Connectivity-Altering Monte Carlo Simulations of the End Group Effects on Volumetric Properties for Poly(ethylene oxide)

Entropic Penalty Switches Li+ Solvation Site Formation and Transport Mechanisms in Mixed Polarity Copolymer Electrolytes

Emerging solid polymer electrolyte (SPE) designs for efficient Li-ion (Li+) conduction have relied on polarity and mobility contrast to improve conductivity. To further develop this concept, we employ simulations to examine Li+ solvation and transport in poly(oligo ethylene methacrylate) (POEM) and its copolymers with poly(glycerol carbonate methacrylate) (PGCMA). We find that Li+ is solvated by ether oxygens instead of the highly polar PGCMA, due to lower entropic penalties. The presence of PGCMA promotes single-chain solvation, thereby suppressing interchain Li+ hopping. The conductivity difference between random copolymer PGCMA-r-POEM and block copolymer PGCMA-b-POEM is explained in terms of a hybrid solvation site mechanism. With diffuse microscopic interfaces between domains, PGCMA near the POEM contributes to Li+ transport by forming hybrid solvation sites. The formation of such sites is hindered when PGCMA is locally concentrated. These findings help explain how thermodynamic driving forces govern Li+ solvation and transport in mixed SPEs.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

Dynamic Heterogeneity of Solvent Motion and Ion Transport in Concentrated Electrolytes

Molecular-level understanding of the cation transference number t₊⁰, an important property that characterizes the transport of working cations, is critical to the bottom-up design of battery electrolytes. We quantify t₊⁰ in a model tetraglyme-based electrolyte using molecular dynamics simulation and the Onsager approach. t₊⁰ exhibits a concentration dependence in three distinct regimes: dilute, intermediate, and concentrated. The cluster approximation uncovers dominant correlations and dynamic heterogeneity in each regime. In the dilute regime, t₊⁰ decreases sharply as increasing numbers of solvent molecules become coordinated with Li⁺. The crossover to the intermediate regime, t₊⁰ ≈ 0, occurs when all solvent molecules become coordinated, and a plateau is obtained because anions enter the Li⁺ solvation shell, resulting in ion pairs that do not contribute to t₊⁰. Transference in concentrated electrolytes is dominated by the presence of cations in a variety of negatively charged and solvent-excluded clusters, resulting in t₊⁰ < 0.

Elucidating the Molecular Origins of the Transference Number in Battery Electrolytes Using Computer Simulations

The rate at which rechargeable batteries can be charged and discharged is governed by the selective transport of the working ions through the electrolyte. Conductivity, the parameter commonly used to characterize ion transport in electrolytes, reflects the mobility of both cations and anions. The transference number, a parameter introduced over a century ago, sheds light on the relative rates of cation and anion transport. This parameter is, not surprisingly, affected by cation-cation, anion-anion, and cation-anion correlations. In addition, it is affected by correlations between the ions and neutral solvent molecules. Computer simulations have the potential to provide insights into the nature of these correlations. We review the dominant theoretical approaches used to predict the transference number from simulations by using a model univalent lithium electrolyte. In electrolytes of low concentration, one can obtain a quantitative model by assuming that the solution is made up of discrete ion-containing clusters-neutral ion pairs, negatively and positively charged triplets, neutral quadruplets, and so on. These clusters can be identified in simulations using simple algorithms, provided their lifetimes are sufficiently long. In concentrated electrolytes, more clusters are short-lived and more rigorous approaches that account for all correlations are necessary to quantify transference. Elucidating the molecular origin of the transference number in this limit remains an unmet challenge.

Electric-Field-Induced Spatially Dynamic Heterogeneity of Solvent Motion and Cation Transference in Electrolytes

While electric fields primarily result in migration of charged species in electrolytic solutions, the solutions are dynamically heterogeneous. Solvent molecules within the solvation shells of the cation will be dragged by the field while free solvent molecules will not. We combine electrophoretic NMR measurements of ion and solvent velocities under applied electric fields with molecular dynamics simulations to interrogate different solvation motifs in a model liquid electrolyte. Measured values of the cation transference number (t_{+}^{0}) agree quantitatively with simulation-based predictions over a range of electrolyte concentrations. Solvent-cation interactions strongly influence the concentration-dependent behavior of t_{+}^{0}. We identify a critical concentration at which most of the solvent molecules lie within solvation shells of the cations. The dynamic heterogeneity of solvent molecules is minimized at this concentration where t_{+}^{0} is approximately equal to zero.

