Rotational Isomeric State Research Articles

Conformational Analysis of Chain Molecules in Liquid Crystalline Phases by a Rotational Isomeric State Scheme with Maximum Entropy Method II. 2H NMR Quadrupolar Splittings from n-Decane and 1,6-Dimethoxyhexane Dissolved in 4′-Methoxybenzylidene-4-n-butylaniline

By a rotational isomeric state scheme with the maximum entropy method [Y. Sasanuma, Polym. J., 10, 883 (2000)], conformational analysis of n-decane and 1,6-dimethoxyhexane dissolved in a nematic liquid crystal 4′-methoxybenzylidene-4-n-butylaniline (MBBA) was carried out based on 2H NMR quadrupolar splittings from perdeuterated compounds at different temperatures and concentrations. All experimental observations were exactly reproduced by simulation. In MBBA, solute chains are more rigid and extended than in the free state. 1, 6-Dimethoxyhexane was found to keep its intrinsic conformational characteristics even in nematic solvent; the gauche fraction of the OC-CC bond was comparatively large. Orientational order parameters ‹SZZ› of the two solutes, plotted against reduced temperature, formed a master curve and were linearly correlated to ‹SZZ› of MBBA within the observed range.

Conformational statistics of macromolecules using generalized convolution

A new technique for generating statistical properties of chain-molecule conformations is presented. Conditional probability density functions (PDFs) describing the frequency of occurrence of the relative position and orientation of frames of reference affixed to selected backbone atoms serve as the inputs. Ensemble statistical properties of whole chains are generated by performing multiple generalized convolutions of these conditional PDFs. The formulation is shown to include classical theories such as the hindered and freely rotating chains, the Gaussian random walk, and the rotational isomeric state model. The convolution model is modified to include the long-range effects of excluded volume. An analytical example is used to illustrate the procedure. A general algorithm to calculate the ensemble properties of an arbitrary chain macromolecule is presented. In this algorithm, each of the N degrees of freedom (e.g. torsion angles) is assumed to have K discrete states. Using the convolution procedure, a chain is divided into P statistical units. The computational requirement is reduced from an O(KN) calculation (corresponding to direct enumeration) to one which is O(P(C+KN/P)) where C is the computational complexity of the convolution procedure. In the case of a homopolymer, computations are reduced further to O(Clog(P)+KN/P).

Conformations and Chain Dimensions of Poly(ethylene oxide) in Aqueous Solution: A Molecular Dynamics Simulation Study

We have performed a molecular dynamics (MD) simulation study of the conformations and chain dimensions of poly(ethylene oxide) (PEO) in aqueous solution. Local conformations were found to depend on temperature and composition in agreement with spectroscopy; in particular, an increase in the C-C dihedral gauche (g) population with decreasing temperature and polymer concentration was observed. In concentrated solution chains were compact relative to the melt due to a decrease in the C-C g dihedral angle and an increase in C-C g population. With dilution chains became more extended. A rotational isomeric state (RIS) model was utilized to examine the influence of local conformations on the dimensions of ideal chains. The RIS chains did not extend with dilution, indicating that this effect is not attributable to changes in local conformations. Additionally, the dimensions of solution chains were found to depend only weakly on temperature despite changes in local conformations that significantly influence RIS chain dimensions. These differences between solution and ideal chains can be attributed to excluded volume and other chain extensional effects in solution. Finally, in contrast to previous simulations and interpretation of some experiments, no tendency for extended helical conformations of the PEO chains was observed despite the large O-C-C-O tgt conformer population. Its wide use, prototypical behavior and simple chemical structure make PEO an excellent candidate for experimental and simulation studies aimed at gaining a better understanding of polymer-water interactions. Our previous simulations revealed that the conformations of glyme and diglyme depend strongly upon temperature and solution composition. In order to determine if the same behavior holds for longer PEO chains and to investigate the influence of local conformations on PEO chain dimensions we have performed MD simulations of H—[ CH2–O–CH2— ] 12 H (PEO-530) using quantum chemistry based atomistic potentials

