Intrinsic Viscosity of Wormlike Chains. Determination of the Shift Factor

Yamakawa, Hiromi; Fujii, Masanori

doi:10.1021/ma60037a024

Cited by 601 publications

(268 citation statements)

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“…Previously, 9 [] data of CTC in THF at 25 C were analyzed by using the theory of Yamakawa, Fujii, and Yoshizaki for the wormlike cylinder model [27][28][29] combined with the quasi-two-parameter theory [29][30][31] for the intramolecular excluded-volume effect to obtain the following wormlike-cylinder parameters: the persistence length q ¼ 10: 5 nm, the molar mass per unit contour length M L ¼ 1110 nm À1 , the cylinder diameter d ¼ 2:2 nm, and the strength of the excludedvolume B ¼ 1:8 nm. The M L value in THF is close to that expected for the energetically stable conformation of the cellulosic chain.…”

Section: Resultsmentioning

confidence: 99%

Local Conformation of the Cellulosic Chain in Solution

Yanai

Sato

2006

Polym J

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ABSTRACT:The temperature and molecular weight dependencies of the intrinsic viscosity [] were investigated for cellulose tris(phenyl carbamate) (CTC) in tetrahydrofuran (THF). By the analysis of the [] data in terms of the wormlike cylinder model, the persistence length q of CTC was determined as a function of the temperature. With decreasing the temperature from 25 to À20 C, q increases from 10.5 to 13.7 nm. This temperature dependence of q was successfully explained by the broken wormlike chain model, where each glucose residue in the cellulosic chain is assumed to take left-handed 3/1 or 2/1 helical state and occasionally a kink state generated by a glucosidic bridge angle fluctuation. While the torsional fluctuation in each glucosidic bond is considerably small, there are two energetically favored helical (3/1 and 2/1) states, so that the cellulosic chain may not be regarded as a regular helix in solution. [DOI 10.1295/polymj.38.226] KEY WORDS Cellulose Derivative / Intrinsic Viscosity / Persistence Length / Broken Wormlike Chain / Local Conformation / Helicity of polymer chains plays important roles in chain rigidity, liquid crystallinity, and chiral discrimination. Recently, several synthetic polymers have been found to take more or less regular helical conformations in solution, and extensive arguments have been made on the relationship among their chemical structure, helicity, chain rigidity, liquid crystallinity, and cholesteric structure. Many review articles deal with recent advances in this subject. [1][2][3][4][5] Cellulose derivatives are known as semiflexible polymers exhibiting liquid crystallinity 6,7 and important materials in chiral chromatography.8 These features imply helical nature in the cellulosic chain. Conformations of cellulose derivatives in solution were studied both experimentally and theoretically for a long time. However, as mentioned in a previous paper, 9 their conformational analysis was not an easy task because both chain stiffness and excluded volume effect must be taken into account simultaneously due to their intermediate chain rigidity. Only recent literature provides proper analyses for the conformation of cellulosic chains 9,10 and also for solution properties (e.g., liquid crystallinity, 11 viscosity, 12 and diffusivity 13 ) based on the properly analyzed conformation. On the other hand, theoretical studies on the conformation of the cellulosic chain were carried out by Brant et al.14-17 in 1970s, who made an extensive conformational energy analysis and found two energetically stable conformations implying left-handed 3/1 and 2/1 helices for the cellulosic chain. However, the characteristic ratio C 1 and its temperature dependence estimated from their conformational energy did not satisfactorily agree with experimental results for cellulose derivatives. 15,16 The disagreement was argued occasionally afterward, 17,18 but satisfactory explanation has not been made yet. Thus, the local conformation of the cellulosic chain is still unclear.In this study, we have revisited...

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Section: Resultsmentioning

confidence: 99%

Local Conformation of the Cellulosic Chain in Solution

Yanai

Sato

2006

Polym J

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“…10 For a more rigid chain, 11 l p can be indirectly estimated from the intrinsic viscosity ([η] θ ). 12 Also note that the developments of electron microscopy 13,14 and AFM [15][16][17] lead to some direct measurements of l p in terms of the conformation change and the force required to extend a polymer chain. It should be emphasized that a combination of the magnetic tweezer and hydrodynamic force can also be used to measure the weaker entropy elasticity of a long and more rigid DNA chain.…”

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confidence: 99%

How Much Force Is Needed To Stretch a Coiled Chain in Solution?

