Molecular Architecture of Non-Linear Polymers: Kinetic Modeling and Experimental Characterization of the System Methyl Methacrylate + Ethylene Glycol Dimethacrylate

A general kinetic approach allowing the prediction of the molecular architecture of non-linear polymers is applied to the study of the copolymerization of methyl methacrylate (MMA) with ethylene glycol dimethacrylate (EGDMA). Dynamic predictions of molecular weight distributions, sequence length distributions and mean square radius of gyration are possible before and after gelation. A set of experiments concerning the copolymerization of MMA and EGDMA was carried out in toluene solution at 60 °C for which classic radical kinetics is a good approximation. The time evolution of key polymer properties was followed using a SEC system with a refractive index detector coupled with MALLS allowing the determination of absolute weight average molecular weight and apparent molecular size distributions as well as z-average radius of gyration. Special focus was given to assess the influence of the initial amount of cross-linker on the dynamics of the non-linear structure build-up of these products. A kinetic scheme comprising 23 different chemical species and 76 chemical reactions was used in the modeling studies of this chemical system. Most of the kinetic parameters used in the simulations have been collected from previous studies. For experiments at low monomer conversion (up to about 0.5) a good agreement between predictions and experimental measurements is observed for molecular weights and z-average radius of gyration by fitting a small number of parameters describing gel effect (with a conversion dependent but chain length independent termination rate parameter) and the relative propagation on pendant double bonds. However, predicted values of weight-average molecular weights and z-average radius of gyration before gelation are too low at higher monomer conversions with non-linear systems. The likely cause is the presence of intramolecular reactions which should not be neglected in these circumstances.     

Spectrum of light scattered from polydisperse polymer solutions

We examine several methods for analyzing the spectrum of light scattered from polydisperse polymer solutions. General expressions are reviewed for the inelastic scattering spectra and integrated intensities due to the pure translational normal mode of motion, using both heterodyne and homodyne detection, in terms of the molecular weights, concentrations, scattering form factors, and diffusion coefficients of the individual polymeric species, These results are used to obtain general expressions for the limiting slopes and intercepts of various rearranged versions of the equation I(v) = (A/π)²/(v² + γ²) that permit linear plotting: I(v) is the intensity of light scattered at frequency v, A is the integrated intensity, and γ is the spectral halfwidth, K²D/2π, where K is the scattering vector and D the diffusion coefficient. These results are applied to the special case of a Schulz-Zimm distribution, neglecting form factors, to obtain explicit expressions relating the average diffusion coefficients determined by these procedures to other measurable quantities: the mean polymer radius; the diffusion coefficient of the weight-average species; and, together with the weight-average sedimentation coefficient, the weight-average molecular weight. Numerical calculations for two particular cases indicate the relative merits of the various data analysis procedures. Homodyne detection gives average values that are closer to weight averages than does heterodyne detection.     

Solution properties of ultrahigh molecular weight polymers. VII. Conformational characteristics of poly(butyl methacrylate)

The paper is concerned with light scattering studies on solutions of ultrahigh molecular weight poly(butyl methacrylate). The dependence of the radius of gyration and of the second virial coefficient on the weight-average molecular weight of the polymers was established in methyl ethyl ketone, dimethylformamide, and CCl₄. Short-range and long-range interactions were discussed in terms of the steric factor σ, of the interaction parameter B, and of the interpenetration function ψ(z).     

The effect of molecular weight heterogeneity on the second virial coefficient of linear polymers in good solvents

The effect of molecular weight heterogeneity on the second virial coefficient A₂ in good solvents is studied for binary mixtures of monodisperse poly(α-methylstyrenes). It is concluded that A₂ for polymer mixtures passes through a maximum with variation of the mixing ration. From comparison with the data, it is concluded that no available theory quantitatively explains both the molecular weight dependence of A₂ of monodisperse polymer and the variation of A₂ of mixtures with the mixing ratio. The interpenetration function for two polymer coils with different molecular weights is discussed on the assumption that the thermodynamic interaction between two polymer coils in good solvents can be approximated by a hard-sphere model.     

Conformation of linear polyethylene in 1-chloronaphthalene: Light scattering characterization of polymers. IV

Light scattering measurements were carried out on a linear polyethylene sample NBS 1475 in 1-chloronaphthalene at 135 and 115°C to determine the weight-average molecular weight, the second virial coefficient A₂, and the z-average mean-square radius of gyration. By use of these results, the system is analyzed in terms of the interpenetration function Ψ for A₂. Observed values of A₂ are rather large but the excluded volume is nevertheless relatively small. Such behavior seem to be similar to that of semiflexible polymers. The characteristic ratio C_n,LS as determined by light scattering is found to be almost twice the literature value of 6.7, which was obtained from viscosity measurements. This discrepancy is explained by comparing the theoretical value of the Flory viscosity parameter Φ at the nondraining limit with values calculated from the light scattering results.     

