Rotational Isomeric State Research Articles

Structure-Property Relationships of Poly(ethylene carbonate) and Poly(propylene carbonate).

Conformational characteristics of poly(ethylene carbonate) (PEC) and poly(propylene carbonate) (PPC) have been revealed via molecular orbital (MO) calculations and nuclear magnetic resonance (NMR) experiments on model compounds with the same bond sequences as those of the polycarbonates. Bond conformations derived from the MO calculations on the models were in exact agreement with those from the NMR experiments. Both PEC and PPC were indicated to adopt distorted conformations including a number of gauche bonds and cover themselves with negative charges, thus failing to form a regular packing and remaining amorphous. The MO data were applied to the refined rotational isomeric state (RIS) calculations to yield configurational properties such as the characteristic ratio, its temperature coefficient, the configurational entropy, and average geometrical parameters of unperturbed PEC and PPC chains. In the RIS calculations on PPC, the regio- and stereosequences were generated according to the Bernoulli trial or Markov stochastic process. In consequence, it was shown that the configurational properties of PPC do not depend significantly on its regio- and stereoregularities. The internal energy contribution to rubberlike chain elasticity, calculated from the temperature coefficient of the characteristic ratio, has indicated the possibility that PEC and PPC will behave as elastomers. The practical applications and potential utilizations of the polycarbonates are discussed on the basis of the conformational characteristics and configurational properties.

Monte Carlo simulation of the stability and structure of polyethylene oxide nanodroplet with different solvent qualities

Monte Carlo simulation for poly(ethylene oxide), PEO, was applied to study the effect of solvent quality on the stability and structure of PEO nanodroplets in the poor solvent regime. The Hamiltonian included intrachain and non-bonded interactions. The intrachain interactions were based on an extended rotational isomeric state (RIS) model, and the non-bonded interactions were based on a discretized form of the Lennard-Jones (LJ) potential. The solvent was included implicitly into the simulations by manipulating the attractive portion of the long-range interactions. The results of the simulations clearly showed that as the solvent became poorer, the nanodroplet became denser, and their interfacial thickness decreased. These changes led to PEO chains assuming more compact conformations to enable better packing in the bulk region of the nanodroplets. The average shape of the nanodroplets changed from spherical to ellipsoidal as the solvent quality decreased. This shape anisotropy was attributed to chains assuming compact conformations while trying to pack more efficiently in the bulk region. The chain end bead distribution was strongly influenced by the solvent quality. As the solvent became poorer, a greater proportion of the end beads were excluded from the bulk region because of the need to achieve better packing. Simulations also suggested the formation of a layered structure as the solvent quality decreased.

A Rigid Hinge Region Is Necessary for High-Affinity Binding of Dimannose to Cyanovirin and Associated Constructs

Mutations in the hinge region of cyanovirin-N (CVN) dictate its preferential oligomerization state. Constructs with the Pro51Gly mutation preferentially exist as monomers, whereas wild-type cyanovirin can form domain-swapped dimers under certain conditions. Because the hinge region is an integral part of the high-affinity binding site of CVN, we investigated whether this mutation affects the shape, flexibility, and binding affinity of domain B for dimannose. Our studies indicate that the capability of monomeric wild-type CVN to resist mechanical perturbations is enhanced when compared to that of constructs in which the hinge region is more flexible. Our computational results also show that enhanced flexibility leads to blocking of the binding site by allowing different rotational isomeric states of Asn53. Moreover, at higher temperatures, this observed flexibility leads to an interaction between Asn53 and Asn42, further hindering access to the binding site. On the basis of these results, we predicted that binding affinity for dimannose would be more favorable for cyanovirin constructs containing a wild-type hinge region, whereas affinity would be impaired in the case of mutants containing Pro51Gly. Experimental characterization by isothermal titration calorimetry of a set of cyanovirin mutants confirms this hypothesis. Those possessing the Pro51Gly mutation are consistently inferior binders.

