Rheological properties of poly(2,6-dimethylphenylene oxide)—polystyrene blends

The viscoelastic (VE) response of freeze-dried blends of polystyrene (PS) and poly-(2,6-dimethyl phenylene oxide) (PPO) has been studied as a function of composition, frequency, and temperature to examine the degree of rheological compatibility. When blended together, the relaxation processes of both molecular species exhibit the same temperature dependence. However, the temperature dependence of the VE response is a function of composition. It is shown that this behavior can be predicted from the measured glass transition temperatures by assuming the additivity of the free volumes of the components. The properties of the blends are compared at equal free volumes. The effective segmental friction factor is found to be independent of composition while the modulus of the rubbery plateau increases with PPO concentration. This result is interpreted as a change in the entanglement molecular weight M_e of the blends. When the changes in M_e are considered, the relationship between the zero-shear viscosity η0 and the 3.4 power of the weight-average molecular weight, commonly found for high molecular weight homopolymers, predicts the compositional dependence of η0 for the PPO–PS blends. It is concluded that the PPO–PS system forms a rheologically compatible blend.     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.     

Effects of chain length distribution on viscoelastic properties of entangled linear polymers: Blending laws for binary blends

The reptation idea of de Gennes and the tube model theory of Doi and Edwards are extended to explain the terminal viscoelastic properties of binary blends in the highly entangled state of two linear monodisperse polymers with different molecular weights M₁ and M₂. A modified tube model is proposed that considers the significance of the constraint release by local tube renewal in accounting for the relaxation process of the higher molecular weight chain. Its relaxation by both reptation and the constraint release is remodeled as the disengagement by pure reptation of an equivalent primitive chain. From knowledge of the longest relaxation times of the blend components, the stress equation is formulated from which blending laws of viscoelastic properties for the binary blends are derived. To force better agreement between theory and experiment at the pure monodisperse limits of the blends, a crude treatment to include the effect of contour-length fluctuation in the equivalent-chain model is also discussed. Theoretical predictions of the zero-shear viscosity and steady-state shear compliance are shown to be in good agreement with literature data on undiluted polystyrenes and polybutadienes over a wide range of the blend composition and M₂/M₁ ratio. The asymptotic of the laws for blends with M₂/M₁ → 1 and 0 are comparable to those from the relaxation spectrum proposed by others earlier on the basis of the tube model.     

Toward a quantitative theory of the rheology of concentrated solutions of stiff polymers

Predictions of the rheological properties of concentrated isotropic solutions of stiff polymers are made that improve on those obtained with the approximate Doi theory. Predictions of the shear-rate and concentration dependence of the viscosity η and the first and second normal stress differences N₁ and N₂ that avoid the closure approximations of Doi are obtained by using a Galerkin numerical solution for the orientation distribution function. The predictions for η and N₁, though they neglect the effects of polydispersity in molecular weight, are shown to be in quantative agreement with recent measurements on solutions of poly-γ-benzyl-L -glutamate (PBLG). The polydispersities of a series of commercial PBLG and PBDG samples are measured by gel permeation chromatography, and found to be broad. An attempt is made to account for the effects of polydispersity on the linear viscoelastic storage and loss moduli for PBLG solutions by using the Marrucci–Grizzuti extension of the Doi theory. The attempt fails. The most probable explanation for the failure is that the rotary diffusive motions of the shorter molecules in the mixture are drastically slowed by the matrix of surrounding longer molecules.     

Numerical calculations of the viscoelastic properties of solutions of branched polymers based on the Zimm-Kilb theory

Numerical calculations were performed for the viscoelastic properties of dilute solutions of branched star polymers with equal branch lengths as formulated in terms of a bead-spring model by Zimm and Kilb without using the integrodifferential equation approximation method to calculate the eigenvalues. The complex modulus and complex viscosity were calculated as functions of frequency for various combinations of the number of branches f (4, 8, and 13), the number of beads in one branch N_b (= N/f; 20 to 100, where N + 1 is the total number of beads, N the number of springs in the molecule) and the reduced hydrodynamic interaction parameter h^* (= h/N^1/2 0.05 to 0.3, where h is the hydrodynamic interaction parameter of Zimm and Kilb). The frequency dependence of the complex modulus in the low-frequency range depends mainly on h^* and not on N_b if N_b is large enough, and it is very close to that calculated from the eigenvalues for h→∞ obtained by Zimm and Kilb, if h^* is about 0.25. As h^* decreases from 0.25, the frequency dependence gradually approaches that of the free-draining cash (h→0). Calculations may be carried out for h^* values somewhat larger than 0.25 and result in a frequency dependence that is not intermediate to the h → 0 and h → ∞ cases as evaluated by Zimm and Kilb. The physical meaning of such “super-non-free-draining” values of h^* is uncertain, however. The intrinsic viscosity ratio g′ = [η]_f/[η]_lin is an increasing function of h^* and changes very slowly with N. For h^* = 0.25, g′ is close to the non-free-draining limit for any value of N.     

