Simplified theory for linear rheology of monodisperse linear polymers

A new version of the tube theory based on the de Gennes–Doi–Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero‐shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman–McLeish model combines self‐consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman–McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed‐form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero‐shear viscosity (η₀). Results of the computations of the zero‐shear viscosity and of the slope of η₀ versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of η₀ versus molecular weight. The possibility of inferring monomer chemistry–dependent parameters from the zero‐shear viscosity remains a difficult task because of the introduction of a constraint‐release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 569–586, 2004     

Dynamic rheological behavior of poly(ether ketone ketone) from solid state to melt state

High performance thermoplastic poly(ether ketone ketone) (PEKK) polymers with various meta phenyl links ratio were investigated by dynamical mechanical analysis. Analyses were carried out in a wide range of temperature from solid state (torsion rectangular mode) to the melt state (torsion parallel plates mode) as function of thermal history and environmental conditions. In the solid state, this study was focused on the secondary relaxations in the vitreous state. A complementary investigation conducted with different poly(aryl ether ketones) allowed us to propose a molecular interpretation of PEKK sub‐vitreous relaxations. In the molten state, storage modulus (G′), loss modulus (G″), storage viscosity (η′), and loss viscosity (η″) were studied to determine zero shear‐rate viscosity (η₀) and thermal activation energy E_a. Master curves were built and the shift factor a_T was determined. Thermal activation energies were extracted from an Arrhenius model on the shift factor temperature's dependency. Finally, E_a and η₀ were determined thanks to the dynamic viscosity fit with Cross model and Cole–Cole representation. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46456.     

Flow properties of ABS (acrylonitrile–butadiene–styrene) terpolymer

ABS (acrylonitrile–butadiene–styrene) terpolymer is a two-phase thermoplastic with SAN (styrene–acrylonitrile) copolymer constituting the continuous phase (matrix). The flow properties of ABS with varying molecular parameters were studied using a capillary viscometer at the shear rate range encountered in its processing. The viscosity-average molecular weights (M_v) of matrix SAN with 26% acrylonitrile content are in the range of 90,000 to 150,000, and M_v of poly-butadiene-are in the range of 150,000 to 170,000. The weight-average molecular weight of the matrix SAN is the main controlling factor for the flow properties of ABS at low shear rate, while the molecular weight distribution of the matrix SAN becomes increasingly important with the increase of shear rate. The presence of SAN grafted polybutadiene increases the melt viscosity of ABS by 40–60% over comparable free SAN copolymer and also decreases the activation energy at constant shear stress to 24–25 kcal/mole from the 33–36 kcal/mole for free SAN. The die swell of ABS and SAN can be correlated with the dynamic shear modulus G′, and the melt fracture of ABS and SAN starts at G′ equal to 3.6 × 10⁶ dynes/cm².     

Viscoelastic properties of suspensions with weakly interacting particles

Rheological characterization of a model suspension containing hydroxyl-terminated polybutadiene and glass beads with filler concentration up to 30% by volume was performed by using a Haake parallel disk rheometer. The rheological tests conducted were the measurement of the storage modulus, G′, loss modulus, G′, and complex viscosity, η*, as functions of the frequency and the steady shear viscosity as a function of the shear rate. The linear viscoelastic region was determined to extend up to 50% strain by measuring G′, G′, and η* as functions of strain amplitude. By using multiple gap separations between the disks, it was found that the suspension did not exhibit slip at the walls of the rheometer. G′ and G′ were used to determine the relaxation times distribution, G_i(λ_i, ⊘) as functions of the relaxation time, λ_i, and the filler content, ⊘. The relaxation moduli, G_i(λ_i, ⊘), decreased with the relaxation time, but increased with the filler content. The Cox–Merz rule was also observed to be valid for these suspensions. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 507–514, 1998     

Radiation degradation of poly(styrene-co-methylmethacrylate). 2. Protective effects of styrene on volatile products,chain scission and flexural strength

The volatile products from γ-irradiation of poly(styrene-co-methylmethacrylate)s at 30°C are found to be the same as from PMMA. The G values are substantially below the values corresponding to linear relationships between the homopolymers. This is attributable to an intramolecular protective effect by the styrene units. Net G(scission) values have been derived from viscosity measurements on the irradiated copolymers after different doses. They also show a protective effect by styrene. The radiation dose (in vacuum) for a 50% reduction in flexural strength increased linearly with mole fraction of styrene from (x_s)_p = 0 to 0.7, above which it increased more rapidly.     

