Formation of dispersed phase in incompatible polymer blends: Interfacial and rheological effects

The formation of dispersed phase in blends of incompatible polymers during melt extrusion with a co-rotating twin screw extruder was studied, using nylon and polyester as the matrix and ethylene-propylene rubbers as the dispersed phase. A master curve is obtained, i.e., Gηmα/γ = 4p^±0.84, where G is the shear rate, γ the particle diameter, η the interfacial tension, η_m the matrix viscosity, η_d the dispersed-drop viscosity, and p = η_d/η_m. The plus (+) sign applies for p > 1, and the minus (?) sign for p < 1. Thus, the dispersed-drop size is directly proportional to the interfacial tension and the ±0.84 power of viscosity ratio. The dispersed drops are the smaller, when the interfacial tension is the lower and the viscosity ratio is the closer to unity. The interfacial tension is largely controlled by the polarities of the two phases, and can be varied over several orders of magnitude by using appropriate dispersants.     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.     

Rheology of a cellulose graft copolymer. Comparison with other closely packed gel thickeners

Hydrolyzed cellulose–polyacrylonitrile graft copolymer is a polyelectrolyte gel suspension with a high viscosity in water. It is a closely packed swollen gel particle suspension in the appropriate concentration range and has similar rheological properties to other thickeners of this type. Viscosities η in either water or salt solution are reduced to a single master curve by use of the reduced viscosity function η/cQ, where c is weight fraction of polymer and Q is swelling volume in excess solvent of the same ionic strength. The effective molecular weight between crosslinks, M_c, determined from shear modulus, corresponds to M_c values for other closely packed gel thickners of similar η/cQ. Among all examples of this class of thickener, the plateau values of η/cQ, which occur at cQ > 2, are approximately inversely proportional to M_c.     

Viskosität hochkonzentrierter Lösungen eines ungesättigten Polyesters in p-Xylol

The viscosity η of a polyester, prepared from maleic anhydride, phthalic anhydride and 1,2-propylene glycol in the acid value range of 30–240 (mg KOH/g) with 2–10% wt.?% of p-xylene in solution, in dependence upon the degree of conversion, was given by η = k₁M?. The viscosity-temperature dependence was satisfactorily described by log η = A + B/T–T₀. The viscosity-polyester content correlation was given by η = C exp (Dx), where C and D are constants, specific for the degree of conversion and of temperature, and x wt.?% of polyester content. In the eq. log η = x₁ log η₁ + x₂ log η₂ + Δ, where x₁ and x₂ are the mole fractions of polyester and p-xylene, η₁ and η₂ their viscosities, Δ was a linear function of M?₀ and the polyester content of the samples. Data from measurements at 100°C are tabulated.     

Pressure dependence of newtonian viscosity

Recently, a new method of generalization of the zero shear viscosity of liquids has been proposed. The method utilizes a modified Doolittle formula and the temperature-dependent volume, as expressed by the corresponding states theory of liquids. Furthermore, the glass-transition temperature has been employed as the scaling parameter. The proposed treatment allowed prediction of the correlation between: (i) viscosity, η, and temperature, T, (ii) η and the molecular weight of polymer, (iii) η and concentration, and (iv) the combined effect of these variables. At present, the method is extended to the pressure, P, effect. Furthermore, by substituting the free volume fraction in the Doolittle formula by the theoretical “hole fraction,” a master-relation is proposed that provides means for predicting η = h(T, P) dependence.     

Effect of concentration on apparent viscosity of a globular protein solution

The viscosity of a globular protein solution as a function of concentration was studied with a cone and plate viscometef (Ferranti-Shirley Viscometer System) using, β-lactoglobulin as a model. An aqueous buffer solution (pH 7, ionic strength 0.04) containing up to 40 percent protein was subjected to rates of shear between 800 and 17,000 sec^?1. Specific viscosity of β-lactoglobulin up to 10 weight percent was proportional to the weight concentration of protein in solution such that: η_s = η₀ [ 1+0.8 (weight percent concentration)] where η₀ and η_s are viscosity coefficients for the pure solvent and the solution, respectively. For 3-40 weight percent, a linear relation of shear rate and shear stress was observed at high shear rates. Linearity began at 3500, 4300, 6800, and 7000 see^?1 for 10, 20, 30 and 40 weight percent concentrations respectively. The apparent viscosity was lower below these critical shear rates.     

