Rotational Isomeric State Research Articles

Generalized Theoretical Study of the Effect of Molecular Bond Optical Tensor Components on the Mean-Squared Optical Anisotropy ⟨γ2⟩ of Model Bead-Spring Linear Homopolymer Chains

The conformationally averaged mean-squared optical anisotropy ⟨γ2⟩ of homopolymer chains under the theta solution condition is simulated using a rotational isomeric state (RIS) scheme with a generalized optical tensor description based on model bead-spring macromolecules. The effect of torsion angle values, number of minimum energy torsion states, probability (statistical weights) of the conformational states, and values of the components of the polarizability tensor for the bead are studied in this manner for the first time. Chains having either one or two interdependent rotatable bonds in the repeat unit are simulated. We find that under certain conditions of the relative orientations and values of the optical polarizability components with regards to the plane of the backbone bond angle, a higher probability for the gauche (less extended) conformation actually leads to a higher value of the optical anisotropy. In other cases, in conjunction with expectations from known experimental results, the optical anisotropy decreases with an increase in the probability of the gauche conformational state consistently over the range of values. We observe that, in most cases, higher values of the difference in the polarizability components lead to higher values of the chain optical anisotropy.

Predicting most probable conformations of a given peptide sequence in the random coil state

In this work, we present a computational scheme for finding high probability conformations of peptides. The scheme calculates the probability of a given conformation of the given peptide sequence using the probability distribution of torsion states. Dependence of the states of a residue on the states of its first neighbors along the chain is considered. Prior probabilities of torsion states are obtained from a coil library. Posterior probabilities are calculated by the matrix multiplication Rotational Isomeric States Model of polymer theory. The conformation of a peptide with highest probability is determined by using a hidden Markov model Viterbi algorithm. First, the probability distribution of the torsion states of the residues is obtained. Using the highest probability torsion state, one can generate, step by step, states with lower probabilities. To validate the method, the highest probability state of residues in a given sequence is calculated and compared with probabilities obtained from the Coil Databank. Predictions based on the method are 32% better than predictions based on the most probable states of residues. The ensemble of "n" high probability conformations of a given protein is also determined using the Viterbi algorithm with multistep backtracking.

Molecular design, synthesis and characterization of aromatic polythioester and polydithioester

Molecular design of poly(ethylene dithioterephthalate) (PETS2) and poly(ethylene tetrathioterephthalate) (PETS4) has been carried out by molecular orbital calculations, NMR experiments, and single crystal X-ray structure analysis for their model compounds and refined rotational isomeric state calculations for the two polymers, and their conformational characteristics, crystal conformations, configurational properties, solubilities, crystallization behaviors, and thermal properties were predicted. For the purpose of the experimental verification, PETS2 and PETS4 were actually prepared and fully characterized. The new polymer, PETS4, was synthesized by an ionic polycondensation reaction using a complex of tetrathioterephthalic acid and piperidinium. The two polymers were characterized by elementary analysis, IR, solubility test, X-ray diffraction, thermal analysis, and solid-state NMR to yield experimental results satisfactorily consistent with the theoretical predictions. Through the actual examples, molecular design of polymers has been proved to be feasible.

Molecular Modelling of the Conformational Flexibility and Elastic Behaviour of Short Poly(ethylene terephthalate) Chains

The Monte-Carlo (MC) rotational-isomeric-state (RIS) method developed previously to model the stress–strain behaviour of poly(ethylene terephthalate) (PET) is now applied to short PET chains of between 42 and 84 skeletal bonds. The effects on the radial and probability density distribution functions of the long, flexible virtual bond used to represent the terephthaloyl unit are investigated. The distribution functions generated, based on finite samples of chains, are found to be discontinuous with subsidiary maxima in their tails. The discontinuities lead to uncertainties in the simulated network elasticity properties and, in order to reduce the uncertainty, it is necessary to truncate the distributions at the values of r where they first become discontinuous. The stress–strain properties calculated from the truncated distributions are shown to be consistent with those presented previously for longer PET chains, for which discontinuities in the sampled functions are not apparent.

