On the factors governing the pressure dependence of the viscosity of moderately concentrated polymer solutions

Viscosity measurements were carried out as a function of pressure and temperature with solutions of polystyrene in eight (endothermal) θ-solvents at the respective critical composition by means of a Searle-type apparatus. A rolling-ball viscometer was used for the investigation of the pure solvents. In all cases the viscosity coefficient increases in a more or less exponential manner when the pressure is raised. For θ-conditions, the volumes of activation of the solutions exceed that of the pure solvent by typically 10–15%. The exact amount of this extra efffect stemming from the presence of the polymer and its variation with temperature can be qualitatively correlated with the heats of mixing. The ratio of the viscosity of the solution at 1000 and 1 bar, respectively, can be varied for a given solvent power (θ-temperature) by the choice of the solvent from ca. 2 (cyclopentane) to 4 (trans-decalin). Within a given system, the maximum effects that can be realized by a change of the solvent power via the variation of temperature ranges from ca. 3 to 6 (tert-butylacetate).     

Huggins' constant and unperturbed parameter of dilute polymer solutions

A novel method developed to evaluate the unperturbed parameter K_θ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, k_Hθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κ_Hθ. All calculations were done by the linear least-squares method. The K_θ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on K_θ can be obtained for polystyrene and poly(vinyl acetate).     

Solubilities and polymer-solvent-nonsolvent θ-compositions of poly (di-n-alkyl itaconates)

In order to establish the prerequisites for the examination of solution properties of poly(di-n-alkyl itaconates), the solubilities of the first 11 members of this polymer homologous series were determined in 70 solvents, and the results correlated with the lengths of the ester substituents of the polymer chain, the solvent solubility parameters and the solvent hydrogen bonding capacities. The relation between solvent strength and the lengths of ester substituents of the monomer units was established quantitatively for several solvents in terms of φ_{2 crit.,} the nonsolvent volume fraction in ternary polymer-solvent-nonsolvent θ-mixtures, and evaluated according to a turbidometric titration method proposed by ELIAS ¹. Both groups of results are a guideline for the probable existance of θ-conditions for particular polymer-solvent pairs and permit the prediction of solubilities of still higher members of the series.     

Studies on melt spinning of nylon 6. I. Cooling and deformation behavior and orientation of nylon 6 threadline

The melt spinning of nylon 6 filament yarns was studied by measuring the filament tensions at the takeup roll, the filament temperatures θ(x), filament diameters d(x), and birefringence Δn(x) as functions of distance x from the spinneret, and by observing how the molecular orientation was affected by these differences in cooling and thinning. Results were as follows: The thinning of the filament line, d(x), is affected little by the spinning temperature or by the degree of polymerization of the yarns taken up; it however depends heavily on the takeup speed V_Tu and the rate Q of production. Trouton viscosity β(T) as a temperature function derived from these experiments on nylon 6 is expressed consistently by the equation β ? 0.34 exp (3250/T), where T is absolute temperature. Nylon 6 filaments exhibit higher Trouton viscosity values than polyester or polypropylene filaments under the same spinning temperature. Filament temperature θ(x) versus distance x agreed well with theoretical values. The speed of molecular orientation was highest in the temperature range from 120°C to 40°C (the latter being the glass transition temperature of nylon 6). Furthermore, the larger the time rate of polymer deformation and the longer the residence time of polymer in the above temperature range, the higher was the orientation of the filament yarns taken up.     

Reaction and diffusion of reactive disperse dye in nylon 6

The diffusion of a reactive disperse dye with a vinylsulfonyl group accompanied by simultaneous reaction with the amino end groups in nylon 6 was examined by the method of cylindrical film roll at 70°C and pH 2.2–8.0. The experimental diffusion profiles of the active and fixed species of the dye in nylon 6 were confirmed to be described by the diffusion equation accompanied by the chemical reaction with substrate taking the limited amount of the end groups into account, where the active species of dye were assumed to react only with the free base of amino end groups. The completion of the reaction with the amino end groups was observed in the first layer from the surface at pH 6.0–8.0. The value of diffusion coefficient was constant (8.0 × 10^?10 cm²/s) at all the pH's. The product of the second-order rate constant, k₂, of reaction of the dye and the dissociation constant, K_a, of the amino end groups was constant (k₂K_a = 4.0 × 10^?9 s^?1) at pH 2.2–8.0. The k₂ values of the reaction with various substrates for vinylsulfonyl and monochlorotriazinyl-reactive dyes were compared and the practical dyeing conditions were discussed.     