Rheological properties of concentrated polymer solution: Polybutadiene in good and θ solvents

The zero shear viscosity, η° of three polybutadiene samples having different molecular weights over a wide range of concentration (1.0–35.0% polymer) in good and θ solvents has been studied. Superposition of viscosity data has been made to give a single composite curve for each solvent by shifting them vertically by a factor (M°/M)^3.4, where M° represents the molecular weight of the reference sample. The shift factor is found to be proportional to M^3.4 in the region of higher concentration, which indicates that the 3.4-power law is valid for the data of polybutadiene. The double-logarithmic plots of relative viscosity η°_r as a function of c⁵M^3.4 yielded a single composite curve approximating a straight line with slope of unity at the higher values of the variables. The results indicate that over a considerable range of the variables (molecular weight and concentration) at a constant temperature, the relative viscosity is a single function of c⁵M^3.4. The results for double-logarithmic plots of zero shear specific viscosity η°_csp as a function of concentration confirmed those observed in polycholoroprene samples studied earlier that the η0_sp values in θ solvents at higher concentration region are found to be higher than those found in good solvents, whereas in the moderately concentrated region the values are just opposite in θ and good solvents. The viscosity crossover in θ solvents is not as sharp as is found in case of polychloroprene samples and that crossover, too, has taken place in the range of concentration of 11.7–31.6% polymer, which is comparatively higher than that of polychloroprene samples (6.06–21.0% polymer). The results indicate some relation between viscosity crossover and polymer polarity, supporting the idea of enhanced intermolecular association in poor solvents. To correlatethe viscosity data obtained in good and poor solvents, two methods, one given by Graessley and the other given by Dreval and coworkers involving the correlating variable c[η], were considered. The plots of relative viscosity η°, versus the correlating variable c[η] in benzene (good solvent) yielded one curve, but in the case of θ solvents (dioxane and isobutyl acetate), the same plots yielded three separate curves instead of a single curve, which is rather unusual. The appropriate correction on the correlating variable for chain contraction in the concentrated region in a good solvent moved the data to a common curve, especially in lower concentration region, but at the higher concentration region a slight overestimation of data seems to have been effected. On the other hand, the plots of log η as a function of correlating variable c[η] yielded a single curve for three samples in the good solvent benzene, but in poor solvents (diozane and isobutyl acetate) the same plots yielded three separate curves for three samples instead of a single curve, the reason for which is not known at present. However, the normalization of the correlating variable c[η] with Martin constant K_M reduced all experimental data of the polymer samples to a common curve. The correlation of the viscosity data by either of the two methods seems to be possible in the case of the nonpolar flexible polymer, polybutadiene.     

Dynamic rheological properties of polyetherimide/polyetheretherketone/liquid crystalline polymer ternary blends

The dynamic rheological properties of poly(etherimide)/poly(etheretherketone)/liquid crystalline polymer (LCP) ternary blends were measured in order to correlate these properties with the morphology obtained after extrusion. The viscosity radio, η_d/η_m, where η_d = disperse phase viscosity and η_m = matrix viscosity, had to be redefined. Below 50 wt% LCP, η_d = η_LCP, η_m = η_PEEK+PEI and η_d/η_m < 1. Above 50 wt% LCP, η_d = η_PEEK+PEI, η_m = η_LCP and η_d/η_m > 1. Fibrillar morphologies were obtained in both cases, except below a concentration of 20 wt% LCP. At low concentrations of LCP the ternary blends had lower viscosities than the component polymers, showing a flow promotion effect of the LCP on the PEI- and PEEK-rich phases.     

