Intermolecular Correlation Functions Research Articles

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water.

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Molecular simulation of an initial stage of the ordered-structure formation of linear and ring polymers upon cooling from the melts

Monte Carlo (MC) simulation of the coarse-grained ring and linear polyethylene (PE) models were employed to study the early stage of the ordered-structure formation upon cooling from the melts. The simulations suggest that the ordered structure with the single domain can be formed for both linear and ring PE chains which have the same mean square radius of gyration in the molten state. Molecular and structural properties evaluated from the simulation are the fraction of trans conformation and the sequence length of trans state, the anisotropic change of chain dimension, the overall orientation correlation function, intra- and inter-molecular bond orientation correlation functions and intermolecular pair correlation function. All these properties reveal an ordering process as the sign of crystallization especially for linear chains whereas it is more difficult for ring polymer to form an ordered phase. For ring chains, the ordered structures were formed with multiple folded conformations and smaller magnitude for the fraction of trans conformation, chain orientation, degree of chain packing, intra- and inter-molecular bond ordering. The simulations suggest that PE chains are needed to stretch to some extent before the chain alignment can proceed. Compared to the linear polymers with comparable molecular size, ring PE chains tend to form the less-ordered crystalline structure, have higher melting temperature and exhibit slower crystallization rates.

Measuring packing length in simulations for different polymer architectures

The packing length p figures prominently in scaling predictions of the entanglement length and bulk modulus for polymer melts and solutions. p has been argued to scale as the ratio of chain displaced volume V and mean square end-to-end distance R2. This scaling works for several cases; however, it is not obvious how to apply it to chains with side groups, and the scaling must fail for sufficiently thin, stiff chains. In this work, we measure the packing length in simulations, without making any scaling assumptions, as the typical distance of closest approach of two polymer strands in a simulated bead-spring melt. We use the intermolecular correlation function to measure the distance up to which a given polymer strand dominates the local volume fraction. Using our measured packing length, we find good agreement of entanglement properties with Lin–Noolandi scaling for flexible polymers of different architectures.

Phase separation of comb polymer nanocomposite melts.

In this work, the spinodal phase demixing of branched comb polymer nanocomposite (PNC) melts is systematically investigated using the polymer reference interaction site model (PRISM) theory. To verify the reliability of the present method in characterizing the phase behavior of comb PNCs, the intermolecular correlation functions of the system for nonzero particle volume fractions are compared with our molecular dynamics simulation data. After verifying the model and discussing the structure of the comb PNCs in the dilute nanoparticle limit, the interference among the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions between the comb polymer and nanoparticles in spinodal demixing curves is analyzed and discussed in detail. The results predict two kinds of distinct phase separation behaviors. One is called classic fluid phase boundary, which is mediated by the entropic depletion attraction and contact aggregation of nanoparticles at relatively low nanoparticle-monomer attraction strength. The second demixing transition occurs at relatively high attraction strength and involves the formation of an equilibrium physical network phase with local bridging of nanoparticles. The phase boundaries are found to be sensitive to the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions. As the side chain length is fixed, the side chain number has a large effect on the phase behavior of comb PNCs; with increasing side chain number, the miscibility window first widens and then shrinks. When the side chain number is lower than a threshold value, the phase boundaries undergo a process from enlarging the miscibility window to narrowing as side chain length increases. Once the side chain number overtakes this threshold value, the phase boundary shifts towards less miscibility. With increasing nanoparticle-monomer size ratio, a crossover of particle size occurs, above which the phase separation is consistent with that of chain PNCs. The miscibility window for this condition gradually narrows while the other parameters of the PNCs system are held constant. These results indicate that the present PRISM theory can give molecular-level details of the underlying mechanisms of the comb PNCs. It is hoped that the results can be used to provide useful guidance for the future design control of novel, thermodynamically stable comb PNCs.

Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs

The methods currently used to calculate atomic pair distribution functions (PDFs) from organic structural models do not distinguish between the intramolecular and intermolecular distances. Owing to the stiff bonding between atoms within a molecule, the PDF peaks arising from intramolecular atom–atom distances are much sharper than those of the intermolecular atom–atom distances. This work introduces a simple approach to calculate PDFs of molecular systems without building a supercell model by using two different isotropic displacement parameters to describe atomic motion: one parameter is used for the intramolecular, the other one for intermolecular atom–atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calculations were done with theDiffPy-CMIcomplex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

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.

Communication: Long-range angular correlations in liquid water

At ambient conditions the intermolecular correlation in liquid water is generally believed to be short ranged as shown in the atomic pair distribution functions (PDFs) obtained from scattering experiments or from theoretical predictions. However, atom-atom PDFs provide only a partial description of the higher dimensional intermolecular correlation function that depends on both the positions and orientations of water molecules. Here we study the atomic PDFs of liquid water as well as the angular correlation function (ACF) using a classical density functional theory. We demonstrate that, different from the PDFs, the ACF exhibits long-range oscillatory decay extending up to tens of molecular diameters. The theoretical predictions are in good agreement with molecular simulations and corroborate recent experimental results from the second harmonic light scattering experiments.

