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.     

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.     

Molecular weight and molecular weight distribution from dynamic measurements of polymer melts

A method for determining the molecular weight distribution (MWD) of a polymer melt has been developed using the dynamic elastic modulus (G'), plateau modulus (G), and zero shear complex viscosity (η). The cumulative MWD was found to be proportional to a plot of (G'/G)^0.5 vs. measurement frequency (ω). Frequency (ω) was found to be inversely proportional to (MW)^3.4, as expected. Results were scaled to absolute values using the empirical relationship η ∝ (M?_w)^3.4, where M?_w is the weight-average MW. M?_w, M?_n (number-average MW) and M?_w/M?_n calculated from melt measurements were found to agree with size exclusion chromatography usually well within 10 percent for broad and bimodal distribution samples. M?_w/M?_n tended to be approximately 20 percent higher for narrow distribution samples (M?_w/M?_n < 1.2) because we did not account for a finite distribution of relaxation times from a collection of monodisperse polymer chains. We also did not account for the plasticizing effect of short chains mixed with long ones which caused peak positions to be closer together for Theological vs, size exclusive chromatography (SEC) determinations of MW for bimodal distribution blends.     

Comparaison des méthodes de fractionnement par chromatographie de perméation et par gradient d'elution pour la détermination des répartitions moléculaires des polypropylénes

Molecular weight distributions for polypropylene samples have been determined by a permeation fractionation method (GPC). Porous silica beads were used as a packing material for the columns. The set of columns allows a good separation of the polypropylene macromolecular chains in a range of molecular weights from 5000 to 1.5 × 10⁶, and the thermal and mechanical stabilities of these beads are very good. The calibration has been carried out with fractions of polypropylene of narrow molecular weight distribution prepared by a large-scale column fractionation. The molecular weights M?_w and M?_n and the ratios M?_w/M?_n calculated from the GPC curves show, in general, good agreement with the ones calculated from the column fractionation curves. However, the M?_w/M?_n ratios are always highter in the case of GPC fractionation. This could be due to diffusion phenomena.     

Hydrolysis of 1,4-cyclohexanedimethanol-based copolyester

The solid state hydrolysis of a copolyester based on a mixture of 1,4-cyclohexanedimethanol and ethylene glycol condensed with terephthalic acid was studied at 100°C and 57 to 96 kPa water vapor partial pressure (55% to 95% relative humidity). The equilibrium water sorption in weight percent (C_∞) was found to be where P is the water vapor partial pressure in kPa. For specimens 0.32-cm thick, it took about 24 h to reach 0.9C_∞. The intrinsic viscosity (IV) was measured and used to calculate the relative change in molecular weight (M?_w) from the relationship IV ∝? (M?_w)^0.7. The decrease in molecular weight was linear with time, and the rate of decrease was found to be proportional to C_∞; the empirical correlation is where the rate constant, k, is in day^?1. A decrease of 50% in M?_w was observed after 22 days at 95% relative humidity.     

Polyether polyols as GPC calibration standards for determination of molecular weight distribution of polyether polyols

Average molecular weights (M_n, M_w and M_p) are important characteristics of oligomers and polymers, and therefore there is a need to have a precise and reliable determination method. A gel permeation chromatography (GPC) coupled with a single refractive index detector was used to determine the molecular weight distributions of commercial polyether polyols calibrated against a series of polyether polyols with known molecular weights and low polydispersity. Results of these GPC analyses were compared to the ones calibrated against the commercially available polystyrene (PS) standards. The number‐average molecular weights (M_n) obtained with GPC using polyether polyols calibration were closer to the theoretical values than the M_n obtained using PS as calibration standards. Hence, these GPC analyses using polyether polyols as calibration standards can provide reliable determination of molecular weight distribution of polyether polyols and can be potentially applied to natural oil‐based polyols, including palm oil‐based polyols. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42698.     

