Molecular weight and chain conformation of amylopectin from rice starch

By using laser light scattering (LS) and size exclusion chromatography combined LS, we have investigated the molecular weight and chain conformation of amylopectin from rice of India (II‐b), japonica (IJ‐b), and glutinous (IG‐b) in dimethyl sulfoxide (DMSO) solution. The weight‐average molecular weight (M_w) and radius of gyration (〈S²〉^½) of amylopectin were determined to be 4.06 × 10⁷ and 128.5 nm for India rice, 7.41 × 10⁷ and 169.6 nm for japonica rice, 2.72 × 10⁸ and 252.3 nm for glutinous rice, respectively. The 〈S²〉^½ values were much lower than that of normal polymers, indicating a small molecular volume of amylopectin, as a result of highly branched structure. Ignoring the difference of degree of branching, approximated dependences of 〈S²〉^½ and intrinsic viscosity ([η]) on M_w for amylopectin in DMSO at 25°C were estimated to be 〈S²〉^½ = 0.30M_w^0.35 (nm) and [η] = 0.331M_w^0.41 (mL g^?1) in the M_w range studied. Moreover, from the 〈S²〉^½ values of numberless fractions obtained from many experimental points in the SEC chromatogram detected with LS, the dependence of 〈S²〉^½ on M_w for the II‐b sample was estimated also to be 〈S²〉^½ = 0.34 M_w^0.347, coinciding with the above results. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Dependence of intrinsic viscosity and molecular size on molecular weight of partially hydrolyzed polyacrylamide

As a typical water-soluble polymer, ultra-high molecular weight (UHMW) partially hydrolyzed polyacrylamide (HPAM) has been widely used in various industries as thickeners or rheology modifiers. However, precise determination of its critical physical parameters such as molecular weight, radius of gyration (R_g) and hydrodynamic radius (R_h) were less documented due to their high viscosity in aqueous solution. In this work, the molecular structure of five UHMW-HPAM samples with different MW was elucidated by ¹H and ¹³C NMR spectroscopy, and their solution properties were characterized by both static and dynamic light scattering. It is found that all the second virial coefficient (A₂) values are positive and approaching zero, indicating of a good solvent of 0.5 M NaCl for UHMW-HPAM. The weight-average molecular weight (M_w) dependence of molecular size and intrinsic viscosity [η] for these series of HPAM polymers with MW ranging from 4.81 to 15.4 × 10⁶ g·mol⁻¹ can be correlated as R_g = 3.52 × 10⁻²M_w^0.51, R_h = 1.97 × 10⁻²M_w^0.51, and [η] = 6.98 × 10⁻⁴ M_w^0.91, respectively. These results are helpful in understanding the relationship between molecular weight and coil size of HPAM polymers in solution, and offer references for quick estimation of molecular weight and screening of commercial UHMW-HPAM polymers for specific end-users.     

Determination of Polymer Branching with Gel Permeation Chromatography. Abstract of a Review

Abstract

The effect of long- and short-chain branching in polymer molecules on GPC separation is reviewed (1–4). The calculation of branched GPC curves is developed from the uiiiversal calibration techniques, which is based on the concept of hydrodynamic volume (M [η]) and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As the branching level increases, the curves arc shown to approach a limiting value. Methods of characterizing branching level3 and molecular-weight distributions of fractions and whole polymers from GPC and intrinsic viscosity data arc prcsentecl. An iterative computer program is described which was written to calculate the degree of branching in whole polymers. Long-chain branching in beveral low-density polyethylene samples was determined, using both the fraction and the whole polymer methods. Effects of various experimental errors and branching models were investigated. For polyethylene, the data show that the effect of branching in intrinsic viscosity is best described by the relationship (g ₃) _w = [η]_br/[η] whre (g _s is the Zimin-Stockmeyer expression for trifunctional branch points in a polydisperse sample.     

