Intramolecular Distribution Functions Research Articles

Polymer free volume and its connection to the entanglement length and the plateau modulus via polymer mode-coupling theory and equation of state

Using a many-chain system of Gaussian chains interacting with each other through the Lennard-Jones (LJ) potential, we demonstrate that there exists a connection between polymer fractional free volume (f) and the entanglement chain length (Ne). Here, f is determined by the generic van der Waals (GvdW) equation of state using the intermolecular radial distribution function [g(r)] of the Gaussian chain generated by the polymer reference interaction sites model while Ne by the polymer mode-coupling theory (PMCT) for strongly coupled macromolecules. The key concept in PMCT is that intermolecular forces experienced by a bead in a chain surrounded by other chains are strongly coupled to the site specific intramolecular radial distribution function. The calculated Gp and η of polyethylene with chain lengths from 500 to 2000 interacting with one another through the LJ potential agree well with experiment and molecular dynamics simulation.

Structure and Conformational Response of Pure and Lithium-Doped Ionic Liquids to Pressure Alterations from Molecular Dynamics Simulations.

The response of ions in ionic liquids (ILs) to elevated external pressure facilitates the induced structural changes that give a chance to understand the change in chemical and physical properties because of perturbation. Employing classical molecular dynamics simulations, we report various structural properties of IL mixtures with Li-salt under varying pressure. Here, we aim to explore the effect of pressure on three ILs N-alkyl-N-methyl-pyrrolidinium bis(trifluoromethanesulfonyl)imide (Pyr1A-TFSI, A = 3, 6, 9) and their mixtures with 30 mol % lithium bis(trifluoromethanesulfonyl)imide (Li-TFSI). The microheterogeneity in these systems was explored by investigating the total and partial structure factors. Intramolecular distribution functions were calculated to study the conformational changes. The distribution of clusters of alkyl chains provides information about aggregation behavior. The calculated total structure factors compliment well with the main features of the experimental results. The prepeak, charge-ordering peak, and main peaks from simulations are in good agreement with the experimental results. The three pure ILs are structurally similar, which show both polarity and charge-ordering peaks. The addition of Li-salt makes the charge-ordering peak disappear. We find that three ILs respond quite differently to the addition of Li-salt. The mesoscopic structure of these ILs is affected by high pressure. The height of the prepeak is diminished significantly with the application of high pressure. This decrease in the height of the prepeak is due to the reduction of alkyl chain aggregation. This motivated us to calculate the aggregation of the alkyl chain quantitatively. The number of alkyl chains present in a given cluster fades with the rise in pressure. The addition of Li-salt decreases the tendency of alkyl chain aggregation. The presence of lithium-ions causes the absence of the charge-ordering peak, which occurs at around 8.0 nm-1 in pure ILs. From the partial structure factors, the charge-ordering is observed to be present in Li-containing mixtures. The conformation change in the ionic entity is also observed; the distance between the nitrogen atom and terminal carbon of the alkyl chain in cation decreases with increasing the pressure. When the Li-ion is present in the mixture, the cis configuration of anions slightly dominates the trans configuration. The conformational change of anions from trans to cis occurs when pressure changes from a low to a high value.

An Insight into molecular structure and properties of flexible amorphous polymers: A molecular dynamics simulation approach

ABSTRACTVisualization of polymer molecules by molecular dynamics simulation remains a challenging area in molecular modeling, as it involves a number of factors like type of force field, simulation time, simulation steps, and so forth. In our present study, we have used the condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, which is specific for polymers and organic molecules, in order to visualize the macromolecular chains of various flexible amorphous polymers: natural rubber, polybutadiene rubber, styrene–butadiene rubber, nitrile rubber, polychloroprene rubber, and fluoroelastomer. The study covered a wide range from nonpolar rubbers to polar rubbers, and the COMPASS force field was promising to understand the local structure and the packing of the chains inside the simulation box. The distance between different adjacent pairs of carbon atoms within the polymer chains was discussed in detail from intramolecular radial distribution function and represented pictorially in the polymer chains. Various bond angles were also examined for further details. In addition, interchain contacts, glass‐transition temperature, and solubility parameter were predicted and compared with the experimental values. The diffusive characteristic of the chains was assessed by mean square displacement which in turn described the polymer chain mobility. In essence, the present study is expected to aid in the vivid conceptualization of molecular orientation of various polymers and would help in predicting various physical properties. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47457

How Meaningful Is the Halogen Bonding in 1-Ethyl-3-methyl Imidazolium-Based Ionic Liquids for CO2 Capture?

