Z-average Molecular Weight Research Articles

On rheological properties of polydisperse polymers

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: η 0 ∼ M α w ; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: θ 0 ∼ M α 1 z , and in the general case α 1 ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.

Conformational change of a natto mucin in solution.

The mucin obtained from a natto sample was found to be composed of 58 % of γ-polyglutamic acid and 40% of polysaccharide. The ratio of l- and d-glutamic acid was determined to be 58:42 using l-glutamic acid decarboxylase. The weight- and z-average molecular weight were 2.08 × 105 and 2.22 × 105, respectively. The distribution curve of the sedimentation coefficient showed a small heterogeneity. The mucin molecule was considered to be randomly coiled at pH 5.0 ~ 8.8 and to be a rod-like molecule in the lower pH region.

Subunit structure and amino-acid composition of crystallized human-muscle glycogen phosphorylase.

The subunit structure and molecular weight of the a and b forms of human muscle glycogen phosphorylase were investigated. Electrophoresis in the presence of sodium dodecylsulfate gave a molecular weight of 94 500 for the monomer. When studied at 1 mg/ml and 20 °C by high‐speed sedimentation equilibrium, sucrose density gradient ultracentrifugation and specific activity‐concentration dependence, both a and b forms of the human enzyme were found to exist as dimers. A slight association of human phosphorylase a was observed in the high‐speed sedimentation equilibrium values of the z‐average molecular weight (262000 for Mmacr;zvs 188000 daltons for Mmacr;w). Some association of the a enzyme was also detected by schlieren sedimentation velocity when the enzyme was studied at 5 mg/ml. Human phosphorylase b could be fully associated to tetramer at 20 °C when Pi, Mg2+ and AMP were added but not in the presence of NaF and AMP which were found to be effective in tetramerizing rabbit phosphorylase b. Another important difference from rabbit phosphorylase was the significantly lower proline content of the enzyme from human muscle.

Purification of Two β-N-Acetyl-d-glucosaminidases from Beef Spleen

Abstract Two enzymes (A and B), each with β-N-acetyl-d-glucosaminidase and β-N-acetyl-d-galactosaminidase activity, were obtained from beef spleen extracts. Final purifications: Enzyme A, 310-fold; B, 260-fold. Purity was confirmed by gel electrophoresis and ultracentrifugation. Only A was bound by DEAE-cellulose, at pH 7.0. The two enzymes had identical weight-average and z-average molecular weights: the latter was unchanged by addition of guanidine hydrochloride or dithiothreitol, but decreased greatly when both were present, indicating more than one peptide chain in each enzyme. Amino acid compositions were similar, but more sialic acid and neutral carbohydrate were present in A than in B. Optical rotatory and circular dichroism spectra also were similar: no Cotton effects were observed at 250 to 300 nm, and rotations and ellipticities were very low at wave lengths l250 nm. Enzyme structure could not be deduced by fitting with calculated curves. Km values were identical but Vmax was slightly greater in A; changes in pH affected Km and Vmax of both enzymes. Kinetic studies showed that the two p-nitrophenyl substrates tested compete for the active sites on both enzymes. Stimulation by bovine serum albumin enhanced Vmax but did not affect Km. Both enzymes were strongly inhibited by various metal ions; neither was affected by sulfhydryl reagents, but activity vanished during treatment with dithiothreitol.

Characteristics of the Protein-Keratan Sulfate Core and of Keratan Sulfate Prepared from Bovine Nasal Cartilage Proteoglycan

