Mark Houwink Sakurada Research Articles

Molecular Weight Distributions in Coupled Polymers UsingZ-Transform

A study of end-to-end coupling reactions of bifunctional linear prepolymers of the Schulz–Flory type is presented by use of Z-transform. The application of Z-transform allows one to derive exact expressions for the change of molecular weight distributions in dependence of the progress of the coupling reaction. After coupling the distribution is also of Schulz–Flory type, however, it depends in a relatively complicated manner on the extent of reaction of the prepolymer and on the extent of the coupling reaction. Further expressions are derived for various dependencies including the influence of the extent of coupling on the average molecular weights, chain lengths, and polymolecularity. By implementation of the Mark–Houwink–Sakurada equation, a correlation between intrinsic viscosity and the progress of coupling reaction is shown.

Rheological properties of poly(trimethylene 2,6-naphthalenedicarboxylate) melts

The rheological properties of poly(trimethylene naphthalene-2,6-dicarboxylate) (PTN) were studied using a dynamic stress rheometer with oscillatory parallel plates. The influence of temperature and molecular weight on the storage modulus, loss modulus, and complex viscosity was investigated. It was possible to express the temperature dependence of the shift factors aT with the Arrhenius equation; the activation energy was found to be 85kJ/mol. A comparison of molecular weight determined: (a) by rheological measurements and (b) by Mark–Houwink–Sakurada equation showed excellent agreement.

The rheological and structural behavior of silylcellulosics derivatives

AbstractThe trimethylsilylcellulose (TMSC) samples were characterized in solution by osmometry, viscometry, and gel permeation chromatography. The Mark‐Houwink‐Sakurada (M‐H‐S) equation coefficients were determined in chloroform, 1,1,1‐trichloroethane, and o‐xylene, in all cases the exponent “a” being higher than unit, this indicating a great stiffness of the macromolecules in solution. Also, the temperature dependence of the limiting viscosity number and M‐H‐S coefficients respectively for TMSC in o‐xylene were studied. The exponent from M‐H‐S equation is also higher than unit, and increases linearly with the temperature. The GPC studies indicates a relative high polydispersity of the studied samples; the polydispersity index being situated between 2 and 3. The change of the crystalline structure as the result of silylation reaction was evidenced, the crystallinity of silyl derivatives depending on the substitution degree (DS), and the molecular weight. The viscous flow parameters for dilute solutions of trimethylsilylcellulose in o‐xylene were determined in the temperature range 30–70°C. The temperature dependence of the dynamic viscosity of the solutions obeys an Arrhenius‐type equation in which the apparent activation energy is linearly dependent on both the solution's concentration and molecular weight. For preexponential factor no significant dependence on concentration and molecular weight was found. This behavior was attributed to the very great stiffness of the macromolecular chains. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2277–2285, 2001

A novel method for estimating unperturbed dimension [ η] θ of polymer from the measurement of its [ η] in a non-theta solvent

A novel method based on the Einstein’s viscosity equation modified by Guth–Simha–Gold and the model on concentration dependence of polymer chain dimension proposed in our previous study has been developed to estimate the unperturbed dimension, [ η] θ , of a polymer (i.e., the intrinsic viscosity at theta conditions) from the measurement of the intrinsic viscosity, [ η], at non-theta conditions only. The [ η] θ values obtained in present method for polystyrene, poly(oxyethylene), poly(methyl methacrylate), poly(vinyl chloride) and poly(isobutene) are good consistent with their experimental values at theta conditions or with their calculated values according to Mark–Houwink–Sakurada equation at theta conditions by the aid of their K θ and molecular weight.

