Unperturbed Chain Research Articles

Reduction of the glass temperature of thin freely standing polymer films caused by the decrease of the coupling parameter in the coupling model

Dramatic reduction of the glass temperature, T g, in freely standing polymer thin films has been found when the thickness of the films become approximately smaller than the average end-to-end distance of the unperturbed polymer chains. The observation of a large molecular weight dependence of the T g reductions provides evidence for the importance of chain confinement effect on the glass temperature of thin polymer films. We propose that for freely standing polymer thin films of high molecular weights, there are: (a) induced orientations of the polymer chains when their average end-to-end distance becomes comparable to the film thickness and (b) decreases of the cooperative length scale for chain segments near the surfaces. As a consequence, the intermolecular constraints of local segmental motions for molecular units are reduced, particularly those located in the vicinity of the surfaces. The reduction of T g is attributed to an attendant decrease of the coupling parameter in the coupling model. This explanation is consistent with a recent photon correlation spectroscopy (PCS) and quartz crystal microbalance (QCM) measurement of the dynamics of local segmental motions in polymer thin films. Calculation of the T g of the thin film studied using the coupling model gives an order of magnitude estimate of the reduction of T g, which is in agreement with experiment.

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio : : , where L 1 ≤ L 2 ≤ L 3 are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7: 12.0 for polyethylene chains.

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio 〈L〉:〈L〉:〈L〉, where L1≤L2≤L3 are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7:12.0 for polyethylene chains.

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

Excluded-Volume Effects in Sodium Hyaluronate Solutions Revisited

Five sodium salt samples of hyaluronic acid ranging in weight-average molecular weight Mw from 1.9×105 to 1.5×106 have been studied by light scattering and viscometry in aqueous sodium chloride at 25°C. The intrinsic viscosity ([η]) data obtained at 10 different NaCl concentrations Cs covering a range from 0.005 to 2.5 M are analyzed along with previous data for lower Mw on the basis of the Yamakawa-Fujii-Yoshizaki theory for unperturbed wormlike chains combined with the quasi-two-parameter (QTP) theory for excluded-volume effects. Fairly satisfactory agreement is observed between theory and experiment at Cs higher than 0.01 M over the range of molecular weight from 3.8×103 to 1.5×106, though the degree of agreement tends to lower with decreasing Cs. When the wormlike chain parameters and the excluded-volume strength estimated from [η] are used, the QTP theory with the known expression for 〈S2〉 (the mean-square radius of gyration) of the unperturbed wormlike chain is found to describe almost quantitatively the measured 〈S2〉 for Na hyaluronate at Cs=0.02, 0.1, and 0.5 M. Thus, it is concluded that this theory for nonionic chains is applicable, in a fairly good approximation, to 〈S2〉 and [η] of the charged polysaccharide in aqueous NaCl unless Cs is lower than 0.02 M.

Dynamic Light Scattering and Dynamic Viscoelasticity of Poly(vinyl alcohol) in Aqueous Borax Solutions. 4. Further Investigation on Polymer Concentration and Molecular Weight Dependencies

Viscosity measurements are made on aqueous borax solutions of poly(vinyl alcohol) (PVA) samples over a wide range of PVA concentration, C, to examine the hydrodynamic properties of associated polymers compared to those of neutral polymers. The dynamic viscoelastic data are reanalyzed using a statistical−mechanical theory for elastically effective chains in transient gels developed by Tanaka and Ishida. The viscosity data are not superposed in the plot of viscosity against C[η] using the Huggins relationship, especially around and over a critical concentration, CN, at which the dynamical behaviors drastically change and an inflection point of a curve in the plot of the viscosity against C is located. On the other hand, when we assume that the chain dimension around CN is the unperturbed one, the viscosity data around CN is well-superposed on a curve in the plot of viscosity against C/C*up, where C*up is the overlapping concentration of the unperturbed chain. The inflection point of this composite curve is ...

Conformational Characteristics of Polymethylene Chains in Melts and in Various Phantom Chains from Explicit Atom Molecular Dynamics Simulations