Effect of microgels on the viscoelastic properties of poly(dimethylvinylsiloxanes)

The course of dynamic viscosity η′ and modulus of elasticity G′ curves versus frequency of oscillations f was compared for poly(dimethylvinylsiloxanes) (PDMVS) samples of similar weight-average molecular weights containing 0.1–0.2% by weight of microgels and free of microgels. It was found that the presence of microgels considerably changes the viscoelastic properties of PDMVS, particularly in the low-frequency range. Only for samples with microgels a linear course of the above-mentioned curves is observed. The content of microgels was determined by the light scattering method, whereas the η′ and G′ versus f values were obtained with the use of the Weissenberg rheogoniometer.     

Co‐(POSS#‐styrene) nanocomposites reduced the glass‐transition temperature,rubbery modulus,and melt viscosity of entangled polystyrene

The addition of polyhedral oligomeric silsesquioxane‐styrene copolymers, co(POSS#‐sty), to entangled polystyrene (PS) reduced (1) the glass‐transition temperature, T_g,blend, (2) the rubbery modulus, and (3) the melt viscosity. POSS#‐sty copolymers with # = 15, 25, and 45 wt% POSS were blended with PS. The blends were miscible and T_g,blend decreased with POSS#‐sty content. Strikingly, POSS#‐sty copolymers also reduced the melt viscosity, up to an order of magnitude reduction. The reductions of T_g,blend and melt viscosity were driven by the type of POSS#‐sty copolymer, POSS45‐sty producing the largest decrease of T_g,blend. Linear viscoelasticity and the time–temperature superposition (TTS) principle (using T_ref = T_g + 50 K to ensure iso‐frictional conditions) revealed that POSS#‐sty induced up to an order of magnitude reduction of the rubbery modulus G_e. The increase of free volume f_g promoted by POSS#‐sty induced the reduction of T_g,blend and G_e, as revealed by TTS analysis. The increase of free volume promoted by POSS#‐sty induced chain intercalation (TEM showed that POSS domains were smaller than the molecular mesh) and these are key factors for the chain disentanglement with the consequent rubbery modulus and melt viscosity reductions. The use of low‐molecular weight polystyrene alone will not produce increase of free volume and tube dilation. POLYM. ENG. SCI., 59:2377–2386, 2019. © 2019 Society of Plastics Engineers     

Thermal analysis of styrene–alkyl methacrylate polymers. II. Thermogravimetric kinetics

The thermal stability and degradation kinetics of several polystyrenes and styrene–alkyl methacrylate copolymers and terpolymers with a number-average molecular weight (M?_n) of 6000–250,000 g/mole have been studied using dynamic thermogravimetry (TG). The degradation kinetics of each polymer sample have been successfully attributed to a sample first-order reaction expression. The results indicate that the thermal stability and degradation kinetics of the polymers are independent of the size of the molecules within the molecular weight range investigated. The steric hindrance effects of the pendent groups appear to be responsible for the improved thermal stability and resistance of C? C bond scission in the styrene–alkyl methacrylate copolymers and terpolymers.     

Dynamic mechanical behavior of copolymers containing carbon black

The storage and loss moduli of random copolymers of styrene and butyl methacrylate containing carbon black of varied surface area were determined by dynamic mechanical analysis at several temperatures about 100°C above the glass-transition temperature, T_g. At low frequencies, the pure polymers exhibit linear double log plots of moduli against frequency, with slopes of unity and approaching two for G″ and G′, respectively. With the addition of carbon black filler, both G′ and G″ become independent of frequency and temperature at low frequencies, consistent with yield behavior arid the formation of a carbon black network. The limiting dynamic complex modulus exceeds the yield stress from steady shear rheology, perhaps indicating the extent of the carbon black network, which was highest for low-molecular-weight copolymer and polystyrene. The filled random copolymers behaved Theologically like similarly filled polystyrenes of comparable molecular weights. Plasticization effects observed in the steady shear rheology of filled copolymers containing small concentrations of carbon black were not observed in dynamic mechanical analysis, although dynamic moduli converge at high frequency.     

Thermal analysis of styrene–alkyl methacrylate polymers. I. Glass transition temperatures

The glass transition temperatures (T_g's) of several polystyrenes and styrene–alkyl methacrylate copolymers and terpolymers were measured using thermomechanical analysis (TMA) and differential scanning calorimetry (DSC). The polymers studied had number-average molecular weights from 3000 to 250,000 g/mole. The results indicate that the composition dependence of the T_g's for the copolymers and terpolymers can be satisfactorily described by a general Fox equation. In general, the measured T_g's of the copolymer and terpolymer samples depend more on the steric effects of the constituent pendent groups than on their molecular weights. The chain flexibility rather than the size of the pendent group is the determining factor in the glass transition properties of the styrene polymers.     