Anionic polymerization of octamethylcyclotetrasiloxane in miniemulsion II. Molar mass analyses and mechanism scheme

Hydroxyl α,ω-functionalized polydimethylsiloxane (PDMS) standards have been synthesized by ring-opening anionic polymerization of octamethylcyclotetrasiloxane (D4)11The notation for the siloxane oligomers throughout the paper is the following: M holds for (CH3)3SiO1/2–, Mv for CH2CHSi(CH3)2O1/2–, MOH for HOSi(CH3)2O1/2– and D for –Si(CH3)2O–. in miniemulsion. Their absolute molar masses as well as Mark–Houwink–Sakurada parameters were then estimated in toluene at 30°C by triple detection size exclusion chromatography (SEC3). MALDI-TOF confirmed the SEC3 results in addition to providing several clues on chain microstructure and evidence of redistribution reactions. Trimethyl and vinyl α,ω-terminated PDMS oligomers were similarly synthesized in miniemulsion in the presence of functional transfer agents and used together with small dihydroxylated PDMS standards to compare the effect of substituents on the SEC calibration curve. Precise measurement of average molecular weights showed that the existing kinetics model could not account solely for mass control below 70% conversion. A thermodynamic explanation is then proposed where the molar mass control is exerted by the surface activity of the chains which drives their reactivity. Small chains rapidly propagate and backbite at the interface. Once the chains reach a critical DP corresponding to their loss of surface tension activity, they penetrate into the particles where side reactions such as redistribution and condensation hardly occur.

Characterization of METHOCEL cellulose ethers by aqueous SEC with multiple detectors

Initial evaluation of a multiple-detector, aqueous SEC technique has shown:•that it is capable of high precision and accuracy;•applicability to the analyses of METHOCEL cellulose ethers;•ability to generate consistent values of RgW, IVW, M̄W,M̄N and polydispersity;•ability to generate dependable Mark–Houwink–Sakurada parameters.Cellulose ethers in this study were commercial products, used ‘as received’, solutions were not dialyzed, corrections were not made for salt content or moisture content and batches were not specially selected. The robustness, convenience and reproducibility of the technique are impressive.

Synthesis, characterization, and crosslinking of novel stars comprising eight poly(isobutylene-azeotropic-styrene) copolymer arms with allyl or hydroxyl termini. II. Stars of eight isobutylene/styrene azeotropic copolymer arms emanating from a calix[8]arene core

Our objective was the precision synthesis of novel stars consisting of a well-defined calix[8]arene core out of which radiate eight poly(isobutylene-aze-styrene) [P(IB-aze-St)] arms fitted with crosslinkable end groups. We reached our objective by preparing the octafunctional calixarene derivative C[8]OCH3, inducing the living azeotropic copolymerization of IB/St charges with the C[8]OCH3/BCl3·TiCl4 initiating system, and end-quenching living IB/St copolymerizations with allyltrimethylsilane. With this strategy, we obtained stars C[8][P(IB-aze-St)CH2CHCH2]8 of various molecular weights. The number of CH2CHCH2 termini of the arms was 8.0 ± 0.2 by quantitative 1H NMR analysis. The eight allyl termini were quantitatively converted to CH2CH2CH2OH termini by hydroboration/oxidation. To confirm that the latter second-generation stars possessed eight primary alcohol end groups, we quantitatively converted the CH2OH termini to OSi(CH3)3 termini, the concentration of which was quantitated by 1H NMR spectroscopy. According to this analysis, the stars contained 8.0 ± 0.3 hydroxyl termini. The glass-transition temperatures of the P(IB-aze-St) arms increased from 59 to 65 °C as the weight-average molecular weights of the arms increased from about 2500 to about 4300 g/mol, respectively. The α and K constants of the Mark–Houwink–Sakurada relationship and the intrinsic viscosity of a representative allyl-telechelic star were determined and compared with a linear azeotropic IB/St copolymer of similar molecular weight. The crosslinking of C[8][P(IB-aze-St)CH2CH2CH2OH]8 stars with 4,4′-methylene bis(phenyl) diisocyanate and 2,4-tolylene diisocyanate in various solvents afforded tightly crosslinked films of potential interest for scratch-resistant coatings, mar-resistant coatings, or both. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1525–1532, 2001

Chain Transfer in the Sulfur-Centered Free Radical Ring-Opening Polymerization of 3-Methylene-6-methyl-1,5-dithiacyclooctane