Effect of Composition on Chain Dimensions of Styrene-Methylmethacrylate Random Copolymers under Theta Condition

Rotational-isomeric-state (RIS)-Metropolis Monte Carlo simulations are performed on poly(styrene-ran-methylmethacrylate) random copolymers to study the intrinsic unperturbed (θ-condition) dimensions. Mean-squared end-to-end distance (⟨r2⟩o ), mean-squared radius of gyration (⟨s2⟩o ), and characteristic ratio (Cn) have been calculated for these copolymers constituted by different overall chemical compositions (styrene fractions 0.29, 0.56, and 0.70). Calculations were carried out with chains of 500 repeating units. With an increase in the styrene content there is an increase in ⟨r 2⟩ o, `, and Cn, in agreement with experimental observations. An increase in the fraction of trans conformational states in the backbone torsion angles is found to be responsible for the exhibited chain expansion behavior. The dimensions calculated by the Monte Carlo simulations agree well with experimental values reported in the literature.

ChemInform Abstract: Computer Simulations of n-Alkane Melts

Stochastic dynamics simulations of n‐alkane melts (C13H28 and C28H58 ) have been performed in order to calculate their static properties. The system consists of linear chains of mass points, which are connected by fixed bond lengths. Each point of a chain is subjected to valence bond and torsional forces. Additionally, nonbonded interactions are taken into account by a truncated, Lennard‐Jones potential. The mean‐square end‐to‐end distance and the radius of gyration of the chains as well as the average fraction of trans conformations were calculated and compared with the results obtained by Monte Carlo simulations and by unperturbed rotational isomeric states model calculations. The comparison exhibits very good agreement between the results of the different approaches, and demonstrates the potential advantages of stochastic dynamics simulations for polymeric systems. An investigation of different torsional potentials exhibited the subtle effect of the curvature of the torsional potential on bulk structures.

Implications of multiscale modeling on sensing predictions in Nafion

Multiscale modeling is used to investigate mechanical stiffness of ionic polymers and thesubsequent implications for electromechanical sensing. Unlike the more common empiricaland gray box approaches this study presents the hypothesis of streaming current asthe fundamental, underlying mechanism responsible for sensing. The approachaccommodates the observation that both stiffness and sensing response can be affectedby cation type and hydration level. Rotational isomeric state (RIS) theory isused to predict the conformation of the hydrophobic backbone of a Nafion, 1200equivalent weight (EW) in lithium and sodium forms. The RIS method generatescrosslink-to-crosslink chain lengths to assess material multiscale stiffness. Both thestiffness and sensing predictions are compared to experiment for validation. It isobserved that the multiscale stiffness does not necessarily evolve in concert withthe global stiffness. However, the implications are consistent with, and offer anexplanation of, experimentally observed water uptake and sensing phenomena.

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.

Monte Carlo simulations of structures and dynamics of cyclic and linear poly(ethylene oxide) melts

A lattice Monte Carlo (MC) simulation of coarse-grained polymer model was developed to study the conformation and diffusion of cyclic and linear poly(ethylene oxide), PEO, blends. Local intrachain interactions were derived from the modified rotational isomeric state (RIS) model and the non-bonded interactions were from a discretized form of Lennard-Jones (LJ) potential energy function. The simulations were performed at 373 K for the chain length from 50 to 200 repeating units. The relative size of linear/cyclic is 〈 R g 2 〉 linear / 〈 R g 2 〉 ring ∼ 2 which was consistent with the theoretical prediction. The diffusion coefficients of cyclic chains were higher than linear chains at high molecular weight. Lower diffusion coefficients of smaller cyclic polymers were attributed to the high local density within molecular volume. The sizes of linear and cyclic chains in binary blends were relatively unchanged at all composition. As the linear fraction increases, the diffusivities of both cyclic ( D C ) and linear ( D L ) decrease. In comparison, D C drops more than D L especially at longer chain length. The decrease in diffusivities was most pronounced at small concentration of linear fraction.

