Temperature dependence of limiting viscosity number and radius of gyration of cellulose diacetate in acetone

Acetone solutions of a cellulose diacetate fraction were studied by viscosity and light scattering methods over the range 12.6–50.3². The temperature dependences of the limiting viscosity number [η], the mean-square radius of gyration 〈s²〉, and the second virial coefficient A₂ were determined. The unperturbed mean-square radius of gyration 〈s²〉_o and the expansion factor α, were estimated by using theoretical relations to the interpenetration function. It was found that dln 〈s²〉_o/dT is ?6.4 × 10^?3 deg^?1, while α, is close to unity over the whole temperature range studied. The viscosity results are interpreted to show that the draining effect is not negligible and the Flory viscosity parameter Φ slightly increases with increasing temperature. It is finally concluded that the value of ?6.9 × 10^?3 deg^?1 for dln [η]/dT can be ascribable to the rapid decrease in 〈s²〉_o.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Moderately concentrated solutions of polystyrene. I. Viscosity as a function of concentration,temperature, and molecular weight

Data on the viscosity η of moderately concentrated solutions of polystyrene are reported. Several solvents were investigated, including cyclopentane solutions over a temperature span between θ_U = 19.5°C and θ_L = 154.5°C. The data were analyzed in terms of a relation giving η as a function of αφM, where α_φ is the expansion factor for the chain dimensions in a solution with volume fraction φ of polymer with molecular weight M. It is shown that values of α_φ so determined decrease as ? lnα_φ/? lnφ = (1 ? 2μ)/6μ for φ greater than φ^* = 0.2M/s³ for moderately concentrated solutions, where s is the root-mean-square radius of gyration and μ = ? ln[η]/? lnM with [η] the intrinsic viscosity.     

Effects of composition on the solution properties of styrene–acrylonitrile copolymers

Short-range interactions between chain units of random copolymers in solution may be influenced by the composition or precisely by the distribution of sequence lengths of the same monomer units. Steric factors were derived for random copolymers of styrene and acrylonitrile with different compositions from the relation between the limiting viscosity number and the molecular weight. Mark-Houwink relations were obtained in methyl ethyl ketone (MEK) or in N,N′-dimethylformamide (DMF) at 30°C. for random copolymers containing 0.383 (Co-1) and 0.626 (Co-2) mole fraction of acrylonitrile, the expressions are: [η] = 3.6 X 10^?4 M _w^0.62, for Co-1 in MEK; [η] = 5.3 X 10^?4 M _w^0.61, for Co-2 in MEK; [η] = 1.2 × 10^?4M _w^0.77 for Co-2 in DMF. With the Stockmayer-Fixman expression, these correlations become, respectively: [η]/M^1/2 = 1.24 × 10^?3 + 8.0 × 10^?7 M^1/2; and [η]/M^1/2 = 1.70 × 10^?3 + 6.3 × 10^?7 M^1/2; and [η]/M^1/2 = 1.68 × 10^?3 + 31.3 × 10^?7 M^1/2. From the unperturbed mean-square end-to-end distances, 〈L²〉₀, determined from the first terms of the latter expressions, together with 〈L²〉_0f calculated by assuming the completely free rotation, gives the steric factor σ = (〈L²〉₀/〈L²〉_0f)^1/2 as 2.25 ± 0.05 for Co-1, and 2.31 ± 0.10 for Co-2. These values of σ are close to those for polystyrene (σ = 2.22 ± 0.05) and for polyacrylonitrile (σ = 2.20 ± 0.05). Therefore, it is concluded that the dimensions of random copolymers of styrene and acrylonitrile in solution are not significantly influenced by the composition. In other words, the unperturbed dimensions are not affected by a change in the alternation tendency between styrene units with phenyl side groups having a large molar volume and acrylonitrile units with nitrile groups responsible for the electrostatic interactions. On the other hand, the long-range interactions reflect the effect of sequence length. The Huggins constant and the second virial coefficient obtained from the light-scattering measurements have optimum values at about 0.5 mole fraction of acrylonitrile, where the greatest tendency for alternation seems to exist.     

