Sakurada Equation Research Articles

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.

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.

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.

Solution properties of poly(di-1′-methylalkyl itaconates)

Di-1′-methylalkyl itaconates and the corresponding poly(di-1′-methylalkyl itaconates) (PD1′Al) containing 2-propyl (PDiPI), 2-butyl (PDiBI), 1′-methylbutyl (PDiAI), 1′-methylpentyl (PDiHI) and 1′-methyiheptyl (PDiOI) groups as side chains were synthesized and characterized. The polymers were fractionated by fractional precipitation. The fractions were characterized by viscometry in THF and acetone, and by light scattering and size exclusion chromatography in THF. The K a and a parameters of the Kuhn—Mark—Houwink—Sakurada equations were determined in THF and acetone. The stiffness of the polymer chain was estimated through the rigidity indices, a, and the characteristic ratio, C α, using the conformational parameter K Θ obtained from the Stockmayer—Fixman plots. The effect of the side-chain structure on the stiffness, conformational behaviour and glass transition temperatures, T g, of these polymers is discussed and the results compared with those corresponding to other related polymer analogues.

Comparative study of wormlike polymer solutions using statistical mechanics, two-parameter theory, and blob theory

Using the Han equation derived from the blob theory we obtain that the chains of wormlike polymers consist of one Kuhn statistical segment at the onset of excluded volume behavior. This holds when these polymers are dissolved in any solvent. This is in accordance with the predictions of Yamakawa–Stockmayer based on the statistical mechanics theory. Combining the same equation of the blob theory with a relation derived from the two-parameter theory, and accepting that at the onset of excluded volume behavior we have one Kuhn statistical segment for the wormlike polymers, we obtain a relation from which we calculate the statistical segment length of these polymers from the K and a_ parameters of the Mark–Houwink–Sakurada equation. The obtained values are in good agreement with the values given in the literature.

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997

Synthesis and Characterization of Rigid Rod Poly(p-phenylenes)

The polymer PP, which consists of a poly(p-phenylene) backbone with sulfonate ester and dodecyl side groups, is synthesized by a Pd-catalyzed coupling of the 1,3-propanediol diester of 2-dodecyl-5-methyl-1,4-benzenediboronic acid with 2,2‘-bis(3,5-di-tert-butylbenzenesulfonato)-4,4‘-dibromobiphenyl. Polymers with various molar masses are obtained, which are soluble without aggregation in conventional organic solvents. The good solubility of this rodlike polymer allows the accurate determination of the molar mass by light scattering, osmometry, and SEC with universal calibration. The dependence of the intrinsic viscosity [η] on the molar mass is determined from both the Mark−Houwink−Sakurada equation and the wormlike chain model. The low value of the persistence length (13 nm) indicates that these polymers are relatively flexible. It is shown that an approximate value of the persistence length, together with the parameters of the Mark−Houwink−Sakurada equation and the wormlike chain model, can be determined using only a single polydisperse sample.

Influence of the degree of acetylation of o‐cresol resin on its molecular conformation in solution

Abstracto‐Cresol‐formaldehyde resin (OC) and five kinds of acetylated OC (AC‐X‐OC; X is the degree of acetylation) were prepared. The Θ‐temperature for each resin was determined by means of the Shultz‐Flory method, and their molecular conformations in both tetrahydrofuran (THF) and Θ‐solvent were estimated from the values of the exponents in the Mark–Houwink–Sakurada equations. The effect of the degree of acetylation on the exponent was negligible in THF, but was remarkable in Θ‐solvent. In THF, the molecular chains of these resins are relatively extended, because the hydrogen bond between phenolic hydroxyl groups is loosely formed. In Θ‐solvent, however, the molecular conformation is compact and the resins are considered to form a pseudo cross‐linked network structure through inter‐ and/or intra‐molecular hydrogen bonds. The Mark–Houwink–Sakurada equation for AC‐100‐OC in 2‐ethoxyethanol at 92.0°C was found to be [η]θ = 0.0773 M̄0.50n, where [η]0 is the limiting viscosity number under the Θ‐condition, and M̄n is the number‐average molecular weight. The unperturbed dimension, (〈r20〉/M̄n)1/2, 〈r20〉 being the unperturbed mean square end‐to‐end distance, for AC‐100‐OC was found to be 0.659×10−8 cm g−1/2 mol1/2.

