Intrinsic viscosity in branched free-radical polymers

The intrinsic viscosity ratio [η]_B/[η]_L was calculated as a function of average branching density for trifunctionally branched, free-radical polymers. Calculations were made for the g^1/2, g^3/2, and h³ rules, using realistic distributions of molecular weights and branches. Experimental data on branched poly(vinyl acetate) lay between the curves obtained from the g^1/2 and h³ relations.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Properties of cellulose acetate in solution. I. Light scattering,osmometry, and viscometry on dilute solutions

Light-scattering, osmotic pressure, and viscometric studies on fractions of cellulose acetate (degree of substitution 2.45) in three solvents are described. The data yield the dependence of the mean-square radius of gyration 〈s²〉, the second virial coefficient Γ₂, and the intrinsic viscosity [η] on molecular weight M and temperature. The results are interpreted to show that excluded volume effects on 〈s²〉 are negligible, even though Γ₂ is large and dΓ₂/dT is positive. The large experimental value of d In [η]/d In M is interpreted in terms of partial draining effects. Data on 〈s₂〉 and [η] for other cellulose esters in the literature are similarly interpreted. Significant aggregation found in solutions of cellulose acetate in many solvents is discussed.     

Synthesis and solution properties of linear,four-branched,and six-branched star polyisoprenes

A number of linear, four- and six-branched regular star polyisoprenes were synthesized by anionic polymerization techniques in benzene using lithium as the counterion and polyfunctional silicon chloride compounds as the coupling agents. Light-scattering measurements in dioxane were performed in order to establish Θ solvent conditions. Determinations of the radius of gyration of the polymers of different structure indicate that g = 〈S²〉_0,br/〈S²〉_0,lin agree closely with random flight calculations for the ratios. Intrinsic viscosities determined in a Θ solvent establish g′ = [η]_br/[η]_lin to be 0.77₃ and 0.62₅ for the four- and six-branched polyisoprenes, respectively. In a good solvent g′ values are slightly lower. These values are compared with theoretical estimates. Viscosities of 19.29% (w/w) solutions of the polyisoprenes in n-decane at 25°C are correlated with the intrinsic viscosities of the polymers under Θ conditions.     

DETERMINATION OF BRANCHING DISTRIBUTION IN HIGH cis-1,4-POLYBUTADIENE BY GPC AND AUTOMATIC VISCOMETRY

Based on the methods reported by Ambler and Kraus, a method has been developed for the determination of long-chain branching distribution in polymers by the combined use of GPC and intrinsic viscosity data of polymer fractions. In this method, g_i, λ_i, G_i, m_i, the weight percentage of polymer that is branched, etc. can be used simultaneously to characterize the distribution, degree and content of branching in polymers. Some relations between molecular weight polydispersity and branching polydispersity in Nickel-based high cis-1,4-polybutadiene samples are discussed. It was found that the number of long branches λ. per unit molecular weight is a function of molecular weight and all of the samples are highly branched at a molecular weight of about 10~6.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.     

Characterization of low-density polyethylene by gel permeation chromatography—II. Study on the Drott method using fractions

Polyethylenes of different structures were fractionated and the fractions characterized by light scattering, gel permeation chromatography and viscometry. Intrinsic viscosities were measured in solvents of different thermodynamical quality including a θ-solvent (diphenyl at 118° for low-density polyethylene and at 130° for high-density polyethylene and ethylene-butene-1 copolymer). The results were used for examining two aspects of the Drott iterative procedure: (a) the relationship between thermodynamical quality of the solvent and depression in the intrinsic viscosity due to branching; and (b) analytical form of expression relating the so-called g-factor to the number of long-chain branches. The ratio of intrinsic viscosities of branched and linear species at a given weight-average molecular weight has been clearly proved to be solvent independent, and the equation relating the g-factor to the number of branches for polymer monodisperse with respect to molecular weights appears to be a fair representation of long-chain branching in low-density polyethylene. For the polymers examined, the branching frequency λ is not independent of molecular weight.     

