Wormlike Model Research Articles

Effects of Hydrophobic Chain Length on the Characteristics of the Micelles of Octaoxyethylene Tetradecyl C14E8, Hexadecyl C16E8, and Octadecyl C18E8Ethers

Size, shape, and flexibility of micelles of octaoxyethylene tetradecyl C(14)E(8), hexadecyl C(16)E(8), and octadecyl C(18)E(8) ethers in dilute aqueous solutions were determined at finite surfactant concentrations c by static light scattering (SLS) and dynamic light scattering experiments at several temperatures T below the critical points. The SLS results were successfully analyzed with the aid of the thermodynamic theory formulated with wormlike spherocylinder model for SLS of micelle solutions. The analysis yielded the molar mass M(w) of the micelles as a function of c and the cross-sectional diameter d. The hydrodynamic radius R(H) and the radius of gyration S(2)(1/2) of the micelles as functions of M(w) were found to be also well-described by the corresponding theories for the wormlike spherocylinder or wormlike chain models. The results of the stiffness parameter lambda(-1) have revealed that the micelles are far from rigid rods but rather stiff compared with typical flexible polymers and they grow in size with increasing T to greater length for longer hydrophobic chains, i.e., alkyl groups of the surfactants. As the alkyl group becomes longer, the d value increased, while the spacings s between adjacent hexaoxyethylene chains on the micellar surface were found to remain substantially constant.

Effects of Hydrophilic Chain Length on the Characteristics of the Micelles of Pentaoxyethylene n-Decyl C10E5 and Hexaoxyethylene n-Decyl C10E6 Ethers

Wormlike micelles of nonionic surfactants pentaoxyethylene decyl ether C(10)E(5) and hexaoxyethylene decyl ether C(10)E(6) in dilute aqueous solutions were characterized by static (SLS) and dynamic light scattering (DLS) experiments at several temperatures T below the critical points. The SLS results were analyzed with the aid of the molecular thermodynamic theory for SLS from micelle solutions formulated with the wormlike spherocylinder model, thereby yielding the molar mass M(w) of the micelles as a function of c and the cross-sectional diameter d of 2.6 nm for both C(10)E(5) and C(10)E(6) micelles. It has been found that the micelles grow in size with increasing c and T, following the relation M(w) proportional, variant c(1/2) in conformity with the theoretical prediction for highly extended polymerlike micelles. The hydrodynamic radius R(H) of the micelles as a function of M(w) was found to be also well described by the corresponding theories for the wormlike spherocylinder model. The results of the stiffness parameter lambda(-1) show that both micelles are rather stiff compared with those formed with other polyoxyethylene alkyl ethers C(i)E(j) but far from rigid rods. The values of the spacing s between two adjacent hexaoxyethylene chains on the micellar surface were found to be substantially the same for both micelles.

Radius of Gyration of Polystyrene Combs and Centipedes in a ϑ Solvent

The molecular weight dependence of the radii of gyration R{sub g} in a {var_theta} solvent (trans-decalin) of one regular branched comb and three regular centipede polystyrenes was studied using a gel permeation chromatography system equipped with a two-angle light scattering detector and a refractive index detector. R{sub g} in trans-decalin for each sample of particular molecular weight was about 25% smaller than that in a good solvent (tetrahydrofuran, THF). On the other hand, they are 20--40% larger than the theoretical values from the Gaussian chain model. This difference can be explained with the wormlike comb model developed by Nakamura et al. (Macromolecules 2000, 33, 8323-8328). Persistence lengths thus obtained for each sample were about half of that determined in THF solution. However, they are significantly larger than that for linear polystyrene. These results suggest that a main chain stiffening effect exists in comb polystyrenes even in a {var_theta} solvent.

