length to the surface tension and we apply non-local classical density functional theory (DFT) based on the perturbed chain statistical associating fluid theory (PC-SAFT) to characterize the curvature dependence of the surface tension of real fluids as well as mixtures. In order to obtain a simple expression for the surface tension, we use a first-order expansion of the Tolman length as a function of droplet radius Rs, as δ(Rs) = δ0 + δ1/Rs, and subsequently expand Tolman's integral equation for the surface tension, whereby a second-order expansion is found to give excellent agreement with the DFT result. The radius-dependence of the surface tension of increasingly non-spherical substances is studied for n-alkanes, up to icosane. The infinite diameter Tolman length is approximately δ0 = -0.38 Å at low temperatures. For more strongly non-spherical substances and for temperatures approaching the critical point, however, the infinite diameter Tolman lengths δ0 turn positive. For mixtures, even if they contain similar molecules, the extrapolated Tolman length behaves strongly non-ideal, implying a qualitative change of the curvature behavior of the surface tension of the mixture. [ABSTRACT FROM AUTHOR]

Predicting thermodynamic equilibrium properties is essential to develop chemical and energy conversion processes in the absence of experimental data. For the modeling of thermodynamic properties, statistical associating fluid theory (SAFT)-based equations of state, such as perturbed-chain polar (PCP)-SAFT, have been proven powerful and found broad application. The PCP-SAFT parameters can be predicted by group-contribution (GC) methods. However, their application to the dipole term is substantially limited: current GC methods neglect the dipole term or only allow for a single dipolar group per substance to avoid handling the molecular dipole moment's symmetry effects. Still, substances with multiple dipolar groups are highly relevant, and their description substantially improves by including the dipole term in SAFT models. To overcome these limitations, this work proposes a vector-addition-based (Vector-)GC method for the dipole term of PCP-SAFT that accounts for molecular symmetry. The Vector-GC employs information on the substance's molecular 3D structure to predict the molecular dipole moment through a vector addition of bond contributions. Combining the proposed sum rule for dipole moments with established sum rules for the remaining parameters yields a consistent GC method for PCP-SAFT for dipolar substances. The prediction capabilities of the Vector-GC method are analyzed against experimental data for two substance classes: nonassociating oxygenated and halogenated substances. We demonstrate that the Vector-GC method improves vapor pressure and liquid density predictions compared to neglecting the dipole term. Moreover, we show that the Vector-GC method enables differentiation between cis- and trans-isomers. The Vector-GC method, hence, substantially increases the predictive capabilities and applicability domain of GC methods. All parameters are provided as JSON and CSV files, and the Vector-GC method is available through an open-source python package. Additionally, the developed regression framework for GC methods for PCP-SAFT is openly available. The regression framework can be employed to regress the Vector-GC method to other substance classes and is easily adaptable to other sum rules for PCP-SAFT., Competing Interests: The authors declare no competing financial interest., (© 2024 The Authors. Published by American Chemical Society.)

Modern equations of state for real nonspherical molecules are often based on Wertheim's first-order thermodynamic perturbation theory (TPT1). A major drawback of TPT1 is that it assumes tangentially bonded spheres. In this work, we develop a Helmholtz energy functional for systems comprising hard heterosegmented chains with arbitrary bond lengths. This is achieved by using hard-sphere fragments (i.e., hard spheres with spherical caps removed at the intersection to their neighbors) as monomers as opposed to full hard spheres. The model is written as a Helmholtz energy functional for inhomogeneous systems and the equation of state for a homogeneous system is determined as a special case. We thereby obtain an equation of state that can be used as a reference to develop statistical associating fluid theory models that more accurately describe the thermodynamic properties of nonspherical molecules. The model is validated against molecular simulation results of bulk pressures and density profiles in slit pores. For the bulk pressures, we show that the equation of state is in excellent agreement with results from molecular simulation for dimers, trimers, and chains of up to 20 segments. The density profiles of individual segments of the chains are regarded in slit pores. Some deviations of the theory from results of molecular simulations are observed for strongly fused chains. Overall, however, good agreement is found for inhomogeneous systems.