Proposed GPC and intrinsic viscosity analyses of randomly crosslinked polymers having primary distributions of the schulz-zimm form

A mathematical treatment is presented for the gel-permeation chromatographic and intrinsic viscosity behavior of randomly crosslinked polymers having primary molecular weight distributions of the Schulz-Zimm form. Kimura's serial solution of the integro-differential equation derived by Saito for randomly crosslinked polymers is employed for the distribution function. The intrinsic viscosity of a molecule containing i crosslinks is assumed related to that of a linear molecule of the same number of units through [η]_br/ = g_i^½[η]_l where g_i = (R_br²)_i/R_l² = {[1 + (i/6)]^½ + (4i/3π)}^?½. R_brand R_l denoting the root-mean-square radii of gyration of branched and linear chains of the same mass. It is also assumed that GPC elution is controlled by the hydrodynamic volumes of the molecules. Representative calculation results are displayed for polymers with a narrow primary distribution and the “most probable” primary distribution. Results for the latter polymers are compared with those previously obtained by a somewhat different mathematical approach.     

Polymerization of vinyl chloride with organolithium compounds. V. Fractionation and solution properties of high molecular weight poly(vinyl chloride)

A sample of high molecular weight poly(vinyl chloride) (PVC) was fractionated by classical precipitation fractionation and gel-permeation chromatography (GPC) on a preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, and by the GPC method. The measured weight-average molecular weights M?_w, intrinsic viscosity [η], and polydispersity index M?_w/M?_n values were used for the determination of the Mark-Houwink equation, [η] = KM^a, for PVC in cyclohexanone (CHX) at 25°C valid for molecular weights from 100,000 to 625,000.     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Chromatographic mass of a polymer and its use for determining the molecular mass characteristics

The method has been proposed for determining the molecular characteristics of flexible-chain polymers that obey the universal calibration principle and for which there are available experimental data on the intrinsic viscosity. This method is based on studying the dependence of the hydrodynamic volume M _n[η], M _w[η], M _z[η], and M _η[η] on parameter a in the Mark-Kuhn-Houwink equation. It has been found that, for parameter a varying in the range from 0.5 to 0.8, the weight-average hydrodynamic volume M _w[η] remains almost unchanged. This allows estimation of M _w based on a single intrinsic viscosity value. The notion of the chromatographic mass of a polymer is advanced and is employed for determining other molecular mass parameters.     

Anionic polymerization of caprolactam. XLIII. Relationship between osmometric molecular weight,viscosity, and endgroups of a polymer

For unfractionated anionic polymers, the following relationship between the osmometric molecular weight and intrinsic viscosity is valid: M?_n = 13200[η]^1.115 (cresol), or M?_n = 13000[η]^1.021 (93.8% H₂SO₄). A comparison of the osmometric and viscometric data with the number of endgroups of a polymer confirmed the finding that under certain conditions, moderately branched molecules can be formed; the above parameters depend on the type of the activator used.     

Solution and thermal properties of poly(1,3-dioxocane)

Poly( 1,3-dioxocane) was synthesized by cationic ring-opening polymerization with triphenyl-methane hexafluoroantimoniate as the initiator and was studied with regard to its solubility, unperturbed chain dimensions, and thermal transitions. The intrinsic viscosity and Flory-Huggins interaction parameter were used to determine the solubility parameter, δ_p = 9.6 cal^1/2cm^?3/2, a value that agrees with that calculated empirically. Fractions were obtained from the solvent/non-solvent system benzene/methanol at 25°C. The number-average molecular weight M_n and intrinsic viscosity [η] were measured in toluene at 25°C. The relation [η] = 1.45₉. 10^?4 M_n^0.79 was found. A value of 5.3 was obtained for the characteristic ratio 〈r²〉₀/nl². Results are correlated with the main thermal transitions of this polyformal.     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

On-line viscometry combined with gel permeation chromatography. II. Application to branched polymers