Light-Scattering Characterization of the Wormlike Micelles of Hexaoxyethylene Dodecyl C12E6 and Hexaoxyethylene Tetradecyl C14E6 Ethers in Dilute Aqueous Solution

The size, shape, and flexibility of hexaoxyethylene dodecyl ether C12E6 micelles and hexaoxyethylene tetradecyl ether C14E6 micelles in dilute aqueous solutions were determined at finite surfactant concentrations, c, by static (SLS) and dynamic light scattering (DLS) experiments at several temperatures T below the critical points. The SLS results were successfully analyzed with the aid of the thermodynamic theory for SLS from micelle solutions formulated with the wormlike spherocylinder model. The analysis yielded the molar mass Mw of the micelle as a function of c and the cross-sectional diameter d of 2.3 nm for the C12E6 micelles and 2.4 nm for the C14E6 micelles. It has been found that micelles grow in size with increasing c and T, following the relation Mw ∝ c1/2. The hydrodynamic radius RH and the radius of gyration 〈S2〉1/2 of the micelles as functions of Mw were found also to be well described by the corresponding theories for the wormlike spherocylinder and wormlike chain models, respectively. The results of the stiffness parameter λ-1 have shown that both micelles are far from rigid rods but rather stiff compared with typical flexible polymers. It has been revealed that the C14E6 micelles grow in size to a much greater length than the C12E6 micelles, presumably because of the thermodynamic reason that attractive interactions among C14E6 molecules are much stronger than those among C12E6 molecules as embodied by the values of the free-energy parameter g2, reflecting the difference in the hydrophobic chain length. The values of d and the spacings s between two adjacent hexaoxyethylene chains on the micellar surface were found to be substantially the same for both of the micelles.

Isotropic−Cholesteric Phase Equilibrium in Solutions of Cellulose Tris(phenyl carbamate)

The isotropic−cholesteric phase boundary concentrations and interfacial tension were measured for tetrahydrofuran (THF) solutions of fractionated cellulose tris(phenyl carbamate) (CTC) samples. The phase boundary concentrations are compared with the scaled particle theory for the hard wormlike spherocylinder model as favorably as those for other stiffer polymer systems, though the theory does not consider effects of the intramolecular excluded-volume and intermolecular multiple contacts, both of which are appreciable for high molecular weight CTC samples. This may be due to cancellation of the two effects in the isotropic−cholesteric phase equilibrium. The interfacial tension γ between the coexisting isotropic and cholesteric phases for the CTC−THF system slightly decreases with molecular weight, and the asymptotic value is higher than those of other stiffer polymer systems. The dependence of the asymptotic γ on the persistence length is consistent with Cui et al.'s theory based on the second virial approximation, but its magnitude is much larger than the prediction of the theory, indicating that higher virial terms in thermodynamic quantities play a significant role in γ.

A Helix in Helices: A Helical Conjugated Polymer That Has Helically Arranged Hydrogen-Bond Strands

The secondary structure of Rh-based stereoregular cis-poly(N-propargylamides) was proposed on the basis of the UV−vis, CD, and IR spectra, the wormlike touched-bead model theory, and a semiempirical molecular orbital calculation. The IR spectra demonstrated the formation of well-ordered intramolecular hydrogen bonding between the pendant amide groups. The relatively red-shified absorption and the intense CD effects indicate that the main chain twists only slightly from coplanarity to exist in a helical conformation with a large helix pitch. Analyzing the intrinsic viscosity of a polymer, (±)-poly(N-propargyl-2-ethylhexanamide), on the basis of the wormlike touched-bead model theory, showed a large helix pitch per monomer unit (h, 0.2 nm), which also supports the above characteristics that the main chain loosely twists. A semiempirical calculation with the AM1 method showed that the helical conjugated backbone is surrounded by two helically arranged hydrogen-bond strands.

Polymer-like structure of lecithin reverse micelles in the lecithin+water+cyclohexane system

The lecithin reverse micelles with and without containing water in cyclohexane at 25.0 °C were characterized by static (SLS) and dynamic light scattering (DLS) experiments. The molar mass M 0 and hydrodynamic radius R H 0 of the micelle determined at infinite dilution have increased with increasing water content W 0, demonstrating that the micelles grow in mass and in size with water uptake into them. The values of R H 0 as a function of M 0 have been successfully analyzed with the use of the wormlike spherocylinder model. The results have revealed that the micelles with containing water assume a shape of rather flexible cylinders with the stiffness parameter λ −1=11.0 nm and the cross-sectional diameter d=5.2 nm. It is also found that the intermolecular distance between hydrophobic tails of two adjacent lecithin molecules on the micellar surface is about 1.2 nm without regard to water content W 0. The micellar growth with increasing lecithin concentration has also been found to occur accompanying the structural evolution by combining information from SLS and DLS results.