Effect of Core Crystallization and Conformational Entropy on the Molecular Exchange Kinetics of Polymeric Micelles.

Here we systematically study the equilibrium molecular exchange kinetics of a series of amphiphilic n-alkyl-poly(ethylene oxide) (Cn-PEO) micelles containing partly crystallized cores. Using differential scanning calorimetry (DSC), we determined the melting transition and extracted the enthalpy of fusion, ΔHfus, of the n-alkyl chains inside the micellar core. Molecular exchange kinetics was measured below the melting point using a time-resolved small-angle neutron scattering technique (TR-SANS) based on mixing deuterated and proteated but otherwise identical micelles. Comparing both kinetic and thermodynamic data, we find that crystallinity within the micellar cores leads to significant enthalpic and the entropic contributions to the activation barrier for molecular exchange. While the former leads to an enhanced stability, the positive entropic gain favors the process. Interestingly, the entropic term contains an excess term beyond what is expected from the measured entropy of fusion. Based on calculations using the Rotational Isomeric State (RIS) model, we suggest that the excess entropy is due to the gain in conformational entropy upon releasing the chain from the confined state in the core. The study thus provides deep insight into the fundamental processes of micellar kinetics and which might be relevant also to other semicrystalline soft matter and biological systems including lipid membranes.

Temperature Dependence of Structural Properties and Chain Configurational Study: A Molecular Dynamics Simulation of Polyethylene Chains

Micro‐structural evolution of polyethylene (PE) across the glass transition temperature (Tg) is investigated by full atom molecular dynamic (MD) simulation. The specific volume as a function of temperature for PE is obtained, through which the volumetric glass transition temperature was determined. The dihedral distribution of the overall bonds of the amorphous polyethylene chain system keeps consistent with the rotational isomeric state scheme. The dependence of isomer probability of skeletal bonds and average radius of gyration on temperature also can be used to estimate the glass temperature. The micro‐structural information obtained from MD simulation should be helpful to understand glass transition mechanism of polymer system.

Sizes and shapes of simulated amorphous cis- and trans-1,4-polybutadiene

Controlling loss modulus can decrease tire rolling resistance. Deformation forces in elastomers depend on chain conformation. As a first step toward screening chemical effects on these, isolated single cis- and trans-1,4-polybutadiene chains of uncorrelated random conformations under unperturbed conditions are generated using Flory's Rotational Isomeric State approach, with discrete rotational states defined by Mark, Abe, and Flory. Averages and distribution of squared end-to-end distance, radius of gyration, and shape parameters are studied for chains ranging from 15 to 120 repeat units at 343 K and for the 50-unit chain at temperatures of 275 K–400 K. The calculated characteristic ratios are in good agreement with experimental and prior computed values. Only small absolute changes in chain size probability densities with temperature are found. A larger relative increase in probability density of unlikely larger chains and a smaller relative decrease in probability density of more likely smaller chains result in increased average chain size and characteristic ratios with increasing temperature. Within subdivisions of the size distribution, larger chains show an increase in characteristic ratio with temperature, while smaller and medium size chains show little change with temperature. This previously unreported effect is stronger for trans than for cis chains. Eigenvalues of the radius of gyration matrix quantify chain shapes along principal directions. Averaged shape measures differ between cis and trans chains, and most shape changes arise along the longest principal direction. Joint correlations between chain size and shape show they are mutually dependent.