Sequence-dependent force response during peeling of single-stranded DNA from graphite

We have analyzed the statistical thermodynamics of peeling single-stranded DNA (ssDNA) from the surface of graphite. Using recently measured parameters, we represent ssDNA as a polymer chain strongly adsorbed to a frictionless substrate using the freely jointed chain, wormlike chain, and rotational isomeric state models. All three models predict steady peeling force under force control, in agreement with single-molecule experiments. We predict that, for finite-length chains, the force response has measurable spikes under displacement control. These force spikes carry information about the underlying sequence of ssDNA, which might thus be measurable with a sufficiently stiff loading system. For the freely jointed chain model, under force control, we have obtained several exact closed-form results and provide relations between the measured peel force and the underlying adhesion free energy.

Predictive elucidation of conformational characteristics and configurational properties of poly(1-methylphosphirane) and poly(1-phenylphosphirane) as a molecular design

Conformational characteristics and configurational properties of poly(1-methylphosphirane) (PMePP) and poly(1-phenylphosphirane) (PPhPP) have been predictively elucidated by the refined rotational isomeric state scheme coupled with ab initio molecular orbital and density functional calculations. The lone pair of the phosphorus atom adopts an sp hybrid orbital. Owing to the high s character (50%), the polyphosphiranes exhibit low proton (hydrogen) affinities, and hence the lone pair does not form any intramolecular attractive interactions with hydrogen. As the meso-diad probability varies from 0 (syndiotactic) to 1 (isotactic), the characteristic ratio of PMePP slightly increases from 6.7 to 7.4, whereas that of PPhPP considerably decreases from 38 to 7.3. The large dimension of syndiotactic PPhPP is chiefly due to π-π attractions formed between adjacent phenyl groups. The trivalent phosphorus atom may be bonded to heavy, noble, and transition metals but readily or gradually oxidized. The usefulness and necessity of the polyphosphiranes have been assessed.

Conformation and conformation-dependent properties of chain molecules

This paper is dedicated to the memory of Professor N.A. Plate for his outstanding contributions to polymer science and his extraordinary leadership in the world scientific community. The long-lasting personal and professional relationship with Nikolai came to the end rather untimely, but his enthusiasm for science and people will always be remembered. The rotational isomeric state treatment has been extended to elucidate conformation and conformation-dependent properties of chain molecules occurring under the condition for which some special care is required. Examples include the odd-even effect of n-alkane chains, dipole moment of polymethylmathacrylate (PMMA), enhancement of optical rotation of vinyl polymers, screw-sense reversal of polyaspartates, and the anisotropy of a flexible spacer involved in the main-chain liquid crystal. Major conclusions are as follows: (1) The distinct odd-even effect is a peculiar character of the methylene sequence -(CH2)n-attributable to its bond angle (tetrahedral) and rotational preference (trans). In the other chains including carbonate linkages or oxyethylene units, the correlation along the chain unnecessarily accompany the odd-even phenomenon. (2) When the meso dyad of the PMMA chain takes the trans-trans conformation, the two adjacent ester groups are situated at a separation of only ca. 0.27 nm. The strong dipole-dipole interaction between the two polar ester groups may be alleviated by taking a staggered arrangement. The importance of such neighbor-dependent correlation in treating dielectric properties has been pointed out. (3) The amplification of conformational asymmetry has been discussed for two seemingly dissimilar examples: i.e., flexible vinyl polymers having asymmetric side chains and tightly hydrogen-bonded α-helical polypeptides. The conformation of the side chain has been elucidated for each of the enantiomeric forms of the backbone. The small free-energy difference between the two forms may cooperatively trigger a drastic effect in these polymeric systems. (4) A long oxyethylene spacer carrying mesogenic units on both terminals can be rather easily accommodated in the nematic LC phase. The nematic conformation of the spacer was found to play a crucially important role in determining the orientational order and the packing entropy of the nematic state.

Computational screening of biomolecular adsorption and self‐assembly on nanoscale surfaces

The quantification of binding properties of ions, surfactants, biopolymers, and other macromolecules to nanometer-scale surfaces is often difficult experimentally and a recurring challenge in molecular simulation. A simple and computationally efficient method is introduced to compute quantitatively the energy of adsorption of solute molecules on a given surface. Highly accurate summation of Coulomb energies as well as precise control of temperature and pressure is required to extract the small energy differences in complex environments characterized by a large total energy. The method involves the simulation of four systems, the surface-solute-solvent system, the solute-solvent system, the solvent system, and the surface-solvent system under consideration of equal molecular volumes of each component under NVT conditions using standard molecular dynamics or Monte Carlo algorithms. Particularly in chemically detailed systems including thousands of explicit solvent molecules and specific concentrations of ions and organic solutes, the method takes into account the effect of complex nonbond interactions and rotational isomeric states on the adsorption behavior on surfaces. As a numerical example, the adsorption of a dodecapeptide on the Au {111} and mica {001} surfaces is described in aqueous solution.

