Unperturbed Chain Dimensions Research Articles

Dynamics of Entangled cis-1,4-Polyisoprene Confined to Nanoporous Alumina

The dynamics of unentangled cis-1,4-polyisoprene confined within self-ordered nanoporous alumina (AAO) is studied as a function of molecular weight (5000–300 g/mol) and pore size (400–25 nm) with dielectric spectroscopy. The main effects are the pronounced broadening of both segmental and chain modes with decreasing AAO pore diameter. This suggests that the global chain relaxation is retarded on confinement. Remarkably, the distribution of relaxation times is broadened even within pores with size 50 times the unperturbed chain dimensions. The glass temperature is unaffected by confinement. These results are discussed in terms of confinement and adsorption effects. Confinement effects are negligible for the studied molecular weights. Chain adsorption, on the other hand, involves time and length scales distinctly different from the bulk that can account for the experimental findings.

Chain Structure and Molecular Weight Dependent Mechanics of Poly(ethylene 2,5-furandicarboxylate) Compared to Poly(ethylene terephthalate)

Solution and melt viscosity relations to molecular weight were obtained for bio-based poly(ethylene 2,5-furandicarboxylate) (PEF) in comparison to poly(ethylene terephthalate) (PET). Furthermore, the rate dependent glassy state tensile properties were explored at varying molecular weights, showing ductile behavior for high molecular weight PEF at low rates. The unperturbed chain dimensions of PEF indicate similar conformational freedom to PET but lower chain packing due to the shorter bond length of 2,5-furandicarboxylic acid (FDCA), inducing a lower entanglement density as corroborated by plateau moduli measurements. The high temperature and shear rate dependence of the melt viscosity as well as the high strain rate dependence of the glassy state yield stress can be explained by this lower entanglement density, although the glassy state may furthermore be subject to chain mobility restrictions.

Chain dimensions and intermolecular interactions of polysilanes bearing alkyl side groups over the UV thermochromic temperature

To elucidate temperature change of intermolecular interactions and chain dimensions for poly(dialkylsilane)s with or without thermochromism, synchrotron-radiation small-angle X-ray scattering and UV-absorption measurements were carried out for relatively low-molar mass poly(n-hexylmethyl)silane (PSi-1), poly(n-decylmethyl)silane (PSi-2), and poly(n-hexylpropyl)silane (PSi-3) samples in isooctane over a wide temperature range down to −94 °C. While the dimensional properties for the three polysilanes were almost irrespective of temperature, the second virial coefficient for PSi-2 and PSi-3 significantly decreased and became negative below the thermochromic temperature at −60 °C and −50 °C, respectively. Analyses in terms of the quasi-two-parameter theory for the wormlike chain showed that conformational change detected by UV-absorption behavior does not cause appreciably the unperturbed chain dimensions of the polysilane samples. Furthermore, aggregates were detected by ultra-small-angle X-ray scattering measurements for high molar mass PSi-3 samples at low temperatures. These results indicate that intermolecular interactions between poly(dialkylsilane) molecules become attractive around the thermochromic temperature.

Dynamics of Unentangled cis-1,4-Polyisoprene Confined to Nanoporous Alumina

The dynamics of unentangled cis-1,4-polyisoprene confined within self-ordered nanoporous alumina (AAO) is studied as a function of molecular weight (5000–300 g/mol) and pore size (400–25 nm) with dielectric spectroscopy. The main effects are the pronounced broadening of both segmental and chain modes with decreasing AAO pore diameter. This suggests that the global chain relaxation is retarded on confinement. Remarkably, the distribution of relaxation times is broadened even within pores with size 50 times the unperturbed chain dimensions. The glass temperature is unaffected by confinement. These results are discussed in terms of confinement and adsorption effects. Confinement effects are negligible for the studied molecular weights. Chain adsorption, on the other hand, involves time and length scales distinctly different from the bulk that can account for the experimental findings.

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.

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.

Molecular simulations of the conformational properties of atactic poly(2-ethylbutyl methacrylate)

RIS Metropolis Monte Carlo (RMMC) simulations were used to determine the unperturbed theta-state chain dimensions of atactic stereoconfigurations of poly (2-ethylbutyl methacrylate) [PEBMA]. Root mean-squared end-to-end distance (〈r2〉o/M)1/2 and characteristic ratio (Cn) were calculated along with the backbone torsion angle distribution. The simulated properties are in very good agreement with experimental results. The values of the PEBMA chain dimensions are in-between those corresponding ones for poly(n-butyl methacrylate) and poly (n-hexyl methacrylate) thereby showing the effect of branching in the side-chain. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Chain Conformation of Poly(alkylene oxide)s Studied by Small-Angle Neutron Scattering

Using small-angle neutron scattering, the unperturbed chain dimensions of a series of poly(alkylene oxide)s (PAO’s) were studied as a function of side-chain length. The PAO’s were obtained using anionic ring-opening polymerization methods. The deuterated monomers were synthesized from commercially available precomponents. A systematic decrease of the chain dimensions with increasing length of the side chains was found. We also compare the PAO’s with the chemically very similar poly(olefin)s with respect to the characteristic ratio C∞, the chain dimensions, and the packing length as a function of the molecular weight per backbone bond. In doing so, we found significant differences between the static properties of the two systems.

