New Interpretations: Molecular Weight Averages for a Polymer

The statement is often made in the polymer literature, without proof, that M _z ≤ M _w ≤ M _n, where M _z, M _w, and M _n are the z-, z weight-, and number-average molecular weights respectively. Four proofs of a generalization of these inequalities are given. It is shown that a higher-order molecular weight average is larger than a lower-order one, regardless of the form of the molecular weight distributions, except for the case when all the molecules have the same molecular weight. A brief discussion of the viscosity-average molecular weight is also included.     

Dilute Solution Properties of Poly(methacrylonitrile-co-styrene) and Poly(acrylonitrile-co-styrene)

Poly(methacrylonitrile-co-styrene) (PMANS) and Poly(acrylo-nitrile- co- styrene) (PANS) having 1:1 composition were prepared with free-radical initiators. The polymers were fractionated into fractions having narrow molecular weight distribution. The dilute solution properties of the fractionated copolymers were studied by light scattering, viscometry, and osmometry in solvents (methyl ethyl ketone, dimethylformamide, and acetone), [n]-M _w and(r²)_w ^l/2?M _w relationships have been established. The validity of the various graphical methods for the determination of Flory′s constant, K _θ were observed.

From the values of the steric factors it was noticed that the copolymer coil of PANS is stiffer than that of PMANS.     

Crystallizable Polyphenylacetylene-Preparation and Solution Properties

The molecular weight distribution (MWD) of crystallizable polyphenylacetylene prepared near room temperature in the presence of ferric acetylacetonate and triethylaluminum was determined through use of fractions characterized by vapor pressure osmometry and gel permeation chromatography (GPC). The number- and weight-average molecular weights (M _n and M _w) are both less than the molecular weight corresponding to the maximum of the weight distribution function, which lacks a high molecular weight tail. M _wandM _n is less than is consistent with models allowing for chain termination characteristic of vinyl polymers. GPC elution volumes are much less than those characteristic of polystyrene of similar molecular weight, and the Mark-Houwink exponent is high (2.4 for M _v 4800 to 6800). These data indicate more rodlike behavior than for polystyrene of equivalent molecular weight. The MWD and other data suggest intramolecular chain termination, possibly associated with the molecule's tendency to form paramagnetic defect states.     

Characterization of Copolymers and Polymer Mixtures by Gel Permeation Chromatography

Abstract

Estimation of molecular weights from GPC data is complicated when the polymer sample consists of a mixture of homopolymers or of statistical copolymers with nonuniform compositions. This is because sizes of solvated polymer coils depend on solvent interaction with both the homo-and hetero-units of the copolymers and because the extent of solvation of different homopolymers can differ. The overall degree of solvation may change effectively with composition and use of a single “average” set of Mark-Houwink constants in calibration procedures will then produce false molecular weight data from the GPC data. A new molecular weight average, M _x, is defined to overcome this problem. This average can be determined from the GPC chromatogram and intrinsic viscosity of the sample in the GPC solvent. Mark-Houwink coefficients are not needed. M _x lies between M _w and M _z.     

Quasiliving Carbocationic Polymerization. II. The Discovery: The α-Methylstyrene System

A detailed analysis of elementary reactions of carbocationic polymerization culminated in the prediction and subsequent experimental demonstration of quasiliving polymerization. Quasiliving polymers are formed in a system provided that the process of chain termination and chain transfer to monomer are absent or reversible, i.e., the propagating ability of the chain end is maintained throughout the experiment, and the molecular weight increases in proportion to the cumulative amount of monomer added. The chain end can be active (carbocation) or dormant (reactivable polymeric olefin or cation source). Chain transfer is suppressed by keeping the monomer concentration low. Quasiliving polymerizations are maintained by continuous slow feeding of dilute monomer to a charge containing the initiating or propagating species (quasiliving polymerization technique). A comprehensive kinetic scheme has been developed that describes quasiliving polymerization in quantitative terms. Quasiliving polymerization was demonstrated experimentally in the “H₂O”/BCl₃/α-methylstyrene and cumyl chloride/BCl₃/α-methylstyrene systems. M _n versus monomer input plots are linear over wide ranges, indicating quasiliving conditions, and poly(α-methylstyrenes) with M _n > 2 × 10⁵ have been obtained, Molecular weight distributions were found progressively to narrow and dispersion ratios M _w/M _n to decrease.     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Copolymers of p-Nitrobenzyl Acrylate with Methyl Acrylate: Synthesis,Characterization, and Monomer Reactivity Ratios

Abstract

Copolymers of p-nitrobenzyl acrylate and methyl acrylate with different feed ratios are synthesized in ethyl methyl ketone using benzoyl peroxide as a free radical initiator at 70 ± 1°C. The copolymers were characterized by IR and ¹H-NMR spectroscopic techniques. Copolymer compositions were determined by ¹H-NMR analysis of the polymers. The monomer reactivity ratios were determined by the application of conventional linearization methods such as Fineman–Ross and Kelen–Tüdös. Gel permeation chromatography was used for determining the molecular weights M _n and M _w, and the polydispersity index. The intrinsic viscosities and the thermal properties of the homo- and copolymers are also discussed.     