Abstract Protein-keratan sulfate core was isolated from bovine nasal cartilage proteoglycan after enzymatically removing chondroitin sulfate with chondroitinase AC from Flavobacterium heparinum. The core preparation exhibited a broad, approximately Gaussian distribution of buoyant densities in CsCl density gradients (between 1.43 and 1.58 g per ml with an average of 1.51 g per ml). Chemical and physical analyses of subfractions from the density gradient indicate that the core macromolecules have a wide polydispersity in molecular weights (350,000 to 550,000, with an average of 450,000). Molecules with larger molecular weights have greater buoyant densities and higher ratios of keratan sulfate to protein. The data suggest that the core molecules contain a protein (or combination of proteins) with a molecular weight of about 200,000 to which different amounts of keratan sulfate are attached. Differences in average keratan sulfate chain lengths and chain numbers appear to contribute to the polydispersity of the protein-keratan sulfate core. Keratan sulfate was isolated from the core preparation after proteolysis with papain and purification with DEAE-cellulose chromatography. Chemical and physical analyses of the keratan sulfate indicate that the polysaccharide exhibits a large polydispersity of molecular weights with a weight average molecular weight of about 8,500 and a z-average molecular weight of about 11,000, and that polysaccharide molecules with larger molecular weights have higher ratios of glucosamine to galactosamine. Alkali treatment of the keratan sulfate selectively destroys threonine and serine as it does for other skeletal keratan sulfates. After alkaline treatment the keratan sulfate chromatographs on Sephadex G-100 with a higher retention volume, Kd = 0.6, than that for the untreated preparation, Kd = 0.3, which indicates that the sizes of the molecules have been significantly reduced. The data are consistent with the hypothesis that the papain-prepared keratan sulfate consists of molecules which contain two polysaccharide chains, each with an average of about six repeat disaccharides, connected through a peptide bridge. Each chain probably contains a terminal sialic acid residue and is attached to the protein with a glycosidic bond between galactosamine and a threonine or serine residue. The high concentration of glutamic acid in the fraction suggests that the polysaccharide chains are also attached in some way to this amino acid. Such a model suggests that the intact proteoglycan macromolecules each contain about 60 keratan sulfate chains of variable lengths built onto the protein core structure.

Polysaccharides of tropical grass species : III. Solution properties of hemicellulose B from setaria sphacelata

The solution properties of hemicellulose B from Setaria sphacelata have been investigated by equilibrium sedimentation and moving-boundary electrophoresis. Values of 40,000, 46,000, and 94,000 have been obtained for the apparent number-, weight-, and z-average molecular weights, respectively, of 0.4% polysaccharide solutions in 0.051 acetate, pH 5.3. Furthermore, the hemicellulose fraction is thought to consist almost entirely of polysaccharide molecules having molecular weights in the vicinity of 38,000, together with traces of much heavier material. Detailed boundary-analysis of the single, symmetrical, electrophoretic peak observed in the same medium indicated a fairly narrow mobility-distribution, at least 80% of the hemicellulose possessing a mobility of −0.7 ±0.2x10 −5 cm 2sec −1volt −1.

Equations for the equilibrium constants of nonideal systems derived from the multinomial theroy using the z-average molecular weight.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSelf-associating systems. 5. Equations for the equilibrium constants of nonideal systems derived from the multinomial theory using the z-average molecular weightMoises DerechinCite this: Biochemistry 1972, 11, 6, 1120–1121Publication Date (Print):March 1, 1972Publication History Published online1 May 2002Published inissue 1 March 1972https://doi.org/10.1021/bi00756a028RIGHTS & PERMISSIONSArticle Views22Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (210 KB) Get e-Alerts Get e-Alerts

Uridine Diphosphate Glucose Pyrophosphorylase: II. POLYMERIC AND SUBUNIT STRUCTURE

Abstract The crystalline enzyme uridine diphosphate glucose pyrophosphorylase from calf liver has been shown to be polydisperse. The more rapidly sedimenting components that are present have been shown to be multimers of the basic pyrophosphorylase molecule. Evidence for multimers has come from (a) ultracentrifugal analysis, (b) protein and activity patterns by polyacrylamide gel electrophoresis and sucrose density gradient ultracentrifugal analysis, and (c) redistribution of the sucrose-separable material. Hydrodynamic studies of the principal component in the ultracentrifuge have yielded extrapolated values of 14.10 to 14.45 S for the sedimentation coefficient and 2.72 to 2.87 x 10-7 cm2 per sec for the diffusion coefficient. Combination of these values yielded a molecular weight of about 480,000. Dissociation in 6 m guanidine hydrochloride and 0.1 m mercaptoethanol has yielded subunits with a sedimentation coefficient of 2.14 S and a diffusion coefficient of 2.90 x 10-7 cm2 per sec. A combination of these values produced a molecular weight of 69,100. Estimates obtained by low speed sedimentation equilibrium were 67,500 for both the weight and z-average molecular weights. Electron micrographs have indicated the presence of tetramers. The results are discussed in relationship to an octomer model.

