Staudinger Equation Research Articles

Molecular characteristics of maltodextrins and rheological behaviour of diluted and concentrated solutions

Low converted products of enzyme and acid hydrolysis of starch, short chain polymer-maltodextrins were produced in well controlled laboratory conditions and together with some commercial industrial products have been tested. Molecular characteristics of these various maltodextrins, such as specific optical rotation, dextrose equivalent, degree of polymerisation, molecular mass and turbidity have been determined. The influence of hydrolysis type, as well as some mutual dependencies between various molecular characteristics (specific optical rotation–dextrose equivalent, turbidity–dextrose equivalent) have been considered. Rheological behaviour of concentrated maltodextrin solutions in the concentration range of 100–500 g dm −3 and temperature range 20–50°C was investigated by rotational viscometry. The flow type was Newtonian, i.e. viscosity was independent of shear rate. Concentration and temperature dependencies of viscosity have been determined, as well as a linear relationship between the viscosity and dextrose equivalent. Viscosities of diluted maltodextrin solutions (concentration 0.002–0.01 g cm −3) were determined at 20°C and intrinsic viscosity (limiting viscosity number) values were calculated. A linear relationship between the intrinsic viscosity and dextrose equivalent has been found. Applicability of the Staudinger equation, [ η]= KM a , to the intrinsic viscosity–molecular mass relationship have been shown. A basis for a viscometric method of the dextrose equivalent determination has been developed.

Influence of added salt on dynamic viscoelasticity of carboxymethylcellulose aqueous systems

AbstractUsing three series of sodium carboxymethylcellulose (NaCMC) in the range of the degree of substitution (the average number of carboxymethyl groups/glucose unit) from 0.5 to 1.3, weight‐average molecular weight Mw was determined by light scattering in solution of triethylenediamine cadmium hydroxide (cadoxene). It was found that the relation between Mw and the limiting viscosity number [η] in 0.1 N sodium chloride (NaCl) aqueous solution can be represented by Staudinger's equation. Dynamic viscoelasticity of aqueous disperse systems of NaCMC with various added salts was measured by means of a cone‐and‐plate rheometer. If the concentration of added salt is less than the concentration at which polymer begins to salt out, frequency dependence curves of the dynamic modulus, which is measured at various salt concentrations, can be superposed into a master curve by horizontal shift only. The shift factor depends on the salt concentration and the kind of salt.

Solution Properties of Marine Humic Acid. I.

The polyelectrolytic properties of the marine humic acid solutions of various degree of neutralization have been studied. The viscosity and the potentiometric titration curve change with time; it takes more than one month to attain the equilibrium for the marine humic acid solution, while commercially available Aldrich humic acid solution becomes the constant state after about 2 d from its preparation. The results indicate that the marine humic acid slowly changes its conformation in the solution like polysoaps.Potentiometric titration curves of the humic acids do not exhibit well-defined equivalence points. The alkaline amount to neutralize the marine humic acid is determined to be 2.9meq/g and for Aldrich's 5.3meq/g.The viscometric behavior of the marine humic acid is similar to a typical flexible polyelectrolyte having charges; in the solution without salt the viscosity rises in the low concentration range and the addition of salt causes the viscosity decrease. The viscosity value of Aldrich's is low because of its small molecular weight. According to the Staudinger's equation, the molecular weight of the marine humic acid is estimated to be 20 times as high as that of Aldrich's.The reduced viscosity vs. concentration plots show discontenuous points which indicate the aggregate formation. The concentration at which aggregation occurs is determined to be 0.1%. It is also estimated by the use of the Fuoss' equation. These results are in good accord with that of the previous work on surface tension measurements.

Viscosity of melanoidins formed by oxidative browning validity of the equation for a relationship between color intensity and molecular weight of melanoidin.

To demonstrate the validity of an equation, E=k1 Mα1 (E:1%1cm E450, absorbance of 1% solution in 1 cm path at 450 run, M: molecular weight, k1, α1: constant), intrinsic viscosity of the color components of melanoidin from a glycine-, diglycine- or triglycine-xylose system and of the color components of shoyu, separated selectively by utilizing their change of elution position on DEAE-cellulose chromatography during oxidative browning, has been investigated in connection with their color intensity or molecular weight. The intrinsic viscosity increased with an increase of molecular weight of the color components from each of melanoidins. The Staudinger's equation, [η]=k2Mα2, was observed to fit the relationship between the intrinsic viscosity ([η]) and molecular weight of color component from each of melanoidins. On the other hand, an experimental equation, E=k3[η]α3 was obtained from a linear relationship between logarithmic intrinsic viscosity and logE of color components from each of melanoidins. The last equation can also be derived from the first two equations. Therefore, the equation, E=k1 Mα1 was judged by this experiment to be valid for these melanoidins. Moreover, these melanoidins including the color components of shoyu was suggested to consist of a homologous series of symmetrically flexible chain polymer with different degrees of polymerization and color intensity, since the equation, [η]=k2 Mα2 was applicable for the melanoidins solutions and none of color components from melanoidins showed optical rotation in visible wavelength region. Mechanism of the representation of color from the chromophore of melanoidin has been also discussed.