Stereospecific and molecular weight‐controlled polymerization of 1,3‐butadiene with Co(acac)3‐MAO catalyst

The polymerization of butadiene (Bd) with Co(acac)₃ in combination with methylaluminoxane (MAO) was investigated. The polymerization of Bd with Co(acac)₃‐MAO catalysts proceeded to give cis‐1,4 polymers (94 – 97%) bearing high molecular weights (40 × 10⁴) with relatively narrow molecular weight distributions (M_w's/M_n's). The molecular weight of the polymers increased linearly with the polymer yield, and the line passed through an original point. The polydispersities of the polymers kept almost constant during reaction time. This indicates that the microstructure and molecular weight of the polymers can be controlled in the polymerization of Bd with the Co(acac)₃‐MAO catalyst. The effects of reaction temperature, Bd concentration, and the MAO/Co molar ratio on the cis‐1,4 microstructure and high molecular weight polymer in the polymerization of Bd with Co(acac)₃‐MAO catalyst were observed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2793–2798, 2001     

Solution characterization of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A series of four well‐defined poly(ferrocenyldimethylsilane) (PFS) samples spanning a molecular weight range of approximately 10,000–100,000 g mol⁻¹ was synthesized by the living anionic polymerization of dimethyl[1]silaferrocenophane initiated with n‐BuLi. The polymers possessed narrow polydispersities and were used to characterize the solution behavior of PFS in tetrahydrofuran (THF). The weight‐average molecular weights (M_w ) of the polymers were determined by low‐angle laser light scattering (LALLS), conventional gel permeation chromatography (GPC), and GPC equipped with a triple detector (refractive index, light scattering, and viscosity). The molecular weight calculated by conventional GPC, with polystyrene standards, underestimated the true value in comparison with LALLS and GPC with the triple detection system. The Mark–Houwink parameter a for PFS in THF was 0.62 (k = 2.5 × 10⁻⁴), which is indicative of fairly marginal polymer–solvent interactions. The scaling exponent between the radius of gyration and M_w was 0.54, also consistent with marginal polymer–solvent interactions for PFS in THF. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3032–3041, 2000     

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.     

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.     

Aromatic poly(amic acids): Fundamental structural studies

Aromatic poly(amic acids) derived from pyromellitic dianhydride and 4,4′,-diaminodiphenyl ether were characterized by dilute solution techniques. Number-average molecular weights M?_n of 13 samples ranged from 13,000 to 55,000 (DP 31–131). Weight-average molecular weights M?_w of 21 samples ranged from 9,900 to 266,000. The ratio M?_w/M?_n was between 2.2 and 4.8. Heterogeneous polymerization yielded higher molecular weight polymer than homogeneous polymerization. The molecular weight could be varied systematically by control of stoichiometric imbalance. Use of very pure monomers and solvent gave polymers of relatively high number-average molecular weight (～50, 000) and the most probable molecular weight distribution M?_w/M?_n = 2. Impure monomers and/or solvent resulted in lower number-average molecular weight (M?_n ? 20,000–30,000) and wider distributions (M?_w/M?_n = 3–5). The Mark-Houwink relation obtained was [η] = 1.85 × 10^?4M?_w^0.80 The exponent is characteristic of moderately extended solvated coils. The unperturbed chain dimensions (r₀² /M)^1/2 were 0.848 A., and the steric factor σ was 1.24 which is close to the limiting value of unity for an equivalent chain with free internal rotations. The sedimentation constant–molecular weight relation was S₀ = 2.70 × 10^?2M?_w^0.39. This exponent is consistent with the Mark-Houwink exponent.     

Characterization of Branched Poly (vinyl Acetate) by GPC and Low Angle Laser Light Scattering Photometry

Abstract

Poly (vinyl acetate), PVAC, synthesized by bulk polymerization over a range of initiator concentrations ([AIBN] = 10^?5 to 4 × 10^?3 g-mole/1), temperatures (50°C, 60°C, 70°C, and 80°C) and conversion levels (3 to > 90%) were characterized using low angle laser light scattering (LALLS) photometry to measure M_w of the whole polymers. A number of these samples were characterized using GPC with a differential refractive index (DRI) and LALLS detector to measure the molecular weight distribution (weight fraction versus M_w). M_w for PVAC samples synthesized at suitably low initiator levels at various conversions were found to agree with classical light scattering measurements after Graessley.