Hydrodynamic Conformation Properties of Poly(1-Trimethylsilylpropyne) Molecules Obtained on NbCl5 Catalyst

Hydrodynamic properties of 10 samples of poly(1-trimethylsilylpropyne) of various molecular weights, obtained with NbCl5 catalyst and containing 60-70% cis C = C bonds, were studied by sedimentation, translation diffusion, and viscometry techniques. The equilibrium rigidity of the polymer molecules was estimated from the viscometric data using the formalism of the intrinsic viscosity theory as applied to the worm-like coil model with excluded-volume effects. For the polymer macromolecules, the Kuhn segment length, thermodynamic parameter e, and hydrodynamic diameter of the chain d were estimated.

Conformation of Polystyrene Chain in Ultrathin Films Obtained by Spin Coating

This article reports a study of the chain conformation in thin films of amorphous polymer prepared by spin coating. Polystyrene chains of two molecular weights Mw, 230 000 and 660 000, are confined in layers of thickness equal to either 1000 A, thus greater than their unperturbed radii of gyration Rg, or 100 A, thus smaller than Rg. The form factor of the chain inside the layer is measured by small-angle neutron scattering. Changes of the scattering are observed as a function of the film thickness in the intermediate scattering vector range. We analyze the data in the frame of the wormlike model. In the 1000 A films, the chain has the same Gaussian conformation as in the bulk. In the films of 100 A, the persistence length of the chain is increased (compared to 9.2 A the value in the bulk) up to 45 A, for both Mw values. However, the corresponding scattering intensity is higher than expected for such an extended chain.

Estimation of conformational characteristics of bisphenol-A based poly(hydroxyethers)

Two samples of bisphenol-A based epoxy resins (poly(hydroxy ethers)) were fractionated by precipitation. The fractions were characterized by the weight-average molecular weight (1.3< M w×10 −3<40) and the intrinsic viscosity in tetrahydrofuran and chloroform. Theories based on the worm-like touched-bead model were used to treat the molecular-weight dependence of the intrinsic viscosity and to estimate the conformational characteristics (Kuhn statistical segment length l K, Flory characteristic ratio C ∞, and steric factor σ). Low values of these characteristics indicating rather high flexibility of the chain are discussed.

Physicochemical studies on xylinan (acetan). III. Hydrodynamic characterization by analytical ultracentrifugation and dynamic light scattering

A laboratory-made sample of the polysaccharide xylinan (acetan) has been further characterized with respect to (i) purity, (ii) molar mass and polydispersity, and (iii) gross conformation by a combination of hydrodynamic measurements (sedimentation velocity and equilibrium analytical ultracentrifugation, viscometry, and dynamic light scattering) in aqueous NaCl (I = 0.10 mol·L−1). Sedimentation velocity diagrams recorded using Schlieren optics revealed highly pure material sedimenting as a single boundary [so20.w = 9.5 ± 0.7) S; ks = (273 ± 112) mL/g]. The hypersharp nature of these boundaries is symptomatic of a polydisperse and highly nonideal (in the thermodynamic sense) system. Low speed sedimentation equilibrium in the analytical ultracentrifuge using Rayleigh interference optics and two different types of extrapolation procedure (involving point and whole-cell molar masses) gave a weight average molar mass Mw of (2.5 ± 0.5) × 10−6 g·mol−1 and also a second virial coefficient, B = (2.8 ± 0.7) × 10−4 mL·mol·g−2, both values in good agreement with those from light scattering-based procedures (Part II of this series). A dynamic Zimm plot from dynamic light scattering measurements gave a z-average translational diffusion coefficient Do20.w = (3.02 ± 0.05) × 10−8 cm2·s−1 and the concentration-dependence parameter kD = (370 ± 15) mL/g. Combination of so20.w with Do20.w via the Svedberg equation gave another estimate for Mw of ≅ 2.4 × 106 g/mol, again in good agreement. Both the Wales-van Holde ratio (ks/[η]) ≅ 0.4 (with [η] = (760 ± 77) mL/g) and the ρ-parameter (ratio of the radius of gyration from static light scattering to the hydrodynamic radius from dynamic light scattering) as ρ > 2.0 all indicate an extended conformation for the macromolecules in solution. These findings, plus Rinde-type simulations of the sedimentation equilibrium data are all consistent with the interpretation in terms of a unimodal wormlike coil model performed earlier. © 1996 John Wiley & Sons, Inc.