Viscosity of polypropylene oxide solutions over the entire concentration range

An empirical equation is presented which describes polymer solution viscosity, η, over the entire concentration range from a knowledge of intrinsic viscosity, [η], Huggins constant, k′, and bulk flow viscosity of polymer, η₀. The equation is: \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\eta _{sp}}}{{C[\eta]}} = \exp \left\{{\frac{{{\rm k'[}\eta {\rm]C}}}{{1 - bC}}} \right\} $\end{document} where solution viscosity, η, is contained in η_sp. No arbitrary parameters are invoked since b can be evaluated at bulk polymer (C = polymer density) where everything else is known. The equation accurately portrays the viscosity of polypropylene oxide (PPG 2025) from infinite dilution to bulk polymer in a very good solvent (benzene) and in a somewhat poorer (～ θ) solvent (methylcyclohexane). The hydrodynamic consequences of the thermodynamic interactions between polymer and solvent are reflected in the constants. This equation should be applicable to other polymer/solvent systems, and thus be immediately useful to those working with concentrated polymer solutions.     

Specific hydroxide ion catalysis of the endwise depolymerization of cellulose

The endwise depolymerization (unzipping reaction) of hydrolyzed cotton cellulose (x = 200) in water under a nitrogen atmosphere was followed at 98°C at several alkalinities in the pH range of 8.0–10.5. The observed apparent first-order rate constant k₁ was invariable at low alkalinity (k₁ = k₀), while above pH 8.5, k₁ increased with pH. The data conform with the expression where [SH] denotes substrate concentration. The specific hydroxide ion catalysis is considered to involve ionization of the anomeric hydroxyl group at the reducing chain end that leads to elimination of the glucosidic oxygen atom bearing the polymer chain from C4 of the terminal D-glucose residue. In this initiation process, the glucosidic oxygen is eliminated as an anion so that rapid propagation of the unzipping along the polymer chain may occur. Thus, entire chains will depolymerize. The kinetic chain length v is defined as the ratio k₁:k_t, where k_t is the pseudofirst-order rate constant for chain terminations, and a value of v ～ 100 D-glucose residues was found at all the alkalinities investigated.     

Effect of photodegradation on dynamic mechanical properties of nylon 6

Changes in the dynamic mechanical properties of nylon 6 (α-form) under ultraviolet light irradiation were investigated. On irradiation with spectrally dispersed ultraviolet light in the wavelength range of 219–415nm, the dynamic modulus E′ and the density of nylon 6 were increased below about 300nm. It was found that the increment in E′ and the density were the result of crosslinking. When E′ was measured with time elapsed during irradiation by light of 253.7 nm, E′ initially decreased with time, increased at a longer time, and then reached a limiting value asymptotically. From the result of the change in E′ with time, it was assumed that the scission and crosslinking reactions occur simultaneously during ultraviolet light irradiation. Thus, the change in E′ with elapsed time was exppressed by the equation E′_t = E′₀ exp (?k₁t) + E′_∞[1 ? exp (?k₂t)], where E′_t is the dynamic modulus at time t, E′₀ is the E′ at t = ₀, E′_∞ is the limiting value of E′, and k₁ and k₂ are the rate constants. The apparent activation energies for k₁ and k₂ were 3.23 and 2.50 kcal/mole, respectively, and the former value agreed with the activation energy for the scission of the amide groups. The effects of the photodegradation on the temperature dispersion of nylon 6 were also investigated. On irradiation with light at 253.7 nm, the α-relaxation which appeared at about 90°C was broadened and the intensity of the γ-relaxation at ?95°C in the tan δ-versus-temperature curve was lowered. The β-relaxation which appeared at ?45°C for the wet nylon 6 decreased its intensity.     