Light-scattering studies on solutions of high and low molecular weight polystyrene mixtures used as models of microgel-containing solutions

Diluted solutions of linear polystyrene (PS) in toluene and dioxane were studied by the light-scattering method. The solutes were mixtures of high-M?_w and low M?_w PS. The dissolved PS mixtures were regarded as polymer solutions containing microgels, the high-M?_w PS being looked upon as the microgel counterpart. The calculation method as proposed by Strazielle¹ and Burchard² was used to evaluate the microgel percentage and particle size, whereby the method could be verified against mixtures with well-known weight composition and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document}. The \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values evaluated for the mixtures from the experimental data were compared with those estimated from the molecular weights of the components, their weight concentrations, and their \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values. The method^1,2 was found to be useful for evaluating the microgel content in a sample, but not for \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values as calculated by Guinier's procedure nor those calculated by Zimm's procedure; the former were low and the latter were even incongruous. A comparative analysis of the theoretical function P^?1(θ)-versus-sin² (θ/2) and experimental (Kc/R(θ))_c=0-versus-sin² (θ/2) curves allowed to discuss the effect of the course of these curves at samll angles from 0° to 30° on M?_w and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} as determined for the high and low molecular weight polystyrene mixtures in toluene as solvent.     

An analytical solution to Tung's axial dispersion equation. Applications in gel permeation chromatography

Equations developed for correcting M_n, M_w, and [μ] for imperfect resolution are generally satisfactory. Choosing the appropriate instrumental spreading function is however a very difcult task. There is need for further research on this problem, in particular with polymer standards for which the DMWD or even M_z is known (in addition to M_n and M_w). A criterion for resolution in GPC which is based on a solution of Tung's axial dispersion equation has been proposed. The operation of GPC in recycle mode appears very promising. Equations have been developed to interpret data obtained in this operational mode. It is probable that a great deal of work will be done in this area in the very near future.     

Copolymerization of 2,6-dimethoxy- and 2,6-dimethylphenol and effect of the copolymer structure on the thermodynamic properties in the solid state

2,6-Dimethoxyphenol and 2,6-dimethylphenol have been copolymerized using the Ag₂O-triethylamine complex as catalyst. The products are random copolymers with wide molar mass distributions, M?_w/M?_n from 2.3 to 3.5. The larger size of the methoxy group than that of the methyl group has no effect on the reaction rate. The heat capacities of the copolymers can be calculated from the values of the homopolymers to an accuracy of within ± 1% from 160 to 280 K. ΔC_p at T_g for the copolymers changes linearly from the value of poly(oxy-2,6-dimethoxy-1,4-phenylene) to that of poly(oxy-2,6-dimethyl-1,4-phenylene) and the glass transition temperatures of the copolymers can be described by the equation of Couchman: \documentclass{article}\pagestyle{empty}\begin{document}$${\rm K} = \Delta {\rm C}_{{\rm p} 2} / \Delta {\rm C}_{{\rm p} 1}.$$\end{document}     

Relationship in polypropylene melt between its linear viscoelasticity and its steady capillary flow properties

It is the object of the present study to obtain clear knowledge of the relations in the polypropylene melt between its linear viscoelasticity and its nonlinear steady capillary flow, paying particular attention to the elastic properties in its capillary flow. By representing the linear viscoelasticity numerically with zero-shear viscosity, η₀, and steady-state compliance, J, evaluation has been made of the properties concerning the elasticity of polymer melt in the capillary flow, such as non-Newtonianity, the entrance pressure loss, the end correction, the Barus effect, and the melt fracture. The steady flow viscosity η, the entrance pressure loss P₀, the critical shear stress, τ_c, and the critical shear rate $\dot \gamma _c$ at which melt fracture begins to occur are subject to η₀ as follows: From the well-known relationship between η and the weight-average molecular weight M?_w, these quantities are governed by M?_w. Meanwhile, for such quantities as structural viscosity index N, end correction coefficient ν, and elastic pressure loss ratio P₀/P, following correlations hold: As η₀ and J are respectively determined mainly by M?_w and the molecular weight distribution MWD, these quantities are governed by both M?_w and MWD. Physical meanings of η₀·J and η₀² · J are, respectively, mean relaxation time and a measure of stored energy in steady flow. The Barus effect has a positive correlation to J, ν, and P₀/P. (The symbol ∝ employed here means positive correlation.)     