A Monte Carlo Simulation on the Effects of Chain End Modification on Freely Standing Thin Films of Amorphous Polyethylene Melts

The effects of chain end modification on freely standing amorphous polyethylene thin films with a thickness 2Rg to 4Rg (radius of gyration) are studied by a Monte Carlo (MC) simulation on a high coordination lattice. The rotational isomeric state (RIS) model is incorporated into the simulation as short-range interactions, and a Lennard-Jones (LJ) potential is used to calculate the long-range interactions. The modification of the chain ends is introduced by changing the well-depth (e) of the LJ potential as compared to the middle beads. Chain ends with eend ≤ emiddle show segregation near the free surface, but chain ends with eend ≫ emiddle prefer to remain in the bulklike region. Both entropy and enthalpy are major factors in the determination of the distribution of the chain ends. The effects of the free surface can extend farther than Rg into the interior of the thin film. However, for the case of relatively attractive chain end (eend slightly larger than emiddle), a fairly large length of isotropic reg...

Conformational Analysis of Amphiphilic Molecules Incorporated in Hexagonal, Lamellar, and Reversed Hexagonal Aggregates of a Ternary System of Sodium Octanoate, 1-Decanol, and Water by the Rotational Isomeric State Scheme Combined with the Maximum Entropy Method

Conformational and orientational characteristics of amphiphiles incorporated in the hexagonal, lamellar, and reversed hexagonal aggregates formed by a ternary lyotropic system of sodium octanoate, 1-decanol, and water have been investigated. Deuterium NMR quadrupolar splittings observed from the randomly and selectively deuterated compounds were simulated by a combined use of the rotational isomeric state scheme and the maximum entropy method. For the individual mesophases, the bond conformations and orientational order parameters of octanoate and 1-decanol were evaluated and related to the aggregate structures. In the lamellar phase, in particular, the 1-decanol chain was found to exhibit peculiar conformations; the C−C bond nearest the OH group is fixed in the gauche state, the adjacent C−C bond also shows a gauche preference, and the second C−C bond from the methyl terminal has a high gauche probability. It follows that the chain length of 1-decanol is almost equal to that of octanoate in the all-trans conformation. Ab initio molecular orbital calculations at the MP2/6-31+G*//HF/6-31G* level for 1-butanol have revealed the inherent conformational preference of the head portion of the alcohol chains; the first C−C bond from the headgroup prefers the gauche state to the trans state by 0.27 kcal mol-1, and the g± g± states in the first and second C−C bonds from the OH group have a comparatively small free energy of 0.42 kcal mol-1 relative to the tt state.

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

A high coordination lattice model for simulating coarse-grained rotational isomeric state (RIS) chains has been under development recently. Initially, the model was developed for chains with symmetric torsional potential energy functions, E(φ)=−E(φ). A single-bead move Monte Carlo algorithm was used and found to be effective in simulating polyethylene chains. A modification was subsequently developed to allow for the simulation of chains with an asymmetric torsional potential, E(φ)≠−E(φ). The single-bead move Monte Carlo (MC) algorithm employed previously was found to be ineffective following this modification. Similar kinetic effects have been seen previously with single-bead MC moves on the cubic lattice, which lead to the Hilhorst–Deutch modification (two-bead crankshaft MC move) of the Verdier–Stockmayer (single-bead move MC) algorithm. A reptation MC move applied to this model appears problematic. A multiple-bead MC move is developed using the pivot algorithm formalism in order to avoid the lattice model specific kinetic effect seen with only single-bead MC moves. This allows for the effective simulation of vinyl polymers with asymmetric torsional potentials such as polypropylene and polyvinyl chloride. Polypropylene (PP) and poly(vinyl chloride) (PVC) chains of varying stereochemical structure are simulated. The chains are found to relax with reasonable efficiency. Polypropylene and polyvinyl chloride chains are reverse mapped back to the fully atomistic description. The solubility parameters of the reverse-mapped atomistic structures are found to agree reasonably well with experimental values.