Practical evaluation of the [η]–M relationship

The Mark-Houwink equation for the relationship between the intrinsic viscosity of a polymer Solution and the molecular weight can be expressed in the more general form: [η] = 32K_θ(M/1000)^a, where the constant K_θ has a theoretical meaning and the constant a is approximately equal to 0.7.     

Fractional coefficient of macromolecules in concentrated solution and in the vicinity of the critical solution temperature. Diffusion and sedimentation studies of polystyrene in toluene and trans-decalin

The concentration dependence of the frictional coefficient (f) in concentrated solutions of well-defined polystyrene fractions has been studied both in a good solvent (toluene) and in a solvent where θ conditions and condition in the vicinity of phase separation can be realized (trans-decalin). f and the self-diffusion coefficient (D⁺) have been calculated from a combination of measured translational diffusion coefficients (D) and osmotic pressure data for the systems; polystyrene $\text{(M = 390 000)}\text{trans-}\text{decalin}$ up to 90 kg/m³ at 20° (θ-conditions), 30° and 40°C; polystyrene $\text{(M = 110 000)}\text{toluene}$ up to 120 kg/m³ at 25°C. Sedimentation measurements are also reported. The main results are: (a) over a concentration interval 0–100 kg/m³, f shows more than a ten-fold and almost linear increase; (b) in trans-decalin when the temperature is raised from 20° (θ-conditions) to 40°C (good solvent conditions), keeping the concentration constant, f increases only slightly, the increase being somewhat more pronounced at higher concentrations; (c) the concentration dependence of the ratio $\text{D}\text{D}{}^{\mathrm{+}}$ is considerable under good solvent conditions but becomes gradually less pronounced when θ-conditions are approached; (d) diffusion/osmosis and velocity sedimentation give identical values of f over the entire concentration interval.     

Contribution of interferometry and mechanical parameters in evaluating molecular orientation for drawn polyester

Mechanical and structural parameters related to the optical properties of polyester (PET) (woollen type) fibres drawn at room temperature have been investigated. The changes in the strain were evaluated to obtain the molecular orientation factors 〈P₂(cos θ)〉 and 〈P₄(cos θ)〉. From the optical orientation, the values of f₂(θ), f₄(θ) and f₆(θ) orientation parameters were calculated. The structure and properties of oriented PET have been studied in the light of the rubber elasticity theory. The dielectric constant, magnetic susceptibility, number N′ of chains between crosslinks per unit volume, optical configuration parameter and the segment anisotropy, were among the calculated parameters. The results of the extension were used to calculate the shrinkage factor. Relationships between the calculated parameters and the draw ratios, together with micro-interferograms, are given for illustration. The present study throws light on how the applied stress changes the molecular orientation factors and the structural parameters. © 1999 Society of Chemical Industry     

Unidirectional fiber–polymer composites: Swelling and modulus anisotropy

The solvent swelling of unidirectional rubber–fiber composites was studied. The amount of matrix swelling was constrained to the extent that would be predicted from the thermodynamic theories of elasticity and polymer–solvent interaction. The geometry of swelling was found to be orthotropic in nature. A simple trigonometric function was derived to relate linear deformation due to swelling to the angle which the direction of its measurement makes with the fiber direction. The validity of the derivation was demonstrated experimentally. Considering swelling to be the imposition of tensile forces of equal magnitude in all directions, and considering a swelling-induced linear deformation to be analogous to a tensile compliance, a simple set of relationships between elastic parameters and their direction of measurement was derived: where E_θ, G_θ, v_θ, and η_θ are Young's modulus, shear modulus, Poisson's ratio, and the shear coupling ratio measured in a longitudinal transverse plane at an angle with the fiber direction, respectively, and E_L, G_LT, and θ_LT are the longitudinal Young's modulus, the longitudinal transverse shear modulus, and the longitudinal transverse Poisson ratio, respectively. Further simplifying the case of combined transverse isotropy and special orthotropy was the conclusion that 1/G_LT = 1/E_T + (1 + 2v_LT)/E_L. The relationships for G and E were experimentally demonstrated.     