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.     

Effects of swelling on the viscoelastic properties of polyester films made from glycerol and glutaric acid

Viscoelastic properties have been determined for poly(glycerol‐co‐glutaric acid) films synthesized from Lewis acid‐catalyzed polyesterifications. The polymers were prepared by synthesizing polymer gels that were subsequently cured at 125°C to form polymer films. The polymers were evaluated for the extent of reaction before and after curing by Fourier transform infrared spectroscopy. They were subsequently immersed in dimethylsulfoxide, tetrahydrofuran, water, methanol, and hexane for 24 h. The amounts of solvent absorbed were monitored and recorded. Dependent up the solvent used, the polymers were able to absorb 9.5–261% of its weight. The effects of the solvent absorption on the viscoelastic properties of the polyester films were evaluated by determining their elastic modulus (G′), viscous modulus (G″), tan δG″/G′, and complex viscosity (η*) by performing oscillatory frequency sweep experiments. The elastic modulus (G′) and viscous modulus (G″) were both higher for the dry polymers than the solvent‐absorbed polymers. However, the polymer films were all higher in elastic (G′) character than viscous (G″) character. Therefore, tan δG″/G′ < 1 before and after immersion in solvents. Values for η* decreased with angular frequency for all of the polyesters tested in this study. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Rheological behavior of styrene‐maleic anhydride/polyol blends obtained through reactive processing

The condensation reaction of styrene‐maleic anhydride copolymer (SMAH) with polytetramethylene ether glycol (PTMEG) in the presence or absence of a hydrated zinc acetate catalyst was studied in a batch mixer. As a control, pure SMAH and an SMAH/catalyst blend were also subjected to the same processing conditions. The reaction characteristics of the blends were investigated by Fourier transform infrared spectroscopy (FTIR) and thermal and rheological analysis. FTIR analysis of the SMAH/PTMEG blend indicated ester formation. The addition of zinc acetate and/or PTMEG to SMAH decreased the glass transition temperature of pure SMAH. Oscillatory shear properties of storage modulus, G′, loss modulus, G″, and complex viscosity, η*, were measured. The SMAH/PTMEG/zinc acetate blend had higher G′, G″, and η* than the blend without the zinc acetate catalyst. The parameters of the relaxation spectra were calculated by using the experimental oscillatory data and the generalized Maxwell model. Zero shear viscosity and the mean relaxation time increased with addition of zinc acetate and/or PTMEG to SMAH as a result of chain extension/branching reactions. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2615–2623, 2002     

Synthesis,properties, and self‐assembly of poly(benzyl ether)‐b‐polystyrene dendritic–linear polymers

Poly(benzyl ether)‐b‐polystyrene dendritic–linear polymers were successfully synthesized using a dendritic chloric poly(benzyl ether) (G₁‐Cl, G₂‐Cl, and G₃‐Cl) as the macroinitiator through the atom transfer radical polymerization process. The structure and properties of the resultant polymers were characterizated by gel permeation chromatography, ¹H‐NMR, Fourier transform IR, thermogravimetric analysis, and differential scanning calorimetry. It was found that the temperature, reaction time, molar ratio of the macroinitiator to styrene, and the generation number of the macroinitiator have significant effects on the molecular weights, conversion, and polydispersities of the resulting polymers. These dendritic–linear block polymers had very good solubility in common organic solvents at room temperature. The terminal group (dendritic segments) of the polymers can affect their thermal stability. These dendritic–linear polymers after self‐assembling in selective solvents (chloroform/acetone) formed core–shell micelles. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1106–1112, 2005     

Dynamic rheological behavior and mechanical properties of PVC/CPE/MAP–POSS nanocomposites