Temperature Dependence of Conformational Relaxation of Poly(ethylene oxide) Melts

The time-temperature superposition (TTS) principle, employed extensively for the analysis of polymer dynamics, is based on the assumption that the different normal modes of polymer chains would experience identical temperature dependence. We aim to test the critical assumption for TTS principle by investigating poly(ethylene oxide) (PEO) melts, which have been considered excellent solid polyelectrolytes. In this work, we perform all-atom molecular dynamics simulations up to 300 ns at a range of temperatures for PEO melts. We find from our simulations that the conformations of strands of PEO chains in melts show ideal chain statistics when the strand consists of at least 10 monomers. At the temperature range of T= 400 to 300 K, the mean-square displacements (⟨Δr2(t)⟩) of the centers of mass of chains enter the Fickian regime, i.e., ⟨Δr2(t)⟩∼t1. On the other hand, ⟨Δr2(t)⟩ of the monomers of the chains scales as ⟨Δr2(t)⟩∼t1/2 at intermediate time scales as expected for the Rouse model. We investigate various relaxation modes of the polymer chains and their relaxation times (τn), by calculating for each strand of n monomers. Interestingly, different normal modes of the PEO chains experience identical temperature dependence, thus indicating that the TTS principle would hold for the given temperature range.

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains.

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model

In this work, a multi-site chain model was incorporated into the polymer reference interaction site model to investigate the structure and properties of atactic polystyrene (aPS) melt and the structural correlations of dilute spherical nanoparticles dissolved in aPS melt. The theoretically calculated X-ray scattering intensities, solubility parameters and intermolecular correlation functions of aPS and its nanocomposites are found to be in agreement with the corresponding molecular simulation and experimental data. The theory was further employed to investigate the distribution functions of different size effects of aPS-nanoparticle system with consideration of the potential of mean force and depletion force. The aggregation of large nanoparticles increases with the increase of the nanoparticle-site size ratio in the infinitely dilute limit. The results show that the present theory can be used to investigate the structure of aPS melt and its nanocomposite, and give a further understanding of the filler dispersion and aggregation. All the observations indicate molecular-level details of the underlying mechanisms, providing useful information for the future design control of new aPS-nanocomposite materials with tailored properties.

Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: methodology and performance

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.

Molecular simulation of the effect of temperature and architecture on polyethylene barrier properties

We present a multiscale approach for calculating the low-concentration solubility, diffusivity, and selectivity of small molecules through polymer matrixes. The proposed modeling scheme consists of two main stages; first, thoroughly equilibrated and representative poly(ethylene) (PE) atomistic melt configurations were obtained through the application of a Monte Carlo (MC) scheme based on advanced chain-connectivity altering moves (linear architectures) or the combination of localized MC moves followed by molecular dynamics. In the second phase, transition-state theory (TST), as proposed by Gusev and Suter [Gusev, A. A.; Suter, U. W. J. Chem. Phys. 1993, 99, 2228], was invoked in a coarser level of description to calculate the barrier properties of the studied macromolecules to small gas molecules at infinite dilution. The multiscale methodology was successfully applied on PE melts characterized by various molecular weights (MW) (from C78 up to C1000) and polydispersity indices at a wide range of temperature conditions. The effect of molecular architecture on the barrier properties was examined through the comparison between linear and short-chain branched structures bearing the same total number of carbon atoms. Simulation results were found to be in very good agreement with available experimental data. Additionally, the new scheme has been further validated by comparing the qualitative behavior of solubility, diffusivity, and selectivity with previously reported trends in the literature based on both experimental and simulation studies. The present study concludes that density plays a dominant role that determines the behavior of the polymer as a barrier material, especially in terms of diffusivity. Additionally, it is evidenced that short-chain branching has a small effect on the barrier properties of PE when the comparison is performed on purely amorphous samples. The hierarchical method presented here not only is faster when compared against conventional molecular dynamics simulations, but in some cases, like the vicinity of the glass transition temperature or for long polymer chain melts, it opens the way to the calculation of the barrier properties at realistic simulation times.

Modeling of aqueous poly(oxyethylene) solutions: 1. Atomistic simulations

The performance of different recently proposed force fields in combination with TIP4P-Ewald (TIP4P-Ew) water in reproducing experimental data of liquid 1,2-dimethoxyethane (DME) and its aqueous solutions for conformer populations, densities of solutions, and self-diffusion coefficients was explored. A modified version of the OPLS force field ("engineered") showed best performance in describing the conformer equilibria, but extremely high interconformational barriers reduce its applicability in dynamical simulations. The TraPPE-united atom force field (TraPPE-UA) by Siepmann et al. (J. Phys. Chem. B 2004, 108, 17596) was found to perform best in reproducing thermodynamic properties, but it showed some deficiency in describing the conformer equilibria. We reparameterized the dihedral potentials to match recent ab initio data by Anderson and Wilson (Mol. Phys. 2005, 103, 89) and could improve significantly the performance of description of conformer populations of DME in water. Subsequently, this modified TraPPE-UA was used in extensive simulations of poly(oxyethylene) oligomers H(CH2OCH2)nH (POEn) with n = 3, 5, 10, 12, 20, 30 repeat units at mass fractions between 3% and 80% at 298 K. Density, radii of gyration, and diffusion coefficients are in very good agreement with available experimental data. We conclude that this force field in combination with the TIP4P-Ew water model is very suitable for simulations of poly(oxyethylene) oligomers in aqueous solution. The application to real polymeric systems on the atomistic level is however hindered by very slow decorrelation of large-scale features and by slow diffusion.