Conformer populations, mean-square chain dimensions, and end-to-end distance distributions for polymethylene (PM) chains, H(CH2)nH with n = 13, 44, and 100, in melts and in various phantom chains have been studied using a parallel computational method of molecular (and Brownian) dynamics simulations with a well-calibrated explicit atom force field. The specific volume−temperature properties of the simulated melt systems are in excellent agreement with experiments. Conformational characteristics of PM chains in melts are identical to those of 1,5 phantom chains, characterized by short-range intramolecular interactions between the atoms separated by up to four skeletal bonds, which correspond to unperturbed chains in ϑ solvents according to recent implicit solvent model results of Sariban et al. and Destrée et al. Moreover, a Gaussian approximation of end-to-end distance distributions is found to be valid only for long PM chains with n greater than 100. According to our simulation results, the characteristic ratio C∞ for unperturbed polyethylene chains is found to be ca. 7.9 at 413 K. This value is larger than the generally accepted value, 6.8 (derived from intrinsic viscosity data for relatively polydisperse polyethylene samples), but is corroborated by recent small angle neutron scattering results (7.8 ± 0.4) for melt chains of nearly monodisperse samples. The fact that PM chains exhibit identical conformational characteristics in melts, 1,5 phantom chains, and ϑ solvents is attributed to the lack of any correlation between local chain conformations and (polymer−polymer or polymer−solvent) intermolecular attractions. Departures from such an ideal behavior seen for other polymers are also discussed.

Thermodynamics of Chain Fluids from Atomistic Simulation: A Test of the Chain Increment Method for Chemical Potential

A formulation is presented for the calculation of the excess chemical potential μex(ntest) of ntest-mer chains mixed at infinite dilution with a bulk n-mer fluid and of the excess segmental chemical potential = μex(n + 1) − μex(n) from detailed atomistic simulations. The formulation is applied for ntest = 6 to 16 in n-hexadecane (C16, n = 16) in the liquid (P = 50 atm) and vapor (P = 1.02 atm) states at T = 580 K using a configurational bias Monte Carlo (MC) scheme. Two different reference states (ideal gas and continuous unperturbed chains) are examined for the definition of μex, and simulations are conducted with two united-atom model representations from the recent literature. In parallel, μex and with reference to the ideal gas are derived from two cubic equations of state (EoS) for the same systems and conditions. Both the MC and the EoS calculations for both models and reference states examined give a linear dependence of μex(ntest) on ntest, confirming that chemical potentials for long chains can be reliably estimated from small test chain and test segment insertions. This confirmation of the “chain increment ansatz” is of great practical value for phase equilibrium calculations in long-chain systems. Predictions for the structure of the C16 liquid and vapor are in good agreement with existing experimental and simulation evidence. Chain conformations in the liquid and vapor are indistinguishable from unperturbed and ideal gas chain conformations, respectively. In lower temperature liquids (T = 450 K, P = 20 atm), insertions of long test chains cannot provide adequate sampling, but the chain increment ansatz remains useful for estimating chemical potentials.

Inclusion Complexes of Chain Molecules with Cycloamyloses. 2. Molecular Dynamics Simulations of Polyrotaxanes Formed by Poly(ethylene glycol) and α-Cyclodextrins

Molecular dynamics (MD) simulations were performed for channel type polyrotaxanes with α-cyclodextrins (α-CDs) threaded onto monodisperse chains of poly(ethylene glycol) (PEG). The polymer captures as much α-CD as its length permits, forming a close-packed structure from the one end to the other. The van der Waals interactions are the main source of the stabilization of these polyrotaxanes. Hydrogen bonds between successive α-CDs slightly favor head-to-head, tail-to-tail sequences over head-to-tail sequences. The α-CDs in polyrotaxanes are more symmetric and less distorted than the isolated α-CDs. The PEG in the polyrotaxane is more extended than an unperturbed chain, because it has a larger population of trans states at internal bonds.

Aqueous solution properties of oligo- and poly(ethylene oxide) by static light scattering and intrinsic viscosity

Conformational properties of ethylene glycol, oligo-, and poly(ethylene oxide) ranging in weight-average molecular weight ( M w) from 62 to 1.1 × 10 7 have been studied by static light scattering and viscometry in salt-free and 0.45 M K 2SO 4 water and in benzene. Above M w = 6 × 10 3, intrinsic viscosity ([η]) and z-average square radius of gyration (〈 S 2〉 2) of PEO in a salt-free solution at 25°C, [η] = 4.33 × 10 −4 M w 0.67 9 dl g −1 and 〈 S 2〉 z = 4.08 × 10 −18 M w 1.1 6 cm 2, respectively. The second virial coefficient is positive in water at 25°C but one order of magnitude smaller than reported by Devanand et al. ( Macromolecules, 1991, 24, 5943). A θ-temperature for PEO in 0.45 M K 2SO 4 aqueous solution is determined to be 34.5°C and above M w = 4 × 10 2, [η] and 〈 S 2〉 z follow the power laws for an unperturbed polymer chain. The characteristic ratio ( C ∞) of PEO is 5.2 ± 0.1. 9.3Åwas determined for the persistence length and 8.7Å −1 for the molar mass per unit contour length of a PEO chain, based on the helical wormlike touched-bead model. The PEO chain in water behaves as a flexible polymer with a relatively large hydrodynamic diameter (9Å) because of the hydration of the PEO chain.