Poly(vinyl chloride)/chlorinated polyethylene (PVC/CPE)/methylacryloylpropyl‐containing polyhedral oligomeric silsesquioxane (MAP–POSS) nanocomposites are prepared. The plastic behavior and dynamic rheological behavior of PVC/CPE/MAP–POSS are investigated. The influences of composition on dynamic storage modulus G′, loss modulus G″, and complex viscosity η* of PVC/CPE/MAP–POSS melts are discussed. The dynamic mechanical properties, mechanical properties, and morphology are determined. The results show that both plastic time and balance torque of the nanocomposites decrease, but the G′, G″, and η* all increase with increasing MAP–POSS content. The maximum value of the dynamic mechanical loss tan δ decreases and elasticity increases when MAP–POSS is added. The impact strength of the nanocomposites increases with increasing MAP–POSS content and has the best value at 10% content of MAP–POSS, which is 5.38 kJ/m² higher than that of the blend without MAP–POSS. The MAP–POSS can be used as an efficient process aid and impact aid for the PVC/CPE blend. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Rheology and water swelling of carboxymethyl starch gels

A series of gels differing in ionic content was prepared by derivatizing starch with varying amounts of carboxymethyl add-on. Some derivatives were lightly crosslinked with epichlorohydrin to reduce soluble material and increase the amount of gel. The gel fraction of each batch was isolated, and viscosity η, shear modulus G, and swelling in water and salt solution were then determined. One gel suspension, examined in more detail, was demonstrated to behave as a closely packed gel thickening agent, thereby warranting use of the three reduced functions: reduced concentration cQ (c is weight concentration of polymer, Q is swelling capacity in excess fluid), η/cQ, and G/c^1/3. At cQ greater than about 2, η/cQ, and G/c^1/3 reach constant plateau values, as is typical of other examples of closely packed gel thickeners. In a comparison among the gel suspensions, plateau values of the reduced viscosity function were nearly proportional to the apparent crosslink density G/c^1/3, in agreement with other closely packed gel thickeners, but were not affected by ionic content of dry polymer. The water swelling capacities of the different gels ranged from 47 to 150 g/g and were correlated with both ionic contents and apparent crosslink densities, but the effects of these variables were less than suggested by theory.     

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.     

Thermorheological behavior analysis of mLLDPE and mVLDPE: Correlation with branching structure

In this article, the correlation between the thermorheological behavior and the molecular structure of two grades of metallocene polyethylene, namely linear low density and very low density polyethylene, is studied. The investigated polymers possess the same molecular weight and polydispersity index, but different levels of short branches. Increasing the number of short branches results in enhanced activation energy and delayed relaxation times of the polymers. Four methods including the time–temperature superposition (TTS), van Gurp‐Palmen and activation energy (E_a) as a function of the phase angle, E_a(δ), and the storage modulus, E_a(G′) are employed to study the thermorheological behavior of the samples. The results indicated that the thermorheologically simple behavior is dominant in the specimens. Both the E_a(δ) and E_a(G′) showed independency toward phase angle and the storage modulus. Moreover, the activation energy values obtained from the TTS principle and the E_a(δ) and E_a(G′) diagrams were in good agreement. The zero‐shear rate viscosity of the samples also followed the equation of the linear polyethylene. Regarding the simple thermorheological behavior and the agreement of the zero shear rate viscosity with the relation of the linear polyethylene, one can conclude that long branches do not exist in the investigated metallocene polyethylenes of this article. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Rheological properties of poly(methyl methacrylate)/rigid ladderlike polyphenylsilsesquioxane blends

A series of poly(methyl methacrylate) (PMMA) blends with rigid ladderlike polyphenylsilsesquioxane (PPSQ) were prepared at weight ratios of 100/0, 95/5, 90/10, 85/15, and 80/20 by solution casting and then hot‐pressing. Their rheological properties have been studied under both dynamic shear and uniaxial elongation conditions. Their rheological properties depend on the compositions. The storage modulus, G′, loss modulus, G″, and dynamic shear viscosity, η*, of the PMMA/PPSQ 95/5 blend were slightly lower than those of pure PMMA. However, the values of G′, G″, and η* for the other PMMA/PPSQ blends are higher than those of PMMA. The G′ values increase with an increase in PPSQ content from 5% through 15% PPSQ at low frequencies and then drop as the PPSQ content increases to 20%. Uniaxial elongational viscosity (η_E) data demonstrate that PMMA/PPSQ blends exhibit slightly weaker (5% PPSQ) and much weaker (10% PPSQ) strain‐hardening than PMMA. In contrast, the PMMA/PPSQ 85/15 blend shows strain‐softening. Neither strain‐hardening nor strain‐softening was observed in the 80/20 blend. The special rheological properties for the 95/5 blend is probably due to a decrease in PMMA entanglements brought by the specific PMMA–PPSQ interactions. Rheological properties of PMMA/PPSQ blends with higher PPSQ content (≥10%) are mainly affected by formation of hard PPSQ particles. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 352–359, 2007