Monte Carlo simulation of the structure of mono- and bidisperse polyethylene nanocomposites

The structure of bidisperse polyethylene (PE) nanocomposite mixtures of 50:50 (by mole) of long and short chains of C160H322/C80H162 and C160H322/C40H82 filled with spherical nanoparticles were investigated by a coarse-grained, on lattice Monte Carlo method using rotational isomeric state theory for short-range and Lennard-Jones for long-range energetic interactions. Simulations were performed to evaluate the effect of wall-to-wall distance between fillers (D), polymer-filler interaction (w) and polydispersity (number of short chains in the mixture) on the behavior of the long PE chains. The results indicate that long chain conformation statistics remain Gaussian regardless of the effects of confinement, interaction strength and polydispersity. The various long PE subchain structures (bridges, dangling ends, trains, and loops) are influenced strongly by confinement whereas monomer-filler interaction and polydispersity did not have any impact. In addition, the average number of subchain segments per filler in bidisperse PE nanocomposites decreased by about 50% compared to the nanocomposite system with monodisperse PE chains. The presence of short PE chains in the polymer matrix leads to a reduction of the repeat unit density of long PE chains at the interface suggesting that the interface is preferentially populated by short chains.

Conformational characteristics and configurational properties of poly(ethylene succinate) and poly(butylene succinate) and structure–property–function relationships of representative biodegradable polyesters

Conformational characteristics and configurational properties of synthetic biodegradable polyesters, poly(ethylene succinate) and poly(butylene succinate), have been investigated by NMR experiments and molecular orbital calculations on their model compounds and the rotational isomeric state calculations for the two aliphatic polyesters. The results have been related to their crystal structures and thermal properties and compared with those obtained previously for poly((R)-3-hydroxybutyrate) and poly(lactic acid) to elucidate structure–property relationships of the representative biodegradable polyesters. In addition, selective affinities to degradative enzymes of the four polyesters have been satisfactorily explained in terms of their conformational characteristics and interactions with the depolymerases.

A multiscale simulation model for poly(ethylene oxide)

An overview of the recent development of a multiscale simulation of amorphous polymeric materials at the bulk density is presented. Poly(ethylene oxide), (PEO), (CH3O-[CH2-CH2-O]nCH3) was selected to illustrate the method. The model starts from an ab initio quantum chemistry to obtain the statistical weights of polymer conformation based on the rotational isomeric state (RIS) theory. PEO chains were then mapped to a coarse-grained model using the modified RIS model onto the second nearest neighbor diamond (2nnd) lattice. The average non-bonded interactions were treated by the discretized Lennard-Jones (LJ) potential. Bulk PEO melts with molecular weight up to 8000 g/mol was generated and equilibrated. The on-lattice properties such as molecular size and conformational statistics agree well with the theory. Fully atomistic amorphous PEO models can be obtained by the reverse-mapping procedure to recover the missing atoms. After an energy minimization step, properties including torsional angle distribution, solubility parameter and static neutron scattering structure factor are in good agreement with experimental results.

Monte Carlo simulation study of the effect of chain tacticity on demixing of polyethylene/polypropylene blends

The molecular origin of the demixing behavior for 50: 50 (wt/wt) polyethylene/polypropylene (PE/PP) with different tacticity of PP at the melts (473 K) was investigated by Monte Carlo simulation of coarse-grained polymer model. Isotactic (iPP), atactic (aPP) and syndiotactic (sPP) polypropylenes were used for blending with PE. Coarse-graining polymer chains were represented by 50 beads, corresponding to C100H202 and C150H302 for PE and PP, respectively. The simulation was performed on a high coordination lattice incorporating short-range intramolecular interactions from the Rotational Isomeric State (RIS) model and long-range intermolecular interactions Lennard-Jones (LJ) potential function of ethane and propane units. Chain dimensions, the characteristic ratio (C n ) and self-diffusion coefficient (D) of PE in the blends are sensitive to the stereochemistry of PP chains. Compared with neat PE melts, PE dimension was relatively unchanged in PE/iPP and PE/aPP blends but slightly decreased in PE/sPP blends. PP dimension was increased in PE/iPP and PE/aPP mixture but decreased in PE/sPP blend in comparison with neat PP melts. In addition, diffusion of PE and PP chains in PE/PP mixture was decreased and increased, respectively, compared to the pure melts. Interchain pair correlation functions were used to detect the immiscibility of the blends. The tendency of demixing of PE/aPP and PE/iPP blends were weaker than that of PE/sPP blend.