Solution properties of perfluoropolyether polymers

Solution properties of fractions of a perfluoropolyether copolymer (PFPE Z) having the structure CF 3(OC 2)F 4) p (OCF 2) q OCF 3have been studied in two solvents, 1,1,2-trichloro-1,2,2-trifluoroethane (CFC 113) and perfluoroheptane, over a large molecular weight range. Two series of fractions having p/q ratio equal to 0.54 and 1.27 were considered. The fractions, which were characterized by light scattering, vapour pressure osmometry and viscosimetry, were found to be narrow. The coefficients of the Mark Houwink—Sakurada equation, [ η] = KM a , were determined for both solvents in the molecular weight range between 8000 and 200 000. CFC 113 turned out to be a theta solvent (the Flory polymer—solvent interaction parameter χ is close to 0.5) while perfluoroheptane behaves as a good solvent ( χ = 0.28). The coil expansion factor α 3 in perfluoroheptane was also measured. The relationship between the hydrodynamic radius and the molecular weight was determined from dynamic light scattering. Finally, a parameter related to the chain stiffness, the characteristic ratio C ∞, was also determined. In the molecular weight range explored it was found that the stiffness is independent of the p/ q ratio. PFPE Z polymer has a chain flexibility similar to that of poly(oxyethylene) and larger than that of poly(tetrafluoroethylene).

Highly isotactic polyacrylonitriles prepared using dialkylmagnesium/water systems as initiators

AbstractAn attempt was made to synthesize stereoregular polyacrylonitrile (PAN) with high molecular weight (e.g. viscosity‐average molecular weight (M̄v) > 1 × 105) by anionic polymerization. The triad tacticities (i.e. the content of mm, mr and rr (m, meso; r, racemo)) of the polymers obtained were analyzed by 13C NMR and their M̄v was determined by viscometry in dimethylsulfoxide at 25°C using Kamide et al.'s Mark–Houwink–Sakurada equation. Highly isotactic and high molecular weight PAN with M̄v > 2.5 × 105 ((mm) ∼ 0.57) was synthesized in anisole at 130°C when the reaction product of di‐n‐hexylmagnesium with water supplied by heating sulfate hydrates (Na2SO4 10H2O, CuSO4 5H2O, and MgSO4 7H2O) was used as a polymerization catalyst. The M̄v of PAN was increased significantly by using the catalyst combined with triethylaluminum (Et3Al). Maximum M̄v attained was 9.7 × 105 ((mm) = 0.64). The main role of Et3Al added is explained as the reduction of OH groups in the catalyst and of residual H2O in the catalyst solution.

Mark–Houwink–Sakurada equation for polyurethane in benzene

Mark–Houwink–Sakurada equation for polyurethane in benzene

Some Dilute Solution Properties of Highly Isotactic Polyacrylonitrile in Aq. Nitric Acid

An attempt was made to investigate the dilute solution properties of highly isotactic polyacrylonitrile (PAN) dissolved in aq. nitric acid and to estimate the molecular parameters, such as the unperturbed chain dimension A and the characteristic ratio C∞. For this purpose a highly isotactic polymer with isotactic triad content of 73.4% was synthesized by irradiating γ-ray on acrylontrile–urea canal complex at −78°C and was subjected to successive precipitation fractionation, using dimethyl sulfoxide as solvent and toluene as precipitant, into 7 fractions. Among them 2 fractions with isotactic triad of 71.0 and 77.9%, respectively were employed for further study. The weight-average molecular weight Mw and the second virial coefficient A2 of these fractions in 70 wt% aq. nitric acid soln. were measured by the light scattering method. The 70 wt% aq. nitric acid soln. was predicted to be able to dissolve perfectly-isotactic PAN with Mw of 1.5–2.6×105 at room temperature. The Mark–Houwink–Sakurada equations in aq. nitric acid solutions differ significantly depending on the stereoregularity of PAN employed, even if highly concentrated acids are used. A 57.5 wt% aq. nitric acid soln. is determined, by the dependence of A2 on the nitric acid concentration, to be a Flory’s theta solvent for PAN with isotactic triad of 71.0% at 25°C. A of PAN increases rapidly with isotactic triad content, especially in the range higher than 50%. C∞ of PAN is always far larger than the calculated value of non-polar Monte Calro chain for polypropyrene [P. J. Flory et al., J. Am. Chem. Soc., 88, 639 (1966)] over the whole range higher than 50% isotactic diad.