Effect of temperature and thermodynamic quality of solvent over unperturbed chain dimensions of nylon 6

AbstractA nylon 6 sample having average molecular mass 4.825 × 105 g mol−1 was fractionated into five different fractions with respect to molecular mass, which ranged from 3691 to 999,000 g mol−1. The light scattering and intrinsic viscosity measurements were made in m‐cresol and its mixture with 1,4‐dioxane. The second virial coefficient, radius of gyration and Mark Houwink's constant and unperturbed chain dimensions were determined by light scattering and viscosity measurement. It has been observed that all these parameters are composition of solvent and temperature dependent. The solvent having composition of 97% m‐cresol and 3% dioxane, was best and it deteriorated with the increase/decrease in percentage of 1,4‐dioxane in m‐cresol. However, its thermodynamic quality was enhanced with the temperature. Such variation in quality of solvent was reflected in all the estimated parameters and showed maxima at this composition of solvent. The unperturbed dimensions obtained by different methods though, differed in values but showed same trend and NA‐MKB method gave close results to the one obtained through [ηo]. A new expression has also been proposed relating ko to solvent quality and temperature and the data obtained by us for nylon‐6 and the one obtained from the literature for dextran obeyed this expression up to large extent irrespective of the solvent composition and temperature. The proposed equations have also been applied to dextran/methoxy ethylene and dextran/ethylene glycol systems and worked well. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.

Intrinsic viscosity and unperturbed dimension of poly(dl-lactic acid) solution

The intrinsic viscosities were determined for poly(DL-lactic acid) (PDLLA) solutions in 1,2-dialkyl phthalate at temperatures ranging from 30 to 60 °C. A series of dialkyl phthalate, in which the alkyl group was changed from methyl to propyl, was used as the solvent to control the solvent quality systematically. The intrinsic viscosity of the PDLLA solution was higher in the better quality solvent, with a higher molecular weight of PDLLA, and at lower temperatures. The unperturbed dimensions of the PDLLA molecule and polymer-solvent interaction parameter of PDLLA in dialkyl phthalate were deduced using extrapolation methods based on the temperature-dependent intrinsic viscosities. Slight shrinkage in the unperturbed chain dimension was observed, which resulted from a change in polymer conformation with temperature. It was also observed that the polymer-solvent interaction became more favorable with the dialkyl phthalate containing a shorter alkyl chain.

Conformation of Single Poly(methyl methacrylate) Chains in an Ultra-Thin Film Studied by Scanning Near-Field Optical Microscopy

The conformation of a single poly(methyl methacrylate) (PMMA) chain was studied by scanning near-field optical microscopy (SNOM). Here we discuss the conformation of PMMA in the confined geometry of the thin film with a thickness less than the unperturbed chain dimension in the bulk state. The direct observation by SNOM was performed for individual fluorescence-labeled PMMA chains dispersed in the thin films of the unlabeled PMMA prepared by the spin coating and Langmuir-Blodgett techniques. We examined the effect of the constraint in the height direction on the radius of gyration in the direction parallel to the film surface, Rxy, i.e., the chain dimension normal to the confinement. In the thickness range of 1–100 nm, Rxy in an ultra-thin film was not significantly altered from that in the bulk state, indicating that the PMMA chain has lowered interchain entanglement in the ultra-thin film.

Temperature Coefficients of Unperturbed Chain Dimensions for Polystyrene and Poly(α-methylstyrene)

The temperature coefficient d ln 0/dT of the unperturbed mean-square end-to-end distance 0 with T the absolute temperature was determined from light scattering measurements for atactic polystyrene (a-PS) with the fraction of racemic diads fr=0.59 and atactic poly(α-methylstyrene) (a-PαMS) with fr=0.72, both in toluene (good solvent) and in the range of temperature 15.0–55.0 °C, on the assumption that the binary-cluster integral and hence the gyration-radius expansion factor do not depend on T. It is then found that d ln 0/dT is definitely negative for a-PS with a weak helical nature but almost vanishes for a-PαMS with a strong helical nature. The results are consistent with the helical wormlike chain theory prediction.