Translational diffusion in Monte Carlo simulations of polymer melts: center of mass displacement vs. integrated velocity autocorrelation function

Translational diffusion has been simulated in monodisperse melts of four linear alkanes, C2xH4x+2, x=6,30,50,158, and two cyclic alkanes, C2xH4x, x=30,50, at 473K. The alkanes are expressed in a coarse-grained representation using x beads on a high coordination lattice, one bead for every two carbon atoms. Short-range intramolecular interactions are controlled by an adaptation of the rotational isomeric state model for unperturbed polyethylene, and the long-range interactions are controlled by a step-wise three-shell potential energy function derived from a continuous Lennard-Jones potential energy function. Acceptance of trial moves, each of which changes the coordinates of a single bead only, is governed by the Metropolis rule. Translational diffusion coefficients, D, are estimated from the mean square displacement of the center of mass and the integral of the velocity autocorrelation function. Both approaches yield the same value for D, which demonstrates that the velocity has been defined in a reasonable manner in the Monte Carlo simulation. A method is proposed for the estimation of D when the trajectory is not quite long enough to have achieved the behavior characteristic of the limit as time approaches infinity.

Evaluations of forcefields for aromatic polysiloxanes, and some applications to poly(diphenylsiloxane)

Two forcefields were evaluated for possible use in polysiloxanes containing aromatic phenyl or phenylene groups, either as side chains or as part of the chain backbone. The criterion was reproducing results on the crystal structure of the cyclic diphenylsiloxane trimer, and both forcefields were satisfactory. The better of the two was used to obtain conformational energies for estimating some of the statistical properties of the corresponding polymer poly(diphenylsiloxane) (PDPS) [Si(C6H5)2–O–]. The calculations were based almost entirely on the rotational isomeric state (RIS) theory, but the possibility of using a Metropolis Monte Carlo method was also considered. Since the stiffness of the chains was of primary interest, the quantities calculated were the unperturbed dimensions and its temperature coefficient and the radii of gyration. Degrees of polymerization ranged from 40 to 400, and temperatures from 300 to 1000K. The “characteristic ratio” (of the mean-square unperturbed dimensions to those of the corresponding freely-jointed chain) was found to be approximately 65 in the limit of very long chains. This is an order of magnitude larger than that of the much studied and very flexible poly(dimethylsiloxane), and the associated chain stiffness this indicates for PDPS seems to be consistent with its high transition temperatures and other properties.

New approach for the generation of initial configurations suitable for molecular dynamics studies of glassy polymers

Initial configurations suitable for molecular dynamics runs are usually assembled according to random values for the torsional angles of the molecules, and thus representing unrealistic conformations of the polymeric chains. In general, this would be acceptable if the system is allowed to run for periods of time long enough for the molecule to fully relax. However, in the current state of molecular dynamics runs, the 3D-periodic systems are usually allowed to run for 100ps, which is too short for the polymeric system to relax. Alternatively, traditional rotational isomeric state approximation (RIS) could be used to generate the initial configurations of the polymeric chains. Unfortunately, RIS does not take into account the possible segment–segment overlap between atoms comprising the polymeric chains. In this work, we investigate the possibility of using the rotational isomeric state approximation to properly construct the initial configuration of 3D-periodic systems, without allowing any segment–segment overlap. In order to ensure that these configurations represent realistically the polymeric system, attempts were made to test the configurational properties of these systems against those determined experimentally. Further, these configurations were used to perform subsequent molecular dynamics runs in order to elucidate the effect of the molecular weight of poly(vinyl chloride) and temperature on some of the important thermodynamic properties such as self-diffusion coefficient, thermal pressure coefficient, heat capacity and dielectric constant.

