Determination of branching distribution by concurrent GPC and sedimentation velocity experiments

A method of determining the distribution of branching in polydisperse polymer samples is proposed. This method uses data from concurrent gel permeation chromatography and sedimentation-velocity experiments. Tedious fractionation, which must precede other methods of determining long-chain branching, is eliminated. An example of use of the method on the data of a sample of styrene–divinylbenzene copolymer is given.     

Effect of long-chain branching on the relation between steady-flow and dynamic viscosity of polyethylene melts

The steady-state viscosity η, the dynamic viscosity η′, and the storage modulus G′ of several high-density and low-density polyethylene melts were investigated by using the Instron rheometer and the Weissenberg rheogoniometer. The theoretical relation between the two viscosities as proposed earlier is:\documentclass{article}\pagestyle{empty}\begin{document}$ \eta \left( {\dot \gamma } \right){\rm } = {\rm }\int {H\left( {\ln {\rm }\tau } \right)} {\rm }h\left( \theta \right)g\left( \theta \right)^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \tau {\rm }d{\rm }\ln {\rm }\tau $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \theta {\rm } = {\rm }{{\dot \gamma \tau } \mathord{\left/ {\vphantom {{\dot \gamma \tau } 2}} \right. \kern-\nulldelimiterspace} 2} $\end{document}; \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} is the shear rate, H is the relaxation spectrum, τ is the relaxation time, \documentclass{article}\pagestyle{empty}\begin{document}$ g\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{\theta \mathord{\left/ {\vphantom {\theta {\left( {1 + \theta ^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 + \theta ^2 } \right)}}} \right] $\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$ h\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} \mathord{\left/ {\vphantom {{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right. \kern-\nulldelimiterspace} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right] $\end{document}. Good agreement between the experimental and calculated values was obtained, without any coordinate shift, for high-density polyethylenes as well as for a low density sample with low n_w, the weight-average number of branch points per molecule. The correlation, however, was poor with low-density samples with large values of the long-chain branching index n_w. This lack of coordination can be related to n_w. The empirical relation of Cox and Merz failed in a similar way.     

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.     

Molecular weight and long-chain branching distributions of some polybutadienes and styrene–butadiene rubbers. Determination by GPC and dilute solution viscometry

A method described for the determination of molecular weight and long-chain branching distributions of polymers requires no prior knowledge of the functional relation between branching frequency and molecular weight. It is based on preparative fractionation and viscometric and gel-permeation chromatographic measurements on both fractions and whole polymer. The technique is applied to several polybutadienes and butadiene-styrene copolymers differing widely in method of synthesis and pattern of long-chain branching.     

GPC,CD and sedimentation analysis of poly-Lys and branched chain poly-Lys-poly-DL-Ala polypeptides

Three different poly-L-lysine (pLys) samples and a branched polypeptide poly-[L-Lys-(DL-Ala)_m] (poly-L-Lys-poly-DL-Ala, AK) were synthetized. Relative molar mass distribution, its average and the degree of polymerisation were determined by sedimentation analysis and gel permeation chromatography (GPC). The conformation of the polymers in solution was studied by circular dichroism (CD) spectroscopy at various pH values and ionic strengths. The data obtained by different methods were compared.A preliminary account of this work was read at the 4^th Conference on Colloid Chemistry, Eger, 1983.     

Molecular flexibility of methylcelluloses of differing degree of substitution by combined sedimentation and viscosity analysis

The flexibility/rigidity of methylcelluloses (MCs) plays an important part in their structure-function relationship and therefore on their commercial applications in the food and biomedical industries. In the present study, two MCs of low degree of substitution (DS) 1.09 and 1.32 and four of high DS (1.80, 1.86, 1.88 and 1.93) were characterised in distilled water in terms of intrinsic viscosity [h]; sedimentation coefficient (s020,w) and weight average molar mass (Mw). Solution conformation and flexibility were estimated qualitatively using conformation zoning and quantitatively (persistence length Lp) using the new combined global method. Sedimentation conformation zoning showed an extended coil (Type C) conformation and the global method applied to each MC sample yielded persistence lengths all within the range Lp(1/4)12-17 nm (for a fixed mass per unit length) with no evidence of any significant change in flexibility with DS.     

Light scattering and intrinsic viscosity investigation of polymethyl-3, 3, 3-trifluoropropylsiloxamer

Solution parameters for the polymer poly-γ-trifluoro-propylmethylsiloxamer has been determined in cyclohexyl acetate, methyl hexanoate, and ethyl acetate. Interpretation of data follows the theory of Fox and Flory. In contrast to poly-dimethylsiloxane, an increased steric hindrance to rotation about the siloxane bond occurs as evidenced by the characteristic ratio of root-mean-square end to end dimensions, (r₀² /r_0f² )^1/2, found to be 1.90 and 1.96 at 25.0 and 72.8°C, respectively. This increase is considered to be primarily due to nearest-neighbor interaction of the polar substituent on the silicon atom. The relation, [η]θ ∝ M^1/2, was observed to hold for this polymer system. The hydrodynamic model appropriate for the polymer is a random coil considerably more permeable to solvent flow than is generally reported for linear polymers. The universal parameter ? was determined to be 1.5 × 10²¹. The effect of temperature on polymer configuration is indicated to be negligible.     