Thermal degradation of polyethylene in a nitrogen atmosphere of low oxygen content. II. Structural changes occuring in low-density polyethylene at an oxygen content less than 0.0005%

Samples of low-density polyethylene, free from additives, were heated at temperatures between 284° and 355°C under high-purity nitrogen. Changes in molecular weight distribution (MWD), molecular weight averages, and degree of long-chain branching (LCB) were followed by gel chromatography (GPC) and viscosity measurements. Other structural changes were investigated by infrared spectroscopy and differential scanning calorimetry (DSC). At 284° and 315°C, the MWD's were shifted toward higher molecular weights and the M?_w values increased. At 333° and 355°C, the MWD's shift toward lower molecular weight, but the high molecular weight, tail is largely retained. M?_w decreases slowly at 333°C. At 355°C, M?_w undergoes a rapid initial drop which levels off. M?_w/M?_n and the degree of LCB increase with heating time and temperature. Olefinic unsaturation increases. The vinyl groups show a larger relative increase than do the trans-vinylene and vinylidene groups. At 355°C, the peak of the unimodal DSC thermogram is shifted to ～3°C higher temperature. A lower melting peak then develops, and after 72 and 90 min the two peaks are about equal in size. The density increases from 0.922 g/cm³ to 0.930 g/cm³ for samples heated at 355°C, and the weight loss was 1.5% after 90 min. A reaction scheme for the thermal degradation of polyethylene is discussed. Initiation is suggested to be accomplished by scission of allylic C? C bonds. Propagation proceeds by both intra- and intermolecular hydrogen abstraction, followed by β-scission. Termination can occur by both combination and disproportionation. Combination reactions are suggested to account for the observed formation of LCB and high molecular weight material. Due to changes in the degree of LCB during the degradation, viscometry alone will not give a proper measure of the changes in molecular weight.     

Molecular architectures of four‐arm star‐shaped styrene‐butadiene copolymer

To understand the molecular architectures of styrene‐butadiene four‐arm star (SBS) copolymers, a size exclusion chromatography combined with laser light scattering (SEC‐LLS) has been used to determine their weight‐average molecular weight (M_w) and radius of gyration (〈S²〉^1/2), and a new method for the establishment of the Mark‐Houwink equation from one sample has been developed. Based on the Flory viscosity theory, we successfully have reduced the 〈S²〉^1/2 values of numberless fractions estimated from many experimental points in the SEC chromatogram to intrinsic viscosities ([η]). For the first time, the dependences of 〈S²〉^1/2 and [η] on M_w for the four‐arm star SBS in tetrahydrofuran at 25°C were found, respectively, to be 〈S²〉^1/2 = 2.62 × 10^?2 M (nm) and [η] = 3.68 × 10^?2 M (mL/g) in the M_w range from 1.4 × 10⁵ to 3.0 × 10⁵. From data of [η] and 〈S²〉^1/2 for linear and star SBS, we have obtained the information about the branching, namely, the ratios (g and g′) of 〈S²〉 and [η] for star SBS to that of the linear SBS of the same molecular weight, which agree with theoretical predictions. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 961–965, 2005     

Small-angle X-ray scattering from sodium hyaluronate in aqueous sodium chloride

Summary Four narrow-distribution samples of sodium hyaluronate with weight-average molecular weights M _w of 3.8 × 10³ to 1.1 × 10⁴ in 0.02 and 0.1 M aqueous NaCl at 25°C have been studied by small-angle X-ray scattering. Data for their z-average radii of gyration <S²>_z ^1/2 and particle scattering functions P(θ), together with previous <S²>_z data from light scattering for high molecular weights, are compared with relevant theories for the wormlike chain with or without excluded volume, using the parameters estimated previously from intrinsic viscosity ([η]) data. It is shown that for M _w lower than 1.1 × 10⁴, <S²>_z, P(θ), and [η] of the polysaccharide in the aqueous salts are all consistently explained by this model without excluded volume. Received: 8 December 1997/Accepted: 26 December 1997     

The relation between melt flow properties and molecular weight of polyethylene

The non-Newtonian behavior of commercial linear polyethylene samples and their fractions were studied at 190°C. The viscosity η versus shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} curves of whole polymers could be superimposed onto a single master curve despite the variations of their molecular weights and molecular weight distributions. For fractions, however, the same master curve was inapplicable, and the sensitivity of the viscosity to shear rate was found to be greater than those of the whole polymers. The zero-shear viscosities η₀ of fractions were related to the 3.42 power of the weight-average molecular weight M_u as follows: For whole polymers, the zero-shear viscosities were found to be considerably higher at the same M_w and markedly lower at the same z-average molecular weight M_z than those of the fractions. Thus, it was concluded that η₀ corresponds to an average of molecular weight between M_w and M_z. It was found that the molecular relaxation time τ is proportional to M_z^5.3 for whole polymers and to η₀M_w for fractions. Using these relations it was possible to relate the flow ratio, the ratio of flow rates at two different shear stresses, with the molecular weight distribution.     