Molecular conformation of a polyaramid in nematic solution from small angle neutron scattering and comparison with theory

Zero-average contrast small angle neutron scattering measurements have been performed on an 11%(w/w) nematic aramid polymer (PPTA) solution in concentrated sulphuric acid. The radii of gyration parallel and perpendicular to the director were determined to be 250 and 70 Å, respectively, at room temperature. In addition, the temperature dependence of the radii of gyration was investigated. The values for the radii of gyration are compared to a worm-like path model for the polymer chain statistics where the segment orientation is described using a Maier–Saupe-type orientational distribution function. From this analysis, it is found that the persistence length of the aramid molecules is the same in the nematic phase as in a dilute isotropic phase, about 290 Å. We conclude that there is no effect of the nematic environment on the polymer chain statistics in this main chain polymer solution. As a consequence, the nematic phase of aramid solutions is expected to contain polymer chains with a substantial number of hairpin defects.

Diffusion Dynamics of Hairy-Rod Polymers in Concentrated Solutions

Photon correlation spectroscopy was employed in the polarized geometry in order to investigate the dynamics of solutions of substituted poly(p-phenylenes) at high concentrations. The total concentration fluctuations were found to exhibit a two-step decay. The fast dominant relaxation was the classical cooperative diffusion, controlled by the osmotic pressure of the system, exhibiting a stronger concentration dependence compared to flexible polymers, and discussed in the framework of the wormlike model. On the other hand, the second diffusive process was not related to self-diffusion (as confirmed by independent pulsed field gradient NMR measurements) and could not be accounted for by the existing theories. The self-friction coefficient was found to exhibit a stronger concentration dependence than the cooperative friction coefficient. At high concentrations, a diffusive cluster process was detected, despite the high solubility of these polymers in different solvents. The characteristics of this mode depend...

Estimation of the Persistence Length of Polymers by MD Simulations on Small Fragments in Solution. Application to Cellulose

A procedure is described to estimate the persistence length and related properties of a persistent polymer by MD simulations of a small fragment, including solvent effects. The procedure is applied to cellulose in aqueous solution, which leads to an upper limit of the persistence length of 145 ± 10 Å. The occurrence of small amounts of folded conformations seems to be indicated by comparison of the theoretical with experimental data. The behavior of the cellulose chain is consistent with the Kratky−Porod wormlike model.

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.

Physicochemical studies on xylinan (acetan). III. Hydrodynamic characterization by analytical ultracentrifugation and dynamic light scattering

A laboratory-made sample of the polysaccharide xylinan (acetan) has been further characterized with respect to (i) purity, (ii) molar mass and polydispersity, and (iii) gross conformation by a combination of hydrodynamic measurements (sedimentation velocity and equilibrium analytical ultracentrifugation, viscometry, and dynamic light scattering) in aqueous NaCl (I = 0.10 mol·L−1). Sedimentation velocity diagrams recorded using Schlieren optics revealed highly pure material sedimenting as a single boundary [so20.w = 9.5 ± 0.7) S; ks = (273 ± 112) mL/g]. The hypersharp nature of these boundaries is symptomatic of a polydisperse and highly nonideal (in the thermodynamic sense) system. Low speed sedimentation equilibrium in the analytical ultracentrifuge using Rayleigh interference optics and two different types of extrapolation procedure (involving point and whole-cell molar masses) gave a weight average molar mass Mw of (2.5 ± 0.5) × 10−6 g·mol−1 and also a second virial coefficient, B = (2.8 ± 0.7) × 10−4 mL·mol·g−2, both values in good agreement with those from light scattering-based procedures (Part II of this series). A dynamic Zimm plot from dynamic light scattering measurements gave a z-average translational diffusion coefficient Do20.w = (3.02 ± 0.05) × 10−8 cm2·s−1 and the concentration-dependence parameter kD = (370 ± 15) mL/g. Combination of so20.w with Do20.w via the Svedberg equation gave another estimate for Mw of ≅ 2.4 × 106 g/mol, again in good agreement. Both the Wales-van Holde ratio (ks/[η]) ≅ 0.4 (with [η] = (760 ± 77) mL/g) and the ρ-parameter (ratio of the radius of gyration from static light scattering to the hydrodynamic radius from dynamic light scattering) as ρ > 2.0 all indicate an extended conformation for the macromolecules in solution. These findings, plus Rinde-type simulations of the sedimentation equilibrium data are all consistent with the interpretation in terms of a unimodal wormlike coil model performed earlier. © 1996 John Wiley & Sons, Inc.