A Molecular Theory of Viscosity of Dilute Polymer Solutions

A theory of viscosity is developed on the basis of Born-Green's distribution-function method. The solutions are considered to be composed of solvent molecules and segments of polymer molecules in contrast with conventional models in which solvents are regarded as continuous structureless media. The stress is obtained in terms of two-body distribution functions n a a , n a b and n b b and potential energy functions φ a , φ b and ϕ, where the subscripts a and b refers to solvent molecules and segments, respectively, provided that ϕ refers to interaction between a solvent molecule and a polymer segment. The viscosity and the intrinsic viscosity are obtained from the stress versus strain rate relation. When the solvent is good Staudinger's equation is got. The equation of viscosity [η]=KM α and [η]= A M 1/2 + B M are derived from two simple assumptions for poor solvents. It is, however, impossible to judge which equation for viscosity is more reasonable since the reasoning for any of assumptions is not clear only from the theoretical standpoint.

STUDIES ON THE PRODUCTION OF ACRYLIC FIBER BY WET SPINNING

The properties of the dope solution of acrylonitrile-methyl acrylate copolymer of 0.95 to 0.05 which was prepared by 50% aqueous solution of NaCNS were studied.(1) The specific gravity of the dope was measured at 30°C in the concentration range from 0.63% to 11.93%.(2) Hygroscopic behaviours of the 50% aqueous solution of NaCNS and the dope sulution with the polymer concentration of 9.5% were measured and compared at the relative humidity of 60% and at 25°C.(3) Microscopic measurement was utilized to evaluate the dissolving rate of acrylonitrile fiber and polymer particle. The minimum concentration of NaCNS to dissolve the polymer is presumed to be around 46%.(4) The viscosity of the dope solution was measured by the ball fall method in the polymer concentration range from 7% to 13%, and in the temperature range from 0.8°C to 65°C. At 30°C, the modified Baker equation obtained is as follows.where η is the viscosity (sec.), M: molecular weight obtained by using the Staudinger equation, ηBP/C=1.5×10-4M (C: 0.5 mole/l), C: the polymer concentration of the dope (%).(5) A linear relationship was observed between the logarithm of the viscosity and the recipr ocal of the absolute temperature in the temperature range from 30°C to 65°C. This relationship did not hold at the temperature below 10°C.(6) The Copolymers of different molecular weights were mixed in various ratios to prepare six dope solutions of the copolymer mixture and the viscosity of the solutions were measured.The relationship of the viscosity of each of the original polymer solution to those of the mixed polymer solutions may be expresed as: where η: the viscosity of the mixed polymer solution (sec.), η1: the viscosities of the original polymer solutions (sec.), W1: the weight fractions of the original polymer solutions (%).

Degradation of cellulose and cellulose derivatives by acid hydrolysis

AbstractThe acid hydrolysis of cellulose and the cellulose derivatives hydroxyethyl cellulose, methyl cellulose and carboxymethyl cellulose have been investigated. The degradation was followed viscometrically and by end group analysis. It was found that the viscoxity‐molecular weight relationship deviated from the modified STAUDINGER equation, the exponent a is increasing with decreasing molecular weight. The influence of acid concentration and temperature on the degradation rate was studied. It was found that the different cellulose derivatives exhibit quite similar degradation characteristics.

Preparation and properties of poly(tetramethyl‐p‐silphenylene‐siloxane)

AbstractImproved methods for the synthesis of p‐bis(dimethylhydroxysilyl)benzene are described. This useful monomer was prepared from p‐bis(dimethylhydrogensilyl)‐benzene which was obtained in 60–70% yields from p‐dibromobenzene and dimethyl chlorosilane by use of an in situ Grignard technique. The great reluctance due to steric factors of the p‐silphenylene‐siloxane configuration to form cyclic structures has been amply demonstrated. The condensation polymerization of p‐bis(dimethylhydroxysilyl)benzene in benzene solution has yielded high molecular weight, crystalline poly‐(tetramethyl‐p‐silphenylene‐siloxanes). The heat of fusion ΔHu of the tetramethyl‐p‐silphenylene‐siloxane was found to be 4350 cal./unit. The modified Staudinger equation relating intrinsic viscosity and weight‐average molecular weight was applicable over a range of 70,000–400,000. These results are summarized in the relationship, [η] = 1.12 × 10−4Mw0.75. Tetramethyl‐p‐silphenylene‐siloxanes were found to be more stable than dimethylsiloxanes both to atmospheric oxidation and degradation through volatile formation in the temperature range 200–305°C.