Characterization of branched polyethylene fractions from the elution column

Fractions from several elution column runs on samples of up to 6 g. of a well-characterized high-pressure polyethylene were analyzed by absolute molecular weight methods and several other techniques. The M_n and M_w integral distribution curves are free from any reversal, as was the viscosity distribution curve. Fractions with M_w as high as 8 × 10⁶ were recovered, more than 20 times higher than the original sample's M_w. The polydispersity of the fractions increases from M_w/M_n = 1.5 or less in the low molecular weight fractions to a nearly constant value of 4.5–5.0 in fractions above 60% cumulative sample weight. Nonetheless, refractionation on the elution column shows that the fractions are narrowly distributed in terms of solubility, while GPC analysis reveals that the fractions have an extremely narrow size distribution. It is concluded from the combined results that long-chain branching plays an important role in determining the equilibrium solubility and, further, that long-chain branching increases the polymer solubility. Sample calculations are provided, which illustrate the effect of fraction polydispersity on calculated original sample molecular weights and the fit of the fractionation results to several model distribution functions.     

Detection of low levels of long‐chain branching in polydisperse polyethylene materials

Creep experiments have been applied to probe the zero‐shear viscosity, η₀, of polyethylene chains directly and precisely in a constant‐stress rheometer at 190°C. Such experiments, when combined with precise measurements of the weight‐average molecular weight, M_w, calibrated relative to linear chains of high‐density polyethylene, are shown to provide a very sensitive approach to detect low levels (0.005 branches per 1000 carbons) of long‐chain branching (LCB). This detection limit is shown to be insensitive to whether the molecular weight distribution (MWD) breadth, M_w/M_n, rises from about two to ten. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Ultra-high strength polyethylene filaments by solution spinning/drawing. 3. Influence of drawing temperature

The influence of the temperature on the drawing behaviour of gel-fibres, which were obtained by spinning of a 2% w/w solution of high molecular weight polyethylene (M_w = 1.1 × 10⁶) in decalin, was studied in the range from 70 to 143°C. It was found that the drawing temperature, like the presence of solvent in the gel-fibres, affected the maximum attainable draw ratio, but did not influence the effectiveness of the hot drawing below the melting point of the polymer.     

Effect of double bonds on the γ-radiation-induced crosslinking of polyethylene

Various low-density polyethylenes ranging in initial weight-average molecular weight (M?_w) from 7600 to 589000 having a ratio of M?_w to number-average molecular weight (M?_n) of about 5 were irradiated by γ-rays in vacuo at 30°C. Gel fractions were determined and analyzed by using the equation derived by Charlesby and Pinner. The following relationships were obtained when M?_w was used as the molecular weight: where r_g represents the gel point dosage (Mrad), [C?C]₀ is the sum of the initial contents of terminal vinyl and vinylidene unsaturations (mole/g polyethylene), and q₀ and p₀ are the probabilities of crosslinking and main-chain scission per monomer unit for a unit radiation dose in Mrad, respectively. Similar relationships to the equations described above were also obtained when M?_n was used. From the results, it was concluded that terminal vinyl and vinylidene unsaturations play an important role for the gel formation in the γ-radiation-induced crosslinking of polyethylene in vacuo at room temperature.     

Size-exclusion chromatography with two-angle laser light-scattering (SEC-TALLS) of high molecular weight and branched polymers

The accuracy and precision of results obtained from light-scattering detection at two angles (TALLS) for size-exclusion chromatography (SEC) are examined for linear narrow molecular weight distribution polystyrenes between 1,290,000 and 20,000,000 MW and for branched polyesters. The ratio of light-scattering intensities at 15° and 90° is used to calculate weight-average molecular weight, M?_w, and an average root-mean-square radius, r?_gu, equivalent to the z-average radius. A shape for the polymer molecule is assumed and an analytical relationship for the particle-scattering function is required. It is shown that analysis of the data using the particle-scattering function for a random coil is valid for both high molecular weight, linear polystyrenes and long-chain branched polyesters. The radius, r?_gu, is determined with high precision by using the ratio of light-scattering signals, which is insensitive to errors in sample concentration and changes in the eluent flow rate. The correct average radius for the whole polymer is obtained despite using low-efficiency, large-particle diameter SEC columns; however, axial dispersion significantly affects molecular weights and radii calculated at each retention volume that can limit the utility of plots used to deduce polymer conformation. © 1995 John Wiley & Sons, Inc.     