Studies on melt spinning. III. Velocity field within the thread

The velocity field within a molten spinning thread was analyzed quantitatively by solving the equations of continuity and momentum for Newtonian liquids. In solving the equations, the viscosity was assumed known and was given by the expression where x and r are distances in cylindrical coordinates. A series solution in velocity v having the expression was obtained when several simplifying assumptions were made on the equations. The series solution was found to converge when cr² < 1 is satisfied. μ₀e^βx and ν₀e^αx above are tangents on semilog paper at x = x to the macroscopic viscosity and velocity profiles μ(x) and ν(x) which were computed separately by means of a technique developed previously by the author.^1,2 The value c was derived from the temperature profile across the thread at x = x computed separately using another technique developed by the author.³ The above series solution showed numerically that under most conceivable spinning conditions the velocity field within the thread is for practical purposes flat across the thread and, in addition, purely extensional.     

The peculiarities of relaxation processes at heating of glasses in glass transition region according to the data of mechanical relaxation spectra (Review)

The results of study of mechanical losses by dynamic methods for silicate, borate, and chalcogenide glasses, metallic glass and glycerol at heating in the glass transition region were analyzed. Essential differences between the dynamic viscosity values η* calculated by means of the Maxwell equation based on the relaxation time at the maximum of losses (ωτ = 1) for labile states of glass, and the experimental values of η for the metastable liquid at the same temperature were revealed. The ratio η*/η was systematized in the framework of kinetic theory of glass transition and thermodynamics. An interpretation of the regularities was proposed based on the theory of dynamic properties of liquids. It was shown that different widths of spectra of relaxation times were the most probable reason of the difference between η* and η. The width of spectrum is determined by the degree of ordering of states of compared metastable liquid and glass at the same temperature; it depends on the thermal prehistory of each state. A wider spectrum of relaxation times corresponds to a more ordered state. For the considered glasses, the ratio of the temperature corresponding to viscosity value η* of the metastable liquid to the temperature of α-relaxation maximum (T _α) is 1.03 ± 0.01 at T _α variation from 190 to 1550 K. It is the evidence that all the relaxation frequencies, constituting both “narrow” and “broad” spectrum are associated with one and the same molecular mechanism. Mechanical losses in the metastable supercooled glycerol are described by the Maxwell equation with high precision for η values from 10¹³ to 10⁵ Pa s.     

Tailoring closely packed gel–particle systems for use as thickening agents

When used as a thickening agent in aqueous suspension, hydrolyzed starch–polyacrylonitrile graft copolymer (H-SPAN) has broadly variable rheological properties, such as viscosity, storage modulus, and stress overshoot characteristics. A series of H-SPAN preparations with variable swelling ratio Q were made by pretreating portions of stock material. As 1% suspensions in water, they had viscosities η that were non-Newtonian. At a constant shear rate, η of the suspensions depended on Q and had a sharp maximum in the midrange of Q. In terms of reduced concentration cQ, where c is weight fraction of polymer, the highest η occurred when cQ was approximately 2. With isoionic dilution, each suspension had a constant reduced viscosity function, η/cQ, provided cQ > 2. The value of η/cQ fell rapidly when cQ approached 1. All thickeners of the closely packed gel–particle type so far examined have this relation of the reduced variables. The shear modulus calculated from measurements of primary normal force and corrected for solvent swelling, according to theory for rubber for elasticity, was essentially constant for each suspension measured during isoionic dilution to cQ = 2. The density of crosslinks calculated from the modulus was extremely low for all samples. The variable rheological properties of the preparations resulted primarily from differences in their low effective crosslink densities.     

Relationship between melt viscosity and dielectric relaxation time for a series of epoxide oligomers

Melt viscosity has been investigated for a series of bisphenol-A type epoxide oligomers with different weight-average mol wts (M?_w), ranging from 388 to 2640. The temperature dependence of the melt viscosity is described by the Williams–Landel–Ferry (WLF) equation. The melt viscosity η is correlated with both the direct current (dc) conductivity σ and the dielectric relaxation time τ. The two relationships between these three properties, σ·η^κ = const (0.63 ≦ κ ≦ 1.12) and η/τ^? = const (0.73 ≦ ? ≦ 1.06), are experimentally derived. Both exponents, κ and ?, depend on the M?_w of the oligomer. The lower M?_w oligomer has the larger value of κ. The κ value is close to unity for the low M?_w oligomer, which agrees with Walden's rule, σ·.η = const, applicable to most low mol wt liquids. The ? value is near unity for the epoxide oligomer with higher M?_w than 2000, which means that the melt viscosity is proportional to the dielectric relaxation time. The low M?_w oligomer (M?_w < 2000), on the other hand, has a smaller value of ? below unity. The result indicates that the melt viscosity is not proportional to the dielectric relaxation time for the low M?_w epoxide oligomer, whose dielectric α-relaxation is not governed by the Debye equation. © 1993 John Wiley & Sons, Inc.     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002     