Min-map bias Monte Carlo for chain molecules: biased Monte Carlo sampling based on bijective minimum-to-minimum mapping

A novel Monte Carlo (MC) simulation scheme based on Theodorou's bijective mapping strategy [D. N. Theodorou, J. Chem. Phys. 124, 034109 (2006)] is introduced. This min-map bias Monte Carlo acts in combination with any other proper, bare MC. It carries over the bare MC move from the original configuration space Omega(0), where trial move acceptance may be low, to a different configuration space, Omega(1), where acceptance is higher. The bare MC move is then performed in Omega(1) and the resulting configuration is finally mapped back to Omega(0). Mappings between Omega(0) and Omega(1) entail weighted selection of trial configurations, the bias of which is subsequently removed in the overall acceptance criterion. The new method is applied, in conjunction with continuum configurational bias as bare MC scheme, to the simulation of explicit hydrogen linear alkanes in the canonical ensemble. Min-map bias MC is found to alleviate the pervasive problem of very low acceptance rates encountered when using an explicit molecular description.

Retention in gas–liquid chromatography with a polyethylene oxide stationary phase: Molecular simulation and experiment

Configurational-bias Monte Carlo simulations in the isobaric-isothermal Gibbs ensemble were carried out to investigate the partitioning of normal alkanes, primary and secondary alcohols, symmetric alkyl ethers and arenes between a helium vapor phase and a polyethylene oxide stationary phase (M(W)=382 g mol(-1)). The united-atom version of the transferable potentials for phase equilibria force field was used to model all solutes, polyethylene oxide and helium. The Gibbs free energies of transfer and Kovats retention indices of the solutes were calculated directly from the partition constants at two different temperatures, 353 and 393 K. Chromatographic experiments on a Carbowax 20M retentive phase were performed for the same set of solutes and temperatures ranging from 333 to 413 K. The predicted retention indices for alcohols, ethers and arenes are overestimated by about 120, 70 and 20 retention index units, respectively, pointing to an overestimation of the first-order electrostatic interactions in the model system. Molecular-level analysis shows that hydrogen-bonding and dipole-dipole interactions lead to orientational ordering for the alcohol and ether analytes, whereas the weaker dipole-quadrupole interactions for the arene solutes are not sufficient to induce orientational ordering. The retention indices of alcohols and ethers decrease with increasing temperature because of the large entropic cost of hydrogen-bonding and orientational ordering. In contrast, the retention indices for arenes increase with increasing temperature because the entropic cost of cavity formation is smaller for arenes than for comparable alkanes.

Investigating pressure effects on structural and dynamical properties of liquid methanol with many-body interactions

Molecular-dynamics simulations utilizing a many-body potential was used to study the pressure dependence of structural and dynamical properties for liquid methanol. The liquid density as a function of pressure agreed well with experiment, and a combination of radial and angular distribution functions were used to analyze molecular structure. From these distribution functions, it was observed that hydrogen bond strength increased with increasing pressure. This observation coincided with an increase in the molecular dipole as a function of pressure, having a significant effect on the observed increased hydrogen bond strength. Also, methanols were found to more strongly favor exactly two hydrogen bonds, with fewer methanols of zero, one, or three hydrogen bonds present at higher pressures. Furthermore, a majority of the compression with increased pressure was found to occur in regions perpendicular to the methanol hydrogen-oxygen bond vector. This was the case despite hydrogen-oxygen nonbonded distances between hydrogen bonding species being shorter, but their stiffer oxygen-hydrogen-(nonbonded) oxygen angle offsets this, resulting in their oxygen-oxygen distances being relatively unaffected. The methanol translational diffusion decreased significantly with increased pressure, while the rotational diffusion decreased at a similar magnitude around the oxygen-hydrogen and oxygen-carbon bond vectors, despite having very different overall diffusion. Finally, the hydrogen bond lifetime increased significantly with pressure, owing to the increased hydrogen bond strength, and the slower translational and rotational dynamics.

Microscopic Origins for the Favorable Solvation of Carbonate Ether Copolymers in CO2

The strong desire for the wide use of carbon dioxide as an environmentally benign process solvent has spurred a large number of attempts to improve its solubility characteristics. Pioneering experimental work by Beckman and co-workers has pointed to carbonate ether copolymers as promising candidates for nonfluorous surfactants. It is demonstrated here that Gibbs ensemble Monte Carlo simulations (using configurational-bias and double-bridging strategies and the transferable potentials for phase equilibria force field) can be employed to accurately predict the phase equilibria of a carbonate ether copolymer with CO2. The simulations indicate that the greater accessibility of the carbonyl oxygen plays a major role for the CO2-philicity of this copolymer surfactant.