Elucidation of spin echo small angle neutron scattering correlation functions through model studies

Several single-modal Debye correlation functions to approximate part of the overall Debey correlation function of liquids are closely examined for elucidating their behavior in the corresponding spin echo small angle neutron scattering (SESANS) correlation functions. We find that the maximum length scale of a Debye correlation function is identical to that of its SESANS correlation function. For discrete Debye correlation functions, the peak of SESANS correlation function emerges at their first discrete point, whereas for continuous Debye correlation functions with greater width, the peak position shifts to a greater value. In both cases, the intensity and shape of the peak of the SESANS correlation function are determined by the width of the Debye correlation functions. Furthermore, we mimic the intramolecular and intermolecular Debye correlation functions of liquids composed of interacting particles based on a simple model to elucidate their competition in the SESANS correlation function. Our calculations show that the first local minimum of a SESANS correlation function can be negative and positive. By adjusting the spatial distribution of the intermolecular Debye function in the model, the calculated SESANS spectra exhibit the profile consistent with that of hard-sphere and sticky-hard-sphere liquids predicted by more sophisticated liquid state theory and computer simulation.

Renormalized one-loop theory of correlations in disordered diblock copolymers

A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)] is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q∗), peak position q∗, and single-chain statistics for symmetric and asymmetric copolymers as functions of χ(e)N, where χ(e) is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q∗) upon χ(e)N for symmetric diblock copolymers in the limit of strong scattering, or large χ(e)N, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q∗) and a decrease of q∗ for large values of χ(e)N, relative to the RPA predictions, but an enhancement of S(q∗) and an increase in q∗ for small χ(e)N. The decrease in q∗ near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q∗ at small values of χ(e)N is a direct result of non-Gaussian single-chain statistics.

Systematic Coarse Graining of 4-Cyano-4′-pentylbiphenyl

A coarse-grained model is derived for a liquid-crystal-forming molecule, 4-cyano-4′-pentylbiphenyl (5CB), from a detailed atomistic model using the iterative Boltzmann inversion (IBI) method in the isotropic phase at 315 K and 1 bar. The coarse-grained model consists of five “superatoms” (one for the cyano group, two for the aromatic rings in the biphenyl moiety, and two for the alkyl tail), which are categorized as three types. A modification of IBI, wherein only one of the effective intermolecular potentials (the one corresponding to the superatom pair whose intermolecular correlation function exhibits the highest deviation from the atomistic one) is updated at each iteration, proves to be necessary to achieve convergence. The coarse-grained model, which enables a savings of a factor of 35 in computational cost relative to atomistic simulation, is used to explore ordering into liquid-crystalline phases at lower temperatures. It is found to yield a first-order ordering transition at 288 K with small hysteresis and negligible system size effects. A detailed investigation in terms of various structural and dynamical measurements indicates that the ordered phase is of the smectic type rather than nematic, as observed experimentally. The ordering temperature can be brought close to the experimental value of 308.5 K through the simple rescaling of the intermolecular effective interaction potentials employed in the coarse-grained model. A nematic ordered phase can be obtained from the coarse-grained model by scaling up the head−head and tail−tail effective interaction potentials obtained by IBI.

A theoretical study of structure–solubility correlations of carbon dioxide in polymers containing ether and carbonyl groups

This work involves a theoretical study to investigate the effects of the structure on CO(2) sorption in polymers, where poly(ethylene oxide) (PEO), poly(propylene oxide) (PPO), poly(vinyl acetate) (PVAc), poly(ethylene carbonate) (PEC) and poly(propylene carbonate) (PPC) were examined. In the theoretical approach, the multi-site semiflexible chain model and the renormalized technique of electrostatic potentials were incorporated into the polymer reference interaction site model (PRISM). To test the theory, molecular dynamic simulations were performed using the TraPPE-UA force field. The theoretically calculated reduced X-ray scattering intensities and intermolecular correlation functions of these five polymers are found to be in qualitative agreement with the corresponding molecular simulation data. The theory was then employed to investigate the distribution functions between CO(2) and different sites of the polymers with consideration of the Lennard-Jones, potential of mean force, and columbic contributions. Based on the detailed structure characteristics of CO(2) in contact with different groups, the CO(2) coordination molecular numbers were obtained and their sorption intensities analyzed. Finally, the sorption isotherms of CO(2) in these five polymers were calculated. The results for PEO, PPO and PVAc are close to the available experimental curves, and the trend of CO(2) solubility is PPC > PEC > PVAc ~ PPO > PEO.

