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     

Evaluation of GPC methods for estimation of Mark–Houwink–Sakurada constants

Constants for the Mark–Houwink–Sakurada relation can be established in principle from GPC measurements on broad distribution polymers. The method requires use of two samples with different intrinsic viscosities or a single polymer for which [η] and M ⁿ M ^w are known. The [η]–M ^w combination is not reliable because M ^v and M ^w are often very similar in magnitude. The [η]M _n method is likewise not recommended because of the influence of skewing and axial dispersion effects on the GPC measurement of M _n. The simplest and safest way to use GPC data to estimate the MHS constants involves the measurement of GPC chromatograms of two polymer samples with different intrinsic viscosities. The method is not confined to the solvent used as the GPC eluant. The MHS constants derived from GPC appear to reflect the molecular weight range of the calibration samples and may not be as widely applicable as those from the more tedious classical methods which employ a series of fractionated samples.     

Randomly branched styrene/divinylbenzene copolymers. I. Preparation,molecular weight characterization,and GPC analysis

A series of randomly branched copolymers of styrene and divinylbenzene were prepared using a benzoyl peroxide-initiated free-radical bulk polymerization at 78°C. DVB contents were varied from 0.01% to 2%. Two samples were polymerized with 0.4% DVB to different conversions: series 9A at 6% conversion and series 9B at 15% conversion (just short of the gelation point). Both samples were fractionated and the fractions characterized by ultracentrifugation, light scattering, osmometry, viscometry, and gel permeation chromatography. The data indicated that the fractions were not of narrow MWD and that the breadth of the MWD of the fractions from series 9B were greater than those of 9A. GPC calibration curves of M, [η], and M [η] were generated for both 9A and 9B fractions by employing curve-fitting techniques to the GPC data. For all of the fractions 9B, the molecular weight calibration provided accurate values of M?_z, M?_w, and M?_n, suggesting that no serious peak spreading had occurred in the GPC experiments. The universal calibration parameter M[η] for the 9A fractions agreed with that of linear polystyrene, while that of the high-conversion series 9B did not. It will be shown in a later paper that series 9B is highly branched, while 9A is lightly branched. Consequently, it is recommended that any GPC analysis of branching units make an allowance for the deviation of highly branched polymers from the linear M[η] calibration curve.     

Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

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     

Evaluation of different branching functions used in the determination of random branching by GPC

Three branching functions are evaluated for use in the measurement of random branching by GPC. Initial evaluations of the functions g^1/2, g^3/2, and h³ were made by computer simulations of GPC experiments using published data of lightly and highly randomly branched polymers. Actual GPC experiments were then performed on characterized samples of lightly and highly branched styrene–divinylbenzene copolymers. The results indicate that h³ adequately predicts branching and molecular weight at all branching densities, whileg^1/2 is accurate only for lightly branched polymers and g^3/2 is accurate only for highly branched polymers. A means for predicting the M–[η] curve for branched polymers from the M–[η] calibration curve for linear polymer is proposed.     

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.     

Eigenschaften thermoplastischer Polyurethanelastomerer in Lösung

Fundamental correlations between the molar mass and the solution viscosity (dimethylformamide (DMF)/1% di-n-butylamine (DBA)) are acquired and discussed on selected polyesterurethanes (PUR-Es) and polyetherurethanes (PUR-Et) with NCO/OH ratios ranging from 955 to 1 030. Static light scattering measurements reveal mass average molar masses in the range 20 000–95 000 g mol^–1; membrane osmometry reveals number average molar masses in the range 15 000–50 000 g mol^–1. Comparative tests with the analytical ultracentrifuge reveal the agreement with respect to the molar mass and the A₂-values; additionally this measurements confirm unimodal Schulz-Zimm molar mass distributions with an average sedimentation constant of S = 1.1 sved (1 sved = 10^–13 s). The results of light scattering und ultracentrifuge measurements show that the solvent mixture DMF/1 wt.-% DBA is well suitable for molar mass measurements and solution viscosity measurements. The linear light scattering Zimm diagram and the sedimentation run exclude microgels and higher molecular associates (for example allophanate and biuret crosslinkage). Because of the good correlation between the determined molar masses and the intrinsic viscosities [η] and the viscosities of the concentrated solutions it was possible to establish a calibration function [η] = K M^a. The exponent a = 0.6–0.9 of the Mark-Houwink-relation indicates that the polymer chains, in diluted solution, are isolated coiled molecules. In concentrated solutions the chains are partly crosslinked, depending on the molar mass. The correlation between the molar mass and the viscosity (Fox-relation) shows an unsteadiness at M_w = 55 000 g mol^–1 (critical molar mass). Above the critical molar mass the solution viscosity increases with the molar mass with an exponent of ϵ = 3.4. Below the critical molar mass of M_w = 55 000 g mol^–1 the solution viscosity increases straight proportional with the molar mass (ϵ = 1).     

