Rotational Isomeric State Approximation Research Articles

Effect of Charge Regulation and Conformational Equilibria in the Stretching Properties of Weak Polyelectrolytes

Weak polyelectrolytes can modulate their charge in response to external perturbations, such as changes in the pH, ionic strength (I), or electrostatic interactions with other charged species, a phenomenon known as charge regulation (CR). On the other hand, it is well established that CR is highly coupled with the conformational degrees of freedom. In this paper, the influence of CR in the stretching properties of weak polyelectrolytes is analyzed, and the possibility of CR induced by mechanical stretching is explored. With this aim, we make use of a minimal model, which captures the fundamental aspects present in the stretching of a flexible weak linear polyelectrolyte: internal angle rotation, bond stretching, bond bending, and proton binding, which is the paradigmatic mechanism of CR. The angle rotation is described by using the rotational isomeric state approximation, while for protonation, the site binding model is assumed. Mechanical stretching is studied by performing semi-grand canonical Monte Carl...

The butane condensed matter conformational problem

From the dipolar couplings of orientationally ordered n-butane obtained by NMR spectroscopy we have calculated conformer probabilities using the modified Chord (Cd) and Size-and-Shape (CI) models to estimate the conformational dependence of the order matrix. All calculation methods make use of G aussian 03 structures for the gauche and trans conformers. Calculations were performed for both the Rotational Isomeric State (RIS) approximation, as well as a continuous gas-phase potential for the dihedral angle rotation. Conformational probability distribution functions for butane as a solute in the ordered liquid–crystal solvent are obtained.

Thermodynamics of polymeric fluids– effect of volume on the configurational entropy of chain molecules

Various conformation-dependent properties of chain molecules have been successfully treated within the rotational isomeric state approximation. The conformation entropy is one of such properties which can be readily defined by the partition function, the sum of all possible configurations of the chain. Flexible polymers often exhibit crystallization and in some cases liquid-crystallization as well. In these first-order transitions, changes in the spatial arrangement of polymer chains are considered to be a major factor involved. In order to explicitly determine the conformational contribution to the melting entropy, the latent entropy observed under the isobaric condition must be corrected for the volume change. The entropy separation involves a hypothetical assumption that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of molecules. Finally thermodynamic significance of the conformation entropy in these transitions is emphasized on the basis of the critical studies of the entropy-volume relation of chain molecules in the liquid state.

Structure and molecular ordering extracted from residual dipolar couplings: A molecular dynamics simulation study

A molecular dynamics (MD) simulation, based on a realistic atom–atom interaction potential, was performed on 4-n-pentyl-4′-cyanobiphenyl (5CB) in the nematic phase. The analysis of the trajectory was focused on the determination of molecular structure and orientational ordering using nuclear dipole–dipole couplings. Three sets of couplings were calculated: C13–13C, C13–1H, and H1–1H. These dipolar couplings were used for investigation of the biphenyl and the ring–chain fragments in 5CB. The models employed in the analysis were based on the rotational isomeric state (RIS) approximation and the maximum entropy (ME) approach. The main questions addressed in this article are: (i) How sensitive are the various sets of dipolar couplings to the long-range orientational order and molecular conformation? (ii) Which model predicts a molecular structure that is in best agreement with the true conformation? Computer simulation is an attractive method to address these questions since the answer is provided: we know the true orientational order and the molecular structure. We found that all sets of dipolar couplings analyzed using the two models predict correct orientational order for the biphenyl fragment. The structure of this moiety was unambiguously determined in all analyses except for the ME method applied on the C13–13C couplings. The RIS approximation failed to discriminate between a large range of possible structures of the ring–chain fragment.

The Energy Profile for Rotation about the C-C Bond in Substituted Ethanes

Encouraging students to appreciate the approximations involved in using the rotational isomeric state approximation and the conditions under which they can be acceptable.

Molecular Modeling of Polyisobutylene. Application of the Modified Rotational Isomeric States Model for Polymers Comprising Four Rotational Isomeric States

Due to the presence of two alternating bond angles in the backbone of the polymeric chains, polyisobutylene (PIB) possesses four different rotational isomeric states. Accordingly, conformations of PIB could be represented by a four-state rotational isomeric scheme with only one adjustable statistical weight parameter. Rotational isomeric states (RIS) were determined at +25°, −25°, +120°, −120°. Conformations were divided into a “+class” and “−class,” with bond conformations tended to be followed by those from the same class and with changes from one class to the other rare. Since the configurational and thermodynamic properties of PIB depend to a great deal on the conformational characteristics of the polymer, a modified rotational isomeric state approximation was used to generate the initial configurations of the polymeric chains without allowing for any segment-segment overlap. Attempts were made to test the configurational properties of these systems against those determined experimentally to ensure that these configurations do represent realistically the polymeric system. Furthermore, these configurations were used to perform subsequent molecular dynamics runs to elucidate the effect of the molecular weight of the polymer and the temperature on some of its important thermodynamic properties, such as self-diffusion coefficient, thermal pressure coefficient, heat capacity, and dielectric constant.