Structure of poly(ethylene glycol)–water mixture studied by polymer reference interaction site model theory

In this work, the polymer reference interaction site model is applied to investigate the structure of poly(ethylene glycol) (PEG) aqueous solution with the strong hydrogen-bond interactions. In the theoretical model, the renormalized technique of electrostatic potentials is combined with our recently proposed multisite semiflexible chain model to describe the inter- and intramolecular correlations. To test the model for the description of hydrogen bonding, the intermolecular correlation functions of water, ethylene glycol (EG), and EG-water binary mixture are calculated. The results are in good agreement with the corresponding simulation or experimental data. The validated model is then employed to predict the intermolecular correlation functions of different sites of the PEG and its aqueous solution. Another priority of the model is that it can obtain the corresponding direct correlation functions directly.

Integral Equation Theory for Gas Sorption and Swelling of Glassy Atactic Polystyrene

On the basis of the polymer reference interaction site model (PRISM), a theoretical approach was proposed to describe gas solubilities in atactic polystyrene (aPS) melt. In the PRISM, our recently developed multisite semiflexible model was applied to derive intramolecular correlation functions. The intermolecular correlation functions for gas−gas and gas−aPS were obtained and further applied to calculate the excess chemical potential of gas−aPS system. The solubility coefficients of a wide range of gases in aPS were predicted at low pressure. These predictions are in good agreement with the experimental data. Particularly, the sorption curves of CO2 in aPS under high pressures were calculated, and the reasonable results were obtained. These results demonstrate that the theoretical model is reliable to describe the sorption properties of small molecules in aPS chain. On the basis of the CO2 sorption isotherms, the swelling of aPS under high pressure were also discussed.

Features of polymer chain dynamics as revealed by intermolecular nuclear magnetic dipole-dipole interaction: Model calculations and field-cycling NMR relaxometry

Proton NMR phenomena such as spin-lattice relaxation, free-induction decays, and solid echoes are analyzed with respect to contributions by intermolecular dipole-dipole interactions in polymer melts. The intermolecular dipole-dipole correlation function is calculated by taking into account the correlation hole effect characteristic for polymer melts. It is shown that the ratio between the intra- and intermolecular contributions to NMR measurands depends on the degree of isotropy of chain dynamics anticipated in different models. This, in particular, refers to the tube/reptation model that is intrinsically anisotropic in clear contrast to n-renormalized Rouse models, where no such restriction is implied. Due to anisotropy, the tube/reptation model predicts that the intramolecular contribution to the dipole-dipole correlation function increases with time relative to the intermolecular contribution. Therefore, the intramolecular contribution is expected to dominate NMR measurands by tendency at long times (or low frequencies). On the other hand, the isotropic nature of the n-renormalized Rouse model suggests that the intermolecular contribution tends to prevail on long-time scales (or low frequencies). Actually, theoretical estimations and the analysis of experimental spin-lattice relaxation data indicate that the intermolecular contribution to proton NMR measurands is no longer negligible for times longer than 10(-7) s-10(-6) s corresponding to frequencies below the megahertz regime. Interpretations not taking this fact into account need to be reconsidered. The systematic investigation of intermolecular interactions in long-time/low frequency proton NMR promises the revelation of the dynamic features of segment displacements relative to each other in polymer melts.

Description of the Structure of Polystyrene with Six-Site Semiflexible Model

In this work, a six-site semiflexible chain model for the polymer reference interaction site model (PRISM) theory was proposed and applied to describe the structure and properties of atactic polystyrene (aPS) melt. In the model, the local monomer structure is composed of six independent sites corresponding to A and B in the backbone and C, D, E, and F in the side phenyl ring group. The intramolecular correlation functions were obtained analytically with the Koyama distribution function and the generator matrix method. To improve the calculation of the intermolecular correlation functions, the potential of mean force was introduced. The calculated X-ray scattering intensity and total radial distribution function were compared with both simulation and experiment data. The results indicate that the model is an effective way to investigate the microscopic structure of styrene polymers.

Role of dipolar correlations in the infrared spectra of water and ice

We report simulated infrared (IR) spectra of deuterated water and ice using Car--Parrinello molecular dynamics with maximally localized Wannier functions. Experimental features are accurately reproduced within the harmonic approximation. By decomposing the line shapes in terms of intramolecular and intermolecular dipole correlation functions, we find that short-range intermolecular dynamic charge fluctuations associated to hydrogen bonds are prominent over the entire spectral range. Our analysis reveals the origin of several spectral features and identifies network bending modes in the far IR range.