Influence of Weak Attractive Interactions on Structures and Properties of Poly(trimethylene terephthalate)

Conformational analysis of poly(trimethylene terephthalate) (PTT) has been carried out by the refined rotational isomeric state (RIS) scheme with ab initio molecular orbital (MO) calculations for a model compound, trimethylene glycol dibenzoate (TMGDB). Bond conformations of the O−CH2−CH2−CH2−O part of TMGDB were determined from 1H and 13C NMR experiments for unlabeled and 13C-labeled TMGDBs. The MO calculations exactly reproduced not only the experimental bond conformations but also the dipole moment and molar Kerr constant observed from TMGDB dissolved in nonpolar solvents. Comparison of the MO calculations with and without electron correlations revealed that a variety of intramolecular attractions, such as π−π interactions, electrostatic attractions, dipole−dipole interactions, and C═O···H−C and C−O···H−C close contacts, are formed in TMGDB and considerably stabilize its folding conformers with g±g∓ sequences in the central CH2−CH2 bonds. The folding conformers may be sources of dimer fluorescence char...

Conformational energies and entropies of peptides, and the peptide–protein binding problem

A novel statistical thermodynamic approach is applied to free-peptide segments in order to classify them according to their conformational energies, entropies and heat capacities. Our approach employs the rotational isomeric state (RIS) model in which the states are described by the Ramachandran map of backbone torsion angles. The statistical weight matrices for the pairwise-dependent states are derived from the torsion angle probabilities of the consecutive dipeptides in a coil library. The partition function is determined for a given sequence via RIS multiplication of the pre-determined matrices. The conformational partition function, Helmholtz free energy, energy, entropy and heat capacity are obtained. The model is applied to randomly produced peptides and also to known peptide inhibitors to analyze their thermodynamic properties. Peptides with low energy, low entropy and low-heat capacity are determined to be essential for a peptide to be a good candidate inhibitor. Free energy changes in peptide binding are also discussed.

Reduced odd–even effects in liquid crystalline carbonate dimers: molecular field analysis

Four liquid crystalline carbonate dimers DCn containing the dimethylbenzalazine mesogen, bis(oxycarbonyloxy)alkane flexible spacers with three to six methylene units and acetate terminal groups were synthesised and their mesogenic behaviour investigated. As compared with the corresponding ester dimers a strong reduction of odd–even fluctuations of nematic–isotropic (N–I) transition entropy is observed. A theoretical analysis of the dimers within the rotational isomeric states (RIS) mean-field approach is also reported. A satisfying agreement between calculated and observed thermodynamic properties is obtained. In fact, the theoretical analysis correctly predicts a significant reduction of the odd–even fluctuations for the core order parameter S as well as for the nematic to isotropic transition entropy △SNI . The calculated distributions of conformers also show reduced differences between even and odd members. In particular, for even dimers the calculated fraction of linear extended conformers in the nematic phase at the N–I transition is around 27%, which is far below that of the corresponding ester dimers (46%).

Conformational transition characterization of glass transition behavior of polymers

The conformational transition behavior of polymer in the amorphous state has been investigated through molecular dynamics simulations across the glass transition temperature (Tg). We find that the conformational transition, a localized and short time dynamics feature, crosses over different barrier heights when the system transforms from the molten state into the glass state and the barrier height in the glass state is markedly lower than that above Tg. In addition to the overall transition behavior, the specific transitions between the rotational isomeric states (RIS) g+, t−, t+ and g− are also investigated in detail. The populations of these specific transitions undergo considerable changes when the temperature decreases; meanwhile, the larger transition rates of the ending torsions get diminished. Besides the rate, the rotation degrees of the dihedrals during the transitions also change their distributions tremendously through Tg, below which most of the larger transition angles (50–100°) were inhibited remaining those sharply around 30°. This possibly explains why below Tg the conformational transition process has a lower effective barrier.

