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.     

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.     

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     

Synthesis and characterization of polyaryloxyphosphazenes

The synthesis, dilute solution characterization, and thermal analysis of seven polyaryloxyphosphazenes are described. Synthesis is accomplished by the ring-opening polymerization of hexachlorocyclotriphosphazene at 245°C, followed by reaction of polydichlorophosphazene with sodium aryloxide salts in solution at 115°C. Polymers prepared and characterized have the general structure [(ArO)₂PN]_n, with Ar = C₆H₅, m- and p-CH₃C₆H₄, m- and p-ClC₆H₄, p-C₂H₅C₆H₄, or p-CH₃OC₆H₄. Elemental and infrared analyses show these polymers are essentially free of reactive chlorine sites. All the polymers displayed high intrinsic viscosities [η] > 1 dl/g, in tetrahydrofuran or chloroform. Closer examination of the dilute solution properties of two polyaryloxyphosphazenes revealed high molecular weights (M?_w> 6 × 10⁵) and broad molecular weight distributions (M?_w/M?_n > 4.7). The experimental values for the Z-average radii of gyration, 〈S²〉_z^1/2, characterized at near theta conditions, are larger than the calculated values for a freely rotating chain, which suggests that these polymers are relatively linear and not highly branched. Thermal analysis revealed second-order glass transitions between ?37 and +13°C and first-order endothermic transitions between 43 and 160°C for the different polymers. Although crystalline structure can persist above this first-order transition, this temperature can be regarded as a melting temperature or softening temperature at which films can be molded. Decomposition temperatures, measured in argon and oxygen, ranged from 250°C to 400°C.     

Polystyrene degradation induced by stresses resulting from the freezing of its solutions

Solutions of polystyrene in p-xylene were frozen in liquid nitrogen. No changes in molecular weight and distribution were caused by freezing solutions for a series of narrow distribution polystyrenes with molecular weights of near 2 × 10⁶ and lower. Likewise a commercial polystyrene of M?_w = 234,000 showed no change, even after 45 cycles of freezing and thawing. However, an ultrahigh molecular weight polystyrene (M?_w = 7.3 × 10⁶) showed appreciable degradation even after a few freezing cycles of its solutions. The changes in molecular weight and distribution were analyzed by gel-permeation chromatography. The results depended very much on the choice of solvent, cooling rate, and concentration. The extent of degradation was found to depend on polymer concentration in two distinct ways. Indeed, two different degradation mechanisms have been distinguished at low and at high concentrations. The change between mechanisms took place between 1.0 and 2.5 g/l. for polystyrene in p-xylene. This appears to provide a rare measure of polymer-polymer interactions (entanglements) in dilute solutions. Degradation in the entanglement region proceeded via a random chain-scission mechanism as tested by the Scott method. In contrast, at low concentrations degradation was characterized by the formation of appreciable amounts of low molecular weight polystyrene. The presence of an antioxidant (Ionol) during freezing did not change the extent of degradation significantly.     

The drawing behavior of linear polyethylene. I. Rate of drawing as a function of polymer molecular weight and initial thermal treatment

The drawing behavior of a series of linear polyethylene homopolymers with weight-average molecular weight (M?_w) ranging from 67,800 to ～3,500,000 and variable distribution (M?_w/M?_n = 5.1?20.9) has been studied. Sheets were prepared by two distinct routes: either by quenching the molten polymer into cold water or by slow cooling below the crystallization temperature (～120°C) followed by quenching into cold water. When the samples (2 cm long) were drawn in air at 75°C using a crosshead speed of 10 cm/min it was found that for low M?_w polymers the initial thermal treatment has a dramatic effect on the rate at which the local deformation proceeds in the necked region. At high M?_w such effects are negligible. An important result was that comparatively high draw ratios (λ > 17) and correspondingly high Young's moduli could be obtained for a polymer with M?_w as high as 312,000. It is shown how some of the structural features of the initial materials (mainly studied by optical microscopy, small-angle x-ray scattering and low-frequency laser Raman spectroscopy) can be interpreted in terms of the molecular weight and molecular weight distribution of the polymers. Although crystallization and morphology can be important at low M?_w, it suggested that the concept of a molecular network which embraces both crystalline and noncrystalline material is more helpful in understanding the drawing behavior over the whole range of molecular weights.     