Generating multichain configurations of an inhomogeneous melt from the knowledge of single-chain properties

Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the mean-field approach and information about the distribution of distance between different molecules is lost. Based on the knowledge of the exact equilibrium single-chain properties in contact with solid substrates, we generate multichain configurations that serve as nearly equilibrated starting configurations for molecular dynamics simulations by utilizing the packing algorithm of [Auhl et al., J. Chem. Phys. 119, 12718 (2003)] for spatially inhomogeneous systems, i.e., a thin polymer film confined between two solid substrates. The single-chain conformations are packed into the thin film conserving the single-chain properties and simultaneously minimizing local fluctuations of the density. The extent to which enforcing incompressibility of a dense polymer liquid during the packing process is able to re-establish intermolecular correlations is investigated by monitoring intermolecular correlation functions and the structure function of density fluctuations as a function of the distance from the confining solid substrates.

Liquid structure of N-butyl- N-methylpyrrolidinium bis-(trifluoromethanesulfonyl) amide ionic liquid studied by large angle X-ray scattering and molecular dynamics simulations

Large angle X-ray scattering of the N-butyl- N-methylpyrrolidinium bis-(trifluoromethanesulfony) amide (P 14 +TFSA −) ionic liquid was measured at 298 K. The total interference function i LAXS( s) and the total pair correlation function G LAXS( r) were successfully obtained. The i LAXS( s) was analyzed in terms of the intra-molecular geometries of the conformational isomers of the P 14 + and TFSA − ions based on the crystal structures, the inter-molecular correlation function G inter LAXS( r) and the inter-molecular radial distribution function as the form D inter LAXS( r) − 4 πr 2 ρ 0 were evaluated. With D inter LAXS( r) − 4 πr 2 ρ 0, the inter-molecular correlation peaks at 3.5, 4.5 and 5–6 Å evidently appeared as the short range interaction, while considerable long range interactions were found as the broad peaks at 10 and 15 Å. Molecular dynamics simulations of the ionic liquid based on the effective pairwise potentials were carried out. The X-ray total interference function derived from the MD simulations i MD( s) was in agreement with the experimental one. According to the inter-molecular partial atom–atom correlation functions from MD simulations, the observed peaks at 3.5, 4.5 and 5–6 Å can be predominantly ascribed to the closest atom–atom correlations between the P 14 + and TFSA – ions such as C···O and C···F. In the inter-molecular partial atom–atom correlation function between terminal methyl carbons of the butyl chain in the P 14 + ion, a peak at 4.0 Å was found as the inter-molecular correlation, suggesting that the ionic liquid shows an alkyl chain aggregation, which is similar to that observed for 1-alkyl-3-methylmidazolium ionic liquids.

Impact of Short Chain Branching on Conformations of Metallocene LLDPE Melts: NMR, Light Scattering and MD Simulation Study

AbstractSummary: The influence of short chain branching on molecular conformations of melts and solutions of metallocene linear Low‐density polyethylene (m‐LLDPE) was studied by nuclear magnetic resonance (NMR) spectroscopy, light scattering, and Molecular Dynamics (MD) simulation techniques. Both T2 relaxation measurements by NMR and MD simulations suggest the loss of molecular order in m‐LLDPE at temperatures >135°C. Similar trends were observed for the radius of gyration as measured by light scattering and calculated from MD simulations vs. branch content (BC) and type. At high BC (>40 branches/1000 C) m‐LLDPE tends towards self assembly. Neither the branch type nor the BC has significant effect on the intermolecular orientation correlation function. This might be attributed to the fact that the high temperature of the melt results in loss of order in the chains. This lack of order is independent of BC or type. This result is in agreement with the results of the dihedral distribution analysis. Also, it is in agreement with our NMR T2 measurements. The radial distribution functions are nearly identical indicating no effect of branch type at low branch density on the correlation between branches and backbone segments. However, increasing the BC to 80 branches/1000C resulted in a change in the correlation between the branches and backbone segments.

How Well Can Coarse-Grained Models of Real Polymers Describe Their Structure? The Case of Polybutadiene.

Coarse-graining of chemical structure of macromolecules in the melt is investigated using extensive molecular dynamics simulation data which are based on a united atom force-field model of polybutadiene. Systematically increasing the number, n, of the united atoms approximated by an effective coarse-grained monomer, we study the influence of degree of coarse-graining on the structure functions such as the segment-segment intermolecular and intramolecular correlation functions. These results are compared to Monte Carlo simulations of the corresponding coarse-grained bead-spring model and Chen-Kreglewski potential for chain molecules. In contrast to the atomistic chemically realistic model of polybutadiene, the bending and torsional potentials are not included into the coarse-grained models. Nevertheless, for a range of intermediate values of n a good qualitative agreement between intra- and intermolecular coarse-grained correlations of the atomistic model and the coarse-grained bead-spring model is found on large and intermediate length scales, but deviations occur on length scales well below one nanometer. The structure functions obtained for the Chen-Kreglewski chains exhibit many artificial features.