Determination of Mark–Houwink–Sakurada equation for phenolic resins and estimation of their molecular conformation in acetone solution

AbstractThe effects of the molecular structure of phenolic resins on the Mark–Houwink–Sakurada (MHS) equation and the conformation in acetone solution were studied. The exponent in the MHS equation was remarkably less than that for linear polymers such as vinyl polymers, cellulose derivatives, and so on. As the cause, the branching and the hydrogen bonding between hydroxyl groups of the neighboring phenolic nuclei were considered. Several kinds of phenol‐p‐cresol and phenol‐p‐tert‐butylphenol cocondensation resins whose composition differs from one another were synthesized. Despite the difference in the degree of branching, the exponent in the MHS equation for each was approximately equal. On the other hand, the exponent for o‐cresol novolak, which was rich in ortho‐para methylene linkages was larger than the all‐ortho novolak and p‐cresol novolak, which were rich in ortho–ortho methylene linkages. Methylation of the phenolic hydroxyl group increased the value of the exponent. From these results, it became obvious that while the hydrogen bonding lowered the exponent in the MHS equation due to molecular conformation compaction in acetone solution, the molecular branching had little effect on the exponent α.

Viscometric determination of the molecular weight of polymers in the low molecular weight region

In order to overcome the difficulty of the determination of the molecular weight of a polymer in the low molecular weight region by viscometry using the Mark–Houwink–Sakurada (MHS) equation, we have proposed the Dondos–Benoit relationship [η]−1 = A2 + AM−1/2, for a number of polymer–solvent systems, for which we give the numerical values of the parameters A1 and A2. Furthermore, we suggest a method for the determination of the above parameters using the MHS constants a and k.

Viscometric and Light Scattering Study in Dimethylacetamide of Linear Segment Polyurethane, Polymerized with Methylene Bis(4-phenyl isocyanate) Polytetramethylene Glycol and Ethylene Diamine

An attempt was made to determine the unperturbed chain dimension A of a segment polyurethane, prepared from polytetramethylene glycol (the number-average molecular weight 1500) methylene bis(4-phenyl isocyanate) and ethylenediamine. A whole polymer was fractionated by successive solution fractionation using dimethylacetamide (DMAc) as a solvent and methylalcohol as a precipitant into 23 fractions. Linearity of the segment polyurethane chain was confirmed by NMR and the solution viscosity change by addition of n-butylamine. The dilute solution properties of eight fractions in DMAc were investigated by the light scattering and viscometry at 25°C. The Mark–Houwink–Sakurada equation for the solution in DMAc at 25°C was [η]=0.101Mw0.59 (cm3 g−1) ([η]; limiting viscosity number, Mw; the weight-average molecular weight). A was found to be 1.02×108 cm for the solution. No significant solvation was observed by adiabatic compressibility measurement.

Dilute Solution Properties of Acrylonitrile/Vinylidene Chloride Copolymer

A copolymer of acrylonitrile (AN) and vinylidene chloride (VDC) was prepared using azobisisobutylonitrile as an initiator and was separated into 20 fractions by successive solution fractionation, using dimethyl sulfoxide (DMSO) as the solvent and toluene as the precipitant. The fractions had essentially the same chemical composition: 59 weight percent in AN. Light scattering for a fraction in dimethylacetamide (DMAc), γ-butyrolactone (γ-BL) and dimethylformamide (DMF) gave the same weight-average molecular weight Mw within an experimental error ±2%, which was evaluated assuming homopolymer. Viscosity and light scattering were measured for 8 fractions in DMAc. The Mark–Houwink–Sakurada (MHS) equations for this polymer at 25 °C were in DMAc, in DMF, in γ-BL, and in 70 wt% aq nitric acid. The molecular weight dependence of the radius of gyration 〈S2〉z1/2 and the second virial coefficient A2 in DMAc at 25°C were represented by 〈S2〉z1/2=3.84×10−9 Mw0.53 and . The unperturbed chain dimension A was determined by Baumann, Stockmayer–Fixman and Kamide–Moore methods. The value of a copolymer of AN and VDC was by ca. 10% smaller than that of polyacrylonitrile.