Dynamics of polypropylene chains in their binary blends of different stereochemical sequences studied by Monte Carlo simulations

The conformational and dynamic properties of polypropylene (PP) for both pure melts and blends with different chain tacticity were investigated by Monte Carlo simulation of isotactic (iPP), atactic (aPP) and syndiotactic (sPP) polypropylenes. The simulation of coarse-grained PP models was performed on a high coordination lattice incorporating short- and long-range intramolecular interactions from the rotational isomeric state (RIS) model and Lennard-Jones (LJ) potential function of propane pairs, respectively. The dynamics of chains in binary PP/PP mixture were investigated with the composition of C150H302 with different chain taciticity. The diffusion rates of PP with different stereochemistry are generally in the order as: iPP > aPP ≫ sPP. For PP/PP blends with 50:50 wt% binary mixtures, immiscibility was observed when sPP was introduced into the mixtures. The diffusion rate of iPP and aPP became slower after mixing, while sPP diffuses significantly faster in the binary mixtures. The mobility of PP chains depends on both intramolecular (molecular size and chain stiffness) and intermolecular (chain packing) interactions. The effect of intramolecular contribution is greater than that of intermolecular contribution for iPP and aPP chains in binary mixtures. For sPP chain, intermolecular interaction has greater influence on the dynamics than intramolecular contribution.

Configurational statistics of poly(L-lactide) and poly(DL-lactide) chains

Conformational characteristics of poly(lactide)s have been investigated by density functional theory and ab initio molecular orbital (MO) calculations and NMR experiments on model compounds. Characteristic ratios, configurational entropies, and internal energies of poly(L-lactide) and poly(DL-lactide), whose stereosequences were generated by Bernoulli and Markov stochastic processes, were calculated under the refined rotational isomeric state scheme with conformational energies and geometrical parameters derived from the MO calculations. In terms of the conformational characteristics thus revealed, we have elucidated the reason why unperturbed chain dimensions determined experimentally for poly(L-lactide) are scattered considerably and, furthermore, discussed crystallization and crystal structures of poly(L-lactide) and molecular characteristics of poly(DL-lactide) synthesized from rac-lactide with stereospecific polymerization catalysts.

The Radius of Gyration of the Products of Hyperbranched Polymerization

The average mean‐square radii of gyration for the products of the linear polymerization, the star‐shaped polymerization, and the hyperbranched polymerization of AB2‐type monomer in the absence or presence of a multifunctional core initiator are investigated using the Dobson‐Gordon's method. The dependence relationships between the average radii of gyration and the average degree of polymerization calculated using the Dobson‐Gordon's method for the linear polymerization products are in good agreement with those obtained from the matrix algebra method of the rotational isomeric state model. The radii of gyration of the star‐shaped and hyperbranched polymers are much smaller than those of the linear polymers if their average degrees of polymerization are equal. The conversion of groups, the core/monomer feed ratio, and the core functionality affect the average radius of gyration of the products. However, compared with the other factors, the degree of polymerization is the most influential factor on the average radii of gyration for the hyperbranched polymer system.

Conformational transitions in the Ramachandran space of amino acids using the dynamic rotational isomeric state (DRIS) model

The dynamic rotational isomeric state model is applied to predict the internal dynamics of the 20 amino acids. Transition rates between rotational isomeric states are calculated from molecular dynamics simulations of Gly-Gly-X-Gly-Gly peptides where X represents one of the 20 amino acids. Predicted relaxation times are in good agreement with fluorescence quenching rate measurements.