Fundamental studies on cationic polymerizations: Molecular weights and molecular weight distributions of polyisobutylenes produced by γ-irradiation (free ions) and chemical catalysis (ion pairs)

The molecular weights (M?_n, M?_v, and M?_w) and molecular weight distributions of polyisobutylenes synthesized by γ-irradiation in the range 29 to ?78°C have been determined. The plots of log M?_n, log M?_v, and log M?_w versus 1/T are linear and parallel (E_M? = ?6.3₆ ± 0.5), and M?_w/M?_n ≈ 3.0 ± 0.5 over this temperature range. The viscosity-average molecular weights of polyisobutylenes obtained by γ-irradiation were compared with those of polymers prepared by BF₃, EtAlCl₂, and AlCl₃. It is found that, at the same polymerization temperature, the M?_v of radiation-induced polyisobutylenes, which propagate by free carbonium ions, is significantly higher than those synthesized by the Lewis acids, which probably propagate via ion pairs. The implications of these findings are discussed, and it is concluded that the counterion in the proximity of the growing cation impedes propagation to a greater extent than it does the competing process of chain transfer to monomer.     

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.     

End-Functionalized polymers by living cationic polymerization. IV. Poly(vinyl ethers) with acidic or basic terminal groups by functional initiator method

Carboxylic acid or primary amine-terminated poly(isobutyl vinyl ethers) were synthesized by living cationic polymerizations with functionalized initiators (CH₃CHIO? CH₂CH₂ ? X; X: that are the adducts of the corresponding vinyl ethers (CH₂ ? CH ? OCH₂CH₂? X) with hydrogen iodide. In the presence of iodine, these initiators induced living cationic polymerization of isobutyl vinyl ether to give polymers with the α-end group of X originating from the initiators. The polymer molecular weights were regulated by the monomer to initiator feed ratio and the molecular weight distributions were very narrow (M _w/M _n ≤ 1.15). Subsequent deprotection of the terminal group X led to polymers with a terminal carboxylic acid or primary amine. ¹H- and ¹³C-NMR analyses showed that the end functionalities of these polymers were all close to unity.     

Direct polycondensation of aromatic dicarboxylic acids and bisphenols with tosyl chloride and N,N-dimethylformamide in pyridine

A Vilsmeier adduct derived from arylsulfonyl chlorides and DMF in pyridine was successfully used as a new condensating agent for the synthesis of aromatic polyesters by the direct polycondensation of aromatic dicarboxylic acids and bisphenols and also of hydroxybenzoic acids. Polymers of high molecular weights (M?_w = 78,000) with relatively narrow molecular weight distribution (M?_w/M?_n ≈ 3.0) were prepared by reacting aromatic dicarboxylic acids with the adduct in pyridine, followed by addition of bisphenols. The polycondensation was significantly affected by the amount of DMF, the nature of the arylsulfonyl chlorides, the conditions of initial reaction of the acids with the adduct, and the rate of reaction with bisphenols. The process was adaptable to the direct polycondensation of hydroxybenzoic acids, affording polymers of high molecular weight (η_inh = 1.73).     

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     

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.     

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.     

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

From the sedimentation-diffusion equilibria of some polymer solutions the average molecular weights M?_n, M?_w, M?_z, and M?_z+1 have been determined in different ways. In particular, the applicability of Fujita's method, which utilizes concentration gradient values at the midpoint of the solution column at a number of rotor speeds, was examined. It appears that if the gradients at some other places in the column are also used, a smaller range of rotor speeds suffices. This method is generally applicable for determining the average molecular weights specified above.     

Living cationic polymerization of isobutyl propenyl ether as β-substituted vinyl ether

Isobutyl propenyl ether [IBPE; CH₃CH=CH? OCH₂CH(CH₃)₂] was polymerized with a mixture of hydrogen iodide and iodine (HI/I₂ initiator) in n-hexane at ?40°C to yield living polymers with a nearly monodisperse molecular weight distribution (MWD) (M?_w/M?_n ≈ 1.1). The number-average molecular weight (M?_n) of the polymers increased proportionally to IBPE conversion and further increased when a new monomer feed was added to a completely polymerized solution. The M?_n was controlled by the initial concentration of hydrogen iodide if the acid was charged in excess over iodine. In polymerization by iodine alone the M?_n of the polymers obtained in nonpolar solvents (n-hexane and toluene) also increased with conversion, but their MWD was broader (M?_w/M?_n = 1.3–1.4) than in the HI/I₂-initiated systems under similar conditions. The iodine-initiated polymerization in polar CH₂Cl₂ solvent, in contrast, led to nonliving polymers with a broad MWD (M?_n/M?_n = 1.6–1.8) and M?_n, independent of conversion. The living polymerization of IBPE was also compared with that of the corresponding isobutyl vinyl ether, to determine the effect of the β-methyl group in IBPE.     