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.     

Molecular weight and arm number of a star‐shaped styrene–butadiene block copolymer synthesized on a pilot‐vessel scale

To improve the rheological properties and processability of industrial rubbers, star‐shaped styrene–butadiene–styrene (SBS) block copolymers were synthesized and characterized in this work. Through the variation of the ratio of divinylbenzene to the diblock anion, a series of SBS samples with three to six arms were prepared. Multi‐angle laser light scattering (MALLS) and size exclusion chromatography (SEC) combined with light scattering (LS) were used to determine the weight‐average molecular weight (M_w), radius of gyration (〈S²〉^1/2), arm number, and chain conformation. The results from MALLS indicated that the M_w values of the star‐shaped SBS copolymers were 9.0, 13.0, 14.9, and 18.1 × 10⁴, which corresponded to three, four, five, and six arms, respectively. There was a lot of M_w and 〈S²〉^1/2 data for the many fractions in the SEC chromatograms of the SBS copolymers in tetrahydrofuran (THF) detected by LS, so the exponent of 〈S²〉^1/2 = KM_w^α was determined to range from 0.59 to 0.30 for the samples having three to six arms. An analysis of the results revealed that the star SBS copolymers existed in a sphere conformation in THF, and their chain density increased with an increase in the arm number. The viscosity of the six‐arm SBS copolymer was reduced significantly, compared with that of the SBS samples having three to five arms, when their M_w values were similar. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1853–1859, 2007     

Statistical moments of elution bands and their application in gel permeation chromatography of polydisperse macromolecules

Equations have been derived that relate the statistical moments of uncorrected and spreading-corrected chromatograms for a general form of the spreading function in gel permeation chromatography of polydisperse macromolecules. The first moment (centroid) of the chromatogram is shown to be directly given by the centroid, In M^*, of a suitably defined molecular weight distribution function of the polydisperse sample, regardless of the position of the calibration dependence, provided it is linear. Both the molecular weight M^* associated with the centroid of the chromatogram and its second central moment (variance) are but little sensitive to the shape of sample molecular weight distribution and can be easily calculated from the polydispersity index M_w/M_n, at least for polymers of a not excessively broad distribution. The derived relations are shown to find application in the calibration of GPC columns by means of characterized, polydisperse standards and in the separation of independent contributions to peak width which originate in sample polydispersity and in band broadening processes in the column. Improved column- and packing performance criteria are also proposed.     

Synthesis and biological activity of phthalimide‐based polymers containing 5‐fluorouracil

The attachment of anticancer agents to polymers is a promising approach towards reducing the toxic side‐effects and retaining the potent antitumour activity of these agents. A new tetrahydrophthalimido monomer containing 5‐fluorouracil (ETPFU) and its homopolymer and copolymers with acrylic acid (AA) and with vinyl acetate (VAc) have been synthesized and spectroscopically characterized. The ETPFU contents in poly(ETPFU‐co‐AA) and poly(ETPFU‐co‐VAc) obtained by elemental analysis were 21 mol% and 20 mol%, respectively. The average molecular weights of the polymers determined by gel permeation chromatography were as follows: M_n = 8900 g mol^?1, M_w = 13 300 g mol^?1, M_w/M_n = 1.5 for poly(ETPFU); M_n = 13 500 g mol^?1, M_w = 16 600 g mol^?1, M_w/M_n = 1.2 for poly(ETPFU‐co‐AA); M_n = 8300 g mol^?1, M_w = 11 600 g mol^?1, M_w/M_n = 1.4 poly(ETPFU‐co‐VAc). The in vitro cytotoxicity of the compounds against FM3A and U937 cancer cell lines increased in the following order: ETPFU > 5‐FU > poly(ETPFU) > poly(ETPFU‐co‐AA) > poly(ETPFU‐co‐VAc). The in vivo antitumour activities of all the polymers in Balb/C mice bearing the sarcoma 180 tumour cell line were greater than those of 5‐FU and monomer at the highest dose (800 mg kg^?1). © 2002 Society of Chemical Industry     

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.     