Thermodynamical approach to polymer rheology

The model of pseudocrosslink is extended to polymer rheology. There exist various sizes b of 4–16 between transition points A and B. Each link is connected with a chain having length n_b and relaxation time τ_b. n_b is equal to b² and τ_b is proportional to n_b². A, B, and C (polymer terminal) divide the stress-relaxation spectrum into four zones. In the AB zone, successive dissociation of links occurs from a small size to a large one and rigidity G is decreased with time t as G ∝? t^?0.5 and viscosity η is increased as G ∝? t^0.5. In the BC zone, dissociation of the B link proceeds along a molecule of length n in a mode of squeezing of molecule and η becomes constant, but G still decreases due to increase of unperturbed end-to-end distance of chain and G ∝? t^?0.5. However, dynamic elasticity becomes constant due to a small amplitude. At high shear, links are loosened and G and η are much decreased. Beyond C, molecule flows and η increases as η ∝? γ^?0.8 n^3.5, but high shear rate γ diminishes the effect of n due to extension of the molecule. Extensional viscosity η^* is affected by the change of shape as η^* ∝? t^1.5 and gives an overshoot. Under load, creep occurs and it is proportional to t^1/2–1/3. © 1995 John Wiley & Sons, Inc.     

Estimation of the inherent friction factor per main-chain friction unit of liquid low-molecular-weight unsaturated polyesters

The temperature dependence (at 323–443 K) of the zero-shear viscosity η of about 30 nonfractionated samples of an unsaturated polyester (300 < M_n < 1500) was analyzed and the parameters of the Vogel equation describing the η(T) dependence were estimated. Their dependence on the molecular weight is discussed. The inherent friction factor per main-chain friction unit, ξ_o, has been evaluated for 15 < Z_n < 70 (where Z_n is the number-average number of main-chain friction units) and compared with the values available for other polymers.     

Self‐assembled structures in d8‐polystyrene‐block‐polyisoprene/polystyrene blends in the weak segregation regime: SAXS and TEM study

BACKGROUND: This paper reports an investigation of the microphase‐separated morphology and phase behaviour in blends of d‐polystyrene‐block‐polyisoprene with homopolystyrene in the weak segregation regime, using small‐angle X‐ray scattering and transmission electron microscopy, as a function of composition, weight‐average molecular weight and temperature. The chain length ratio parameter r_M = M_H/M_C (where M_H and M_C are the weight‐average molecular weights of the homopolymer and corresponding block copolymer chain) was selected to encompass all possible types of mutual homopolymer/block copolymer sizes. RESULTS: In the weak segregation regime the polystyrene block chains behave as a ‘wet brush’ for r_M < 1 similarly to the intermediate and strong segregation regimes. For r_M > 1 a macroscopic phase separation occurs. The domain spacing D increases systematically in the range 0 < r_M ≤ 1 with increasing concentration of homopolymer w_P and increasing r_M regardless of the implemented specific morphology, but the slope of the periodicity D versus w_P relation is smaller than in the intermediate and strong segregation regimes. CONCLUSION: The criterion for ‘wet and dry brush’ morphologies has been applied to explain the changes in microdomain morphology during the self‐assembly process. It has been shown that the parameters r_M and χ^3/2N (where χ is the Flory–Huggins parameter and N the number of segments per chain) characterize the slope of the D versus w_P relation in the weak and intermediate segregation regimes. Copyright © 2009 Society of Chemical Industry     