Conformational Transition of the Poly(ethylene oxide) Chain near the Critical Point of the Tetrahydrofuran/Water Mixed Solvent System

Inherent viscosities were measured for poly(ethylene oxide) (PEO) in tetrahydrofuran/water (THF/WT). The measured temperature range covered the range from 35 °C close to the lower critical solution temperature Tc of THF/WT system. It was found that near the critical temperature, the inherent viscosities contract down to about one-third of the value at 35 °C. The overall contraction behavior agrees well with de Gennes' theory, but two observations contradict his prediction. First, the reduced ϑ temperature, τϑ, at which the unperturbed chain dimension is observed strongly depends on the molecular weight. Second, we observed only the contraction behavior instead of the contraction-and-reswelling on approaching close to the critical point. The expansion factors αη3(=[η]/[η]ϑ) for the different molecular weight samples fall on one master curve when plotted as a function of [log τ − log τϑ] Mw1/2. Here τ (=(Tc − T)/Tc) and Mw are the reduced temperature and the weight-average molecular weight, respectively.

Estimation of the Unperturbed Chain Dimensions of Poly(Vinyl Chloride) Polymer by Various Methods

Flory Fox, Kurata-Stockmayer, Berry, Inagaki-Suzuki-Kurata, Stockmayer-Fixman and Ahmad-Baloch methods based on the excluded volume theory have been applied to poly(vinyl chloride)-cyclohexanone system to obtain Kq and the radius of gyration. A discussion on the reliability of these methods is given. The Stockmayer-Fixman and Ahmad-Baloch methods are found to be equally applicable.

Chain dimensions and scattering function of (1 → 3)- β- d-glucan simulated by the Monte Carlo method

A Monte Carlo method was used to evaluate the chain dimensions and scattering function of (1 → 3)- β- d-glucan in solution. Monte Carlo samples of the glucan chain were generated on the basis of a conformational energy map of the dimeric subunit, i.e. β-laminarabiose. The effect of the excluded volume was introduced into the model by placing hard spheres with a radius R ex at the center of mass of each glucose unit in the chain sequence. The results for the chain length dependence of the quantity 〈S 2〉 x (〈S 2〉 is the mean square radius of gyration and x is the degree of polymerization) and the radial distribution of the end-to-end distance have confirmed that the unperturbed (1 → 3)- β- d-glucan chain shows non-Gaussian-type behavior in the region of x < 200, above which the chain behaves in a Gaussian manner in its overall conformational character. However, local helical character was observed throughout the x range. In contrast with the unperturbed chain, the perturbed chain is characterized by non-Gaussian behavior over the chain length examined ( x ≤ 2000). The experimental 〈S 2〉 x vs. x data of the curdlan fractions in water-diluted cadoxen, evaluated by light scattering, were found to be simulated by perturbed chains with an excluded volume R ex = 1.0 A ̊ . The scattering function was calculated from the ensemble of generated (1 → 3)- β- d-glucan chains as a function of x ( x ≤ 40) in the q range up to 1.0 A ̊ −1 ( q is the scattering vector). The scattering function in the range 0.1 ≤ q ≤ 0.8 A ̊ −1 , where the scattering function is sensitive to the local chain conformation, reveals an appreciable oscillation. The calculated scattering function and 〈 S 2〉 for the Monte Carlo chains with x = 2–7 were in reasonable agreement with preliminary experimental results obtained by small-angle X-ray scattering for the corresponding laminara-oligosaccharides in water.

Electrostatic Contributions to Chain Stiffness and Excluded-Volume Effects in Sodium Hyaluronate Solutions

Intrinsic viscosities [η] for sodium hyaluronate in aqueous sodium chloride at 25°C were determined for 12 samples ranging in weight-average molecular weight Mw from 3.8×103 to 3.5×105 at NaCl concentrations Cs between 0.005 and 2.5 M. They were analyzed on the basis of the Yamakawa-Fujii-Yoshizaki theory for [η] of an unperturbed wormlike chain combined with the Yamakawa-Stockmayer-Shimada theory for excluded-volume effects to estimate the total persistence length q and the excluded-volume strength B as functions of Cs. At any Cs studied, excluded-volume effects on [η] became appreciable when Mw exceeded 1×104–2×104. The Cs dependence of q yielded 4.0 nm for q0 (the intrinsic persistence length) of the polysaccharide chain at infinite ionic strength. It was found that the values of q−q0 (i.e., the electrostatic contribution to q) at Cs<0.02 M were roughly 70% larger than predlcted by the Le Bret theory and the Odijk-Skolnick-Fixman theory. On the other hand, the estimated B values agreed fairly well with Fixman and Skolnick’s theory for the excluded-volume interaction between a pair of charged rodlike segments unless Cs was lower than 0.05 M.