We report on several parameters that can be used to describe the 1-ethyl-3-methyl-4,5-(X2)imidazolium cations (where X = H, Br, and I) within the Canongia-Lopez and Padua Force Field (CL&P) framework. Geometrical parameters like intramolecular distances and radial distribution functions are close to the experimental structure. Density values obtained with our force field are within the expected ones from CL&P calculations in related systems. This information is used to simulate through molecular dynamics the solubilization of CO2 by these ILs. For pure ILs, the addition of halides in position 4 and 5 promotes an enhanced hydrogen bond interaction at position 2 with the oxygen atoms in the anion. It is found that CO2 should be in the interstices of the anion-cation 3D network with longer distances than those found in other reports at ab initio levels, suggesting that halogen bond, if present, may be not the driving force interaction in these systems. Therefore, it seems that CO2 interacts linearly via an oxygen atom with the cation and with the anion through a π-stacking or hydrogen-bonded fashions. Solvation enthalpies compare well with the experimental data, thereby suggesting that halogenated ILs dissolve more efficiently in CO2 than C2C1Im+ derivatives. This result suggests that halogenated ILs can be considered as reliable candidates for CO2 capture.

Parametrization of Chain Molecules in Dissipative Particle Dynamics.

This paper presents a consistent strategy for parametrization of coarse-grained models of chain molecules in dissipative particle dynamics (DPD), where the soft-core DPD interaction parameters are fitted to the activities in solutions of reference compounds that represent different fragments of target molecules. The intercomponent parameters are matched either to the infinite dilution activity coefficients in binary solutions or to the solvent activity in polymer solutions. The respective calibration relationships between activity and intercomponent interaction parameter are constructed from the results of Monte Carlo simulation of the coarse-grained solutions of reference compounds. The chain conformation is controlled by the near neighbor and second neighbor bond potentials, which are parametrized by fitting the intramolecular radial distribution functions of the coarse-grained chains to the respective atomistic molecular dynamics simulations. The consistency, accuracy, and transferability of the proposed parametrization strategy is demonstrated drawing on the example of nonionic surfactants of the poly(ethylene oxide) alkyl ether (CnEm) family. The lengths of tail and head sequences are varied (n = 8-12 and m = 3-9), so that the critical micelle concentration ranges from 10 to 0.1 mM. The surfactants are modeled at different coarse-graining levels using DPD beads of different diameters. We found consistent agreement with experimental data for the critical micelle concentration and aggregation number, especially for surfactants with relatively long hydrophilic segments. Depending on the system, we observed surfactant aggregation into spheroidal, elongated, or core-shell micelles, as well as into irregular agglomerates. Using the models at different coarse-graining levels for the same molecules, we found that the smaller the bead size the better is agreement with experimental data.

A new perturbed-chain equation of state for square-well chains in fluid and solid phases

Considering the hard-chain system as reference, a perturbed-chain equation of state (EOS) is developed. The second-order thermodynamic perturbation theory EOS is applied to the reference system. Monte Carlo simulation data for average intra-molecular and inter-molecular segment-segment radial distribution function of hard-chain systems with a chain length of 3-10 in the range of packing fraction between 0.1 and 0.72, covering both fluid and solid phases, are reported. A disordered solid phase structure is considered in this work. These customized data are used to develop the perturbation term of square-well (SW) attractions. The performance of perturbed-chain EOS is tested against computer simulation data from the literature for compressibility factor and phase equilibrium in the systems of SW chains. Results within good accuracy are obtained for all the test cases. Global vapor-liquid-solid equilibrium diagrams for SW chain systems predicted by the new EOS are reported.

Conformation of a flexible chain in explicit solvent: Exact solvation potentials for short Lennard-Jones chains

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.

Effective density terms in proper integral equations

Two complementary routes to a new integral equation theory for site-site molecular fluids are presented. First, a simple approximation to a subset of the atomic site bridge functions in the diagrammatically proper integral equation theory is presented. This in turn leads to a form analogous to the reactive fluid theory, in which the normalization of the intramolecular distribution function and the value of the off-diagonal elements in the density matrix of the proper integral equations are the means of propagating the bridge function approximation. Second, a derivation from a topological expansion of a model for the single-site activity followed by a topological reduction and low-order truncation is given. This leads to an approximate numerical value for the new density coefficient. The resulting equations give a substantial improvement over the standard construction as shown with a series of simple diatomic model calculations.

Comment on “The effect of density on the properties of short chain fluids” [J. Chem. Phys. 122, 094906 (2005)

In a recent work [J. Chem. Phys.122, 094906 (2005)], Porter and Lipson present a Born-Green-Yvon integral equation approach for computing the intramolecular distribution functions of a flexible interaction-site chain in a monomeric solvent. Although this Born-Green-Yvon construction appears to work for a hard-sphere chain-in-solvent system, here we show that the approach yields quantitatively incorrect results for the square-well chain-in-solvent system.