Bone-Tissue-Engineering Material Poly(propylene fumarate): Correlation between Molecular Weight, Chain Dimensions, and Physical Properties

Poly(propylene fumarate) (PPF) is an important biodegradable and cross-linkable polymer designed for bone-tissue-engineering applications. For the first time we report the extensive characterization of this biomaterial including molecular weight dependences of physical properties such as glass transition temperature Tg, thermal degradation temperature Td, density rho, melt viscosity eta0, hydrodynamic radius RH, and intrinsic viscosity [eta]. The temperature dependence of eta0 changes progressively with molecular weight, whereas it can be unified when the temperature is normalized to Tg. The plateau modulus and entanglement molecular weight Me have been obtained from the rheological master curves. A variety of chain microstructure parameters such as the Mark-Houwink-Sakurada constants K and alpha, characteristic ratio Cinfinity, unperturbed chain dimension r0(2)/M, packing lengthp, Kuhn length b, and tube diameter a have been deduced. Further correlation between the microstructure and macroscopic physical properties has been discussed in light of recent progress in polymer dynamics to supply a better understanding about this unsaturated polyester to advance its biomedical uses. The molecular weight dependence of Tg for six polymer species including PPF has been summarized to support that Me is irrelevant for the finite length effect on the glass transition, whereas surprisingly these polymers can be divided into two groups when their normalized Tg is plotted simply against Mw to indicate the deciding roles of inherent chain properties such as chain fragility, intermolecular cooperativity, and chain end mobility.

An Assessment of the Role of Quenched Randomness in the Stereochemical Sequences of Atactic Vinyl Polymers

The influence of the quenched randomness in the stereochemical sequences of atactic chains on the mean-square unperturbed end-to-end distance, 〈r2〉0, is assessed. The method uses a rotational isomeric state (RIS) model based on virtual bonds between the centers of mass of the C6 rings in polystyrene. This virtual bond model is derived from a conventional RIS model expressed in terms of the C−C bonds in the main chain. The zeroth-approximation virtual bond model, which retains only the most probable conformations of each tetrad, correctly finds 〈r2〉0 ∼ n in the limit as n → ∞ if the probability for a meso diad, pm, is 0 < pm < 1, although the same zeroth-approximation model yields 〈r2〉0 ∼ n2 if pm is either 0 or 1. The values of 〈r2〉0 at intermediate pm are surprisingly close to the ones deduced from a full, C−C bond based RIS model. This achievement of the zeroth-approximation model demonstrates the important role of the quenched randomness of the stereochemical sequences in determining the unperturbed dimensions of atactic chains. Excellent agreement with the 〈r2〉0 from the full RIS model based on C−C bonds over the entire range of stereochemical composition, 0 ≤ pm ≤ 1, can be achieved in a first-approximation virtual bond model, which includes the next most probable conformations at each tetrad and refines slightly some of the conformations by minor adjustments in soft degrees of freedom.

Synthesis and Rheological Properties of Poly(5‐n‐hexylnorbornene)

AbstractSummary: Poly(5‐n‐hexylnorbornene) (PHNB) was obtained in high molecular weight and high yields by vinyl‐type polymerization of 5‐n‐hexyl‐2‐norbornene (endo/exo = 77/23) with [NiBr(NPMe3)]4/B(C6F5)3 as catalyst precursor. The combination of size exclusion chromatography with on‐line light scattering and intrinsic viscosity measurements allowed the Mark‐Houwink expressions to be evaluated in tetrahydrofuran. The unperturbed chain dimensions for poly(5‐n‐hexylnorbornene) were estimated via the extrapolation procedure of Burchard‐Stockmayer‐Fixman. This evaluation of the unperturbed chain dimension in turn permits the calculation of the entanglement molecular weight and the plateau modulus via the packing length model. This allows the determination of rheological properties for these materials where conventional rheology measurements are difficult, or impossible.[η]‐M data for PHNB in THF at 35 °C.magnified image[η]‐M data for PHNB in THF at 35 °C.

Influence of Syndiotactic Propylene Units on the Rheological Parameters of Poly(ethylene−propylene) Copolymers

The plateau modulus has been measured for a trio of amorphous poly(ethylene−propylene) copolymers where the mole fraction of ethylene ranged from 0.57 to 0.67. These materials were prepared by using a living catalyst system involving bis(salicylaldiminato)titanium activated by methylaluminoxane. This catalyst with propylene yields highly syndiotactic (rr = 0.98; rrrr = 0.96) homopolymer. s-Polypropylene is known to have a plateau modulus and unperturbed chain dimension that are markedly larger than the values shared by the atactic and isotactic counterparts. The enhancement in the unperturbed chain dimension translates into an entanglement molecular weight for s-polypropylene that is ∼1/3 that of the atactic and isotactic counterparts. Thus, within the confines of the packing length notion, these empirical observations raise the question as to whether the rheological characteristics of the s-polypropylene will carry over into the random copolymer format. The copolymers with s-polypropylene segments yield ...