Viscoelastic properties of dilute polymer solutions: The effect of varying the concentration

Dynamic viscoelastic behavior was investigated for solutions of polystyrene in tricresyl phosphate, a good solvent, at concentrations, c, less than the coil‐overlapping concentration, c*. At the infinite dilution limit, the behavior was in accord with the theory of Doi and Edwards involving the excluded volume potential and hydrodynamic interaction (HDI). Thus, the viscoelastic functions were completely derived from the intrinsic viscosity–molecular weight relation. At finite c, the complex modulus was represented by the sum of two terms. One was a Rouse–Zimm (RZ) term conveniently represented by the Zimm theory with an arbitrarily chosen value of the HDI parameter. The other was a term with a single relaxation time, longer than the longest RZ relaxation time, and with a high‐frequency modulus proportional to the square of c [the long‐time (LT) term]. The behavior of the RZ term indicated the stronger screening of HDI with increasing c. Using the experimental c dependence of the longest RZ relaxation time to get the relevant parameter, we compared the RZ viscoelastic function with the Muthukumar–Freed theory. The agreement was good at low concentrations, c < c*. The contribution of the LT term, which was not included in the theory, was quite significant at low frequencies; about 60% of the Huggins coefficient was attributable to this term. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 211–217, 2001     

Conformation of poly(methacrylic acid) in alcohol–water mixtures. III. Dependence on molecular weight

Poly(methacrylic acid) has been studied in 0.002N HCl–ethanol mixtures as a function of molecular weight. A different dependence on molecular weight is noted at different alcohol concentrations. Since the intrinsic viscosity passes through a series of extrema with changes in alcohol concentration, the dependence on molecular weight has been considered in two regions of alcohol concentration in particular. The region of the first minimum and the region of the second minimum (or overall maximum). In the region of the first minimum, intrinsic viscosity is proportional to M^½, just as in 0.002N HCl. The Huggins coefficient k′ is large (ca. 60) but drops to about 10 when the molecular weight exceeds 320,000. In the region of the second minimum the dependence on molecular weight is complex. Intrinsic viscosity is proportional to molecular weight both at low and at high molecular weight and thus indicates freely draining structures. There is a conformational contraction, however, at molecular weight about 320,000 leading from one type of structure to the other. The structure at higher molecular weight may involve a specially strong bond between specifically grouped segments in the chain. The positions of the extrema along the alcohol concentration axis are not molecular weight dependent, particularly above 320,000. Results available for molecular weight dependence in methanol agree well with this picture. The present results confirm prediction inherent in the model of Silberberg and Priel and Silberberg.     

Flow properties of poly(methyl methacrylate) solutions

Viscosity and normal stress behavior were measured for poly(methyl methacrylate) samples of various average molecular weights in diethyl phthalate solution at 30 and 60°C. All samples conformed approximately to the most probable distriution (M?_w/M?_n = 2). Concentrations ranged from 0.113 to 0.38 g/ml, and M?_w from 53,800 to 1,620,000. Despite considerable evidence in the literature of unusual linear viscoelastic behavior for this polymer, its nonlinear properties appear to be rather conventional. The viscosity–shear rate master curve was similar to that found earlier for concentrated solutions of polystyrene and poly(vinyl acetate) of comparable molecular-weight distribution. The viscosity time constant τ_o parallels τ_R, the characteristic time of the Rouse model, although the residual dependence of τ_o/τ_R on concentration and molecular weight appears to be slightly different from that for polystyrene and poly(vinyl acetate). Similar conclusions apply to the recoverable compliance J_e,^o estimated from the normal stress behavior of each solution, and its relationship to the Rouse model compliance J_R.     