Jin

et al. 2009

Macromolecules

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In the 1970s, de Gennes and Pincus 1,2 used the Rouse model 3 to show that linear polymer chains in a good solvent could undergo a first-order coil-to-stretch transition to pass through a pore much smaller than its coiled size under an elongation flow field with a sufficient hydrodynamic force, independent of both the chain length and the pore size. Namely, a coiled polymer chain can pass through a small pore as long as the flow rate (q) is higher than a threshold [q c = k B T/(3πη)], where k B , T, and η is the Boltzmann constant, the absolutely temperature, and the solvent viscosity, respectively.On the other hand, it has been suggested that the electrostatic blob model for a polyelectrolytes chain would also be applicable for the coil-to-stretch transition of a neutral chain in an ultrafiltration experiment. 4,5 In principle, the stretching of a neutral chain under an elongational flow and the extension of a polyelectrolyte chain under the electrostatic repulsion have a similar physical nature, but not identical. Namely, a neutral chain can be stretched as a string of blobs under an elongational flow. The blob size decreases as the shear rate increases. Finally, each blob can be fully stretched with a sufficiently strong shear force.It is not difficult to realize that the passing through a small pore occurs only when the blob size (ξ b ) of a stretched chain in a flow filed is smaller than the pore size (D). Therefore, the critical flow rate is associated with the relative size of the blob to the pore. Whether a coiled chain can pass through a small pore is related to its local deformability, i.e., the entering of the first blob into the pore, at which the entropic confinement force (k B T/D) is overcame by the hydrodynamic force (3πηq c /D), where it has assumed that each blob is a nondraining ball with a diameter identical to the pore size (D). 1,2 Note that here only the short-range interaction is relevant. In principle, one can reversibly use q c to characterize the local deformability. To our knowledge, the predicted chain-length and pore-size independence of q c has not been confirmed in experiments because such a first-order coil-tostretch transition has not been observed for a long time. Recently, we have observed such a discontinuous first-order transition by ultrafiltrating linear polystyrene chains through specially constructed small pores (20 nm). 6

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“…Substitution of Equation (2) into a relationship derived by Yamakawa 75 for the overall persistence length led to Equation (3), which was the final model for polyelectrolytes in solution containing added low molar mass salt. In Equation (3) η intrHS is the intrinsic viscosity without electrostatic influence (achieved at high added salt concentrations), M is the polymer molecular weight, m o is the average molecular weight of a monomer unit, and l m is the length of a monomer unit.…”

Section: Polyelectrolyte Solution Theorymentioning

confidence: 99%

“…The method for determining η intrHS was previously described. 78 In order to determine the value of Φ at each real solution condition, calculations were performed using the Yamakawa-Fujii theory 75 . An iterative routine was employed in which the solution intrinsic viscosity at each condition, along with the theoretical value of the Flory-Fox factor, Φ o = 2.86 x 10 23 , was inserted into Yamakawa's equation relating intrinsic viscosity to polymer persistence length.…”

Section: Polyelectrolyte Solution Theorymentioning

confidence: 99%

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For Stimul-Responsive Polymers With Enhanced Efficiency in Reservoir Recovery Processes

McCormick

Hester²

2004

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This report contains a series of terpolymers containing acrylic acid, methacrylamide and a twin-tailed hydrophobic monomer that were synthesized using micellar polymerization methods. These polymer systems were characterized using light scattering, viscometry, and fluorescence methods. Viscosity studies indicate that increasing the nonpolar character of the hydrophobic monomer (longer chain length or twin tailed vs. single tailed) results in enhanced viscosity in aqueous solutions. The interactions of these polymers with surfactants were investigated. These surfactants include sodium dodecyl sulfate (SDS), cetyl trimethylammonium bromide (CTAB), Triton X-100. Viscosity measurements of DiC 6 AM and DiC 8 AM mixtures indicate little interaction with SDS, gelation with CTAB, and hemimicelle formation followed by polymer hydrophobe solubilization with Triton X-100. The DiC 10 Am terpolymer shows similar interaction behavior with CTAB and Triton X-100. However, the enhanced hydrophobic nature of the DiC 10 polymer allows complex formation with SDS as confirmed by surface tensiometry. Fluorescence measurements performed on a dansyl labeled DiC 10 Am terpolymer in the presence of increasing amounts of each of the surfactant indicate relative interaction strengths to be CTAB>Triton X-100>SDS.A modified model based on Yamakawa-Fujii and Odjik-Skolnick-Fixman theories was found to describe the contribution of electrostatic forces to the excluded volume of a polyelectrolyte in solution. The model was found to be valid for flexible polymer coils in aqueous salt solutions where intermolecular interactions are minimal. The model suggested that a dimensionless group of parameters termed the dimensionless viscosity should be proportional to the dimensionless ratio of solution screening length to polyion charge spacing. Several sets of experimental data from the literature and from our laboratory have been analyzed according to the model and the results suggest that the two dimensionless groups are indeed related by a universal constant. This model has identified the parameters that are important to fluid mobility, thereby revealing methods to enhance solution performance when using polyions solutions as displacing fluids in oil reservoirs. 5 EXECUTIVE SUMMARYTo date, our synthetic research efforts have been focused on the development of stimuli-responsive water-soluble polymers designed for use in enhanced oil recovery (EOR) applications. These model systems are structurally tailored for potential application as viscosifiers and/or mobility control agents for secondary and tertiary EOR methods. The goal of previous synthetic work has been to design novel polymers that exhibit large dilute solution viscosities in the presence of the adverse conditions normally encountered in oil reservoirs (such as high salt concentrations, the presence of multivalent ions, and elevated temperatures). The polymers are also designed to have "triggerable" properties that can be elicited by external stimuli, such as changes in pH and/or sal...

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Intrinsic Viscosity of Wormlike Chains. Determination of the Shift Factor

Cited by 601 publications

References 8 publications

Local Conformation of the Cellulosic Chain in Solution

Local Conformation of the Cellulosic Chain in Solution

How Much Force Is Needed To Stretch a Coiled Chain in Solution?

For Stimul-Responsive Polymers With Enhanced Efficiency in Reservoir Recovery Processes

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