Conformational Analysis of Chain Molecules in Liquid Crystalline Phases by a Rotational Isomeric State Scheme with Maximum Entropy Method I. 1H-1H Dipolar Couplings from n-Alkanes Dissolved in a Nematic Solvent

For conformational analysis of chain molecules incorporated in nematic fields, a rotational isomeric state (RIS) scheme was revised for use with the maximum entropy method. Analysis thus based proceeds as follows. 1) All possible conformations are enumerated within the RIS approximation. 2) The principal Axes of inertia, determined for each conformer, are considered molecular axes, and orientational order parameters are evaluated from dimensions of a rectangular parallelepiped closely fitted to the conformer. 3) Conformational statistical weight factors of first- and second-order interactions are adjusted and order parameters are scaled so as to reproduce experimental observation and maximize the information entropy regarding conformer populations. By this method, 1H-1H dipolar couplings observed from n-hexane, n-heptane, n-octane, n-nonane, and n-decane dissolved in a nematic liquid crystal Kodak EK11650 p-pentylphenyl-2-chloro(4-benzylbenzoyloxy)-benzoate [M.E. Rosen, S.P. Rucker, C. Schmidt, and A. Pines, J. Phys. Chem. 97, 3858 (1993)] were analyzed. For all n-alkanes, good agreement between theory and experiment was attained. Anisotropic conformers were slightly more populated than in the free state. The present results were quantitatively comparable to those of analysis using the mean-field theory.

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.

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...

Nucleation in n-alkanes: A density-functional approach

A density-functional theory for a polyatomic system is applied to gas–liquid nucleation in n-butane and n-heptane, employing an interaction site model and the rotational isomeric state approximation. Effects of chain length and flexibility on equilibrium properties and nucleation are discussed. It is shown that the n-alkane systems cannot be well approximated by a system with the spherically symmetric Lennard-Jones potential, giving a nucleation rate scaled by the classical rate smaller by six orders of magnitude.

The polyoxyethylene chain—on the origin of its conformational flexibility

Polyoxyethylene (POE) is known to be highly flexible, a variety of spatial configurations being permitted. Like many other conventional polymers, the conformation of the POE chain can be treated within the framework of the rotational isomeric state (RIS) approximation using a limited number of RIS parameters. An unambiguous assignment of numerical values to statistical weights such as σ and ω has not been achieved for the chain occurring under various conditions: σ for the rotation around the C—C bond and ω for the so-called second-order interaction taking place between the methylene group and the oxygen atom separated by four bonds. In this work, we have attempted to demonstrate the role of these two parameters in determining the conformation-dependent properties of the POE chain. Various RIS parameter sets reported in literature have been compared with a model calculation, in which σ and ω are varied over a wide range, the other parameters being kept invariant. A comprehensive analysis provides a rational explanation for the long lasting question why so many RIS parameter sets effectively reproduce the conformational characteristics of the identical polymer molecule. Finally, it is emphasised that a critical assessment of ω and/or σ is required to establish an unambiguous RIS description of the POE chain.

Chain Dynamics and the Simulation of Electron Spin Resonance Spectra from Oriented Phospholipid Membranes

A model previously developed for describing the dynamics of flexible alkyl chains that is based on Flory's rotational isomeric state approximation is adapted and applied to the analysis of electron spin resonance (ESR) spectra obtained from a phospholipid spin label in a macroscopically aligned phospholipid membrane. In this model, rotation around each C−C bond of the labeled alkyl chain is characterized by three inequivalent minima, with one end of the chain fixed to mimic the phospholipid headgroup, and with the dynamic effects of the nitroxide label explicitly included. This model is integrated with that for the overall rotation of the phospholipid in the mean orientational potential of the aligned membrane, and it is incorporated into the stochastic Liouville equation which describes the ESR line shape in the presence of these dynamic processes. The analysis is simplified by introducing the fact that the relatively rapid internal modes of motion can be treated by motional narrowing theory and a time scale separation can be made with respect to the much slower overall motions of the phospholipid. A series of ESR spectra from the spin label 16-PC in the lipid dimyristoylphosphatidylcholine were obtained over a range of temperatures (35−65 °C) in the Lα phase for various orientations of the normal to the bilayer plane relative to the magnetic field. Very good agreement with experiment is obtained from this model by using least squares fitting procedures for the overall motional dynamics. One finds an order parameter of 〈 〉 that is constant throughout the phase and the perpendicular component for rotational diffusion, R⊥, that ranges from about 1−3 × 107s-1 (which corresponds to the ESR slow motional regime). Fits to the ESR spectra were also obtained from a simple but standard model wherein a single overall rotational diffusion tensor is used to describe the combined effects of internal and overall dynamics. These fits were almost as good, but they lead to a much larger R⊥ ≈ 3−6 × 108 s-1 and a smaller 〈 〉 = 0.1, since these parameters now include the composite effects of both types of processes. New ESR experiments are proposed to provide more critical tests of these models.