Flow birefringence of short-chain molecules: Cellulose tricarbanilates in benzophenone

Measurements of flow birefringence of cellulose tricarbanilates were carried out on nine fractions (0.27 × 10⁵ < M ≤ 12 × 10⁵) in a temperature range of 55–110°C, with benzophenone as a matching solvent (dn/dc = 0). The ratio of Maxwell constant to intrinsic viscosity, which has been found to be independent of molecular weight for the limiting case of Gaussian molecules, is successfully interpreted as a function of molecular weight in terms of the recent theory of Gotlib and Svetlov (based on the wormlike chain model of Kratky and Porod). From the measurements at 55°C a number of 36.6 monomer units per random link is deduced. This is in accord with results of small-angle x-ray scattering. For the extinction angle curves a clear transition is observed from rodlike to statistical molecules when the molecular weight is increased. At high molecular weights the master curves obtained for anionic polystyrenes and cellulose tricarbanilates coincide. Implications of this observation on the kinetic stiffness of the cellulose tricarbanilate chain are discussed. The intrinsic viscosity-molecular weight relationship is considered. From a comparison with the results of the theory of Eizner and Ptitsyn it is concluded that the cellulose tricarbanilate chain must be highly solvated in benzophenone.     

Static ultrasonic oscillations induced degradation and its effect on the linear rheological behavior of novel propylene based plastomer melts

The ultrasonic degradation of novel propylene based plastomer (DP) melts with different melt viscosities was conducted in a “static” ultrasonic device where the samples were taken from various distances from the tip of an ultrasonic probe. The effects of ultrasonic time, oscillation temperature, ultrasonic intensity and the distance from the ultrasonic probe tip on the degradation behavior of DP melts as well as the ultrasonic degradation effect on the linear rheological behavior of DP melts were studied. The results show that the increase of initial melt viscosity of DP (higher molecular weight) has greater impact on the ultrasonic degradation of DP melt. The molecular weight and intrinsic viscosity of DP decrease with the increase of ultrasonic oscillation time and they approach to a limiting value. The molecular weight distribution of DP increases after ultrasonic degradation. Decreasing oscillation temperature and distance from probe tip and increasing ultrasonic intensity lead to an increase in the degradation of DP melt. The linear rheological behavior measurements of the samples obtained near the ultrasonic probe tip show that ultrasonic oscillations decrease the complex viscosity, zero shear viscosity, viscoelastic moduli, cross modulus, relaxation time and the slope of log G′ − log G″ for DP melts.     

Reduced viscosity, rheology and morphological properties of sulfonated poly (ether ether ketone): Polyetherimide blends

Blends of poly (ether ether ketone) (SPEEK) and polyetherimide (PEI) were prepared in five different weight ratios, using N,N-dimethylacetamide (DMAc) as solvent. Reduced viscosity and rheological parameters of these blends were investigated. Cannon–Fenske viscometer was used to study the viscoelastic parameters of the salt-free polyelectrolyte blends and the data obtained was fitted in Fuoss–Strauss equation. Effects of temperature and concentration have been investigated. It was observed that the storage modulus (G′) and dynamic viscosity (η′) of the blends varies significantly as compare to pure SPEEK and PEI. Surface morphology and thermal behavior of the membranes were studied using scanning electron microscopy (SEM) and differential scanning calorimetry (DSC). Form SEM results it was observed that the phase separation occurs at 25% PEI contents in blends.     

Steady-shear viscosity of polydimethylsiloxanes over the range from the lower to the upper Newtonian region

The mechanism of non-Newtonian behavior for flow from the lower to the upper Newtonian region is explained by a modification of Graessley's theory. In the theory proposed here, a viscosity η_fric, which is based on friction between polymer segments and is almost shear-independent, is introduced in addition to Graessley's entanglement viscosity η_ent, which decreases with increasing shear rate. The theory is applied to previously obtained data on steady flow of polydimethylsiloxanes of different molecular weights. The agreement between calculated and experimental results is good. In polymers with the molecular weight above the critical molecular weight for entanglement M_c, the major contribution to viscosity near zero shear rate is η_ent. As the shear rate increases, the flow curve has an inflection where η_fric cannot be disregarded in comparison with η_ent. In the upper Newtonian region, η_fric has more influence on the viscosity than η_ent. The theory can also explain the experimental results on flow of polymers with molecular weight below M_c, which were shown to be slightly non-Newtonian in the previous paper.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.     