Dilute solution properties of cellulose in LiOH/urea aqueous system

Cellulose was dissolved rapidly in 4.6 wt % LiOH/15 wt % urea aqueous solution and precooled to –10 °C to create a colorless transparent solution. ¹³C‐NMR spectrum proved that it is a direct solvent for cellulose rather than a derivative aqueous solution system. The result from transmission electron microscope showed a good dispersion of the cellulose molecules in the dilute solution at molecular level. Weight‐average molecular weight (M_w), root mean square radius of gyration (〈s²〉_z^1/2), and intrinsic viscosity ([η]) of cellulose in LiOH/urea aqueous solution were examined with laser light scattering and viscometry. The Mark–Houwink equation for cellulose in 4.6 wt % LiOH/15 wt % urea aqueous solution was established to be [η] = 3.72 × 10^?2 M in the M_w region from 2.7 × 10⁴ to 4.12 × 10⁵. The persistence length (q), molar mass per unit contour length (M_L), and characteristic ratio (C_∞) of cellulose in the dilute solution were given as 6.1 nm, 358 nm^?1, and 20.8, respectively. The experimental data of the molecular parameters of cellulose agreed with the Yamakawa–Fujii theory of the worm‐like chain, indicating that the LiOH/urea aqueous solution was a desirable solvent system of cellulose. The results revealed that the cellulose exists as semistiff‐chains in the LiOH/urea aqueous solution. The cellulose solution was stable during measurement and storage stage. This work provided a new colorless, easy‐to‐prepare, and nontoxic solvent system that can be used with facilities to investigate the chain conformation and molecular weight of cellulose. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3093–3101, 2006     

Chain dimensions and transport coefficients of sodium poly(isoprenesulfonate) in aqueous sodium chloride

Sodium poly(isoprenesulfonate) (NaPIS) fractions consisting of 1,4‐ and 3,4‐isomeric units (0.44:0.56) and ranging in molecular weight from 4.9 × 10³ to 2.0 × 10⁵ were studied by static and dynamic light scattering, sedimentation equilibrium, and viscometry in aqueous NaCl of a salt concentration (C_s) of 0.5‐M at 25 °C. Viscosity data were also obtained at C_s = 0.05, 0.1, and 1 M. The measured z‐average radii of gyration 〈S²〉_z^1/2, intrinsic viscosities [η], and translational diffusion coefficients D at C_s = 0.5‐M showed that high molecular weight NaPIS in the aqueous salt behaves like a flexible chain in the good solvent limit. On the assumption that the distribution of 1,4‐ and 3,4‐isomeric units in the NaPIS chain is completely random, the [η] data for high molecular weights at C_s = 0.5 and 1 M were analyzed first in the conventional two‐parameter scheme to estimate the unperturbed dimension at infinite molecular weight and the mean binary cluster integral. By further invoking a coarse‐graining of the NaPIS molecule, all the [η] and D data in the entire molecular weight range were then analyzed on the basis of the current theories for the unperturbed wormlike chain combined with the quasi‐two‐parameter theory. It is shown that the experimental 〈S²〉_z, [η], and D are explained by the theories with a degree of accuracy similar to that known for uncharged linear flexible homopolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2071–2080, 2001     

Solution and thermal properties of poly(1,3-dioxocane)

Poly( 1,3-dioxocane) was synthesized by cationic ring-opening polymerization with triphenyl-methane hexafluoroantimoniate as the initiator and was studied with regard to its solubility, unperturbed chain dimensions, and thermal transitions. The intrinsic viscosity and Flory-Huggins interaction parameter were used to determine the solubility parameter, δ_p = 9.6 cal^1/2cm^?3/2, a value that agrees with that calculated empirically. Fractions were obtained from the solvent/non-solvent system benzene/methanol at 25°C. The number-average molecular weight M_n and intrinsic viscosity [η] were measured in toluene at 25°C. The relation [η] = 1.45₉. 10^?4 M_n^0.79 was found. A value of 5.3 was obtained for the characteristic ratio 〈r²〉₀/nl². Results are correlated with the main thermal transitions of this polyformal.     

Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity

In order to explain the observed nonvanishing limiting value of dynamic intrinsic viscosity of polymer solutions at ω = ∞ one has considered the necklace model with finite resistance to the rate of coil deformation introduced long ago by Cerf for the study of gradient dependence of intrinsic viscosity and streaming birefringence. The calculation need not take into account change of hydrodynamic interaction as a consequence of coil deformation because the experimental data are always either obtained at very low gradient or extrapolated to zero gradient so that in the experiment the macromolecule has the same conformation as in the solution at rest. The model indeed yields a finite [η]′_{ω = ∞} in good agreement with experiments on polystyrene in Aroclor. According to the theory [η]′_{ω = ∞}/[η]₀ decreases with increasing molecular weight as M^?1 and M^?1/2 for the free-draining and impermeable coil, respectively. The absolute limiting value [η]_∞′, therefore turns out to be nearly independent of M, at least for small values of internal viscosity. From the observed value [η]_∞′/[η₀] one can obtain the coefficient of internal viscosity of the macromolecule. The value for polystyrene in Aroclor calculated from dynamic experiments on rather concentrated solutions is close to that derived by Cerf from streaming birefringence observations of polystyrene in a series of solvents of widely differing viscosity.     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Synthesis and solution properties of linear,four-branched,and six-branched star polyisoprenes

A number of linear, four- and six-branched regular star polyisoprenes were synthesized by anionic polymerization techniques in benzene using lithium as the counterion and polyfunctional silicon chloride compounds as the coupling agents. Light-scattering measurements in dioxane were performed in order to establish Θ solvent conditions. Determinations of the radius of gyration of the polymers of different structure indicate that g = 〈S²〉_0,br/〈S²〉_0,lin agree closely with random flight calculations for the ratios. Intrinsic viscosities determined in a Θ solvent establish g′ = [η]_br/[η]_lin to be 0.77₃ and 0.62₅ for the four- and six-branched polyisoprenes, respectively. In a good solvent g′ values are slightly lower. These values are compared with theoretical estimates. Viscosities of 19.29% (w/w) solutions of the polyisoprenes in n-decane at 25°C are correlated with the intrinsic viscosities of the polymers under Θ conditions.     

The solubility of cellulose in liquid ammonia/salt solutions

The dissolution of cellulose in solutions of liquid ammonia and ammonium thiocyanate is discussed. Viscosity measurements on dilute solutions of cellulose in this solvent over a range of shear rates and shear stresses are reported. A four-bulb Ubbelohde suspended level viscometer was used for the measurements. Plots of log [η] versus log M gave Mark-Houwink coefficients of a = 0.95 and K = 6.686 × 10^?5 at 25°C for [η] as dl/g. The Bloomfield equation was used to calculate effective bond lengths (b) from limiting viscosity numbers of cellulose in solutions of ammonia/ammonium thiocyanate and Cuene, respectively. Results indicate that cellulose may have similar configurations in both solvents and also that the ammonia solutions are true cellulose solutions. Miscibility of the cell- ulose/ammonia/ammonium thiocyanate solutions with organic solvents, such as glycerol, is also reported. Further, a few interesting characteristics of the liquid ammonia/ammonium salt solutions, discussed briefly, are the convenient boiling point, the rheological behavior, and the relatively high concentration of cellulose obtainable.     

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Unperturbed dimension of poly-N-vinylcarbazole

Osmotic-pressure, viscosity, and light-scattering measurements have been carried out on dilute solutions of poly-N-vinylcarbazole fractions (4 < 10^-4M < 230) in toluene, dioxane, and benzene. The theta temperature for poly-N-vinylcarbazole in toluene solutions has been found to be 37 ± 1°C. The intrinsic viscosity of poly-N-vinylcarbazole in toluene at 37°C is represented by [η]θ = 76.2 × 10^?3M?_n^0.50. Values of the characteristic ratios (〈L²〉₀/M)^1/2 and σ = (〈L²〉₀/〈L²〉_0f)^1/2 have been obtained as 633 × 10^?11 and 2.85, respectively. It appears that the large σ value is due to the steric repulsion between large side groups.     

