Upturn effect in the Non-Newtonian intrinsic viscosity of polymer solutions. II. Polyisobutylene in polybutene oil

With an increasing gradient, the intrinsic viscosity of a high molecular weight polyisobutylene (M?_n = 7 × 10⁶) in polybutene oil L.100 (η_s = 5 poise) first drops to a minimum and then rises again. The minimum occurs at β = M[η]₀η_sG/NkT = 240, which is about ten times the value predicted by the dumbbell model. Such a shift to larger gradient is in good agreement with the more realistic necklace model of macromolecules in a good solvent. The increase of intrinsic viscosity after the minimum is nearly linear with the gradient and continues beyond the value at zero gradient. Experiments with capillaries of different length-to-diameter ratios yield identical flow curves so that one may exclude the possibility that the observed upturn is an artifact caused by end effects or time dependence of viscosity.     

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.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

The Newtonian Viscosity of Polymer Solutions

Viscosity measurements of cellulose acetate and polyisobutylene over a wide range of concentrations and molecular weights have been made. The data so obtained and the data taken from the literature for schizophyllan show that the viscosity varies smoothly with concentration of the polymer for the whole range of concentrations and molecular weights investigated. The characteristic concentrations, C_ch , of the polymers are calculated by the following equations: C_ch = 0.77/[η] or C_ch = 1.08/[η]. The relationship between molecular weight and intrinsic viscosity is obtained by fitting the data by the method of least squares. By plotting the reduced viscosity versus the reduced concentration, superposition curves are obtained for both cellulose acetate and polyisobutylene. It is not possible to obtain superposition curves for schizophyllan, which is a more rigid polymer.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Hydrophobically modified polyelectrolytes I. Dilute solution properties of fluorocarbon-containing poly (acrylic acid)

Dilute solution viscosity of fluorocarbon‐containing hydrophobically modified poly (acrylic add) was measured in aqueous solutions of various NaCl concentrations. The intrinsic viscosity ([η]) and Huggins coefficient (k_H) were evaluated using Huggins equations. It is found that, at low Nacl concentration, the modified polymers exhibit values of intrinsic viscosity ([η]) and Huggins coefficient (k_H) similar to those of unmodified polymers. For both of the modified and unmodified polymers, the intrinsic viscosity decreases with increase of NaCl concentration, while the Huggins coefficient increases upon addition of NaCl. But the variation of [η] and k_H is more significant for the modified polymers, which reflects the enhanced intra‐ and intermolecular hydrophobic association at higher Nacl concentration.     

Contribution of Polymer‐Solvent Interactions to Dynamics of Linear Polymers in Dilute Solutions

In this work a theoretical approach to dynamics of linear vinyl polymers in dilute solutions of high viscosity solvents is presented. The calculations for the relaxation time spectra, polymer intrinsic viscosity [η (ω)], complex elastic modulus G*(ω), total intrinsic viscosity [η^T (ω)] and specific heat capacity C (ω) were carried out in the non‐free‐draining limits. The relaxation time spectrum calculated for dynamics of low frequency modes exhibits a Rouse‐like character. Its position and shape corresponds to the ultrasonic relaxation time spectrum observed in the system at 10⁶ Hz. On the other hand, the relaxation time spectrum associated with moderate frequency mode dynamics is narrower and typical for ultrasonic relaxation observed at 10⁷ Hz. The polymer intrinsic viscosity [η (ω)] and elastic modulus G*(ω) are shown to be represented by the model within a low‐frequency range. In turn, the specific heat capacity C (ω) is displayed as a representation of the model in the acoustic region mentioned above. In the high‐frequency range the dynamics is described by the total intrinsic viscosity [η^T (ω)] tending to a plateau where the value is equal to the sum of the single‐bead intrinsic viscosity [η_N] and effective solvent viscosity [η_eff].     

Application of the porous-sphere hydrodynamic model to dilute polymer solutions

The porous-sphere model of Debye–Brinkman–Bueche is applied to predict the limiting frictional coefficient f₀ and intrinsic viscosity [η] of polystyrene fractions in tetrahydrofuran and random protein coils in 6M guanidine hydrochloride. Following the formulation of Wiegel and Mijnlieff, the molecular permeability is modeled to increase exponentially as the square of the distance from the center of the molecule. A method is developed to obtain this permeability from the translational diffusion coefficient. The experimental values of f₀ and [η] are in satisfactory agreement with the calculated values. Also, this analysis predicts values of the Mandelkern–Flory–Scheraga parameter for flexible coils which are significantly smaller than the minimum values permitted by the Kirkwood–Riseman theory. This is in accord with the experimental evidence.     

Studies on reactions of the N-phosphonium salts of pyridines. XIV. Wholly aromatic polyamides by the direct polycondensation reaction by using phosphites in the presence of metal salts

Poly-p-benzamide of high molecular weight (η_inh = ～ in H₂SO₄) was obtained by the direct polycondensation reaction of p-aminobenzoic acid (p-ABA) by means of diphenyl and triaryl phosphites in N-methylpyrrolidone (NMP)-pyridine solution containing lithium and calcium chlorides. Molecular weight of polymer varied with the amount of these salts, showing maximum values at the concentration of about 4 wt-% of LiCl or about 8 wt-% of CaCl₂ in the reaction mixture. The reaction temperature at around 80°C gave a polymer of the highest viscosity. The polycondensation reaction was also affected by monomer concentration, solvents, and tertiary amines like pyridine. Similarly, aromatic polyamides with high molecular weight (η_inh values up to 1.34 in H₂SO₄) were prepared from isophthalic acid and aromatic diamines, whereas terephthalic acid gave only low-viscosity polymers.     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Thermodynamic properties of N,N-dimethylformamide + water

The excess viscosities, η^E, and excess energy of activation (ΔΕ_η)^Ε of dynamic viscosity have been investigated by using dynamic viscosity measurements for N,N-dimethylformamide + water (DMFW) mixtures over the entire range of mole fractions at five different temperatures. The results were also fitted with the Redlich–Kister equation. This system exhibited very large positive values of η^E and (ΔΕ_η)^Ε due to the increased dipole–dipole interactions and correlation length between unlike molecules. The activation parameters ΔΗ_σ and ΔS_σ have been also calculated, and they show that the critical region has an important effect on the dynamic viscosity properties. The results obtained are discussed from the viewpoint of the existence of interactions between the components.     