Conformational and Orientational Characteristics of Chain Molecules Placed in Nematic Fields. Part II

Deuterium NMR quadrupolar splittings and 2 H - 2 H dipolar couplings observed from perdeuterated 1,6-dimethoxyhexane (CD 3 O(CD 2 ) 6 OCD 3 ) dissolved in a liquid crystal 4'-methoxybenzylidene-4-η-butylaniline (MBBA) were analyzed using the single-ordering-matrix (SOM) and the Photinos-Samulski-Toriumi (P-S-T) models. Within the framework of the rotational isomeric state approximation, intramolecular interactions up to the third-order (between atoms and groups separated by five bonds) were considered. The geometrical parameters and intramolecular interaction energies determined from ab initio molecular orbital calculations were employed. The two simulation models yielded fair agreement between theory and experiment, but were found to give quite different images of the solute chain: (the SOM model), the solute becomes rigid and extended to conform itself to the nematic field; (the P-S-T model), the solute has almost the same degree of flexibility as in the free state, but populations of the anisotropic conformers are selectively enhanced. To reveal the true conformational characteristics of chain molecules in nematic fields, experimental techniques to enable direct and quantitative measurements of the bond conformations are necessary.

Generalized Flory theory for hard alkane fluids

Generalized Flory-dimer (GF-D) theory is extended to hard n-alkane fluids modelled as fused hard spheres constrained according to the rotational isomeric state approximation. Theoretical predictions for the second to the fifth virial coefficients for each conformer from n-butane to n-octane are compared with numerical results. Predictions for the second viral coefficient are in excellent agreement with recent simulation results; however, GF-D theory systematically overpredicts the third virial coefficient and underpredicts the fourth and the fifth virial coefficients. GF-D predictions for the compressibility factor for n-alkanes from n-butane to n-octane are compared with molecular dynamic simulation results for a closely related model. Despite the over- and underprediction of the individual virial coefficients, excellent agreement is observed between theory and simulation for the compressibility factors of n-butane and n-pentane using no adjustable parameters. However, in the cases of n-hexane, n-heptane and n-octane, GF-D theory slightly underpredicts the pressure at high volume fractions. Theoretical considerations suggest that probably the predictions of GF-D theory will deteriorate with increasing chain length.

Generalized Flory theory for hard alkane fluids

Generalized Flory-dimer (GF-D) theory is extended to hard n-alkane fluids modelled as fused hard spheres constrained according to the rotational isomeric state approximation. Theoretical predictions for the second to the fifth virial coefficients for each conformer from n-butane to n-octane are compared with numerical results. Predictions for the second viral coefficient are in excellent agreement with recent simulation results; however, GF-D theory systematically overpredicts the third virial coefficient and underpredicts the fourth and the fifth virial coefficients. GF-D predictions for the compressibility factor for n-alkanes from n-butane to n-octane are compared with molecular dynamic simulation results for a closely related model. Despite the over- and underprediction of the individual virial coefficients, excellent agreement is observed between theory and simulation for the compressibility factors of n-butane and n-pentane using no adjustable parameters. However, in the cases of n-hexane, n-heptane and n-octane, GF-D theory slightly underpredicts the pressure at high volume fractions. Theoretical considerations suggest that probably the predictions of GF-D theory will deteriorate with increasing chain length.