Intra- and Intermolecular Packing in Polyolefin Blends

The response of chain packing for four saturated hydrocarbon polymers, poly(ethylene−propylene), poly(ethylene−butene), isotactic polypropylene, and head-to-head polypropylene, to changes in environment are considered. The changes arise from mixing each material with the three others in the series. Intra- and intermolecular packing are considered separately by using molecular dynamics simulation, where unambiguous separation of the two is possible. We assess changes from the pure state in chain dimensions [radii of gyration and end-to-end distances], the intramolecular pair distribution functions, and the intermolecular pair distribution functions of each component [the A/A and B/B distributions]. Although it cannot be compared to the melt, the cross [A/B] intermolecular pair distribution function is also considered. We find that chain dimensions and intramolecular packing are insensitive to mixing. Regardless of the nature of the second component, these quantities are invariant within our ability to meas...

Structure and thermodynamic properties from molecular dynamics simulations of the polyethylene crystal

This paper describes the results of molecular dynamics simulations of polyethylene crystal at two temperatures in the absence of periodic boundary conditions. We report the profiles of the temperature and pressure tensor along two directions in the crystal. We check that the two different methods (IK) and (MOP) for calculating the pressure tensor give similar profiles, which are constant in the middle of the crystal. In addition, we compare the data resulted from the pressure profiles with the values obtained from the virial route. The internal structure of the polyethylene is visualized through the intramolecular and intermolecular radial distribution functions.

Analytical expression for the correlation function of a hard sphere chain fluid

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein—Zernike integral equation theory with the polymer Percus—Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D (D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Chandler—Silbey—Ladanyi integral equation theory for semiflexible molecules

Extension of Chandler—Silbey—Ladanyi (CSL) integral equation theory for the fluid of semi-flexible site—site molecules is proposed. The Percus—Yevick type of the closure is used to describe the structural properties of the fluid consisting of semiflexible linear chain triatomic molecules. Results for the site—site intramolecular and intermolecular radial distribution functions (RDFs) are compared with the corresponding computer simulation results and results of self-consistent reference interaction site model (RISM) theory. In general both theories give reasonably good agreement with corresponding Monte Carlo simulation data. The exception is the RDF between the terminal sites, for which none of the theories is satisfactory. The present version of CSL theory appears to be slightly more accurate than the self-consistent RISM approach.

The Excluded Volume Problem in the Polymer Reference Interaction Site Model

An intramolecular distribution function for lattice chains, accounting for the long range excluded volume, has been derived employing an Ornstein−Zernike-like integral equation approach, initially investigated for off-lattice chains by Curro, Blatz, and Pings. The intramolecular distributions, obtained for 16-, 30-, and 60-mers, are compared to theoretical results for the freely jointed chain model and to Monte Carlo simulation data. The new single chain intramolecular distribution function accurately matches the Monte Carlo data whereas the ideal chain structure factor overestimates the short-range intramolecular correlations. Upon increasing density the simulated intramolecular distributions gradually evolve toward the ideal chain results although the latter are never actually reached. The intermolecular distributions for athermal and interacting 30-mers at several densities have been calculated by combining the investigated intramolecular distribution functions with the lattice-PRISM theory. Furthermore, the equation of state for athermal 20- and 30-mers and the liquid−vapor spinodal for 16-mers have been investigated. It is found that the ideal chain distribution function results in unphysical thermodynamic behavior, reflected in the equation of state as well as in the liquid−vapor spinodal. The predicted intermolecular distribution is quite reasonable, considering the simplicity of the ideal chain model. The combination lattice−PRISM/excluded volume intramolecular distribution function offers at least qualitatively correct results both for the thermodynamic properties and intermolecular correlations. abstract

Some exact results for isolated hard-disc chain and ring molecules

In this paper we study two-dimensional flexible interaction-site molecules composed of n tangent hard discs. In particular, we obtain exact results for the n-site probability function for isolated tangent-hard-disc chains and rings with n⩽6. All configurational properties of the chain and ring n -mers can be determined from this probability function. We present analytical and ‘exact’ numerical results for the mean-square site–site separations, mean-square radii of gyration, average shape and two-site intramolecular distribution functions.