Studies in condensed phosphates. Part II. Viscosities of simple and complex sodium metaphosphate solutions

AbstractThe viscosity‐average molecular weights M̄w of [Na4Ca(PO3)6]n and [Na4Ba(PO3)6]n polymers determined by Staudinger's equation in 0.0035N NaCl solution were found to be lower than their number‐average molecular weights M̄n determined by endgroup titration. The above anomaly has been shown to be owing to the effect of bivalent cations liberated in equilibria of the type: This has been further confirmed by measurments of M̄w by the light scattering method. In aqueous solutions the greater change in viscosity of [Na4Ca(PO3)6]n solution with dilution is also ascribed to the secondary dissociation of the polymeric anions at lower concentrations.

A viscosity–molecular weight relationship for polydimethylsiloxanes

AbstractThe relationship of intrinsic viscosity [η] to the weight‐average molecular weight M̄w of polydimethylsiloxane in toluene at 25°C. has been determined. The modified Staudinger equation, [η] = KM̄wa, with K = 2.43 × 10−5 and a = 0.84, describes the relationship for the above polymers in the range of weight‐average molecular weight from 18,900 to 124,500 (as determined by light‐scattering measurements). These constants differ from the values reported by Barry, where K = 2 × 10−4 and a = 0.66 were obtained. The difference is attributed to the fact that Barry dealt with number‐average rather than weight‐average molecular weight.

Ultrasonic degradation of polymer molecules in solution: Some comments on recent papers

AbstractRecent papers on the ultrasonic degradation of polymer molecules in solution are discussed. It is pointed out that the use of the Staudinger equation to derive weight‐average degrees of polymerization from the viscosities of benzene solutions of polystyrenes is a source of error, since these solutions have been found to obey the Houwink equation. Some measurements of degradation rates by the use of diphenyl picryl hydrazyl as a free radical scavenger are considered, and it is concluded that they can be fitted almost equally well by two different rate equations.

Determination of constants in the intrinsic viscosity–molecular weight equation

AbstractIn the modified Staudinger equation, [η] = Km[Mv]α, the constants Km and α are usually found from measurements of [η] and Mv. As the latter cannot be determined directly, the method adopted in the past has been to prepare fractions, determine Mn or Mw by such absolute methods as osmometry and light scattering, and then to assume that the fractions are sufficiently monodisperse to justify writing Mv = Mn = Mw. An alternative approach has been suggested in this paper, making use of the fact that, for a distribution arising from random degradation, Mv = constant × Mn; it has been shown that the appropriate distribution results from the heterogeneous hydrolysis of cotton. The method has been applied to the case of cellulose triacetate in chloroform and the following results have been obtained: Km = 2.51 × 10−4; α = 1.02.

SOME CONSIDERATION ON THE STAUDINGER'S CONSTANT OF CELLULOSE NITRATE

Km value of cellulose nitrates in acetone is measured in relation to their degree of nitration and degree of polymerisation.(1) Km value varies respectively with the degree of nitration and degree of polymerisation.(2) Following relations hold for nitrogen content of about 13.8% N, which is obtained usually with nitration mixture containing HNO3-H3PO4-P2O5.(a) DP below 600_??_η_??_=11×10-4•P, (c:g/l)(b) DP 600_??_3000_??_η_??_=0.1+92×10-4•P, (c:g/l)(3) DP-distribution curves of some linters and wood pulps calculated from Staudinger's equation and above formulas, (a) and (b) were compared. Curves of high DP region are respectively different.

Molecular Weight of Jute Alpha-Cellulose

MUCH work has been done on the determination of the molecular weight of cotton and wood celluloses. Staudinger and Feuerstein1 reported 1,920 as the degree of polymerization of jute cellulose (which corresponds to a molecular weight of 311,040). But Chowdhury and Bardhan2 obtained 516; their value was calculated from Staudinger's equation: where ηsp is the specific viscosity, C the concentration, Km a constant and M the molecular weight. Km was taken to be 10 × 10−4. Since Km is now accepted as 5 × 10−4, their figure has to be doubled (that is, the degree of polymerization becomes 1,032).