Partitioning of proteins between an aqueous solution and a weakly-ionizable polyelectrolyte hydrogel

To predict partitioning of proteins between a temperature- and pH-sensitive hydrogel and its surrounding aqueous solution, it is appropriate to use Schnitzer's method for determining solute partitioning based on size exclusion and the cell model for polyelectrolyte solutions. The mean-pore size of the hydrogel is calculated using the method of Peppas et al. The charge of the network, which depends on pH and salt concentration, is calculated using weak-polyelectrolyte-titration theory. De Gennes' scaling relation and Odijk's wormlike model are used to determine the persistence length and the radius of gyration of the polyelectrolyte chain in the hydrogel. For N-isopropylacrylamide gels copolymerized with sodium acrylate or 2-dimethylaminoethyl methacrylate, predicted partition coefficients for cytochrome-C are in semiquantitative agreement with experiment.

Molecular Characteristics of Poly(methacrylamidod-Glucose)1

Abstract The fractions of poly(methacrylamido D-glucose) with molecular weights 7< M·10-4< 550 have been studied in water by the methods of molecular hydrodynamics. Kuhn-Mark-Houwink equations were obtained. The hydrodynamic invariant and the sedimentation parameter were also calculated. The equilibrium rigidity and the hydrodynamic diameter of molecules modeling macromolecules in solution were evaluated on the basis of the theory of the wormlike necklace model with the effects of excluded volume taken into account at different values of the excluded-volume parameter. The effect of fraction polydispersity on the quantitative values of exponents in the equations of the Kuhn-Mark-Houwink type and the Kuhn segment length is discussed.

Orientation-Dependent Interactions in Polymer Systems. 5. Thermotropic Liquid Crystalline Transition of Tri-O-heptylcellulose

Fairly narrow fractions of tri-O-heptylcellulose (THC) covering a wide range of degrees of polymerization (DP) were prepared and studied by viscometry and light scattering to determine the wormlike model parameters of the polymer to be q= 43.2 exp(-0.0050T) nm and M L = 880 nm -1 , where q is the persistence length, M L is the shit factor, and T is the absolute temperature. The same fractions were studied with their thermal properties to determine the anisotropic-isotropic transition temperature T i and transition entropy ΔS as a function of DP. Both T i and ΔS increased with increasing DP to approach a limiting value for large enough DP. These trends were favorably compared with the predictions of the statistical models with the above-noted parameter values. It was shown that the main factor that causes the thermotropic transition and the chain-length dependence of T i in bulk THC is the temperature-dependent flexibility of the polymer

DNA Extension under the Action of an External Force

We computed the extension-force dependence for the wormlike model of a polymer chain. The dependence that we obtained differs essentially from the corresponding well-known dependence for the freely jointed chain when the extension exceeds half of the chain contour length. We used the computed results to analyze the measurements of extension of individual DNA molecules under the action of force made recently (Smith, S. B.; Finzi, L.; Bustamante, C. Science 1992,258, 1122). We took into account the electrostatic interaction between DNA segments for a very low salt concentration. The theoretical dependencies obtained are in very good agreement with the experimental data