Rotational isomeric state study of molecular dimensions and elasticity of perfluoropolyethers: Differences between Demnum-, Fomblin-, and Krytox-type main chains

Molecular dimensions and elasticity of Demnum-, Fomblin-Z-, and Krytox-type perfluoropolyether (PFPE) molecules were studied by rotational isomeric state (RIS) and RIS Monte Carlo (MC) methods. The mean square of end–end distance, 〈R2〉, that of the radius of gyration, 〈Rg2〉, and the characteristic ratio Cn of the molecules were calculated by the RIS method. In the RIS calculations, the number of main chain atoms, N, was increased to about 100. The RIS results show that the Demnum- and Fomblin-Z-type molecules have similar 〈R2〉, 〈Rg2〉 and Cn values. However, the Krytox-type molecule has correspondingly smaller values at every N. The molecular elasticity of the molecules was evaluated by the RIS-MC method by estimating the force–elongation relation of the molecules. These RIS-MC calculations clarified that the Demnum- and Fomblin-Z-type molecules have similar molecular elasticity, but the Krytox-type molecule is more elastic. These distinct features of the Krytox-type molecule are attributed to the distorted rotational potential of its CF(CF3)–O bonds. These calculations were compared with experimental results obtained with a surface force apparatus (SFA), and it is concluded that the Krytox-type molecule is the most desirable for boundary lubrication.

The influence of flexible side chains on the dimensions of flexible polymers

Molecular dynamics simulations of single chains in vacuo have been used to investigate the role of flexible branches on the dimensions and in particular the backbone rigidity of flexible polymers. A series of isotactic poly-α-olefin chains was chosen as a model system to study because of their simplicity of structure. Θ-conditions were simulated for each branched chain by careful adjustment of the Van der Waals parameters, and properties such as end-to-end length, radius of gyration and persistence length were measured. As expected the backbone rigidity of the polymers was found to be determined by a balance between the coiling of the backbone induced by a gauche state at the branch point and the size of the side chain. Trends in persistence length with branch content compared favourably to the previous Rotational Isomeric State and experimental measurements of the characteristic ratio. The stiffening of the backbone under good solvent conditions was also investigated and it was found that the persistence length could be systematically increased by increasing the size of the side group, with the shape of the side group also making a small difference to the sampled backbone conformations.

The stress optical behavior of PET fibers and films

The use of stress-optical measurements to characterize oriented PET fibers is reviewed. The implications of a molecular network for the development of orientation in spun fibers, cold drawn and hot drawn fibers are also considered. Early research made use of the Kuhn and Grun theory of photoelasticity, and their model has been shown by many workers to be a useful starting point for understanding the development of molecular orientation in PET provided that it is suitably modified for high chain extension at high draw ratios. The principal thrust of recent research at Leeds has been to explore the applications of more precise molecular modelling using the Monte Carlo rotational isomeric state model developed by Stepto and Taylor, and applying it to the development of optical birefringence with strain, as well as the shrinkage stress. It has been shown that the Kuhn and Grun theory, where the actual network is replaced by a model network of freely jointed random links, cannot provide a consistent description of the shrinkage stress and the optical birefringence.

Thermoelastic and stress-optical behavior of aromatic-aliphatic polyester networks

Thermoelastic networks were prepared by crosslinking hydroxyl terminated poly(pentamethylene glycol isophthalate) with tri(p-isocyanate-phenyl)-thiophosphate. The thermoelastic and stress-optical behavior of the networks were studied at several temperatures in the range of 10–70 °C. The values of the temperature coefficient of the unperturbed dimensions, d ln〈r2〉/dT, and the optical configuration parameter Δa were −4.5×10−3 K−1 and 22.7×10−24 cm3, respectively. Theoretical calculations carried out with the rotational isomeric state model gives values of d ln〈r2〉/dT in very good agreement with the experimental results. However, the theoretical values of Δa are nearly one order of magnitude lower than the experimental ones. No reasonable modification of conformational energies or contributions to the anisotropic part of the polarizability tensor would achieve agreement between theory and experiments. The discrepancy between theoretical and experimental results may be qualitatively explained by intermolecular interactions.

Equilibrium Spatial Distribution of Aqueous Pullulan: Small-Angle X-ray Scattering and Realistic Computer Modeling

A rotational isomeric state model has been developed for the polysaccharide pullulan dissolved in water. The model is consistent with the mean-square radius of gyration and Debye scattering function as measured for pullulan oligomers containing 3, 6, 9, and 12 glucose residues by small-angle X-ray scattering. It is also consistent with the unperturbed chain dimensions of high molecular weight aqueous pullulan and the temperature coefficient of the unperturbed dimensions. The model is based on identification of an initial set of rotational isomeric states using the AMBER* molecular mechanics force field in conjunction with a continuum model for aqueous solvation. The relative weights of the rotational isomeric states were subsequently adjusted to achieve an optimized fit to the data. Three important rotational isomeric states (encompassing together more than 77% of the probability distribution) are identified for the (1→6)-linkage while a single state is recognized for the (1→4)-linkage. One of the states ...