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.     

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.     

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.     

Estimation of some parameters of the exchange mechanism of luminescence decay

The rates of variations of the relative yield (α_η) and decay time (α_τ) with the acceptor concentration (C_A) have been calculated in the vicinity of C_A = 0. On the basis of the equations obtained, the ratio α_η/α_τ has been found and a simple scheme of experimental data analysis proposed.     

Mark-Houwink relations for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene

The parameters in the Mark-Houwink relationship, [η] = K′M?_v^a, for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene at 130°C have been estimated. They were found by measuring the limiting viscosity numbers of a series of fractions with molecular weights ranging from less than 10,000 to almost 700,000. The results are for 1-chloronaphthalene, [η] =0.0555 M?_v^0.684 (with a standard error of 0.0064 in K′ and 0.010 in a) and for 1,2,4-trichlorobenzene, [η] = 0.0392M?_v^0.725 (with a standard error of 0.00703 in K′ and 0.015 in a), where [η] is expressed in ml/g. The unperturbed end-to-end distance calculated from the viscosity-molecular weight data agrees with the theoretically expected value.     

Viscometric Analysis of Miscibility and Interactions for Binary,Ternary Polycarbonate/Brominated Polystyrene + Chloroform Systems at Different Temperatures

Viscosities of ternary systems consist of polycarbonate (PC)/brominated polystyrene (PBrS) in chloroform and their corresponding binary systems were measured at different temperatures (20, 25, and 30°C). All the measurements were carried out at the concentration ranges of 0.1–0.6 g·dL^?1. The mass ratio of PC to PBrS was selected as 75:25, 50:50, and 25:75 in the ternary solutions. Two empirical expressions of Huggins and Kraemer equations with three-parameters were used for reproducing of the experimental viscosity data. The fitting parameters were obtained for the corresponding temperatures. The miscibility criteria on the basis of the sign of Δ[η]_m based on the difference between experimental and ideal values of [η]_m, was calculated by applying the Garcia et al., theoretical equation. The effect of temperature on the viscosity data was also studied. The results from this method were correlated with the miscibility data obtained for the same system by differential scanning calorimeter (DSC) findings.     

Anionic polymerization of caprolactam. XLIII. Relationship between osmometric molecular weight,viscosity, and endgroups of a polymer

For unfractionated anionic polymers, the following relationship between the osmometric molecular weight and intrinsic viscosity is valid: M?_n = 13200[η]^1.115 (cresol), or M?_n = 13000[η]^1.021 (93.8% H₂SO₄). A comparison of the osmometric and viscometric data with the number of endgroups of a polymer confirmed the finding that under certain conditions, moderately branched molecules can be formed; the above parameters depend on the type of the activator used.     

Modified graessley theory for non-newtonian viscosities of polydimethylsiloxanes and their solutions

A deviation from Graessley's theory of entanglement viscosity appears at very high shear rates when the flow of polydimethylsiloxanes of various molecular weights and their solutions with various concentrations is measured by the capillary method. In order to explain this deviation, a modified Graessley theory is proposed according to the previously reported suggestion that frictional viscosity appears not to be negligible at high shear rates. A reducing procedure taking a frictional viscosity parameter into account was performed. All of the reduced data are combined to give a master curve in spite of a wide range of molecular weight, concentration, and shear rate (from the lower Newtonian to very highest non-Newtonian flow region). The findings from the reducing procedure completely explain the mechanism of non-Newtonian flow for the bulk polymers with various molecular weights, including those below the critical molecular weight for entanglement, and for polymer solutions at any concentration. The viscosity of the linear polymer system consists of the shear-dependent entanglement term η_ent proposed by Graessley and the shear-independent frictional term η_fric. The non-Newtonian behavior depends on the ratio of η_ent/η_fric at the shear rate of measurement. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric and the critical shear rate for onset of the non-Newtonian flow may be used as a measure of the non-Newtonian behavior of the system and a measure of capability for its rising, respectively. The Graessley theory is to be included in the present modified theory and is applicable to the case of η_entη_fric ? 1.     

Molecular dimensions of polydipropylsiloxamer

The molecular dimensions of polydipropylsiloxamer were studied by intrinsic viscosity measurements in toluene and in 2-pentanone. The relationships between the molecualr weight and the intrinsic viscosity were found to be: [η]_25°C., toluene = 4.35 × 10^?4 M^0.58; [η]_θ(10°C.), toluene = 1.09 × 10^?3 M^0.5; [η]_θ(76°C.), 2-pentanone = 8.71 × 10^?4 M^0.5. This held reasonably well for molecular weights from 25,000 to 3000,000. The root-mean-square end-to-end length ratio, (r₀² /M)^1/2 as calculated from the constant K, exceeds the free rotation value by approximately 100%. The disparity is greater than that found with polydimethylsiloxamer, indicating a lower degree of flexibility for the polydipropylsiloxamer. This is largely due to the short range steric interaction between near neighboring units of the chain. Gel permeation chromatography was also employed to demonstrate the lower degree of flexibility for polydipropylsiloxamer as compared with polydimethylsiloxamer.