Molecular weights of styrene–maleic anhydride copolymers

A dual-calibration method for the determination of molecular weights and molecular weight distribution of styrene–maleic anhydride copolymers (S/MA) by gel permeation chromatography (GPC) is introduced. It might be applicable to copolymers of other type. A linear relationship of intrinsic viscosity [η] and weight-average molecular weight (M?_w) for unfractionated S/MA in tetrahydrofuran (THF) at 25°C can be expressed by the equation The maleic anhydride content of the copolymers ranges from 5 to 50 mole-%, and the M?_w range is from 2 × 10⁴ to 7 × 10⁶. The plot of log [η] M?_w versus GPC elution volume of the S/MA copolymers falls on the same curve as that of the polystyrene standards in THF.     

The reactive modification of polyethylene. I: The effect of low initiator concentrations on molecular properties

Commercial samples of high density, linear low density, and low density polyethylene were modified by injection of low concentrations of free radical initiator during extrusion. Molecular properties monitored included molecular weight distribution, degree of unsaturation, and branching. When the polyethylene teed to this reactive extrusion process had similar values of M_w, but varying polydispersity, degree of branching and degree of unsaturation, the magnitude of the change in molecular weight distribution was found to be in the following order: HDPE 1 > LDPE2 > LLDPE. In general, terminal vinyls enhanced molecular weight increase, and branching promoted degradation. However, for a second high density polyethylene sample with M_w = 154,000 (rather than the previous sample's M_w of 85,600), the change in molecular weight distribution was small and located at the lower molecular weight end. This work provided data for the kinetic model development detailed in Part II.     

Order-Disorder Conformation Change of Succinoglycan in Aqueous Sodium Chloride as Studied by Static and Dynamic Light Scattering

Summary Static and dynamic light scattering measurements have been made on a sodium salt sample of succinoglycan in 0.01 M aqueous NaCl at different temperatures between 25 and 75°C where the polysaccharide undergoes a thermally induced change from an ordered (helical) to disordered conformation with raising temperature T. The weight-average molecular weight M _w, the z-average radius of gyration, and the hydrodynamic radius sharply decrease in a relatively narrow T range (around 55°C) in which the specific rotation was previously found to change sigmoidally with T. In particular, the value of M _w (4.55 × 10⁵) in the ordered state at 25°C is twice as large as that (2.27 × 10⁵) in the disordered state at 75°C, giving decisive evidence that the helical structure of the polysaccharide in aqueous NaCl is composed of paired chains. It is concluded that this structure is a double-stranded helix and breaks directly into two disordered chains with increasing T. Received: 6 July 2001 / Accepted: 24 July 2001     

In-chain functionalization by alternating anionic copolymerization of styrene and 1-(4-dimethylaminophenyl)-1-phenylethylene

Anionic copolymerizations of styrene (M₁) with excess 1-(4-dimethyl-aminophenyl)-1-phenylethylene (M₂) were conducted in benzene at 25°C for 24h, using sec-butyllithium as initiator. Narrow molecular weight distribution copolymers with M?;_n = 16.1 × 10³ g/mol (M?_w/M?_n = 1.04) and 38.2 × 10³g/mol (M?_w/M?_n = 1.05), and 24 and 38 moles of M₂ per macromolecule, respectively, were characterized by size exclusion chromatography, ¹H NMR spectroscopy and DSC. The monomer reactivity ratio, r₁ = 5.6, was obtained from the copolymer composition at complete consumption of M₁, assuming that the rate constant k₂₂ =0,i.e. r₂ =0. The polymers exhibited T_g values of 128 and 119°C, respectively, which correspond to an estimated T_g = 217°C for the hypothetical homopolymer of M₂.     