The effects of pressure and temperature upon the viscosities of liquids with special reference to polymeric liquids

From a consideration of the work required for expansion of a liquid, the following relationship between viscosity η, pressure P and temperature T is put forward. For unassociated liquids with molecules which are not too large, V* is taken as the parachor, log₁₀ (η* in Ns/m²) is ?3.88, P* is 8.58 × 10⁶ N/m², R is the gas constant, and T* is a constant characteristic of each liquid. The equation can be applied to polymeric liquids if V* and η* are taken as disposable constants. For example, for polystyrene V* is found to be 3 × 10^?3 m³ mol^?1 and log₁₀ (η* in Ns/m²) to be 3.4 log₁₀ M?_w ?10.2 where M?_w is the weight-average molecular weight (kg/mol) from 5 kg/mol upwards. In the equation, the same constants serve for the variation of viscosity with pressure and with temperature. The viscosity under a high pressure can therefore be estimated from viscosities all measured at normal pressures but at different temperatures. The viscosities of a number of polymers have been measured over a range of temperature and pressure and the results support the equation. Support is found for the view that segments are involved in the flow of polymeric liquids and V* gives a measure of the volume of the segment. The size of the segment seems to increase as the flexibility of the polymer chain decreases. The lowest values for V* are found for polysiloxanes in which the segment seems to be only four atoms long. Larger values of V* are found for polymers with units of the type –CH₂–CHR-. Larger values still of V* are given by polymers with units of the type –CH₂-CR₁R₂- and even larger V* values are found for those polymers with benzene rings constituting a major part of the main chain. As V* rises the viscosity of the polymeric liquid becomes much more dependent upon pressure and temperature. Thus whilst the polysiloxanes have viscosities which are relatively insensitive to pressure and temperature, the aromatic polysulphones and poly(2,6-dimethylphenylene oxide) have viscosities which are very sensitive to pressure and temperature.     

Long-chain branching in low-density polyethylene

A sample of a commercial low-density polyethylene was fractionated and values of number ? M_n and weight-average M_w, molecular weights obtained together with intrinsic viscosities [η], measured in decalin at 135° and in a theta-solvent, diphenyl at 118°. Results are compared with those obtained using samples of high-density polyethylene, of narrow molecular weight distribution, in decalin at 135° and in diphenyl at 125°. Values of the z-average mean square radius of gyration (S^?2)_z, are converted to the weight-average unperturbed state. The branching parameters g and g¹ thus obtained, indicate that long-chain branching increases with increasing molecular weight. Intrinsic ivscosities under theta-conditions for the low-density polyethylene fractions lead to a relationship [η]_θ = K _w^0·20, agreeing with the treatment of Zimm and Kilb. Some of the approximations involved in the estimation of long-chain branching are discussed.     

Estimation of Mw from dilute solution viscosity

The viscosity-average molecular weight, M_v, of a polymer is given operationally through its limiting viscosity number [η] and the Mark-Houwink equation [η] = KM_v^α, where K and α are empirical constants. If [η] is measured under different conditions, α and M_v will vary for the same sample. M_v^α is the α-order moment about the origin of the differential weight distribution of the polymer. Practically, the results of a series of M_v measurements on the same polymer are equivalent to a cluster of fractional moments of the weight distribution, with orders between 0.55 and 0.80. It is shown that the first moment of this distribution, M_w, may be estimated reliably by a straightline plot of M_v against α-extrapolated to α equals 1. This simple expedient is effective although there are probably no molecular weight distributions in which the relation is strictly linear and there are no mathematical distributions for which the αth root of the αth moment is a linear function of α for all α. The deviation from linearity is small enough, however, that the real curve can be represented by a straight line over a short range of α. Thus, M_w can be measured accurately, but M_n, M_z, or the breadth of the distribution is not accessible by this method. Experimental and literature examples show that the precision of M_w estimated by this method compares well with that of primary methods for measuring this molecular weight average. If a linear relationship is observed with reliable α values, this appears to be a sufficient condition for estimation of a valid M_w.     