The Behavior of Horse Liver Alcohol Dehydrogenase in Guanidine Hydrochloride Solutions

Abstract The z-average molecular weight of horse liver alcohol dehydrogenase in dilute neutral buffer is 78,200 by sedimentation equilibrium. Guanidine hydrochloride, 1 m, reversibly inhibits enzymatic activity. The inhibition with nicotinamide adenine dinucleotide is competitive and with ethanol is mixed. When ethylenediaminetetraacetate is added to the enzyme in 1 m guanidine hydrochloride, zinc is removed, followed by aggregation. Sedimentation velocity experiments indicate that no subunit is formed under these conditions. In 3 m guanidine hydrochloride, the sedimentation equilibrium data suggest the presence of a reversible association-dissociation system. Ethylenediaminetetraacetate removes zinc but has no effect on sedimentation equilibrium behavior of the enzyme in 3 m guanidine hydrochloride. Reduction and alkylation of the enzyme in 3 m guanidine hydrochloride results in almost complete dissociation into two subunits. Thus, it appears that sulfhydryl residues may be involved in subunit association, whereas zinc plays little or no role. After correction for guanidine binding, the z-average molecular weight of the enzyme in 5 m guanidine hydrochloride containing mercaptoethanol is 41,000. Measurements of molecular weight, sedimentation coefficient, and intrinsic viscosity of the enzyme in 5 m guanidine hydrochloride all indicate that the structure of horse liver alcohol dehydrogenase is composed of two subunits.

Self-associating systems. 3. Multinomial theory for ideal systems using the z-average molecular weight.

Self-associating systems. 3. Multinomial theory for ideal systems using the z-average molecular weight.

Sedimentation equilibrium and other physicochemical studies on the lysine-rich fraction of calf thymus histones.

1. The lysine-rich fraction (Ia+Ib, or f1) of calf thymus histones was isolated as the sulphate by acid extraction. 2. Sedimentation-equilibrium measurements with interference optics showed that this fraction was monodisperse with a molecular weight of 19500+/-2000. 3. The ;apparent molecular weight' calculated from the sedimentation-equilibrium studies varied markedly with concentration. The large second virial coefficient implied by such variation was attributed to the very high charge/mass ratio of this relatively small protein. Estimates of the charge were made from the values of this virial coefficient. 4. The very large value of the virial coefficient explains anomalies in the earlier reports of the molecular weight of this histone and also why the z-average molecular weight can appear to be lower than the weight-average molecular weight. 5. The differences of the specific refractive increments, and the partial specific volumes, between dialysed and undialysed solutions of this histone fraction could also be attributed to its high molecular charge, which was estimated from these differences and agreed, within the expected limits, with the value deduced from the second virial coefficient. 6. Sedimentation-velocity measurements combined with the known molecular weight imply that lysine-rich histone has a high frictional ratio and an extended shape. Optical-rotatory-dispersion measurements indicated that it had a low helical content.

Molecular weight distribution and swell properties of some low‐pressure polyethylenes

AbstractThe molecular weight distribution of some low‐pressure homopolymers of ethylene intended for use in blown bottles have been determined by using a modified sand column technique. A correlation is indicated between the Z‐average molecular weight M̄z and the postextrusion swelling of the resin as measured by the weight of a bottle blown from that polymer.