Interplay between electrophoretic mobility and intrinsic viscosity of polypeptide chains

The present work is motivated specifically by the need to find a simple interplay between experimental values of electrophoretic mobility and intrinsic viscosity (IV) of polypeptides. The connection between these two properties, as they are evaluated experimentally in a formulated dilute solution, may provide relevant information concerning the physicochemical characterization and separation of electrically charged chains such as polypeptides. Based on this aspect, a study on the relation between the effective electrophoretic mobility and the IV of the following globular proteins is carried out: bovine carbonic anhydrase, staphylococcal nuclease, human carbonic anhydrase, lysozyme, human serum albumin. The basic interpretation of the IV through polypeptide chain conformations involves two unknowns: one is the Flory characteristic ratio involving short-range intramolecular interactions and the other is the Mark-Houwink exponent associated with large-range intramolecular interactions. Here, it will be shown via basic and well-established electrokinetic theories and scaling concepts that the IV and global chain flexibility of polypeptides in dilute solutions may be estimated from capillary zone electrophoresis, in addition to classical transport properties. The polypeptide local chain flexibility may change due to electrostatic interactions among closer chain ionizing groups and the hindrance effect of their associated structural water.     

Influence of polydispersity and long chain branching on the melt viscosity of polycarbonate

The Newtonian and non-Newtonian melt viscosities of bisphenol A polycarbonate (PC) at 280°C were treated according to the generalized multivariable power function, where the average molecular weights, polydispersity degree and branching degree are considered as variables. The shear rate was also considered as a variable for non-Newtonian conditions. In the same way, the melt fluidity was treated as a multivariable power function. It has been found that the same melt flow properties of polymer can be obtained by an appropriate combination of Newtonian melt viscosity (being a function of molecular weight) and long chain branching. The experimental data on PC agree with the theoretical approach of Bucche and Graessley.     

Effect of temperature on the intrinsic viscosity and conformation of different pectins

The effects of temperature on the intrinsic viscosity and on the conformation of pectin obtained from Citrus, Apple and Sunflower in a 0.17M NaCl solution were studied. Mark-Houwink plots for Orange, Apple and Sunflower pectin were obtained using HPSEC with online light scattering and viscosity detection. The intrinsic viscosity and flow activation energy E _a of pectin from the sources studied were measured over the temperature range 20–60°C. E _a values were 0.67, 0.69, 1.34, and 1.44 × 10⁷ J/(kmol) for commercial Citrus, Orange, Sunflower and Apple pectin, respectively. Intrinsic viscosity decreased linearly with increasing temperature, for all pectins except Apple one. These results clearly indicated that Apple pectin underwent structural changes that were more drastic than those that occurred for pectin from the other sources. E _a increased with decreasing weight average molar mass M _w indicating that pectin with low M _w were more asymmetric than pectin with higher values of M _w. Changes in the Huggins coefficients K _h with temperature for pectin from the various sources were attributed to the ability of pectin to aggregate, disaggregate and re-aggregate according to the temperature at which it was stored.     

The relation between the molecular weight and intrinsic viscosity of polymethyl acrylate

Summary A series of unfractionated and fractionated samples of polymethyl acrylate of different low molecular weights have been prepared by homogeneous solution. polymerization in dimethyl formamide in presence of , '-azo-(-cyano-n-valeric acid) as initiator under a variety of conditions. The number-average molecular weights have been determined by end-group titrations and vapour pressure osmometry. The following []-M relationships for polymethyl acrylate have been obtained.[] = 33.5 x 10^–5M^0.63 for unfractionated samples in benzene at 25 °C. [] = 3.89 x 10^–5M^0.843 for fractionated samples in benzene at 35 °C.With 2 tables     

Relation between preferential solvation and intrinsic viscosity of polymers in solvent mixtures

Preferential solvation and intrinsic viscosity measurements are reported for three systems: polystyrene + benzene + methanol, polystyrene + carbon tetrachloride + methanol, and poly(2-vinylpyridine) + ethanol + cyclohexane. Plots of the coefficient of preferential solvation λ′ as a function of variation of the segment density Δ_ρ for a given ternary system, give a single curve for a large range of molecular weight and solvent mixture composition. This correlation between λ′ and Δ_ρ is verified in previously published data.     

The relation between the molecular weight and intrinsic viscosity of polyvinyl alcohol

Summary A series of unfractionated and fractionated samples of polyvinyl acetate were prepared by homogeneous solution polymerization of vinyl acetate in N,N-dimethylformamide at 90 °C. in presence of , -azo-(-cyano-n-valeric acid) as initiator under a variety of conditions. A portion of each sample was hydrolysed to polyvinyl alcohol. The number average molecular weights have been determined by end-group titrations. The following molecular weight-intrinsic viscosity relationships for polyvinyl alcohol have been obtained. [] = 33.88 X 10^–5 M ^0.716 — for unfractionated samples in water at 30 °C. [] = 29.51 X 10^–5 M ^0.716 — for fractionated samples in water at 30 °C.With 1 figure and 2 tables