Statistics of star-shaped molecules III. Stars with branched nuclei

Number and weight average molecular weights and scattering behaviour of star molecules with extended branched nuclei are calculated by application of cascade theory. The nuclei considered arise from random polycondensation of monomers of the A₃ or of the A—B/C type. Nuclei of the first type are characterised by very large molecular polydispersities (M_w/M_n α M_w), while nuclei of the second type have less broad molecular weight distributions (M_w/M_n α M_n). The rays of the stars are assumed to be either monodisperse or to obey the Schulz—Flory “most probable” length distribution. Analytic expressions are given for M_w, M_n, 〈S²〉_z and the particle scattering factor P_z(h) which was averaged over the ensemble. The results are compared with stars of spherical and uniform nuclei whose molecular weights and mean square radii of gyration equal M_wN and 〈S²〉_zN from the other two types of nuclei. In the limit of very large ray lengths the scattering behaviour is determined solely by the number of branches z. At shorter chain length of the rays structure and polydispersity of the nuclei have marked influence. This influence is still easily noticed from the angular dependence of scattered light at chain lengths where no differences in the 〈S²〉_z versus M_w plot are detectable. The mean square radius of gyration depends only weakly on the number of rays and eventually becomes independent of it if z 15. In that limit 〈S²〉_z depends virtually on the length of the rays alone and its distribution. Stars whose rays have a most probable length distribution exhibit 〈S²〉_z values twice as large as stars with monodisperse rays. A procedure is suggested and discussed for the determination of the number and length of the rays if the scattering behaviour of the isolated nucleus and the isolated linear chains is known.     

Melt rheology of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites during capillary extrusion

The melt flow properties during capillary extrusion of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites were measured by using a Rosand rheometer to identify the effects of the filler content and operation conditions on the rheological behaviour of the sample melts. The experiments were conducted under the following test conditions: temperature varied from 220 to 240 °C and shear rate ranged from 10 to 10⁴ s^?1. The filler volume fractions were 0, 10, 20, 30, 40 and 50%. The results showed that the shear flow did not strictly obey the power law under the test conditions, and that the entry pressure drop (ΔP_en) and the extension stress (σ_e) in entry flow increased nonlinearly, while the melt shear viscosity (η_s) and extension viscosity (η_e) decreased with increasing the wall shear stress (τ_w) at constant test temperature. The dependence of the melt shear viscosity on the test temperature was approximately consistent with the Arrhenius expression at fixed τ_w. When τ_w was constant, η_s and η_e increased while ΔP_en and σ_e decreased with the addition of the filler volume fraction. © 2002 Society of Chemical Industry     

Synthesis and phase behavior of chiral side‐chain liquid‐crystalline polysiloxanes containing two mesogenic groups

The synthesis of chiral side‐chain liquid‐crystalline polysiloxanes containing both cholesteryl undecylenate (M_I) and 4‐allyloxy‐benzoyl‐4‐(S‐2‐ethylhexanoyl) p‐benzenediol bisate (M_II) mesogenic side groups was examined. The chemical structures of the obtained monomers and polymers were confirmed with Fourier transform infrared spectroscopy or ¹H‐NMR techniques. The mesomorphic properties and phase behavior of the synthesized monomers and polymers were investigated with polarizing optical microscopy, differential scanning calorimetry, and thermogravimetric analysis (TGA). Copolymers IIP–IVP revealed a smectic‐A phase, and VP and VIP revealed a smectic‐A phase and a cholesteric phase. The experimental results demonstrated that the glass‐transition temperature, the clearing‐point temperature, and the mesomorphic temperature range of IIP–VIP increased with an increase in the concentration of mesogenic M_I units. TGA showed that the temperatures at which 5% mass losses occurred were greater than 300°C for all the polymers. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2670–2676, 2002     

Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties

A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (M?_w/M?_n <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of M?_w/M?_n and the Mark-Houwink exponent a. The resulting value of S₂/S (where S₁ = Στ_p/τ₁, S₂ = Σ(τ_p/τ₁)², the τ_p's being the relaxation times and τ₁ the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.