Physical and Chemical Properties of β-Methylaspartase

1. A modified purification procedure for β-methylaspartase from Clostridium tetanomorphum, which gives electrophoretically pure enzyme in almost 50% yield, is described. 2. The z-average molecular weight of the native enzyme was determined to be 100,000 by the sedimentation equilibrium technique. The molecular weight was invariant in the pH range, 5.9 to 9.7, and was also not affected by ethylenediaminetetraacetate (10-4 m ) or by Mg++ and K+ at concentrations which are optimal for catalytic activity. 3. Under a variety of experimental conditions similar to those used in the sedimentation equilibrium studies, sedimentation velocity experiments yielded an s020,w value of 6.05 S for the native enzyme. 4. Trailing boundary sedimentation experiments showed that the sedimentation coefficient associated with β-methylaspartase activity was very close to 6.05 S. This result established that the enzyme species having an s020,w value of 6.05 S and a molecular weight of 100,000 was present, and catalytically active, under the conditions we have commonly used in steady state kinetic studies of the reaction. 5. The value of e279 was 5.63 x 104 m -1 cm-1 and the molar turnover number at pH 9.7, with Mg++ and K+ as activators, was 650 sec-1. 6. All catalytic activity was lost when 2 sulfhydryl groups, out of a total of 20 in the enzyme molecule, had reacted with p-chloromercuribenzoate.

Sedimentation equilibrium in aqueous solutions of a nonionic detergent

The micelle molecular weight of polyoxyethylene oetylphenylether with 20 moles of ethylene oxide in aqueous solution has been determined by the sedimentation equilibrium method. The critical micelle concentration is found to be 0.075 g. d1. −1, in agreement with that from surface tension measurements. The micelle molecular weight obtained is 35,600, which corresponds to the association number, 32.4. The solution is almost ideal and the micelles are homogeneous in size. The equilibrium constant and the standard free energy for the micelle formation have been estimated. From the sedimentation equilibrium data the number-, weight-, and z-average molecular weights have been obtained at given concentrations, and they are compared with those calculated from the equilibrium constant between monomers and micelles.

Molecular Weight Distribution and Melt Rheological Properties for High Density Polyethylenes

High density polyethylene (HDPE) has each its distinctive features in the rheological properties according to its manufacturing process. The present work proposes to present a quantitative relationship between its molecular weight distribution and the melt viscoelastic properties for some samples of HDPE.The samples have been fractionated by both the elution column technique and the precipitation technique. The number-average, weight-average and Z-average molecular weights have been calculated from the smoothed molecular weight distribution curve for each sample by the method of summation.The viscoelastic properties of some series of the commercial HDPE have been measured by means of a concentric cylinder type rheometer at different temperatures (150∼230°C). The angular frequency (ω) ranges from about 10-2 to 50sec-1. The ratio of flow rate at shear stress 106dyne/cm2 to at 105dyne/cm2 (=flow ratio; FR), which gives a good indication of the non-Newtonian property of samples, have been measured by means of a melt indexer type rheometer.The results are as follows;(1) The linear relationship is found between Mw/Mn and Mz/Mw for only a series of samples made by the same manufacturing process.(2) FR is found to be related to Mz/Mw, not to Mw/Mn. log FR=0.137Mz/Mw+1.04(3) Dynamic viscosity (η') and dynamic regidity (G') can be superposed according to the temperature-time superposition principle, and shift factors aT from η' and G' are practically the same.Agreement with constancy of shift factor for various molecular weights (Mv=5∼10×104) and distributions is good, and the apparent activation energy (ΔHa) calculated from the shift factor is 6-7kcal/mol. ΔHa of copolymer is also of the same value.(4) Master curves also are constructed with respect to the molecular weight for measurements of η' and G' versus ω for only those samples in which Mz/Mw are equal to each other.Shift factors aM from η' and G' are the same.The relationship must also be right in the steady flow viscosity, and confirms that HDPE with the same Mz/Mw have equal FR.(5) The relationship between η0 and Mw is effected by the molecular weight distribution.log η0=3.5log Mw+log (Mz/Mw)-12.7