The variations of the configurational and solvency properties of low molecular weight sodium polyacrylate with ionic strength

The configurational and solvency properties of low molecular weight sodium polyacrylate have been determined for a wide range of ionic strength solutions, from intrinsic viscosity data in the polymer literature.The variations of the polymer properties with ionic strength (I) are described very well by simple mathematical expressions. Thus, a linear relationship was found between the solvency parameter and 1/I ^(1/2), while the variations of the expansion factor and the radius of gyration with 1/I ^(1/2) were described by second order polynomials.LowI solutions (i.e. < 0.01) have a high solvency for sodium polyacrylate. In such solutions the polymer is in a highly expanded configuration. Thus, the radius of gyration of a typical, low molecular weight (ca. 5000 g mol^–1) sodium polyacrylate approaches the limiting value of ca. 4.5 nm atI<0.01.Conversely, high ionic strength solutions (i.e. >0.10) have a low solvency for sodium polyacrylate. In such solutions the polymer is in a virtually unexpanded configuration. Thus, the radius of gyration of a typical, low molecular weight sodium polyacrylate approaches the limiting value of ca. 2.0 nm atI>0.10.     

Cyclopolymerization of diallylamine derivatives in dimethyl sulfoxide

Diallyl quaternary ammonium chlorides, bromides and N-alkyldiallylamine hydrochlorides were polymerized with ammonium persulfate (APS) in dimethyl sulfoxide (DMSO). The dependences of yield and molecular weight of polymers on polymerization conditions were examined and quaternary ammonium chlorides were found to have better polymerizability than bromides. The poly(diallyl quaternary ammonium chlorides) obtained with APS—DMSO system are expected to have quite high molecular weights, as determined from the measurement of limiting viscosity numbers of the polymers in NaCl aqueous solution.     

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.     

The synthesis and solution properties of some rigid-chain,water-soluble polymers: Poly[N,N′-(sulfo-phenylene)phthalamide]s and poly[N,N′-(sulfo-p-phenylene)pyromellitimide]

Poly[N,N′-(sulfo-phenylene)phthalamid]es and poly[N,N′-(sulfo-p-phenylene)pyromellitimide] were prepared in water-soluble form and were found to have unique solution properties, similar in some respects to xanthan. The polymer most investigated, poly[N,N′-(sulfo-p-phenylene)terephthalamide] (PPT-S), is produced as the dimethylacetamide (DMAC) salt by the solution polymerization of 2,5-diaminobenzenesulfonic acid with terephthaloyl chloride in DMAC containing LiCl. The isolated polymer requires heating in water to dissolve; the resulting cooled solutions are viscous or gels at concentrations as low as 0.4%. They are highly birefringent, exhibit circular dichroism properties, and are viscosity-sensitive to salt. Solutions of this polymer mixed with those of guar or hydroxyethyl cellulose give significantly enhanced viscosity. The polymer is relatively low molecular weight, ca. 5000 estimated from viscosity data. Some meta and para isomeric analogs of PPT-S were prepared; these polymers have similar properties except they are more soluble in water, and higher concentrations are required to obtain significant viscosity. Poly[N,N′-(sulfo-p-phenylene) pyromellitimide] (PIM-S) was prepared similarly from 2,5-diaminobenzenesulfonic acid and pyromellitic dianhydride. Its aqueous solution properties are similar to those of PPT-S. It appears that these relatively low-molecular-weight rigid-chain polymers associate in water to form a network that results in viscous solutions at low concentrations.     

Chain collapse by lattice simulation

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(In N)^3/11, as predicted by the renormalization group theory.     

The viscoelasticity of polymer solutions: Comparison of theory and experiment

The theory of the preceding paper is compared with previously unpublished experimental results on the viscoelastic properties of two polystyrene fractions of molecular weight 1.9 × 10⁶ and 1.2 × 10⁶ in nitropropane, which is very nearly a theta solvent, and in toluene, a good solvent. At the concentrations used, around 1%, the theory predicts extensive departures from non-draining toward free-draining behavior; these effects are observed. The theory similarly fits experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in decalin and dioctyl phthalate in the same concentration range.     

Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions

Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N‐dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant‐to‐hydrophobe molar ratio, that is, the number of hydrophobes per micelle (N_H). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (N_H = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady‐flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the N_H value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (N_H = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004