Dilute solution characterization of polyfluoroalkoxyphosphazenes

Results from the dilute solution characterization of polyfluoroalkoxyphosphazenes in Freon ether (E2) solutions are reported. Anomalous viscosity data suggest that polymer aggregation sometimes occurs in E2 and may be caused by the presence of relatively few anomalous polar groups on the polymer backbone. Since small amounts of acetone added to the E2 solutions inhibit aggregate formation, samples are also characterized in an E2-acetone mixed solvent. Light scattering and osmometry indicate that E2 and E2-acetone (9.09% by volume) are theta solvents for the polymers. High molecular weights (M?_w < 3 × 10⁶) and unusually broad molecular weight distributions (M?_w/M?_n < 16) are found. One polymer is fractionated by extracting solutions in 1,1,2-trichloro-1,2,2-trifluoroethane with acetone. Although the samples are highly polydisperse, intrinsic viscosities correlate with number-average molecular weights satisfying the Mark-Houwink relation with the exponent a ≈ 1/2. The z-average mean-square radius of gyration increases linearly with molecular weight so that 〈S²〉_g/M?_w ≈ 0.098. Because of the large polydispersity and unknown form of the distribution function, a quantitative interpretation of characterization results relating dilute solution parameters to polymer skeletal structure is not possible. The tentative conclusion is that the fluoroalkoxy-substituted phosphazene polymers are relatively linear and therefore that the broad distribution of molecular weights must be due to some polymerization mechanism other than branching.     

Molecular weights and molecular weight distribution of polymers by equilibrium ultracentrifugation. Part II. Molecular weight distribution

A method has been developed for determining the molecular weight distribution of a polymer sample from the sedimentation–diffusion equilibrium data for a solution under pseudo-ideal conditions. From some theoretical examples it appears that the method works well and that the molecular weight distribution can be determined with a reasonable degree of resolution. From three polymer samples (polyethylene, polystyrene, and polycaprolactam) the molecular weight distribution was determined in this way. The average molecular weights, M?_n, M?_w, M?_z, and M _z+1, calculated from these distribution functions agree well with those calculated directly from the equilibrium data.     

Estimation of polydispersity in polymers and colloids by field-flow fractionaion

Various methodologies of sedimentation, thermal, and steric field-flow fractionation for the estimation of the polydispersity in polymers and colloids are presented. These are based either on retention and/or on zone-spreading data. The reference materials used are nearly monodisperse and polydisperse submicron polystyrene and PVC latex beads, nearly monodisperse spherical particles of hematite, and polydisperse irregular particles of strengite (FePO₄·2H₂O) and PS polymers of various molecular weights. The results found are compared with those determined by other techniques or given by the manufacturers.     

Application of the flory-mandelkern equation to individual unfractionated polymer samples

A method is developed for the application of the Flory-Mandelkern equation to the determination of the weight-average molecular weights of individual, broad, unfractionated polymer samples. The method includes appropriate averaging of the sedimentation constants and of the intrinsic viscosity of an unfractionated polymer sample in a θ solution from the velocity sedimentation data. By means of the method, individual samples of polystyrene, poly(isooctyl methacrylate) and of the copolymer of styrene with 20% isooctyl methacrylate prepared under the same emulsion polymerization conditions from commercial monomers have been investigated. Appropriate θ solvents have been found by the Elias method. Equations for the dependence of the sedimentation constants and of the intrinsic viscosities in the θ solvents on the molecular weights have been established for the polymers without fractionation. Osmometric and light-scattering measurements as well as Archibald experiments have shown that by the proposed method the molecular weight cut-off effect is eliminated in the above equations and in the polydispersity parameter M _w/M _n. Molecular weight distributions have been determined for the polymer samples.     

Molecular weight distribution in random branching of polymer chains

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight-average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T-shaped junctions) without assistance of crosslinkages (H-shaped junctions).     