Polymerization by oxidative coupling. IV.. Synthesis and properties of poly(2-methyl-6-phenylphenylene ether)

Copper-amine catalyst systems which polymerize 2-methyl-6-phenylphenol to high molecular weight polymer are described. With CuCl and N,N,N ′,N′-tetramethyl-1,3-butanediamine (TMBD), an intrinsic viscosity of 1.56 dl/g was obtained. Faster rates of polymerization resulted with a CuBr-TMBD catalyst. Catalysts from other tertiary amines and mixtures of tertiary amines also produced high polymer. Pyridine and diethylamine catalyst were less active. Samples of polymer were isolated at different stages of the polymerization. Measurements of viscosity, osmotic pressure, light scattering, gel permeation, hydroxyl groups, nitrogen content, and chemical reactivity were made on the samples. Below a molecular weight value of M?_n 60,000, M?_n/M?_w was 2.0. At higher molecular weights, there was a broadening in molecular weight distribution. No major change in the molar concentration of the “;head” endgroups with increasing molecular weight was detected by infrared analysis. However, nitrogen analyses, chemical reactivity studies, and the M?_n/M?_w ratio suggested the chemical nature of the “head” end had changed. The relationships between intrinsic viscosity in chloroform at 25°C and M?_n and M?_w for unfractionated polymer samples are log [η] = ?4.26 + 0.84 log M?_n and log [η] = ?3.86 + 0.70 log M?_w.     

Living cationic polymerization of 2-vinyloxyethyl phthalimide: Synthesis of poly(vinyl ether) with pendant primary amino functions

Cationic polymerization of 2-vinyloxyethyl phthalimide ( 1 ) in CH₂Cl₂ at ?15°C with hydrogen iodide/iodine (HI/I₂) as initiator led to living polymers of a narrow molecular weight distribution (M?_w/M?_n = 1.1–1.25). The number-average molecular weight of the polymers was in direct proportion to monomer conversion and could be controlled in the range of 1000–6000 by regulating the 1 /HI feed ratio. However, when a fresh monomer was supplied to the completely polymerized reaction mixture, the molecular weight of the polymers was not directly proportional to monomer conversion. The polymerization of 1 by boron trifluoride etherate (BF₃OEt₂) in CH₂Cl₂ at ?78°C gave polymers with relatively high molecular weight (M?_w > 20,000) and broad molecular weight distribution (M?_w/M?_n ～ 2). The HI/I₂-initiated polymerization of 1 was an order of magnitude slower than that of ethyl vinyl ether, probably because of the electron-withdrawing phthalimide pendant. Hydrazinolysis of the imide functions in poly( 1 ) gave a water-soluble poly(vinyl ether) ( 3 ) with aliphatic primary amino pendants.     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Synthesis,light emission,and photovoltaic properties of perylene‐containing polyacetylenes

Perylene (Py)‐containing polyacetylenes with different skeleton structures ? [HC?C(C₆H₄)CO₂? Py]_n? (P 1 ), ? [HC?C(CH₂)₈CO₂? Py]_n? (P 2 ), and ? {[(C₆H₅) C?C(CH₂)₉NH₂]? co? [(C₆H₅)C?C(CH₂)₉? Py]}_n? (P 3 ) are synthesized in satisfactory yields by Rh‐catalyzed polymerization (for P 1 and P 2 ) and polymer reaction (for P 3 ). All the polymers are soluble and possess high molecular weights (M_w up to 2.8 × 10⁵). Their structures and properties are characterized and evaluated by IR, NMR, UV, TGA, PL, and photovoltaic (PV) analyses. The polymers are thermally stable, losing little of their weights when heated to 330 °C. When their solutions are irradiated, their perylene pendants emit intense red fluorescence at 610 nm. PV cells with a configuration of ITO/PEDOT:PSS/polymer/LiF/Al are fabricated, which show maximum current density of 10.3 μA/cm². The external quantum efficiency is sensitive to the polymer structure, with P 3 exhibiting the highest value of 0.23%. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2025–2037, 2008     

Living cationic polymerization of vinyl ethers with a functional group. VII. Polymerization of vinyl ethers with a silyloxyl group and synthesis of polyalcohols and related functional polymers

Living cationic polymerizations of two silicon-containing vinyl ethers, 2-(t-butyldimethyl-silyloxyl)ethyl vinyl ether (tBuSiVE) and 2-(trimethylsilyloxyl)ethyl vinyl ether (MeSiVE), have been achieved with use of the hydrogen iodide/iodine (HI/I₂) initiating system in toluene at ?15 or ?40°C, despite the existence of the acid-sensitive silyloxyl pendants. The living nature of the polymerizations was demonstrated by linear increases in the number-average molecular weights (M?_n) of the polymers in direct proportion to monomer conversion and by their further rise upon addition of a second monomer feed to a completely polymerized reaction mixture. The polymers obtained in these experiments all exhibited very narrow molecular weight distributions (MWD) with M?_w/M?_n around or below 1.1. Desilylation of the polymers under mild conditions (with H⁺ for MeSiVE and F^? for tBuSiVE) gave poly(2-hydroxyethyl vinyl ether), a water-soluble polyalcohol with a narrow MWD. The living processes also permitted clean syntheses of amphiphilic AB block copolymers and water-soluble methacrylate-type macromonomers, all of which bear narrowly distributed segments of the polyalcohol derived from the silicon-containing vinyl ethers.