Coupling of conformational and ionization equilibria in linear poly(ethylenimine): a study based on the site binding/rotational isomeric state (SBRIS) model

The conformational and ionization properties of linear poly(ethylenimine) are studied by combining the site binding model (SB) with the rotational isomeric state (RIS) model, developed by Flory to calculate the conformational properties of neutral linear molecules. The resulting approach (the SBRIS model) is used to rationalise the experimental poly(ethylenimine) titration curves. By fitting the experimental macroconstants, conformational and binding parameters are obtained. The obtained values are consistent with previous binding and structural information. The emergence of triplet interaction between protonated sites is explained as a natural consequence of the coupling between binding and conformational equilibria. When only nearest neighbour interactions are considered, transfer matrix techniques are used in the calculations. In order to account for excluded volume and long-range electrostatic interactions, Monte Carlo simulations are performed. The results indicate that at high ionic strengths, long-range interactions have a very limited impact on the titration curves. However, for long chains, they have a significant influence on the radius of gyration.

Temperature Dependence of Polypropylene Configurations

The temperature dependence of the chain configurations of amorphous polypropylenes is investigated by means of molecular dynamics (MD) simulations. The temperature gradient of the specific volume can be used to estimate the glass temperature of the amorphous polypropylene chain system. The dihedral distribution of the overall bonds of the amorphous polypropylene chain system at the various temperatures maintains the rotational isomeric state (RIS) scheme. The occurrence frequency of the isomeric state also can be used to locate the glass temperature. The average occurrence frequency of the trans or gauche states is almost unchanged below the glass temperature and the trans fraction decreases with increasing temperature above the glass temperature. The RIS calculations developed for an isolated chain conflicts with configurational parameters in amorphous bulk or melt state, although it is successful to explain the observation for the dilute and θ‐solution. The average molecular dimension of polypropylenes obtained by MD simulation is almost independence of temperature in amorphous bulk and melt, which is in agreement with the experimental observation.

Solution SAXS measurements over a wide temperature range to determine the unperturbed chain dimensions of polystyrene and a cyclic amylose derivative

The mean-square radii of gyration <S2> of two polystyrene (PS) samples with weight-average molar masses Mw of 2.18 × 104 and 3.88 × 104 in toluene and 2-butanone and of a cyclic amylose tris(phenylcarbamate) (cATPC) with a Mw of 4.73 × 104 in tetrahydrofuran were determined by synchrotron radiation small-angle X-ray scattering measurements over a wide range of temperatures from −77 °C to 70 °C. Both PS and cATPC are sufficiently soluble to enable SAXS measurements even at −77 °C in the solvents used. The <S2> of cATPC does not depend on temperature over the range investigated here. This result may be reasonable for such rigid ring polymers. In contrast, the radii of PS depend on temperature to a significant degree, whereas the second virial coefficient is mostly temperature independent. The resulting characteristic ratio C∞ for PS in toluene decreases monotonically with increasing temperature, as predicted both by the rotational isomeric state (RIS) and by (helical) wormlike chain models. However, C∞ in 2-butanone exhibits a minimum ∼10 °C and increases with increasing temperature, suggesting that the RIS energy parameters should be affected by the intermolecular interactions between the polymer and solvent. Mean-square radii of gyration <S2> for two polystyrene samples in toluene and 2-butanone and a cyclic amylose tris(phenylcarbamate) (cATPC) sample in tetrahydrofuran were determined by SAXS between −77 and 70 °C. Whereas <S2> of cATPC does not depend on temperature over the range investigated, those for polystyrene depend to a significant degree. The characteristic ratio for polystyrene in toluene monotonically decreases with increasing temperature. However, that in 2-butanone has a minimum ∼10 °C, suggesting that the RIS energy parameters are affected by the intermolecular interactions between the polymer and solvent.