Laser light-scattering characterization of gelatin in formamide

Laser light scattering (LLS) including angular dependence of absolute integrated scattered intensity (static LLS) and of the spectral distribution (dynamic LLS) has been used successfully to characterize gelatin in formamide at room temperature. In static LLS, the use of formamide as a single solvent instead of an aqueous salt solution avoids the well-known problem of preferential sorption of salts in the domain of gelatin molecules. Therefore the true weight-average molecular weight M_w, the z-average radius of gyration, and the second virial coefficient have been determined. In dynamic LLS, precise measurements of the intensity-intensity time correlation function permit a Laplace inversion to obtain an estimate of the normalized characteristic linewidth distribution which could be reduced to a translational diffusion coefficient distribution, G(D). This report shows that the calibration between D and M can be established from M_w and G(D) by using only two broadly distributed gelatins instead of a set of narrowly distributed gelatin standards. After establishing a calibration between D and M, we were able to estimate the molecular weight distribution of gelatin from G(D). © 1994 John Wiley & Sons, Inc.     

Effects of molecular weight distribution in drag reduction and shear degradation

A reduction of frictional drag in turbulent flow was obtained in benzene by using three monodisperse polystyrene samples having weight-average molecular weights of 1.8, 4.1 and 7.1 × 10⁶. By testing these polymers individually and in mixtures, data were obtained for samples with known molecular weight distributions. The drag reduction of these samples was studied as a function of polymer concentration and flow rate so that a generalized picture of the effects of polydispersity could be obtained. These results are used to help explain much of the behavior that was observed for polystyrene and other polymers. This includes the fact that the polystyrene samples exhibit a remarkably high resistance to the loss of drag reduction via degradation in turbulent flow. Such experiments indicate that drag reduction and degradation depend strongly on molecular weight distribution. Thus a molecular level interpretation of experimental results cannot be made unless the effects of the distribution are considered.     

Flow behavior of narrow-distribution polydimethylsiloxane

The flow behavior of α,ω-dihydroxypolydimethylsiloxanes, having a weight-average number-average molecular weight ratio of 1.1–1.2, was studied with a Cannon-Manning viscometer and an Instron rheometer. Comparison of the flow behavior of samples with narrow and broad molecular weight distributions indicated that the onset of non-Newtonian behavior occurred at a much higher shear rate for narrow-distribution polydimethylsiloxanes than for polydisperse polydimethylsiloxanes. A plot of reduced viscosity versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \eta _0 {M \mathord{\left/ {\vphantom {M T}} \right. \kern-\nulldelimiterspace} T} $\end{document} gave two experimental master curves, one for polymer of narrow distribution and the other for polydisperse polymer. The experimental master curve obtained from the narrow-distribution polymer was found to fit the theoretical master curve derived from Graessley's entanglement theory. The viscosity–molecular weight relationship for the higher molecular weight polydimethylsiloxanes was found to be the same for both hydroxydimethylsilyl- and trimethylsilyl-endblocked polymers. However, at low molecular weight, the viscosity–molecular weight curve deviated from linearity because of the association of polydimethylsiloxanols, which apparently is not significant at higher molecular weights. The critical molecular weight of entanglement, M_c, was found to be about 30,000.     

A novel scheme of heterogeneous polymerization of ethylene

The heterogeneous polymerization of ethylene initiated by radiation in tert-butyl alcohol was studied. The polymerization was carried out in a 100-ml reactor at 25–100°C and pressures of 200–300 kg/cm² in the presence of 50 ml of tert-butyl alcohol containing 7 wt-% water. The amounts of polymerized monomer, the average molecular weight of polymer formed, and the molecular weight distribution of polymer were measured at various stages of reaction and at various temperatures. The molecular weight distribution was found to be very much dependent on the reaction time and temperature. For the polymer formed at 50–60°C in the very early stages of reaction, the molecular weight distribution is unimodal, and in the intermediate stage a shoulder appears at a molecular weight higher than the first peak which increases as the polymerization proceeds; eventually a bimodal curve is formed. The bimodal distribution curves were analyzed to determine the fractions and average molecular weights of the each peak. On the basis of these data for the molecular weight distribution and kinetic behavior, a new scheme for the heterogeneous polymerization is proposed which indicates that the polymerization proceeds via propagating radicals in two different physical states, namely, loose and rigid states.     

Dependence of Polymer Chain Entanglements on the Solution Concentration

For the viscometric determination of molecular weights of polymers, sufficiently dilute solutions have to be used so that entanglements of the polymer chain are absent. The concentration of the polymer should be such that the relative viscosity (η_r) lies in the range 1.1–1.5 [1]. Similarly, for molecular weight determination by light scattering, the suggested concentration for polymer with weight-average molecular weight ( M _w ) > 10⁵ is 0.5 wt%; for those with M _w < 10⁵, up to 1% may be used [2].