Theory for the Phase Behavior of Polyolefin Blends: Application to the Polyethylene/Isotactic Polypropylene Blend

A microscopically realistic theory for modeling the structure, thermodynamics, and phase behavior of polyolefin blends is developed on the basis of the polymer reference interaction site model (PRISM theory). The thermodynamics of mixing is treated using perturbation theory with the corresponding athermal mixture as the reference system. As an illustration of the approach we modeled the polyethylene/isotactic polypropylene blend (PE/i-PP). The polypropylene monomers were constructed from three independent interaction sites representing the CH 2 , CH, and CH 3 united atom groups constituting the monomer. Likewise polyethylene monomers consisted of two identical interaction sites, each representing a CH 2 moiety. The intramolecular structure functions, required as input to PRISM theory, were determined from single-chain Monte Carlo simulations using the rotational isomeric state approximation. The Suter-Flory rotational isomeric state parameters were used for isotactic polypropylene. PRISM theory was used to compute the ten independent intermolecular pair correlation functions needed to characterize the intermolecular packing of the athermal blend. The enthalpic contribution to the free energy was then computed from first-order perturbation theory. The entropy of mixing, heat of mixing, and spinodal curve were computed as a function of composition for the blend consisting of PE and i-PP chains of 200 monomer units. The blend was found to be highly incompatible with UCST behavior. Local or short range correlations were found to significantly increase the heat of mixing, resulting in critical temperatures approximately 10-15 times larger than predicted on the basis of Flory-Huggins theory under the assumption of random mixing.

Conformation of 1,3-dimethoxypropane in the gas phase and in solution: rotational isomeric state simulation of NMR vicinal coupling constants

Conformation of 1,3-dimethoxypropane has been studied in the gas phase (approximately 120–180°C). Vicinal coupling constants 3 J HH and 3 J CH determined by 1H and 13C NMR were analysed within the rotational isomeric state approximation. The trans and gauche couplings required in this analysis were set equal to J G = 2.8 Hz and J T = 13.7 Hz for 1HCC 1H, and J G = 2.0 Hz and J T + J′ G = 16.0 Hz for 13COC 1H. The conformational energy parameters of the chain were conventionally defined as Eσ and Eϱ for the gauche state around the CH 2CH 2 and OCH 2 bond, respectively, and Eω for the repulsive second-order interaction (g ±g ∓) for the OCH 2CH 2CH 2O fragment. The experimental values of the coupling constants were found to be reproduced by a variety of combinations of Eσ and Eω, Eϱ being kept at 1.03 kcal mol −1. Adoption of Eω = 1.97 kcal mol −1, as calculated by a molecular mechanics method, led to Eσ = −0.84 kcal mol −1. Alternatively, by setting Eσ = −0.58 kcal mol −1 as calculated, Eω = 0.40 kcal mol −1. Assuming Eω > 1 kcal mol −1 for the gas phase, a value of Eσ from −0.7 to approximately −0.9 kcal mol −1 was proposed. The conformation, and thus conformational energies, varied quite sensitively with the polarity of the medium. The results were compared with those observed in solution.

Even-odd effects in liquid crystal dimers with flexible spacers: a test of the rotational isomeric state approximation?

In this work we analyse the consequences of relaxing the rotational isomeric state (RIS) approximation in predicting the transitional properties of nematogenic systems formed by two mesogenic moieties linked by a flexible spacer, as in the homologous series of α,ω-bis(4′-cyanobiphenyl-4-yl)alkanes and α,ω-bis(4′-cyanobiphenyl-4-yloxy)alkanes, generically referred to as CB dimers. Comparison is made therefore between predictions of the nematic-isotropic transition temperatures, entropy changes, and order parameters obtained from the RIS model, and those by taking into account the full distribution of torsional angles. The continuous model predicts a damping of the even-odd effects for long chain systems, with entropy changes and order parameters at the nematic-isotropic transition tending to those of the corresponding monomers.

NMR relaxation in long-chain quaternary ammonium ions: the role of torsional flexibility

Abstract The conformational dynamics of alkyl chains is usually analysed within the framework of the rotational isomeric state (RIS) approximation, where only the conformers corresponding to the configurational potential minima are considered, and torsional fluctuations about the minima are ignored. In order to test the validity of this procedure, 13 C NMR T 1 relaxation times have been measured in the series of symmetric tetra- n -alkylammonium ions (C N H 2 N +1 ) 4 N + , with N = 8, 10, 12, 16 and 18, and compared with theoretical results predicted by the RIS model. Spin relaxation rates of the terminal carbon atoms show a tendency to level off for increasing chain length, in contrast with the monotonic increase predicted by the RIS model. The experimental behaviour reveals that deviations from RIS results appear for chains with more than ten carbon atoms.

Conformational dynamics and the rotational isomeric state approximation for alkyl chains

The assumption of a timescale separation between conformational kinetics and torsional modes, implicit in the rotational isomeric state approximation, is analysed on the basis of asymptotic solutions of a multidimensional diffusion equation.