Gel permeation chromatography (GPC) combined with on-line flow time measurements have been applied to the analysis of branching in polymers. Three sets of branched polymers were examined: polybutadienes lightly crosslinked by high energy radiation, a styrene-divinyl benzene copolymer and several of its fractions, and polyvinyl acetates branched by polymer transfer reactions during polymerization. The reduction in intrinsic viscosity due to branching was determined for each GPC fraction of the polybutadiene samples. The branching frequency in these fractions was known from other information, so the results were used to establish a relationship between viscosity ratio G and the theoretical size ratio g. This relationship was then used to calculate the distribution of branching and M _w in the styrene copolymers and the polyvinyl acetates. The results were compared with independent information on these polymers. The agreement was generally good.     

Molecular characterization of a hyperbranched polyester. I. Dilute solution properties

A hyperbranched polyester was fractionated by precipitation to produce 10 fractions with molecular weights between 20 × 10³ and 520 × 10³ g mol^?1. Each of these fractions was examined by size exclusion chromatography, dilute‐solution viscometry, intensity, and quasi‐elastic light scattering in chloroform solution at 298 K. High‐resolution solution‐state ¹³C NMR was used to determine the degree of branching; for all fractions this factor was 0.5 ± 0.1. Viscometric contraction factors, g′, decreased with increasing molecular weight, and the relation of this parameter to the configurational contraction factor, g, calculated from a theoretical relation suggested a very strong dependence on the universal viscosity constant, Φ, on the contraction factor. A modified Stockmayer–Fixman plot was used to determine the value of (〈r²〉_o/M_w)^1/2, which was much larger than the value for the analogous linear polymer. The scaling relations of the various characteristic radii (R_g, R_h, R_T, and R_η) with molecular weight all had exponents less than 0.5 that agreed with the theoretical predictions for hyperbranched polymers. The exponent for R_g was interpreted as fractal dimension and had a value of 2.38 ± 0.25, a value that is of the same order as that anticipated by theory for branched polymers in theta conditions and certainly not approaching the value of 3 that would be associated with the spherical morphology and uniform segment density distribution of dendrimers. Second virial coefficients from light scattering are positive, but the variation of the interpenetration function, ψ, with molecular weight and the friction coefficient, k_o, obtained from the concentration dependence of the diffusion coefficient suggests that chloroform is not a particularly good solvent for the hyperbranched polyester and that the molecules are soft and penetrable with little spherical nature. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1339–1351, 2003     

Association of polyacrylonitrile prepared by low-temperature,solution polymerization with an organometallic catalyst

The weight-average molecular weights of polymers of acrylonitrile prepared by a free-radical initiator and an organometallic catalyst have been determined by lightscattering measurements in N,N-dimethylformamide, dimethyl sulfoxide, and dimethylacetamide at 25°C. and in dimethyl sulfoxide at 140°C. The apparent molecular weights of the polymers prepared with the NaAlEt₃S(i-Pr) catalyst in DMF at ?78°C. (referred to as high-melting polymers) changed from 54,800, 82,700, and 480,000 when measured in DMF at 25°C. to 36,000, 41,600, and 225,000 when measured in DMSO at 140°C., whereas the molecular weights of the free-radical polymers remained unchanged. Furthermore, from results obtained in DMSO at 140°C., The intrinsic viscosity–molecular-weight relationships were found to be identical for the high-melting and the free-radical polymer and in substantial agreement with an equation reported by Cleland and Stockmayer. The apparent decrease in molecular weight of the high-melting polymer from 25 to 140°C. indicates rather clearly that the high-melting polymers are associated in DMF at 25°C. The “aggregates,” even though present only at low concentrations, raised the weight-average molecular weight markedly but affected the number-average molecular weight only slightly, thus giving a high M?_w/M?_n ratio. It appears likely that when temperature and solvent are such that association does not occur, linear PAN's will have approximately the same intrinsic viscosity–molecular weight relationship (subject of course to slight change by polydispersity). The often reported abnormal molecular weight of samples prepared by solution polymerization especially at low temperatures, may be attributed to branching, or to an association, as reported here. The nature of association of PAN in dilute solution is also discussed.