3-Methylene-6-methyl-1,5-dithiacyclooctane (MDTO, 1) was polymerized in both the presence and absence of a number of chain transfer agents, viz. 1-butanethiol (BuSH), dibutyl disulfide (BuSSBu), and dibutyl sulfide (BuSBu). Mark−Houwink−Sakurada (MHS) constants for poly(MDTO) were found to be K = 23 × 10-5 dL g-1 and α = 0.67. Using these parameters, chain transfer constants were obtained at 60 °C and are reported as 0.13 (BuSH), 0.19 (BuSSBu), and 0.0025 (BuSBu). These values are compared to the corresponding chain transfer constants obtained for styrene (STY) and methyl methacrylate (MMA). Subsequently, the chain transfer activity was measured over a range of temperatures (40−80 °C), and Arrhenius parameters were determined. Significant differences in chain transfer activity between carbon- and sulfur-centered radicals were observed. In addition, the extent of transfer to monomer was determined across the range of temperatures 40−100 °C, yielding a value for CM of 55 × 10-4 at 60 °C. The likely extent o...

A new relation between the intrinsic viscosity and the molecular mass of polymers derived from the blob model: determination of the statistical segment length of flexible polymers

Using the relation between the unperturbed dimensions parameter on one hand and the intrinsic viscosity and the statistical segment length of the polymers on the other, as predicted by the two-parameters theory, we have modified Han's equation [Polymer, 20 (1979) 1083], which is derived from the blob theory. According to the proposed equation, plotting [η]/M1/2 versus M3ν−1.5, where ν is the exclude volume index, we obtain straight lines from the slopes of which we calculate the statistical segment length of flexible polymers. The value of ν is obtained from the value of the exponent of the Mark–Houwink–Sakurada equation. The proposed method is useful in the high molecular mass region in which the Stockmayer–Fixman–Burchard equation is not valid.

Effect of H-bond active sites on transport properties of poly(ethylene oxide) dissolved in its monomers: Shear viscosity and diffusion coefficient studies

The possibility of dissolving poly(ethylene oxide) [PEO:H–(O–CH2–CH2)n–OH] in its monomeric liquid ethylene glycol [EG:H–(O–CH2–CH2)–OH] represents the only way to verify the complex polymer–monomer interactions, through the OH end groups, resulting in the scaling law R∝Nν. We report viscosity results, in conjunction with photon correlation spectroscopy data, on different molecular weight PEO samples, in a wide range of concentrations, dissolved in EG. In order to distinguish among various interaction mechanisms, we also studied PEO dissolved in EG monomethyl ether [EGmE:CH3–(O–CH2–CH2)–OH] and EG dimethyl ether [EGdE:CH3–(O–CH2–CH2)OCH3], the latter not having in its chemical structure OH hydroxylic groups available to give rise to hydrogen bond interactions. In particular, the quality (good-theta-poor) of the solvents has been analyzed by verifying the well-known Mark–Houwink–Sakurada scaling law and the effects of the polymer–solvent interactions on the coils diffusive properties.

Degradation of cellulosic insulation in power transformers. Part 1: Factors affecting the measurement of the average viscometric degree of polymerisation of new and aged electrical papers

The degree of polymerisation (DP) of electrical insulation paper is an invaluable tool for assessing its condition and is extensively used in laboratory tests to assess the life expectancy of transformer insulation. Accurate and reproducible determinations are essential if the results are to be used to calculate a meaningful life. Publication IEC 450 was prepared in 1974 as a standard for the measurement of the DP of new and aged electrical papers (the equivalent US standard is ASTM D4243). However, experience across a number of laboratories has indicated the need for further clarification in the experimental method, whichever standard is adopted. Errors arise during preparation of solutions, measurement of viscosity and calculation of DP, due to oxidative degradation of the solution, inconsistencies in the measurement temperature and the conversion of intrinsic viscosity to DP using the Mark Houwink Sakurada relationship. This paper quantifies errors associated with DP measurement which are not described in existing standards.

Microstructure of 2,3 erythro di-isotactic polynorbornene from atomistic simulation

A new RIS model was developed for erythro di-isotactic polynorbornene that included long-range steric interactions that are needed to properly model its conformation. These interactions were included by extracting RIS states from an approximate energy state map for the heptamer of this polymer. The RIS model predicted a novel helix-kink conformation for this polymer in which helices were occasionally disrupted by a backbone kink and a value of approximately 1.9 for the exponent “a” from the Mark–Houwink–Sakurada equation at the θ condition. These RIS results were consistent with independent single chain Monte Carlo simulations and were also used to generate bulk periodic structures of this polymer. The results of these simulations compare well to both experimental viscometry and wide angle X-ray diffraction results for two polymer samples synthesized using Pd and zirconocene homogeneous polymerization catalysts. These results indicated that the likely stereochemical configuration for polymers produced using these catalysts is the erythro di-isotactic form. They also suggested that polymers of similar structure such as cis poly(t-butyl acetylene) may also adopt this kink-helix conformation.