Effect of molecular weight distribution on melt flow properties of low-pressure polyethylene

A series of low-pressure Ziegler polyethylene samples has been fractionated by the sand column technique. The molecular weight distributions have been determined by the Schulz-Dinglinger approximation. The number-average, weight-average, and z-average molecular weights have been calculated from the fractionation data for each sample by the method of summation. Melt indexes and melt flow ratios have been determined by standard techniques. The melt index is found to be related to the reciprocal of the fifth power of the weight-average molecular weight, and the melt flow ratio is proportional to the z-average molecular weight.

Effects of molecular weight distribution and branching on rheological parameters of polyethylene melts. Part II. Fractions and blends

AbstractStudies of the rheological properties of fractions of linear and branched polyethylenes have shown that the melt recovery of linear polyethylene fractions is very small and independent of molecular weight over a wide range. Fractions containing high degrees of long‐chain branching, on the other hand, have high melt recoveries. The melt recovery of a fraction can therefore be used as an index of long‐chain branching. Alternatively, if no long‐chain branching is present, the melt recovery is a unique function of the molecular weight distribution. This effect is illustrated by blends of fractions. The log of the critical shear rate is a linear function of the log melt viscosity of the fraction for both linear and branched polyethylenes. This would indicate that the critical shear rate of polydisperse samples would depend primarily on the weight‐average of Z‐average molecular weight of the polymer. This is confirmed by previous studies on polydisperse samples. It also appears that critical shear rate is highly dependent on the homogeneity of the sample. Blends of the same fractions had quite different critical shear rates, depending on the procedure used to prepare them, even though their molecular weight distributions were identical. The change in viscosity with shear rate is not a unique function of molecular weight or melt viscosity. Fractions of linear polyethylene show a greater change in viscosity with shear rate than branched fractions of similar low shear melt viscosity. This suggests that the effect is related to chain entanglement or coordinated segmental motion.

A simplified method for the calculation of the Z-average molecular weight from ultracentrifuge data

A modification of the method of Lansing and Kraemer for obtaining Z-average molecular weights from ultracentrifuge measurements under equilibrium conditions is described. By employing the differrential form of the equation normally used for homogeneous materials, in conjunction with numerical differentiation, the amount of computation involved in obtaiining a Z-average molecular weight is greatly reduced. The modified treatment yields essentially the same values of the Z-average as does the original treatment, and the computation error is slightly less in the modified method than in the original. It is also shown that the Z-average molecular weight at each point in the cell can be derived directly from the Archibald equation relating concentration to distance in the cell. Tentative molecular weight averages of 80 000 (Z-average) and 76 000 (weight-average) are assigned to a sample of crystalline yeast aldolase.

MOLECULAR SIZE AND CONFIGURATION OF CELLULOSE TRINITRATE IN SOLUTION

Viscosity and light-scattering measurements were made on several fractions and two unfractionated samples of cellulose trinitrate. The samples were prepared from bleached ramie, unbleached ramie, and cotton linters. The solvents were acetone and ethyl acetate. Viscosity was measured in a multishear viscometer designed for the purpose. Light-scattering measurements were made in a Brice-Phoenix Light-scattering Photometer modified to accommodate a cell which could be ultracentrifuged.The range of molecular weight investigated was from 6.5 × 105 to 25.0 × 105 The relationship between the z-average mean-square radius of gyration, [Formula: see text] and the z-average molecular weight was approximately linear in both solvents. The ratio of [Formula: see text] (where [Formula: see text] is the value of [Formula: see text] in the unperturbed state) was found constant in acetone but to increase with [Formula: see text] in ethyl acetate. This indicated that, whereas in acetone random coil configuration was attained, a configurational transition occurred in ethyl acetate in the molecular weight range investigated.The value of the exponent a in the relationship between intrinsic viscosity and molecular weight was found to be lower than unity but approximately equal in both solvents.The significance of the experimental data is discussed.