Distribution Function P(S) of Uniform Star Polymers

In this paper, the probability density distribution function P(S) of the radius of gyration of the unperturbed star polymer chains is investigated using Monte Carlo method. We find that the distribution function P(S) for ideal star-shaped polymer may also expressed in the form of P(S)− −S2aexp(−(a+0.5)S2/〈S2〉), and the parameter a only depends on the number of branches f, which is similar to the Flory-Fisk expression P(S) for ideal linear polymer chain.

GdfidL: a finite difference program for arbitrarily small perturbations in rectangular geometries

A FD-program for calculating the resonant fields in a perturbed chain of rectangular cavities is presented. The unperturbed cavity chain can be discretized exactly by standard FD-programs that operate on regular grids. Discretizing a perturbed chain exactly with such a grid would lead to a computation time inversely proportional to the perturbation. GdfidL does not represent the grid as a matrix but as a linked list. This allows discretizing arbitrarily small perturbations of a certain class without increasing the time for the solution. As a nice side-effect, only interesting volumes are discretized, reducing the computation time further.

Conformations and Structures of Poly(oxyethylene) Melts from Molecular Dynamics Simulations and Small-Angle Neutron Scattering Experiments

An ensemble of H(CH2OCH2)12H chains has been studied by molecular dynamics simulations as both melt chains and unperturbed phantom chains as a model system to investigate condensed phase effects on chain conformations of poly(oxyethylene) (POE). In addition, conformations of high molecular weight POE chains in the melt have been determined by small-angle neutron scattering (SANS) experiments over a temperature range of 347−459 K. Our simulations show that POE chains in the melt are more extended than the phantom chains which represent the unperturbed chains in ϑ solution. Moreover, the melt chains exhibit a negative temperature coefficient of chain dimensions in contrast to a positive value for the phantom chains. The difference in chain dimensions and the difference in the temperature dependence of chain dimensions between melt and phantom chains are corroborated by the results of our SANS measurements when they are compared with experimental results for POE chains in ϑ solution. We attribute these signi...

Chain Stiffness and Excluded-Volume Effects in Dilute Polymer Solutions: Cellulose Tris[(3,5-Dimethylphenyl)carbamate

Nineteen fractions of cellulose tris[(3,5-dimethylphenyl)carbamate] (CTDC) ranging in weight-average molecular weight Mw from 2.5 × 104 to 7.5 × 106 have been studied by static light scattering, sedimentation equilibrium, and viscometry in 1-methyl-2-pyrrolidone at 25 °C. Since this cellulose derivative exhibits pronounced optical anisotropy, light-scattering data are corrected for the anisotropy effect on the basis of Nagai theory for the Kratky−Porod (KP) wormlike chain with cylindrically symmetric polarizabilities. It is shown that the data for 〈S2〉z (the z-average mean-square radius of gyration), δ (the optical anisotropy factor), and [η] (the intrinsic viscosity) and those reported previously for 11 fractions are described accurately by the known theories for the unperturbed KP chain if Mw is lower than 7 × 105. From the comparison, the persistence length and the monomeric projection of the CTDC chain are estimated to be 7.8 and 0.52 nm, respectively. When Mw exceeds 106, i.e., when nK (the Kuhn segment number) increases above 50, excluded-volume effects on 〈S2〉z and [η] become experimentally observable. Though such a large nK value for the appearance of volume effects has been considered inconsistent with the Yamakawa−Stockmayer−Shimada (YSS) theory for KP or helical wormlike chains, the observed excluded-volume effects are found to be explained quantitatively in the YSS scheme, i.e., by the YSS perturbation theory combined with the Domb−Barrett function for the radius expansion factor and the Barrett function for the viscosity expansion factor. Thus, this theoretical scheme should have a wider applicability than what might be anticipated from earlier studies.

Dynamics of Concentrated Weakly Charged Polyelectrolyte Solutions

The static and dynamic structure factors of weakly charged polyelectrolytes in concentrated solutions are derived in the random phase approximation. The effects of polymer stiffness, excluded volume, charge fraction, and salt concentration are obtained and compared with the small angle neutron scattering experiments on poly(acrylic acid) gels. An accurate description of the short range interactions in the unperturbed polymer chain together with consideration of a moderate excluded volume effect is required to approximate the complicated experimental behavior.