Intrinsic viscosity-molecular weight relationship for chitosan

The intrinsic viscosity–molecular weight relationship for chitosan was determined in 0.25 M acetic acid/0.25M sodium acetate. Chitosan samples with a degree of acetylation (DA) between 20 and 26% were prepared from shrimp-shell chitosan by acid hydrolysis (HCl) and oxidative fragmentation (NaNO2). Absolute molecular weights were measured by light scattering and membrane osmometry. Size exclusion chromatography (SEC) was used to determine average molecular weights (Mn, Mv, and Mw) and polydispersity. The following Mark–Houwink–Sakurada equation (MHS) is proposed for chitosan of Mw in the range of 35–2220 kDa: The value of the MHS exponent a suggests that chitosan behaves as a flexible chain in this solvent. Examination of MHS constants obtained in this work and those available in the literature with other solvents indicates that a and K are inversely related and that they are influenced by DA, and pH and ionic strength of the solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2591–2598, 2000

Solution properties of poly(dimethyl siloxane)

The solution properties of poly(dimethyl siloxane) (PDMS) were studied with light scattering (LS), gel permeation chromatography/light scattering (GPC/LS), and viscometry methods. PDMS samples were fractionated, and the weight-average molecular weights, second virial coefficient, and the z-average radius of gyration of each fraction were found according to the Zimm method with the LS technique. In this work, the molecular weight range studied was 7.5 × 104 to 8.0 × 105. Molecular weights and molecular weight distributions were determined by GPC/LS. The intrinsic viscosities of these fractions were studied in toluene at 30 °C, in methyl ethyl ketone (MEK) at 20 °C, and in bromocyclohexane (BCH) at 26 °C and 28 °C. The Mark–Houwink–Sakurada relationship showed that toluene was a good solvent, and MEK at 20 °C and BCH at 28 °C were θ solvents for PDMS. The unperturbed dimensions were calculated with LS and intrinsic viscosity data. The unperturbed dimensions, expressed in terms of the characteristic ratio, were found to be 6.66 with different extrapolation methods in toluene at 30 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2678–2686, 2000

Effect of temperature and concentration on viscosity of orange peel pectin solutions and intrinsic viscosity–molecular weight relationship

The effects of temperature and concentration on the viscosity of orange peel pectin solutions were examined at five different temperatures between 20 and 60°C and five concentration levels between 2.5–20 kg/m 3. The effects of temperature was described by an Arrhenius-type equation. The activation energy for viscous flow was in the range 19.53–27.16 kJ/mol, depending on the concentration. The effect of concentration was described by two types of equation, power-law and exponential. Equations were derived which describes the combined effects of temperature and concentration on the viscosity for two different models in the range of temperatures and concentrations studied. Orange peel pectin was extracted by using HCl (pH 2.5, 90°C, 90 min) ammonium oxalate (0.25%, pH 3.5, 75°C, 90 min) and EDTA (0.5%, 90°C, 90 min) extraction procedures. The best result was obtained with ammonium oxalate extraction in which the pectin content of the final product was 30.12%, although the efficiency among the procedures varied.The average molecular weight was measured by light scattering technique. Magnitudes of intrinsic viscosity and molecular weight of pectins obtained by extraction with HCl, ammonium oxalate and EDTA were 0.262, 0.281, 0.309 m 3/kg and 84 500, 91 400, 102 800 kg/kgmol, respectively. The molecular weight dependence of the intrinsic viscosity of the orange peel pectin solutions was expressed by Mark–Houwink–Sakurada equation. The data were fitted to equation as η i=2.34×10 −5( M w,ave) 0.8224 which helps to evaluate the average molecular weight of pectin solutions from orange peel with a knowledge of their intrinsic viscosity.