Synthesis and Properties in Solution of Gaussian Homo Asymmetric Polysiloxanes with a Bulky Side Group

Ring opening polymerization (ROP) of 1,3,5-tri-n-hexyl,1,3,5-trimethylcyclotrisiloxane (D ₃ ^Hexa ) and 1,3,5-tri-n-heptyl,1,3,5-trimethylcyclotrisiloxane (D ₃ ^Hepta ) was promoted by acid-treated synthetic silica–alumina to obtain Gaussian homo asymmetric polysiloxanes. M_w was above 70?kg/mol, meaning that homo asymmetric bulky side-group polysiloxane chains with high molecular weight were obtained. The material was treated in an acidic medium to improve the contents of acid sites and successfully tested as an inorganic acidic catalyst for ROP of D ₃ ^Hexa and D ₃ ^Hepta cyclosiloxanes. The samples of poly(methylhexylsiloxane) (PMHS) and poly(methylheptylsiloxane) (PMHepS) obtained were structurally characterized mainly by ²⁹Si NMR. All the experimental values including the refractive index increment (dn/dc), the second virial coefficient (A₂), the square root of the mean square radius of gyration ( $ \langle {{\text{RMS}}_{\text{radius}}}^{ 2} \rangle^{ 1/ 2} $ ), the average molecular weight (M_w), the average molecular numeral (M_n), and the weight polydispersity (M_w/M_n) were obtained using a gel permeation chromatography/light scattering (GPC/LS) coupled system. The A₂ experimental value for the two polymers (between 4 and 6.5?×?10^?4?mol/mL?g²) indicated that toluene was a good solvent. In addition, PMHS and PMHepS $ \langle {{\text{RMS}}_{\text{radius}}}^{ 2} \rangle^{ 1/ 2} $ were greater than 30?nm, indicating that larger chains of high molecular weight were obtained.     

Emulsion polymerization kinetics and reactor design. IV. Continuous-flow operation with recycling

A new mathematical model with a correction for radical capturing efficiency in a continuous emulsion polymerization with recycle flow has been proposed. These performance equations predict the conversion as well as molecular weight distribution of the polymer product during the continuous-flow operation. Experimental results obtained with vigorous mixing associated with a premixer are in best agreement with the theoretical prediction. In certain situations, the recycling provides a means for obtaining a higher degree of back-mixing with a normal flow reactor. However, it is difficult to obtain a high conversion of monomer by a continuous emulsion polymerization operation even with a long residence time. Theoretical and experimental average degrees of polymerization of polymer leaving the reactor are progressively displaced toward smaller values with greater mean residence time. According to the calculations based on our kinetic model the ratio M?_w/M?_n in the continuous emulsion polymerization remains constant regardless of mean residence time.     

Dispersion in gel permeation chromatography. A rapid numerical solution to Tung's integral equation

A rapid iteration method has been developed to correct the molecular weight averages calculated from raw GPC data for dispersion. Though simple in its performance, it covers the general case that the instrumental spreading characteristics (Tung's resolution factor h) depend on the elution volume. Moreover, it is irrelevant whether the calibration curve, being the logarithmic plot of the molecular weight versus the elution volume, is linear or not. The method has been applied to a number of well-characterized polystyrene mixtures and yields molecular weight averages which agree with those predicted theoretically. The effect of asymmetry exerted by the dispersion on both molecular weight averages M?_n and M?_w is also discussed.     

Predicting elastic moduli of heterogeneous polymer compositions

A new method for predicting elastic moduli M of heterogeneous polymer compositions is proposed. It is based on a phenomenological adjustment between parallel and series models for upper and lower bound moduli M_U and M_L. Thus, where ?_H is the volume fraction of hard phase, ?_S is the volume fraction of soft phase, and n is the only adjustable parameter since the upper and lower bound moduli are given by and where M_H and M_S are the moduli of the pure hard and soft phases, respectively. Predicted values of M are in agreement with measured values in a number of systems which include polyblends and composite materials of fixed morphology. The significance of n is discussed relative to concentrations in the area of a phase transition for the polyblends or relative to phase morphology in the case of fixed morphology compositions. Interestingly, the relationship, by analogy, is in agreement with measured values of polyblend melt viscosities.     

A phenomenological master curve for viscosity—structure data for two phase polymer systems in simple shear flow

A master curve hypothesis is established based on a mass balance and an assumption of continuous stress through interfaces for well dispersed two phase systems with “defined” zero shear viscosity. The master curve, which is in reasonable accordance with experimental data is represented in a double logarithmic plot of log (η_T/_T,0) against log \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{\eta _{T,0} M_C H\rho}}{{c^2 RT}}\dot \gamma _T} \right) $\end{document}. M_c is the molecular weight between entanglements, H = M?_w/M?_n, ρ is the density, c is the polymer concentration, all defined for the continuous phase. η_T and η_T,0 are the viscosity and zero shear viscosity of the blend, η_T is the apparent shear rate, R the gas constant, and T is absolute temperature.     