Athermal Lattice Polymers: A Comparison of RISM Theory and Monte Carlo Simulations

Polymer-RISM theory is applied to study athermal polymeric lattice fluids. The inter- molecular segmental distributions and the compressibility equation of state (EoS) have been obtained within the approach for three different intramolecular distribution functions, i.e., the random flight, the non reversal random walk, and an intramolecular distribution obtained from Monte Carlo simulations. Both the intermolecular segmental distributions and the EoS are also compared to Monte Carlo simulations. From the comparison to the simulations it is seen that the polymer-RISM theory is well able to reproduce the intermolecular segmental distributions, but it underestimates the density dependence of the EoS: the EoS is worse than the classical Huggins EoS for the same model, and only for the computer simulated intramolecular distribution we find reasonable agreement between calculated and simulated EoS. The absence of liquidlike ordering effects in a lattice fluid allow us to show to what extent the deviations are due to the incomplete incorporation of excluded volume in the intramolecular distribution functions.

Some exact results for isolated hard-disc chain and ring molecules

In this paper we study two-dimensional flexible interaction-site molecules composed of n tangent hard discs. In particular, we obtain exact results for the n-site probability function for isolated tangent-hard-disc chains and rings with n⩽6. All configurational properties of the chain and ring n -mers can be determined from this probability function. We present analytical and ‘exact’ numerical results for the mean-square site–site separations, mean-square radii of gyration, average shape and two-site intramolecular distribution functions.

Small-angle X-ray scattering reveals differences between the quaternary structures of oxygenated and deoxygenated tarantula hemocyanin

Small-angle X-ray scattering (SAXS) curves have been recorded for the oxygenated and deoxygenated states of the 4 × 6-meric hemocyanin from the tarantula Eurypelma californicum. A comparison of the curves shows that the quaternary structures of the two states are different by three criteria, which all indicate that the hemocyanin is less compact in the oxygenated compared to the deoxygenated form: (a) The radius of gyration is 8.65 ± 0.05 nm for the deoxy- and 8.80 ± 0.05 nm for the oxy-form. (b) The maximum particle dimension amounts to 25.0 ± 0.5 nm for the deoxy- and to 27.0 ± 0.5 nm for the oxyform. (c) A dip in the intramolecular distance distribution function p( r) is more pronounced and shifted to larger distances in the oxy-form. The p( r) functions based on SAXS measurements were compared to p( r) functions deduced from published electron microscopical images of three different 4 × 6-meric hemocyanins from closely related species. The p( r) functions of SAXS and electron microscopy were similar in one case, whereas in the other two cases the distance between the two 12-meric half-molecules had to be changed by 1–1.5 nm to obtain good agreement. The differences between the p( r) functions of oxygenated and deoxygenated 4 × 6-meric tarantula hemocyanin are much larger than one would expect from a comparison of X-ray structures of the oxygenated and deoxygenated states of a closely related 6-meric hemocyanin. Thus, the conformational changes upon oxygenation occur at various levels of the quaternary structure, as postulated by hierarchical theories of allosteric interactions.

Collapse of a polymer chain: A Born–Green–Yvon integral equation study

A Born–Green–Yvon (BGY) type integral equation is developed for the intramolecular distribution functions of an isolated flexible polymer chain. The polymer is modeled as a linear array of n identical spherical interaction sites connected by universal joints of bond length σ. In particular we study chains composed of up to n=400 square-well spheres with hard-core diameters σ and well diameters λσ (1≤λ≤2). Intramolecular distribution functions and the resulting average configurational and energetic properties are computed over a wide range of temperatures. In the high temperature (good solvent) limit this model is identical to the tangent hard-sphere chain. With decreasing temperature (worsening solvent) the square-well chain undergoes a collapse transition identified by a sudden reduction in chain dimensions and a peak in the single chain specific heat. Extensive comparison is made between the BGY results and Monte Carlo results for square-well chains with λ=1.5. The BGY theory is extremely accurate for square-well 4-mers at all temperatures. For longer chains the theory yields reasonably accurate results for reduced temperatures greater than T*≊1 (expanded and theta states) and qualitatively correct behavior for T*<1 (collapsed state). Very accurate values for the theta temperatures for square-well chains with 1.25≤λ≤2.0 are also obtained.

Configurational statistics for isolated square-well chain molecules: exact results for short chains

Exact results are obtained for the configurational statistical properties of isolated square-well chain molecules of lengths 3 and 4. The chain molecules considered here are composed of square-well spheres with hard-core diameter σ and well diameter λσ (1 ˇ- λ ˇ- 2) connected by ‘universal joints’ with bond length σ. Exact analytical and semi-analytical expressions are obtained for the intramolecular site-site distribution functions for these chain molecules. From the intramolecular distribution functions one can determine all average equilibrium configurational and energetic properties. In particular, the mean-square site-site separations, mean-square radius of gyration, average energy, and specific heat are calculated. With decreasing temperature the chain molecules undergo a collapse transition identified by a sudden reduction in chain dimensions and a peak in the specific heat. For both square-well 3-mers and 4-mers the reduced transition temperature is in the range 0·2 ≲T c* ≲ 0·5.