An electronic device and a technique which optimizes the sensitivity and the signal-to-noise ratio of the LALLS photometer throughout the molecular weight distribution (MWD) of the GPC chromatogram were devised. These considerably simplify the operation of the LALLS for both offline and online operation with GPC.

Most importantly it was unambiguously shown that the commonly used universal calibration parameter (UCP) with GPC, [n]M_w, is incorrect for polymers with molecules having the same hydrodynamic volume but different molecular weights, i. e., those with only chain branching (LCB), copolymers with compositional drift, and polymer blends. The correct UCP was found to     

Ruthenium‐catalyzed fast living radical polymerization of methyl methacrylate: The R?Cl/Ru(Ind)Cl(PPh3)2/n‐Bu2NH initiating system

A fast living radical polymerization of methyl methacrylate (MMA) proceeded with the (MMA)₂? Cl/Ru(Ind)Cl(PPh₃)₂ initiating system in the presence of n‐Bu₂NH as an additive [where (MMA)₂? Cl is dimethyl 2‐chloro‐2,4,4‐trimethyl glutarate]. The polymerization reached 94% conversion in 5 h to give polymers with controlled number‐average molecular weights (M_n's) in direct proportion to the monomer conversion and narrow molecular weight distributions [MWDs; weight‐average molecular weight/number‐average molecular weight (M_w/M_n) ≤ 1.2]. A poly(methyl methacrylate) with a high molecular weight (M_n ～ 10⁵) and narrow MWD (M_w/M_n ≤ 1.2) was obtained with the system within 10 h. A similarly fast but slightly slower living radical polymerization was possible with n‐Bu₃N, whereas n‐BuNH₂ resulted in a very fast (93% conversion in 2.5 h) and uncontrolled polymerization. These added amines increased the catalytic activity through some interaction such as coordination to the ruthenium center. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 617–623, 2002; DOI 10.1002/pola.10148     

Controlling the molecular weight of poly(2,5-bis[N-methyl-N-hexylamino]phenylene vinylene) using nitrobenzene as an inhibitor

Poly(2,5-bis[N-methyl-N-hexylamino] phenylene vinylene) (BAM-PPV) has been studied for several decades as an anti-corrosion coating. Although the polymer is readily synthesized via base-promoted radical chain polymerization, BAM-PPV exhibits poor solubility at high-molecular weights (M_w > 100 kDa), which limits its applications. In this work, the molecular weight of BAM-PPV was modulated with nitrobenzene. At nitrobenzene loading as low as 0.9 mol%, the polymerization reaction produced low-molecular weight BAM-PPV (M_w = 5–46 kDa). The polymerization of BAM-PPV was systematically studied via size-exclusion chromatography (SEC), liquid chromatography–mass spectrometry (LC-MS), and ¹H NMR spectroscopy, which revealed suppression of the dimer intermediate before chain polymerization. Collectively, this work could expand the practical applications of BAM-PPV for use in optoelectronic devices or corrosion inhibition coatings.     

Effects of the thermal history and concentration on the aggregation of Erwinia gum in an aqueous solution

The aggregation of Erwinia (E) gum in a 0.2 M NaCl aqueous solution was investigated by multi‐angle laser light scattering and gel permeation chromatography (GPC) combined with light scattering. The GPC chromatograms of five fractions contained two peaks; the fractions had the same elution volume but different peak areas, suggesting that aggregates and single chains coexisted in the solution at 25 °C. The apparent weight‐average molecular weights (M_w) of the aggregates and single chains for each fraction were all about 2.1 × 10⁶ and 7.8 × 10⁴, respectively. This indicates that the aggregates were composed of about 27 molecules of E gum in the concentration range used (1.0 × 10⁻⁶ to 5.0 × 10⁻⁴ g/mL). The weight fraction of the aggregates (w_ag) increased with increasing concentration, but the aggregates still existed even in an extremely dilute solution. The fractionation process and polymer concentration hardly affected the apparent aggregation number but significantly changed w_ag. The E‐gum M_w decreased sharply with an increase in temperature. When the E‐gum solution was kept at 100 °C, w_ag decreased sharply for 20 h and leveled off after 100 h. Once the aggregates were decomposed at a higher temperature, no aggregation was observed in the solution at 25 °C, indicating that the aggregation was irreversible. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1352–1358, 2000     