Viscometric Behavior of Solution of Polyisobutylene in Hexane and Cyclohexane Solvents: Viscosity-Molecular Weight Relationships

The behavior of three different high molecular weight polyisobutylenes (PIB) in solutions of hexane and cyclohexane at 30°C has been investigated by viscometry. Mark–Houwink relations have been examined, the polymer–solvent interaction is discussed in terms of the calculated Huggins constant, k; parameter a of the Mark–Houwink equation; and equivalent hydrodynamic volumes V _e. The molecular weights of the three sample of polyisobutylene are remarkably well fitted with the intrinsic viscosity data.     

Interaction parameters in ternary polystyrene solutions at high temperature

A combination of dilute solution viscometry and Rayleigh light scattering has been used to evaluate experimentally the interaction parameters χ_ij in solutions comprising tetralin (1), polystyrene (2) and 3-methyl cyclohexanol (3). The measurements were carried out at 371.5 K, where binary solutions of the polymer in 3-methyl cyclohexanol are under θ-conditions and tetralin is a thermodynamically good solvent for polystyrene. For polymer-solvent interaction, values of χ₁₂ = 0.40 ± 0.01 and χ₂₃ = 0.50 were obtained. The solvent-solvent interaction parameter χ₁₃ was composition dependent, having limiting values of 0.52 and 0.73 at X₁ = 0 and X₁ = 1, respectively, where X₁ is the mol fraction of liquid 1 in binary mixtures of liquids (1) and (3).     

The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

Estimation of the Surface Energy of Polymer Solids

The methods to estimate the surface tension of polymer solids using contact angles have been reviewed in the first part. They are classified into the following three groups depending on the theories or the equations applied: (1) the methods using the Young's equation alone, (2) the methods using the combined equation of Young and Good-Girifalco, and (3) the methods using the equations of work of adhesion. Some notes and comments are given for each method and results are compared with each other. The two-liquids method for rather high energy surface is also introduced.

Next, some new possibilities to evaluate the surface tension of polymer solids are presented by our new contact angle theory in consideration of the friction between a liquid drop and a solid surface. The advancing and receding angles of contact (θ _a and θ _r ) are explained by the frictional tension γ_F and accordingly two kinds of the critical surface tension γ_C (γ_Ca and γ_Cr ) are given.

This work has shown that one of the recommendable ways to evaluate γ_S is either the maximum γ_LV cos θ_a or the maximum γ_C using the advancing contact angle θ_a alone, and another way is the arithmetic or the harmonic mean of the γ_Ca and γ_Cr . A depiction to determine the γ_C such as ln(1 + cos θ₀ ) vs. γ_LV with cos θ₀ = (cos θ₀ + cos θ_r )/2 has also been proposed.     

Effect of temperature and thermodynamic quality of solvent over unperturbed chain dimensions of nylon 6

A nylon 6 sample having average molecular mass 4.825 × 10⁵ g mol^?1 was fractionated into five different fractions with respect to molecular mass, which ranged from 3691 to 999,000 g mol^?1. The light scattering and intrinsic viscosity measurements were made in m‐cresol and its mixture with 1,4‐dioxane. The second virial coefficient, radius of gyration and Mark Houwink's constant and unperturbed chain dimensions were determined by light scattering and viscosity measurement. It has been observed that all these parameters are composition of solvent and temperature dependent. The solvent having composition of 97% m‐cresol and 3% dioxane, was best and it deteriorated with the increase/decrease in percentage of 1,4‐dioxane in m‐cresol. However, its thermodynamic quality was enhanced with the temperature. Such variation in quality of solvent was reflected in all the estimated parameters and showed maxima at this composition of solvent. The unperturbed dimensions obtained by different methods though, differed in values but showed same trend and NA‐MKB method gave close results to the one obtained through [η_o]. A new expression has also been proposed relating k_o to solvent quality and temperature and the data obtained by us for nylon‐6 and the one obtained from the literature for dextran obeyed this expression up to large extent irrespective of the solvent composition and temperature. The proposed equations have also been applied to dextran/methoxy ethylene and dextran/ethylene glycol systems and worked well. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.     