The limits of polymer concentration for such measurements are not clearly known. On dissolution, the polymer molecules adopt a more or less extended configuration whose shape depends on the structure and molecular weight of the polymer, the properties of the solvent, and the temperature

[3]. The molecules of flexible linear polymers acquire a coiled configuration due to free rotation about the C-C bonds. When a dilute solution satisfies theta conditions, the polymer molecules are free from all kinds of interaction and move freely. Then their solution properties could possibly be related to their end-to-end distance. Based on this concept, our attempt to establish the permissible limits of polymer concentration for dilute solutions of several polymers of different molecular weights is reported here.     

Static light scattering from poly(ethylene oxide) in methanol

Static light scattering measurements were performed on dilute solutions of monodisperse poly(ethylene oxide) (PEO) in methanol at 25°C. PEOs of five different molecular weights ranging from nominal M_w = 8.6 × 10⁴ to 9.13 × 10⁵ were used. Linear Zimm plots were obtained for all the PEO samples: no downturn was observed at small angles, indicating that no large aggregates of PEO molecules exist in the solution. From the plots, values of the weight-average molecular weight, M_w, the radius gyration, R_G, and the second virial coefficient, A₂, were successfully determined for respective PEOs. Observed relationship between R_G and M_w indicates that methanol is certainly a good solvent for the polymer. © 1996 John Wiley & Sons, Inc.     

Molecular structure of synthetic rubber. I. Light-scattering properties of styrene–butadiene copolymers

The discrepancy between the values reported for the weight-average molecular weight and molecular weight distribution of cold-type styrene-butadiene rubber is examined. The results obtained indicate that aggregation of the rubber due to hydrogen bonding or cluster formation is not a contributing factor to the high weight-average molecular weights obtained. The very broad molecular weight distributions, the M?_w/M?_n of the order of 10–20, are attributable to the presence of a few per cent of very high molecular weight fraction microgel in samples polymerized to moderate conversions. This microgel has been removed to various degrees by several methods: (1) mastication, (2) treatment with CaSO₄, (3) ultracentrifugation, and (4) ultrafiltration. The nature of this microgel is examined in terms of its light-scattering property, intrinsic viscosity, and concentrated solution viscosity. The weight-average molecular weight obtained by light scattering on these samples after removal of microgel are lower by as much as an order of magnitude. The operational definition of the weight-average molecular weight, M?′_w, is therefore introduced, corresponding to the one obtained after removal of the microgel. It is suggested that the actual and the operational weight-average molecular weights be used in conjunction in the characterization of these copolymers.     

A Study of the Molecular Weight and Chain Length Distribution of Cyclocopolymers of Divinyl Ether and Maleic Anhydride

Some physical properties of a cyclocopolymer formed by an intra-inter-molecular polymerization mechanism were studied. The cyclic copolymer of divinyl ether and maleic anhydride was chosen for study. Intrinsic viscosities were determined in two solvents. The weight-average molecular weight was determined by light-scattering measurements and the number-average molecular weight was determined by osmometry. Results from a sedimentation velocity pattern indicated that the chain length distribution is much broader than random, which is in agreement with the ratio of the two molecular weight determinations. The polymer was fractionated by precipitation from acetone with hexane as precipitant. Addition of sodium tetraphenyl boron was necessary to obtain separation. Correlation of intrinsic viscosity and weight-average molecular weights was not obtained because of anomalous solubility effects preventing light-scattering determinations.     

High-resolution gel-permeation chromatography

The resolution attainable in gel-permeation chromatography (GPC) was investigated by using columns packed with polystyrene gel particles of about 5 μ diameter and mixtures of two monodisperse poly-α-methylstyrene samples studied previously. The resolution of GPC was found comparable to that of the sedimentation velocity method and slightly better than that of precipitation chromatography. Standard polystyrene samples obtained from Pressure Chemical Co. also were measured with the same columns. It was found that weight-average to number-average molecular weight ratios (M?_w/M?_n) of these samples with molecular weight in the range 97,000–411,000 are smaller than 1.006. For samples with molecular weight of 10,000–51,000 and 498,000–860,000, M?_w/M?_n is larger than 1.006, and the width of molecular weight distributions of these samples differed. In particular, molecular weight distributions of samples with molecular weights 19,800 and 51,000 were shown to be bimodal. It is therefore concluded that GPC is useful for samples of very narrow molecular weight distribution if high-resolution columns are used.