Light Scattering and Viscometric Study of Cellulose in Aqueous Lithium Hydroxide

An attempt was made to determine molecular parameters of cellulose dissolved in simple solvents. Cellulose regenerated from a cuprammonium solution of acid-hydrolized cotton linters was found to dissolve molecularly, without suffering molecular degradation, into 6 wt% aqueous LiOH solution by choosing an adequate condition. The apparent weight-average molecular weight Mw*, of cellulose obtained by light scattering in a non-dialyzed aqueous LiOH, was converted into the correct weight-average molecular weight Mw with the aid of the data on Mw* and Mw for a dialyzed cadoxen solution of cellulose. The Mark–Houwink–Sakurada equation for cellulose in aq LiOH was [η]=2.78×10−2 Mw0.79 at 25°C {[η]; limiting viscosity number}. The Flory’s viscosity parameter Φ for this system was significantly smaller than the theoretical value for unperturbed chains at non-draining limit, showing a molecular weight dependence. The linear expansion factor for the radius of gyration was always below 1.04 as estimated from the penetration function. The unperturbed chain dimensions were estimated by various methods using the light scattering and/or viscometric data. Cellulose was found to be semiflexible in aq LiOH.

The Mark–Houwink–Sakurada Equation for the Viscosity of Atactic Polystyrene

In this review, the second in a series, the viscosity–molecular weight (Mark–Houwink–Sakurada) relationships have been critically evaluated for atactic polystyrene for a variety of solvents often used for viscosity measurements. These are benzene, toluene, 1,2,4-trichlorobenzene, tetrahydrofuran, o-dichlorobenzene, 2-butanone, and two theta solvents, cyclohexane and decalin. In addition, the Mark–Houwink–Sakurada parameters for several other solvents, not used as frequently, are provided.

Light Scattering and Viscometric Study on Polyacrylonitrile in Dimethylformamide, Ethylene Carbonate/Water Mixture, and Aqueous Nitric Acid

An attempt was made to determine the Flory theta solvents and the unperturbed chain dimension A of polyacrylonitrile (PAN). A sample of PAN, polymerized using redox catalyst and having isotactic triad of 26% and syndiotactic triad of 24%, was fractionated by successive solution fractionation method to give a series of fractions with the ratio of weight- to number- average molecular weight Mw/Mn of 1.15—1.41. A mixture of ethylene carbonate (EC) and water containing 85 wt% EC and aq. 55 wt% nitric acid was identified by the light scattering method to be Flory theta solvents at 25°C whose second virial coefficients were zero. The Mark–Houwink– Sakurada (MHS) equations were determined in various solvents. In the theta solvents, the radius of gyration 〈S2〉z1/2 was proportional to Mw1/2 and the exponent a in MHS equations was always 0.5. The Flory viscosity parameter Φ was 2.3×1023 in DMF and 2.8×1023 in theta solvents, independent of Mw. The unperturbed chain dimension parameter A, the conformation parameter σ and the characteristic ratio C∞ were determined by thermodynamic and hydrodynamic methods. Both methods gave consistent results. The solvent dependence of these parameters was demonstrated.

The Mark–Houwink–Sakurada Equation for the Viscosity of Linear Polyethylene

In this review, the parameters K and α found in the literature for the Mark–Houwink–Sakurada equation relating viscosity to molecular weight have been critically evaluated for linear polyethylene, and values have been recommended for six commonly used solvents. These are decalin, 1,2,4-tricholorobenzene, 1-chloronaphthalene, tetralin, o-dichlorobenzene, and p-xylene. In addition, the literature values of K for several different theta solvents are presented.