Optomechanical variations in cold‐drawn thermally treated polypropylene fibers

A two‐beam polarizing interference microscope with a microstrain device was used for measuring some optical and mechanical parameters for polypropylene (PP) fibers at room temperature (28 ± 1°C). The changes in the molecular orientation were evaluated to obtain orientation factors f₂(θ), f₄(θ), f₆(θ), 〈P₂(cos θ)〉, 〈P₄(cos θ)〉, and crystalline and amorphous orientation functions F_c and F_a, respectively. The shrinkage factor, uniaxial tension, true stress, molar refractivity R, surface reflectivity R′, the crosslink density N_s, the chain entanglement density N_c, the segment anisotropy γ_s, and the number of chains N′ were calculated. In addition, the shrinkage stress was found to increase with the increase of draw ratio. The dielectric constant ε, the dielectric susceptibility η, the average work per chain w′, and the constants of the stress–birefringence equation were obtained. Comparison between Hermans's optical orientation functions and the corrected formulas by de Vries are given. The values of fully oriented refractive indices n₁ and n₂ were found. The generalized Lorentz–Lorenz equation given by de Vries was used to determine the structural parameters of PP fibers. An empirical formula was suggested to correlate the changes in the evaluated parameters with different draw ratios, and its constants were determined. The study demonstrated changes on the molecular orientation factors and evaluated microstructural parameters as a result of an applied cold‐drawing process. Relationships between the calculated parameters and the draw ratios, together with microinterferograms were presented for illustration. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 729–738, 2003     

Radiation-induced graft polymerization of 4-vinyl pyridine to styrene–butadiene–styrene triblock copolymer

The radiation-induced graft polymerization of 4-vinyl pyridine to styrene–butadiene–styrene triblock copolymer (SBS) was investigated. Relations between the rate of grafting and the dose rate when SBS was irradiated in 4-vinyl pyridine–methanol solution, and between the rate of grafting and 4-vinyl pyridine concentration of 4-vinyl pyridine–methanol solution have been investigated. An experiment that had been carried out on SBS immersed in various 4-vinyl pyridine concentration of 4-vinyl pyridine–methanol solutions showed that the extent of swelling of SBS by the various 4-vinyl pyridine–methanol solutions increased with increasing 4-vinyl pyridine concentration. The largest rate was found at 20 vol % 4-vinyl pyridine–methanol solution. The rate was smaller at the volume percent of 4-vinyl pyridine higher or lower than 20 vol %. On the assumption that the theory of homogeneous homopolymerization could be applied to this grafting reaction, the value of k_p²/k_t was obtained, where k_p and k_t are the propagation and termination constant, respectively. The value of k_p²/k_t greatly decreased with increasing adsorbed concentration of vinyl pyridine–methanol solution. This decrease of k_p²/k_t was explained by the fact that 4-vinyl pyridine and methanol absorbed in SBS acted as a plasticizer which increased the molecular motion of the polymer. The solvent effect on the graft polymerization was also investigated. The result was explained by solubility parameter. When the chosen solvent had better solubility with the polymer, the degree of grafting was smaller. That was connected with the extent of the polymer chain mobility.     

Development of macrostructural effects of cold drawing on nylon 6 fibers

This work reports measurement of the molecular orientation by two techniques for nylon 6 fibers drawn at room temperature. The changes in the strain and optical parameters are used to obtain some macrostructural parameters to evaluate the cold‐drawing process values of the mechanical orientation functions, [P₂(cos θ)], [P₄(cos θ)], amorphous and crystalline orientation functions (F_c and F_a), and the molar number of chain segments per unit volume (N_e). Also the crosslink density (N₀), the chain entanglement density (N_s), the average optical orientation F_av, the dielectric constant (ε), the dielectric susceptibility (η), the shrinkage stress (k_s), and other parameters were calculated. Relationships between the calculated parameters are given. The present study demonstrates changes in the molecular reorientation factors and the obtained new physical properties resulting from cold‐drawing process. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 287–295, 2004