Fundamental solution and single‐chain properties of polylactides

AbstractPolylactides (PLA) have been known for several decades and are recently of considerable commercial significance. However, the literature on basic chain properties and solution characterization is divided and inconsistent. In this study, a comprehensive and well‐controlled set of experiments is combined with rigorous quantitative analysis to resolve existing apparent contradictions. Homopolymers and copolymers spanning wide ranges of molecular weight and stereoisomer proportions were prepared by ring‐opening polymerizations of L‐ and D‐lactides using stannous octanoate as the catalyst. Samples were characterized by means of: (1) dilute‐solution viscometry in three different solvents; (2) size exclusion chromatography in tetrahydrofuran (THF) with light scattering detection; (3) static multiangle light scattering in a mixed acetonitrile–dichloromethane solvent; (4) variable‐angle spectroscopic ellipsometry; and (5) melt rheology. The data imply that PLA are typical linear flexible polymers; unperturbed PLA chain dimensions are describable in terms of a characteristic ratio of 6.5 ± 0.9, regardless of stereoisomer content. The Schulz‐Blaschke and Mark‐Houwink constants for dilute PLA solutions in chloroform and in THF are determined. For chloroform at 30°C, the correct values are kSB = 0.302, K = 0.0131 (mL/g), and a = 0.759, while for THF at 30°C, the correct values are kSB = 0.289, K = 0.0174 (mL/g), and a = 0.736. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3100–3111, 2005

Thermorheological Properties of Hydrogenated Pseudorandom Styrene−Butadiene Copolymers

Rheological properties of amorphous hydrogenated styrene−butadiene copolymers (HSBC) were investigated. The structure corresponds to styrene−ethylene−1-butene terpolymers. Entanglement molecular weights (Me) of 2380−3270 g/mol were obtained at 50 °C for HSBCs containing 49.5−68.9 wt % of styrene. These values were closer to polyethylene rather than polystyrene. The vertical shift factor, bT, showed quite different temperature dependence from the classical expression of bT = ρT/ρ0T0, where ρ and ρ0 are the densities at temperature T and a reference temperature T0, respectively. This had also been observed in poly(ethylene-co-1-butene) and could be attributed to the temperature coefficient of unperturbed polymer chain dimension, κ = d ln 〈R2〉0/dT, by using the packing model. The temperature dependence of bT indicated the temperature dependence of Me for HSBCs. The Me at 140 °C were estimated as 3100−4200 g/mol for HSBCs containing 49.5−68.9 wt % of styrene, which was about 30% higher than at 50 °C. Plateau ...

On the rheology of ethylene-octene copolymers

It has previously been shown that the plateau modulus, G N p , and thus the entanglement molecular weight, M e, of flexible polymers can be correlated to the unperturbed chain dimension, <R 2>o/M, and mass density, ρ, via the use of the packing length, p. For polyolefins, a method was recently proposed whereby knowledge of the average molecular weight per backbone bond, m b, allows <R 2>o/M and consequently G N o and M e to be estimated. This is particularly valuable for polyolefin copolymers since the melt chain dimensions are often unknown. This work corroborates these theoretical predictions by studying the rheology of a series of carefully synthesized ethylene/octene copolymers with varying octene content (19–92 wt%). Furthermore, the results reported herein also allow the advancement of rheological characterization techniques of polymer melts. For instance, based on the analysis of the linear viscoelastic properties of these copolymers, it has been found that several rheological parameters scale with the copolymer comonomer content. Analysis of the viscoelastic material functions in terms of the evolution of the phase angle, δ, as a function of the absolute value of the complex modulus, |G*|, (the so-called van Gurp-Palmen plots), provides a fast and reliable rheological means for determining the composition of ethylene/α-olefin copolymers. The crossover parameters, G co(=G′=G″) and gco(=1/ω co) also scale with copolymer composition.

Unmixing of Polymer Blends Confined in Ultrathin Films: Crossover between Two-Dimensional and Three-Dimensional Behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 </= N </= 256 effective monomers per chain) and film thicknesses (2 </= D </= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt densities there are pronounced "correlation hole effects", in particular for the smaller values of D. Also the components of the radius of gyration and end-to-end distance parallel and perpendicular to the confining walls are analyzed and their scaling behavior is studied. Evidence is presented that for strictly two-dimensional polymers (as occur for D = 2) the average number of intermolecular contacts scales with chain length N as z(c) proportional, variant N(-3/8) and therefore the critical temperature scales as T(c) proportional, variant N(5/8), whereas for values of D that exceed the excluded volume screening length, z(c) remains nonzero for N --> infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.