Rheology of silicon carbide/vinyl ester nanocomposites

Silicon carbide (SiC) nanoparticles with no surface treatment raise the viscosity of a vinyl ester resin much more intensely than micrometer‐size SiC particles. An effective dispersant generally causes a reduction in the resin viscosity attributed to its surface‐active properties and thereby increases the maximum fraction of particles that can be introduced. This article assesses the rheological behavior of SiC‐nanoparticle‐filled vinyl ester resin systems with the Bingham, power‐law, Herschel–Bulkley, and Casson models. The maximum particle loading corresponding to infinite viscosity has been determined to be a 0.1 volume fraction with the (1 ? η_r^?1/2)–? dependence (where η_r is the relative viscosity and ? is the particle volume fraction). The optimum fractional weight percentage of the dispersants (wt % dispersant/wt % SiC) is around 40% for 30‐nm SiC nanoparticles, which is much higher than 1–3% for micrometer‐size particles. SiC nanoparticles at a concentration of 9.2 wt % (0.03 volume fraction) cause a fourfold increase in the resin viscosity. The addition of a dispersant at the optimum dosage lowers the viscosity of SiC/vinyl ester suspensions by 50%. The reduction in the viscosity is substantial to improve the processability of SiC/vinyl ester nanocomposites. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 4365–4371, 2006     

Rheological properties of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

Steady-state shear rheological properties of liquid crystalline solutions of four ethyl celluloses (ECs) were determined at a low shear rate (1 s^?1) and at relatively high shear rates by using two rheometers (cone-plate and capillary types), and were compared with those of liquid crystalline hydroxypropyl cellulose (HPC). The effect of molecular weight (MW) on the viscoelastic behavior was also determined. The viscoelastic behavior was also determined. The viscometric behavior of EC solutions was similar to that of HPC solutions: (1) with respect to temperature, the shear viscosity (η) at shear rate of 1 s^?1 exhibited a minimum (η_min) and a maximum (η_max), and the concentration–temperature superposition for η could be applied; (2) the behavior of η at relatively high shear rates as a function of shear rate or polymer concentration was typical of lyotropic liquid crystals. The MW dependence of η_min was greater than that of η_max for EC solutions. The behavior of the elastic parameters such as Bagley correction factor (v), entrance pressure drop (ΔP_ent), and die swell (B) at relatively high shear rates for EC solutions was essentially similar to that for HPC solutions: (1) the shear rate or stress dependence of the elastic parameters was greatly dependent on whether the polymer solution was in a single phase or biphase; (2) with respect to concentration the elastic parameters showed a maximum and a minimum and the maximum or minimum point for each parameter was not always identical to each other. η for the isotropic or fully anisotropic solutions at a given concentration (C) increased, whereas η for the solutions in the vicinity of the biphasic region showed a minimum, with respect to MW. The slope of η at a given shear rate vs. CM _w depended on shear rate, and this slope for the isotropic solutions appeared to be greater than that for fully anisotropic solutions. ΔP_ent and v at a given concentration showed either a monotonical increase or a maximum or minimum with MW, and this behavior was not fully consistent with that of η. B for the isotropic solutions increased and B's for both biphasic and fully anisotropic solutions were almost constant, with MW.     

Influence of two-step process and of different stoichiometric ratios on morphologies generated in castor oil epoxy resins

Phase separation during polymerization was studied in a model system consisting of a diepoxide based on diglycidyl ether of bisphenol A (DGEBA), variable amounts of ethylenediamine (EDA) and the mass of castor oil (CO) necessary to obtain a mass fraction equal to 0-15 in a final system where the stoichiometric ratio of amine to epoxy equivalents, r, was equal to 1. A two-step polymerization process was performed by curing first a system with r = 0-5, during variable times before phase separation, and then carrying the system to r = 1. Thermodynamic analysis of samples with different r values led to a linear relationship between the Flory-Huggins interaction parameter and r. The concentration (P) and average size (D?) of dispersed-phase particles followed opposite trends, i.e. P increased while D? decreased, when either r was increased or the time of curing in the first step of a two-step process was decreased. This was explained by assuming that the competition between nucleation and growth was determined by the viscosity at the cloud point, η_cp. Low values of η_cp favoured growth over nucleation and led to fewer but larger particles.