A Case for Characterizing Polymers with the Kerr Effect

We briefly summarize Kerr effect studies of dilute polymer solutions, taken from our own work, for the purpose of emphasizing their unique ability to characterize polymer microstructures. In cases where at least one of their monomer repeat units is polar or at least reasonably and anisotropically polarizable, the molar Kerr constants, mK, of polymers obtained from the electrical birefringence measured for their dilute solutions are demonstrated to be exquisitely sensitive to their microstructures, including the tacticities of homo- and copolymers and the comonomer sequences of copolymers. In addition, because the mKs expected for polymers with given or known microstructures can be calculated if their conformational characteristics have been established, comparison of observed and calculated mKs can also be used to confirm or derive their conformational characteristics, such as those embodied in their rotational isomeric states (RIS) models. From such comparisons of observed and calculated mKs, we were able to conclude that, among all characterization techniques, Kerr effect studies of dilute polymer solutions are clearly the most sensitive to both their microstructures and their conformations. This is largely a consequence of the fact that the mKs of small molecules range over more than 4 orders of magnitude and, in addition, may be either positive or negative in sign. Several additional potential applications of the Kerr effect are suggested for polymers that interact/complex with each other or with certain small molecules in solution and also for polymers at interfaces, e.g., polymer brushes bathed/swollen in solvents. Finally a call (a plea really) is made for polymer samples containing polar or anisotropically polarizable repeat units for further evaluating the Kerr effect as a sensitive means to characterize both their microstructures and conformations. This request is made because of our soon to be achieved and unique capability to measure mKs of polymers in solution on a state-of the-art Kerr effect instrument nearing completion in our laboratory.

Conformational Characteristics, Configurational Properties, and Thermodynamic Characteristics of Poly(ethylene terephthalate) and Poly(ethylene-2,6-naphthalate)

Conformational analysis of poly(ethylene terephthalate) (PET) and poly(ethylene-2,6-naphthalate) (PEN) has been carried out by the refined rotational isomeric state (RIS) scheme coupled with ab initio molecular orbital (MO) calculations for a model compound, ethylene glycol dibenzoate (EGDB). 1H and 13C NMR experiments for unlabeled and 13C-labeled EGDBs yielded bond conformations of the central O−CH2−CH2−O bond sequence. The MO calculations satisfactorily reproduced not only the experimental bond conformations but also the dipole moment and molar Kerr constant observed from EGDB. The aromatic ring and ester group of EGDB render its intramolecular interactions more complicated than those of poly(ethylene oxide) with the same O−CH2−CH2−O bonds; C═O···H−C and C−O···H−C close contacts and dipole−dipole interactions are simultaneously formed in EGDB. The characteristic ratio of PET, derived from the refined RIS calculations using the MO energies for EGDB, exactly agree with those determined from small angle neutron scattering experiments for the melt. Thermodynamic quantities on PET and PEN, evaluated from the RIS calculations, have well characterized melting and crystallization behaviors of these polyesters.

The introduction of hydrogen bond and hydrophobicity effects into the rotational isomeric states model for conformational analysis of unfolded peptides

Relative contributions of local and non-local interactions to the unfolded conformations of peptides are examined by using the rotational isomeric states model which is a Markov model based on pairwise interactions of torsion angles. The isomeric states of a residue are well described by the Ramachandran map of backbone torsion angles. The statistical weight matrices for the states are determined by molecular dynamics simulations applied to monopeptides and dipeptides. Conformational properties of tripeptides formed from combinations of alanine, valine, tyrosine and tryptophan are investigated based on the Markov model. Comparison with molecular dynamics simulation results on these tripeptides identifies the sequence-distant long-range interactions that are missing in the Markov model. These are essentially the hydrogen bond and hydrophobic interactions that are obtained between the first and the third residue of a tripeptide. A systematic correction is proposed for incorporating these long-range interactions into the rotational isomeric states model. Preliminary results suggest that the Markov assumption can be improved significantly by renormalizing the statistical weight matrices to include the effects of the long-range correlations.