Conformational Properties of Poly(vinylidene fluoride). A Quantum Chemistry Study of Model Compounds

The molecular geometries and conformational energies of model molecules of poly(vinylidene fluoride) (PVDF) have been determined from high-level quantum chemistry calculations and have been used in parametrization of a six-state rotational isomeric state (RIS) model for PVDF. The model molecules investigated were 1,1,1,3,3-pentafluorobutane, 1,1,1,3,3,5,5,5-octofluoropentane, 2,2,4,4-tetrafluoropentane, and 2,2,4,4,6,6-hexafluoroheptane (HFH). Analysis of the conformations of these molecules revealed split trans minima (t+ = 195°, t- = 165°), as was seen in previous studies of perfluoroalkanes. In contrast, the gauche minima, which split in perfluoroalkanes, did not do so in the PVDF model compounds. The lowest energy conformer of HFH, g+g+g+g+, was found to be at least 0.4 kcal/mol lower in energy per backbone dihedral than any of the conformers of HFH resembling crystalline polymorphs of PVDF, indicating that intermolecular interactions are important in stabilizing conformations of PVDF in the crystalline phases. A six-state RIS model was able to accurately reproduce the conformer energies of the PVDF model compounds. The RIS analysis revealed that, as in n-alkanes and perfluoroalkanes, the trans conformation of the backbone dihedral is intrinsically lower in energy than the gauche conformation in the PVDF model compounds. However, very large unfavorable second-order interactions between fluorine atoms occur in −CH2− centered t+t+ sequences and, to a lesser extent, t+g+ and t+g- sequences. The quantum chemistry based RIS model yielded a characteristic ratio for PVDF in good agreement with experiment, but with significantly different conformer populations than predicted by earlier RIS models, including a much higher gauche probability. The high gauche probability of 65% for unperturbed PVDF chains (at 463 K), greater than that for poly(ethylene) and much greater than that for poly(tetrafluoroethylene), is a consequence of the unfavorable second-order interactions occurring in −CH2− centered sequences containing trans conformations.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 16. Theoretical and experimental investigations of cyclics prepared from poly(decamethylene fumarate) and poly(decamethylene maleate) ring-chain equilibrium reactions

The molar cyclisation equilibrium constants K x for cyclics [OCOCHCHCOO(CH 2) 10] x (with x=1–7) in two closely related polyester systems, poly(decamethylene maleate) and poly(decamethylene fumarate), were measured experimentally using gel permeation chromatography. The corresponding theoretical K x values were calculated by two methods. The first applied a rotational isomeric state model to describe the statistical conformations of chains forming rings and it assumed that such chains obey Gaussian statistics. The second approach used MSI's program Insight II to perform the Monte Carlo Metropolis calculations. When the expected chain expansion effects in a good solvent media was considered, a good agreement between experiment and theory for all the cyclics with x≥2 was found.

Conformational and Packing Modeling of Optically Active Polyesters. 2. Helical Structure of an Isotactic Polylactone

Optically active poly(α-methyl-α-n-propyl-β-propiolactone) (PMPPL) crystallizes in a 21 helical conformation, but its conformational structure and packing symmetry have not been solved and refined yet. On the basis of the rotational isomeric state approximation and the conformational algorithm for polymer helices, optimum conformational models derived from single helices were used as a starting point in building crystal structures. Both intra- and intermolecular interactions were simultaneously optimized. Semiempirical molecular mechanics calculations of an isotactic single chain having fixed experimental helical parameters revealed that the preferred conformation for PMPPL entails the ttg-g- backbone chain conformation with a g-t side-chain orientation. Crystal models compatible with the observed orthorhombic lattice dimensions (a = 10.6, b = 11.1 A) were built and refined against electron diffraction data, X-ray powder diffraction spectra, and structure factor calculations. The favored structure contain...