Evaluation of light-scattering detectors for size exclusion chromatography. II. Light-scattering equation selection

A new multiangle laser light-scattering (MALLS) detector for size exclusion chromatography promises simultaneous measurement of both weight-average molecular weight (M_w) and radius of gyration (r_g) at each retention volume across the chromatogram. However, there are a variety of ways of interpreting the raw data to provide these results. This study examines variations of three different rearrangements of the basic light-scattering equation. Data from a room temperature analysis of polystyrene and a high-temperature analysis of polyethylene were used. The degree of fit of each equation to the data and the precision of the M_w and r_g values are evaluated. To define precision, joint confidence regions (JCRs) were calculated and compared to simple confidence intervals based upon standard deviations in order to see the effect of interdependence of M_w and r_g. Results showed that the Debye equation was superior to the inverse Debye equation (similar to the Zimm plot) for the interpretation of MALLS data. The effect of the quantity of data included in the regression model was also assessed. Use of only the most precise four detector angles was compared to use of a full set of 15 angles. Precision of weight-average molecular weight values was found to be improved as the detector angle decreased because of the shortened extrapolation to zero angle. Precision at room temperature was much superior to that at high temperature. Use of simple confidence intervals was shown to provide only a fair approximation to the more accurate JCR. The “natural scatter” of data shown by the JCR generally shows the same trend as do plots in the literature of M_w vs. r_g. Thus, it is concluded that JCRs should be more often calculated in light-scattering studies in order to distinguish random scatter from meaningful correlations of these values. © 1993 John Wiley & Sons, Inc.     

Synthesis of poly(D,L‐lactic acid) modified by triethanolamine by direct melt copolycondensation and its characterization

Using D ,L ‐lactic acid (LA) and multifunctional group compound triethanolamine (TEA) as starting materials, a novel biodegradable material poly(D ,L ‐lactic acid‐triethanolamine) [P(LA‐TEA)] was directly synthesized by simpler and practical melt polycondensation. The appropriate synthetic condition was discussed in detail. When the molar feed ratio LA/TEA was 30/1, the optimal synthesis conditions were as follows: a prepolymerization time of 12 h; 0.5 weight percent (wt %) SnO catalyst; and melt copolycondensation for 8 h at 160°C, which gave a novel star‐shaped poly(D,L ‐lactic acid) (PDLLA) modified by TEA with the maximum intrinsic viscosity [η] 0.93 dL g⁻¹. The copolymer P(LA‐TEA) as a different molar feed ratio was characterized by [η], Fourier transform infrared spectroscopy (FTIR), proton nuclear magnetic resonance (¹H‐NMR), gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and X‐ray diffraction (XRD). Increasing the molar feed ratio of LA/TEA, T_g and M_w increased. However, all copolymers were amorphous, and their T_g (12.2°C–32.5°C) were lower than that of homopolymer PDLLA. The biggest M_w was 9400 Da, which made the biodegradable polymer be potentially used as drug delivery carrier, tissue engineering material, and green finishing agent in textile industry. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Dynamic light-scattering characterization of the molecular weight distribution of a broadly distributed phenolphthalein poly(aryl ether ketone)

Using a recently developed laser light-scattering (LLS) procedure, we accomplished the characterization of a broadly distributed unfractionated phenolphthalein poly(aryl ether ketone) (PEK-C) in CHCl₃ at 25°C. The laplace inversion of precisely measured intensityintensity time correlation function from dynamic LLS leads us first to an estimate of the characteristic line-width distribution G(T) and then to the translational diffusion coefficient distribution G(D). By using a previously established calibration of D (cm²/s) = 2.37 ×10⁻⁴M^−0.57, we were able to convert G(D) into a differential weight distribution f_w(M). The weight-average molecular weight M_w calculated from f_w(M) agrees well with that directly measured in static LLS. Our results indicate that both the calibration and LLS procedure used in this study are ready to be applied as a routine method for the characterization of the molecular weight distribution of PEK-C. © 1996 John Wiley & Sons, Inc.     

Rheological properties of polypropylenes with different molecular weight distribution characteristics

Relationships between the rheological properties and the molecular weight distribution of two polypropylene series with different molecular weight distribution characteristics were studied. The end correction coefficient in capillary flow is determined by the molecular weight M_w and the molecular weight distribution M_w/M_n, and is higher as both characteristic values are larger. The die swell ratio at a constant shear rate depends on M_w, M_w/M_n, and M_z/M_w, and is higher as the three characteristic values are larger. The critical shear rate at which a melt fracture begins to occurs depends on the molecular weight M_w and the molecular weight distribution M_z/M_w, and is proportional to M_z/M_w² in a log–log plot. The critical shear stress does not depend on the molecular weight, and is higher as M_z/M_w is higher. The zero‐shear viscosity is determined by a molecular weight of slightly higher order than M_w, and the characteristic relaxation time is determined by M_z. The storage modulus at a constant loss modulus scarcely depends on the molecular weight, and is higher as the molecular weight distribution M_w/M_n is higher. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2128–2141, 2002