Living Carbocationic Copolymerizations. V. Synthesis of Isobutylene/p-Methylstyrene Copolymers with the Constant Copolymer Composition Technique in the Leidenfrost Reactor

Abstract

Living copolymerization of the isobutylene (IB)-p-methylstyrene (pMeSt) monomer pair in combination with the constant copolymer composition (CCC) technique produces high molecular weight ( M _n ≈ 100,000 g·mol^?1) and narrow molecular weight distribution ( M _w/ M _n ≈ 1.45) compositionally uniform IB/pMeSt copolymer molecules in the industrially important IB/pMeSt = 97–99/3–1 mol% composition range. Syntheses were carried out with TiCl₄ coinitiator in n-butyl chloride homogeneous solution at ?85°C by the use of the Leidenfrost reactor (i.e., by direct cooling of the charge with liquid nitrogen). In order to carry out the CCC technique it was necessary to obtain reliable copolymerization reactivity ratios. These investigations led to r_IB = 0.5 ± 0.1 and r _pMeSt = 10 ± 4. The attainment of CCC and living copolymerization conditions has been quantitatively demonstrated by dedicated diagnostic plots. Specifically, the attainment of CCC conditions was proven by the analysis of composite rate plots (comonomers input and corresponding copolymer formed versus time) and composition plots (comonomer composition in feed and copolymer formed versus weight of copolymer formed, W _p), and living copolymerization was proven by linearly ascending number-average molecular weight of copolymer ( M _n) versus W _p plots starting at the origin.     

Atom Transfer Radical Polymerization of Styrene Using Multifunctional Iniferter Reagents as Initiators

Summary: Two multifunctional iniferters, 1,4-bis-(α-N,N-diethyldithiocarbamyl-isobutyryloxy)-benzene (BDCIB) and 1,3,5-tris-(α-N,N-diethyldithiocarbamyl-isobutyryloxy)-benzene (TDCIB), were successfully synthesized and used as initiators to initiate the polymerization of styrene in the presence of a CuBr/PMDETA complex. The polymerization results demonstrated that the kinetic plots in all cases were first-order to the monomer, the molecular weight of the polymers increased linearly with the monomer conversion; meanwhile, the molecular weight distribution of the polymer was kept to a very low value (M_w/M_n ≤ 1.35). Furthermore, the measured molecular weights were very close to the calculated values, which indicated the high efficiency of the initiator for the polymerization of styrene. The effect of catalyst concentration and initiator concentration was not obvious and the influence of polymerization temperature was apparent, and the polymerization rate increased with the polymerization temperature. The results of chain-extension and ¹H NMR analysis proved that the polymer obtained was capped with diethylthiocarbamoylthiy (DC) group.     

Intramolecular cyclization in the polymerization of ABx monomers: Approaches to the control of molecular weight and polydispersity in hyperbranched poly(siloxysilane)

Different approaches to control the molecular weight of hyperbranched poly(siloxysilane) have been explored. Because the intramolecular hydrosilylation competitively consumes the vinyl groups of the monomer and other oligomeric intermediates, the conventional single-batch bulk process generally affords polymer with a relatively low molecular weight (M_w = 5000) in ca. 60% yield. We have developed a progressive slow addition process that effectively increases the molecular weight of the final polymers and improves preparation yield by reducing the occurrence of cyclization. Using this gradual growth method, polymers with molecular weights in the range of 6–86,000 (M_w) and polydispersities in the range 2–15 were easily obtained in yields of ca. 70–80%. More importantly, both the molecular weight and the polydispersity could be controlled by changing the rate of addition or the amount of monomer fed. The slower the addition, or the larger the amount of monomer added, the higher the molecular weight and polydispersity of the resulting polymer. In seeded polymerizations, a similar trend was observed with a maximum M_w near 84,000 and a yield of 80%, values that are very significantly higher than those obtained by the single batch process described earlier. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3193–3201, 1999     

Polymerization of 4-phenyl-1-butyne catalyzed by metathesis and Ziegler–Natta catalysts

The polymerization of 4-phenyl-1-butyne was carried out using metathesis and Ziegler-Natta catalysts. Especially, the Fe(acac)₃-AlEt₃ catalyst with toluene as a solvent produced an extremely high molecular weight polymer of M_w ≈ 10⁶. Solubility of the polymers at room temperature in organic solvents such as benzene, toluene, dichloromethane, chloroform, and THF was excellent despite their high molecular weights. It has been indicated that the polymer prepared by the Fe(acac)₃-AlEt₃ catalyst is of cis form with a high stereoregularity. © 1993 John Wiley & Sons, Inc.