Scalings of fluorine‐containing polyimides in cyclopentanone

Eight 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride‐4,4′‐diamino‐3,3′‐dimethylbiphenyl (6FDA‐OTOL) fractions and seven 2,2′‐bis[4‐(3,4‐dicarboxyphenoxy) phenyl] propane dianhydride‐4,4′‐diamino‐3,3′‐dimethylbiphenyl (BISADA‐OTOL) fractions in cyclopentanone at 30 °C were characterized by a combination of viscometry and static and dynamic laser light scattering (LLS). In static LLS, the angular dependence of the absolute scattered intensity led to the weight‐average molar mass (M_w), the z‐average root mean square radius of gyration, and the second virial coefficient. In dynamic LLS, the Laplace inversion of each measured intensity–intensity time correlation function resulted in a corresponding translational diffusion coefficient distribution [G(D)]. The scalings of 〈D〉 (cm²/s) = 8.13 × 10⁻⁵ M_w^−0.47 and [η] (dL/g) = 2.36 × 10⁻³ M_w^0.54 for 6FDA‐OTOL and 〈D〉 (cm²/s) = 3.02 × 10⁻⁴ M_w^−0.60 and [η] (dL/g) = 2.32 × 10⁻³ M_w^0.53 for BISADA‐OTOL were established. With these scalings, we successfully converted each G(D) value into a corresponding molar mass distribution. At 30 °C, cyclopentanone is a good solvent for BISADA‐OTOL but a poor solvent for 6FDA‐OTOL; this can be attributed to an ether linkage in BISADA‐OTOL. Therefore, BISADA‐OTOL has a more extended chain conformation than 6FDA‐OTOL in cyclopentanone. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2077–2080, 2000     

Zur Reaktion von tert-Butyl-phosphaalkin mit Molybdänkomplexen

Reaction of tert -Butyl-phosphaalkyne with Molybdenum Complexes The reaction of tBuC≡P with [(CH₃CN)₃Mo(CO)₃] leads to the complex [Mo(CO)₄〈Mo(CO)₂(η⁴-P₃CtBu){η⁴-P₂(CtBu)₂}〉] 1 as well as to the alkyne complexes [Mo(CO)₄〈{P₃(CtBu)₂}{Mo(CO)₂(CtBu)}{η³-P₂(CtBu)₂}〉] 2 and [Mo(CtBu){η⁴-P₂(CtBu)₂(CO)}{η⁵-P₃(CtBu)₂}] 3 . All compounds are characterized by X-ray structural analysis, by NMR- and IR spectroscopy and by mass spectrometry. In complex 1 a 1,3-diphosphacyclobutadiene and a 1,2,4-triphosphacyclobutadiene are connected by two molybdenum carbonyl centres. In 2 a 1,3-diphosphacyclobutadiene is π- and a novel 1,2,4-triphospholyl ligand is σ-bonded at two Mo centres. A characteristic feature of 3 besides a π co-ordinated 1,2,4-triphospholyl ligand is a 3,4-diphosphacyclopentadienone as ligand, formed via CO insertion during the cyclodimerisation of two phosphaalkynes.     

Characterization of poly(styrene-co-divinylbenzene) microgels

Tightly cross-linked poly(styrene-co-divinylbenzene) microgels with molecular weights in the range 10⁷ to 10⁸ g mole^?1 were studied in solution in dimethylformamide containing 7 g dm^?3 LiBr. Laser light scattering photon correlation spectroscopy (PCS) was used to measure z-average translational diffusion coefficients D?_z and dilute solution viscometry to measure intrinsic viscosities [η]; values of the equivalent hydrodynamic radii 〈R〉${}_{\text{η}}^{\text{?}}$ and 〈R_D^?1〉 were derived. Weight-average molecular weights M?_w and z-average mean-square radii of gyration 〈S²〉_z were determined by conventional light scattering. The microgels were investigated by gel permeation chromatography, and molecular weight data obtained using the [η]M calibration procedure were in satisfactory agreement with results obtained by electron microsocopy and conventional light scattering.