A Rapid Determination of the Average Molecular Weight of Rubber in Hevea Latex

Abstract A method is described for determining viscometrically the molecular weight of rubber in freshly tapped latex. For this purpose the latex is dissolved in a toluene-pyridine mixture. From the intrinsic viscosity of this solution the molecular weight of the rubber can be determined by the Staudinger equation and a known viscosity constant. Molecular weights varying between 238,000 and 480,000 have been found, depending on the kind of clone. Rubber in fresh latex does not have a lower molecular weight than in old preserved latex.

The polymerization of styrene sensitized by acetyl radicals.

A study has been made of the polymerization of styrene in the liquid phase, initiated by acetyl radicals from the photolysis of diacetyl. The rate of consumption of monomer was proportional to the square root of the rate of light absorption; the rate of consumption of diacetyl was proportional to the first power of the rate of light absorption. The ratio of the rate constant for chain propagation to the square root of the rate constant for chain termination was found to be 3.9 × 10−3 liter1/2 mole−1/2 sec.−1/2 at 20°C. The quantum yield of diacetyl consumption was 4.0 × 10−3. By relating the kinetic data to the observed intrinsic viscosities, the exponent of the number average molecular weight in the modified Staudinger equation was found to be 0.65. The values of the corresponding K factors for homogeneous and heterogeneous polymers were 6.5 × 10−3 and 8.2 × 10−3, respectively, when the assumption was made that chain termination was by recombination; for chain termination by disproportionation the values were 8.7 × 10−3and 12.9 × 10−3, respectively, for concentrations in base moles per liter.

A rapid determination of the average molecular weight of rubber in hevea latex

AbstractA method is described for determining viscometrically the molecular weight of rubber in freshly tapped latex. For this purpose the latex is dissolved in a toluene‐pyridine mixture. From the intrinsic viscosity of this solution the molecular weight of the rubber can be determined, using the Staudinger equation and a known viscosity constant. Molecular weights have been found, varying between 238000 and 480000, depending on the kind of clone. Rubber in fresh latex does not have a lower molecular weight than in old preserved latex.

キチンに關する研究

Following points were found from our experiments concerning the viscosity of the aqueous solution of glycol chitin. (1) The relation between the intrinsic viscosity, -[η], and the degree of polymerisation; P, for glycol chitin was found to agree with H. STAUDINGER's equation as follows: [η]=lim[ηspC]=Km•P C=0 Where η sp is for the specific viscosity; C for the concentration of the solution in grams per liter; and Km for a constant characteristic for each polymeric series. The value of Km for glycol chitin was 12×10-4 which was perfectly in agreement with that of water soluble cellulose derivatives such as glycol cellulose or methyl cellulose. Thus, it was concluded that chitin was similar to cellulose, a long chain molecule formed from β-1, 4-glu cosidic linkage of acetyl glucosamine. (2) The degree of polymerisation of glycol chitin was 851 which was calculated from the above equation, where Km is 12×10-4. Accordingly, it is sure that the degree of poly-merisation of natural chitin would be comparable to that of natural cellulose.

キチンに關する研究

Following points were found from our experiments concerning the viscosity of the aqueous solution of glycol chitin. (1) The relation between the intrinsic viscosity, -[η], and the degree of polymerisation; P, for glycol chitin was found to agree with H. STAUDINGER's equation as follows: [η]=lim[ηspC]=Km•P C=0 Where η sp is for the specific viscosity; C for the concentration of the solution in grams per liter; and Km for a constant characteristic for each polymeric series. The value of Km for glycol chitin was 12×10-4 which was perfectly in agreement with that of water soluble cellulose derivatives such as glycol cellulose or methyl cellulose. Thus, it was concluded that chitin was similar to cellulose, a long chain molecule formed from β-1, 4-glu cosidic linkage of acetyl glucosamine. (2) The degree of polymerisation of glycol chitin was 851 which was calculated from the above equation, where Km is 12×10-4. Accordingly, it is sure that the degree of poly-merisation of natural chitin would be comparable to that of natural cellulose.

Viscometric Investigation of Dimethylsiloxane Polymers

The intrinsic viscosities of an extended series of linear methyl polysiloxane fluids, having dimethylsiloxane (Me2SiO) as the repeating unit, have been determined in toluene solution. These values have been correlated with their molecular weights, determined chemically and by osmotic pressure and light scattering measurements. The Staudinger equation was found applicable only for fluids of relatively low molecular weights, i.e., up to about 2500; for the higher polymers, the best correlation of intrinsic viscosity with number average molecular weight was found to be: [η]=2×10−4Mn0.66. This held reasonably well for molecular weights from 2500 to about 200,000. The bulk viscosities of the polysiloxane fluids were found to conform to the Flory relationship for melt viscosities; the expression: log visc. (cs. at 25∘C)=1.00+0.0123 Mn12appears to be reasonably valid for molecular weights above 2500.