Dynamic and static properties of polyoxymethylene chains

The dynamics and conformational-dependent properties of polyoxymethylene (POM) chains are studied using the modified bond-fluctuation model and the rotational-isomeric state model. In our bond-fluctuation model, a Kuhnian bond includes four carbon-oxygen bonds. Each Kuhnian bond may have different energy, and the Kuhnian bond energy is calculated using the tetrahedral lattice model as it gives a reasonable approximation to the carbon–oxygen backbone bond of the POM chain. Our statistical mechanics properties of chains are in good agreement with the theoretical results. The relaxation times τ 1 increase with chain length N by a power law of the form τ 1( N)≈ N 2 in the absence of excluded volume and τ 1( N)≈ N 2.16 in the presence of excluded volume, and the diffusion coefficients D behave as D≈1/ N in the absence and presence of excluded volume.

Detection of the onset of demixing in simulations of polypropylene melts in which the chains differ only in stereochemical composition

Simulations have been performed at 480 K for pure melts of atactic, isotactic and syndiotactic polypropylene chains with a degree of polymerization of 50 and composition C150H302, and also for the three 50:50 mixtures of two of these species. The simulations are performed on a high coordination lattice, with incorporation of short range intramolecular interactions from a rotational isomeric state model of polypropylene, and incorporation of long range interactions defined by a Lennard-Jones potential energy function for the interaction of pairs of molecules of propane. Both the rotational isomeric state model and Lennard-Jones parameters were taken directly from the literature (Suter et al. and Prausnitz, respectively). The efficiency of the simulation on the sparsely occupied high coordination lattice facilitates the equilibration of the one- and two-component melts within accessible computer time. Onset of a tendency for demixing of isotactic and syndiotactic polypropylene is apparent in the intermolecular pair correlation functions. No such demixing occurs with isotactic and atactic polypropylene. Both of these predictions from the simulation are consistent with experimental results in the literature (Maier et al. and Lohse, respectively). The simulation produces an ambigious prediction for the melt of atactic and syndiotactic polypropylene. This melt has been reported (Maier et al.) to exhibit phase separation, but less strongly than the isotactic-syndiotactic system, for which the simulation makes an unambiguous (and correct) prediction. The physical origin of the tendency for demixing in the simulations is identified as the differences in the preferred local conformations of polypropylene chains with various stereochemical sequences. This driving force is an example of “conformational asymmetry” induced solely by differences in stereochemical sequence.

A second generation of mapping/reverse mapping of coarse-grained and fully atomistic models of polymer melts

Recently the rotational isomeric state model for unperturbed polymers has been combined with potential energy functions designed for the description of the interactions of pairs of molecules in the gaseous state for the purpose of reversibly bridging between simulations of coarse-grained (on-lattice) and fully atomistic (in continuous space) models of polymers. The first generation of this method is reviewed here. This method has been applied to the conformation, energetics, structure, and dynamics of melts, free-standing thin films, and fibers, as well as to the cohesion of two thin films. Then the second generation is presented for the first time. When applied to a polyethylene melt, the first generation method maps every second carbon atom of the chains onto a high coordination lattice, which is derived from a diamond lattice. Physical densities are obtained with occupancies of about 1/6 of the sites on the high coordination lattice. The second generation utilizes every fourth carbon atom in the chains, and requires occupancy of only 1/12 of the sites. The short-range intramolecular interactions are controlled by an adaptation of the classic rotational isomeric state model for polyethylene, and the intermolecular interactions come from a discretization of a continuous Lennard-Jones potential, designed for the description of the interaction of pairs of hydrocarbons with 2 or 4 carbon atoms, for the first and second generation, respectively. Reversibility is demonstrated between the first-and second-generation models. In view of the prior demonstration of recovery of the fully atomistic model in continuous space from the first generation model, reversible interconversion of the first and second generation models demonstrates that the latter model can be reverse-mapped to the fully atomistic model in continuous space.