Preparation and glass transition temperature of hyperbranched poly[allyl methyl maleate‐co‐N‐propyl maleimide]

The kinetics and molecular weight averages of the hyperbranched polymers formed by the alternating copolymerization of equimolar allyl methyl maleate (AMM) and N‐n‐propyl maleimide (PMI) were investigated. The yields, molecular weight averages, and polydispersity indices as well as the branching degrees of the produced copolymers increased with increasing initiator concentrations and prolonged polymerization time. The trends of the experimental molecular weights as determined by size exclusion chromatography were in good agreement with the theoretical predictions. The molecular weight distribution indices fit the curve given by M_w/M_n = 1/(1‐x_D), and the molecular weights fit the curve given by M_w = 4076/(1‐x_D)², where x_D was the conversion of vinyl groups. DSC studies demonstrated a nonlinear relation of T_g values to the reciprocal of molecular weight (M), and T_g values decreased with the increase of molecular weight. For the T_g values of highly branched polymers in high molecular weight range, a relation of T_g = T + k/M was obtained, where T was obtained by extrapolating to infinite molecular weight and k was a constant. T was 136°C, and k = 2.9 for this work. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1941–1947, 2005     

Molecular Weight Distribution of Low Molecular Weight Polyols Derived from Fatty Acid Methyl Esters

A series of commercial polyether polyols with well-defined molecular weights (MW) was used along with propylene glycol and dipropylene glycol as gel permeation chromatography (GPC) calibration standards to determine the MW and oligomeric composition of the synthesized low MW fatty acid methyl ester (FAME) polyols, having an MW of lower than 600 Da. This GPC analysis was compared to the one calibrated against the commercially-available polystyrene (PS) standards and to the number-average molecular weight (M _n) obtained via vapor pressure osmometry (VPO) technique. The MW of FAME polyols obtained with GPC calibrated against polyether polyols were closer to the M _n values obtained via VPO than the MW obtained via GPC calibrated against PS standards. Using the reliable GPC calibration, the MW distribution and the hydroxyl functionality of FAME polyols were determined with greater confidence.     

Studies on determination of molecular weight for ultrahigh molecular weight partially hydrolyzed polyacrylamide

The molecular weight characterization of partially hydrolyzed polyacrylamide (HPAM) for enhanced oil recovery use is rather difficult because of its ultrahigh molecular weight copolymer and polyelectrolyte behaviors in solution. In this work the effects of aqueous NaCl solution concentration and degree of hydrolysis of polymer on molecular dimension were studied. A simple and precise method for determining molecular weight of HPAM is presented. The molecular weight of HPAM with any degree of hydrolysis can be calculated from the [η]−M_w equation of unhydrolyzed PAM in an H₂O system by measuring , of HPAM obtained in aqueous NaCl solutions by extrapolating salt concentration to infinity. Because the values of of HPAM of different degrees of hydrolysis are all equal to the corresponding [η] value of the unhydrolyzed PAM of the same degree of polymerization, the molecular weight of HPAM of any degree of hydrolysis can thus be calculated from the [η] − M_w equation for PAM homopolymer. © 1996 John Wiley & Sons, Inc.     

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.     

Gel permeation chromatography in the study of the molecular weight distribution of the copolymer vinyl chloride–vinyl acetate

A sample of the commercial copolymer vinyl chloride–vinyl acetate was fractionated by the GPC method in the preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, GPC in the analytical scale, chemical analysis, and IR spectroscopy. They were compared with those obtained by precipitation fractionation. The M?_w and [η] values from the light scattering and viscometry of fractions of the commercial copolymer were employed for the calculation of the Mark-Houwink equation valid in THF at 25°C for a copolymer with vinyl acetate content of 10–13%. Universal calibration of the [η]·M type was confirmed experimentally for the above polymer. Effects which could change the correct interpretation of the GPC data were discussed in detail. Correct interpretation of the GPC data showed an agreement between the GPC, light scattering, and viscometric data within 6–7%.