Evaluation of chain rigidity of poly(diisopropyl fumarate) from light scattering and viscosity in tetrahydrofuran

Poly(diisopropyl fumarate) (poly(DiPF)) was prepared by radical polymerization in bulk or in benzene with an azo initiator at 60°C, and fractionated with tetrahydrofuran (THF) or methanol as the solvent and water as the non-solvent. The selected nine fractions with a relatively narrow molecular weight distribution were used for the viscometric, light scattering and gel permeation chromatography experiments. The light scattering and viscosity studies using several kinds of solvents revealed that the intrinsic viscosity of poly(DiPF) changed less sensitively to the nature of the solvent used, in contrast with the second virial coefficient which was strongly dependent on the solvent. The Mark–Houwink–Sakurada equation was determined as follows: [η]=5.18×10−4Mw0.98 in cm3/g in THF at 30°C. The persistence length (q) of poly(DiPF) was evaluated from the viscosity data in THF using the Bohdanecký plot. The q and the molecular weight per unit contour length (ML) were 11 nm and 1340 nm−1, respectively. These values were compared with those for typical semiflexible polymers reported in literature.

Assessment of errors in the determination of Mark-Houwink-Sakurada and Stockmayer-Fixman constants using size-exclusion chromatography with on-line viscometric detection: Analyses of poly(p-substituted styrenes) in tetrahydrofuran

In this work, we present values for the Mark-Houwink-Sakurada (MHS) and Stockmayer-Fixman (SF) constants for a series of homopolymers of para-substituted styrenes (4-X-styrene; X = OCH3, OCH2CH3, CH3, F, Cl, and Br) in THF at room temperature. The respective values of K (in 10(-5) dL/g) and alpha were: 0.685 and 13.2; 0.662 and 14.1; 0.740 and 8.41; 0.781 and 5.24; 0.726 and 8.95; 0.700 and 7.79. The respective values for K-theta (in 10(-4) dL/g) and K' (in 10(-7) dL/g) were: 6.01 and 16.1; 6.22 and 9.07; 7.64 and 17.4; 5.59 and 23.7; 6.29 and 17.3; 4.44 and 10.3. These constants were measured using size-exclusion chromatography with on-line viscometry. As part of this work, we investigate the applicability of common model fitting procedures to this method of measuring MHS/SF constants and the effect of uncertainties in their estimated values on the accuracy of molecular weight analysis. (C) 1999 John Wiley & Sons, Inc.

Molecular characterization of α,β-poly(asparthylhydrazide) a new synthetic polymer for biomedical applications

α,β-Poly(asparthylhydrazide) (PAHy) is a new synthetic polymer that exhibits interesting properties and is a candidate for biomedical applications. In this article the characterization of PAHy polymer by multi-angle laser light scattering (MALS) and single-capillary viscometer (SCV) detectors on-line to a size exclusion chromatography (SEC) system is reported. The SEC–MALS–SCV system furnishes exhaustive and consistent characterization of the PAHy polymer. Further, it is possible to characterize the PAHy polymer through conventional SEC and universal calibration. The universal calibration method gives intrinsic viscosity and dispersity very close to those measured by the absolute detectors; instead the weight-average molar mass is approximately 8% lower. This finding means that the chromatographic separation of PAHy polymer is fundamentally based on its hydrodynamic volume. By the SEC–MALS–SCV system the constants of the Mark–Houwink–Sakurada equation were also estimated.

On the relation between the Mark–Houwink–Sakurada constants

On the relation between the Mark–Houwink–Sakurada constants

A simple and rapid method for evaluation of Mark–Houwink–Sakurada constants of linear random coil polysaccharides using molecular weight and intrinsic viscosity determined by high performance size exclusion chromatography: application to guar galactomannan

A rapid method for establishing the constants in the Mark–Houwink–Sakurada equation, relating intrinsic viscosity and molecular weight (MW), of guar galactomannan is described. Following partial acid hydrolysis, the galactomannan was analyzed using high performance size exclusion chromatography employing viscosimetry and right angle light scattering detectors. In this way, a large number of samples of polysaccharides with a wide range of MW distributions were prepared, without need for isolation, and intrinsic viscosity and MW rapidly determined. The a and K values found for guar galactomannan were 0.72 and 5.13×10 −4 ([ η] in dl/g) respectively, in good agreement with previously published values.