Conformational characteristics and configurational properties of poly(butylene terephthalate) and structure–property relationships of aromatic polyesters

Conformational analysis of poly(butylene terephthalate) (PBT) has been carried out by the refined rotational isomeric state scheme combined with ab initio molecular orbital (MO) calculations and NMR experiments on its model compound, tetramethylene glycol dibenzoate (TetMGDB). Two conformers of TetMGDB, showing intramolecular phenyl–phenyl close contacts, yielded so small free energies at the MP2 level that the overestimated MP2 stabilization for the π–π attraction was compensated by addition of the hemi-MP3 term. The altered MO energies satisfactorily reproduced the NMR and dipole moment data on TetMGDB. The energy correction was also applied to poly(trimethylene terephthalate) (PTT), and configurational properties of PBT and PTT were evaluated from the altered energies. Fluorescence emissions observed from poly(ethylene terephthalate) (PET), PTT, PBT, and their model compounds were well correlated with the spacer conformations. Configurational, thermal, and optical properties of the aromatic polyesters of industrial importance are discussed herein in terms of their conformational characteristics.

Elucidation of conformational characteristics and configurational properties of poly((R)-3-hydroxybutyrate) by ab initio statistical mechanics

Conformational free energies and geometrical parameters derived from ab initio molecular orbital (MO) calculations for monomeric and dimeric model compounds of poly((R)-3-hydroxybutyrate) (PHB) were introduced into the refined rotational isomeric state (RIS) scheme to yield the characteristic ratio, configurational entropy, configurational internal energy, bond conformations and averaged geometrical parameters of PHB. The reliability of the MO calculations was confirmed through comparison with 1H and 13C nuclear magnetic resonance experiments for the monomeric model compound. The characteristic ratio (5.60) derived from the refined RIS calculations for the unperturbed PHB chain at 25 °C is in satisfactory agreement with the experimental values (6.1–6.3). The crystalline PHB chain is known to adopt the ttg+g+ conformation in the repeating unit. A previous study revealed that a trimeric (R)-3-hydroxybutyrate substrate bound on a PHB depolymerase lies in the ttg+g+ and tg−tt conformations. In our MO calculations, the former conformation is the most stable, and the latter is metastable but further stabilized by intermolecular C=O⋯H−N and C=O⋯H−O hydrogen bonds on the enzyme.

Reversible Copper(II)/(I) Electrochemical Potential Switching Driven by Visible Light-Induced Coordinated Ring Rotation

We here describe the first metal complex system in which electronic signals can be repeatedly extracted by converting bistable states related to an intramolecular ligand rotational motion, which is fueled by visible light. The molecular structure for relating an electron transfer and a motion consists of a copper center and a coordinated unsymmetrically substituted pyrimidine derivative, whose rotational isomerization causes an electrochemical potential shift. To harness light energy effectively through metal-to-ligand charge transfer (MLCT) excitation, we prepared a simple copper(I) complex coordinated by a 4-methyl-2-(6'-methyl-2'-pyridyl)pyrimidine and a bulky diimine. The thermodynamic and kinetic parameters of redox and rotational reactions were analyzed by cyclic voltammograms at variable temperatures, by considering four stable isomers related to copper(II)/(I) states and rotational isomeric states. The key feature of this compound is that the rotation is frozen in the copper(I) state (rate constant for the rotation, k(Ii→o) = 10(-4) s(-1)) but is active in the copper(II) state (k(IIi→o) = 10(-1) s(-1)) at 203 K. The compound makes a bypass route to the isomeric metastable copper(I) state, via a tentative copper(II) state formed by photoelectron transfer (PET) in the presence of a redox mediator, decamethylferrocenium ion (DMFc(+)), or upon a partial oxidation of the complex. Light- and heat-driven rotation in the copper(I) state with a potential shift (ΔE°' = 0.14 V) was analyzed by electrochemical measurements of the complex in the solution state. The rotor could be reset to the initial state by heating, thereby completing the cycle and enabling repeated operation fueled by light energy. A significant redox potential shift associated with the copper(II)/(I) transition accompanied the rotation, thereby providing a new type of molecular signaling system.