Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

The elastic properties of sodium montmorillonite suspensions

Shear wave rigidity moduliG have been determined using a shear wave propagation technique for sodium montmorillonite suspensions. Measurements were made as a function of time at various values of pH, NaCl concentration (C) and solids concentration and the data used to estimateG _e the value of the modulus att=. The dependency ofG _e on pH,C and solids concentration is interpreted in terms of the mode of interaction between particles and the associated volume filling structure. The results suggest that whether a coagulated or dispersive structure develops in these suspensions depends not only on pH andC but also on the degree of delamination of the clay.     

有机蒙脱土对端羧基聚丁二烯凝胶流变行为的影响

在恒定剪切速率下,利用旋转流变仪研究端羧基聚丁二烯/蒙脱土纳米复合凝胶的流变行为,同时利用X-射线衍射(XRD)和透射电镜(TEM)等表征手段研究其微观结构.研究结果表明,该体系在26～116℃的升-降温过程中,观察到不可逆转变和可逆转变两种流变行为,其中不可逆转变流变行为归因于蒙脱土片层的剥离过程,而可逆转变流变行为...     

Surface modification of clay and its effect on the intercalation behavior of the polymer/clay nanocomposites

Melt intercalation of the methylsilylated organoclays with polar polymers such as SAN was examined to verify the adhesive role of guest polymeric chains between hydrophilic clay layers, so-called “glue effect” on intercalation behavior. Once methylsilylated organoclay was melt-blended with SAN, it was found that the mixture presented significant retardation of increase of interlayer spacing, d₀₀₁ with heating time, and a noticeable decrease of d₀₀₁ after the methylsilylation of organoclay, implying that the diffusion of SAN was highly suppressed by the decrease of polar interaction force caused by conversion of OH to methylsiloxyl groups. However, when applying shear force for the methylsilylated organoclay/SAN nanocomposites during melt intercalation, a noticeable increase of d₀₀₁ was observed, expressing that intercalation of clay by SAN occurred much more effectively because of the reduction of gluing force between host clay and guest polymers, which was well supported by dramatic improvements of mechanical properties after methylsilylation of organoclays. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2367–2372, 2004     

Synthesis,rheology, and morphology of nylon‐11/layered silicate nanocomposite

Exfoliated nylon‐11/layered silicate nanocomposites were prepared via in situ polymerization by dispersing organoclay in 11‐aminoundecanoic acid monomer. The original clay was modified by a novel method with 11‐aminoundecanoic acid. In situ Fourier transform infrared spectroscopy results show that stronger hydrogen bonds exist between nylon‐11 and organoclay than that of between nylon‐11 and original clay. The linear dynamic viscoelasticity of organoclay nanocomposites was investigated. Before taking rheological measurements, the exfoliated and intercalating structures and the thermal properties were characterized using X‐ray diffraction, transmission electron microscopy, differential scanning calorimetry, and thermogravimetric analysis. The results show that the clay was uniformly distributed in nylon‐11 matrix during in situ polymerization of clay with 4 wt % or less. The presence of clay in nylon‐11 matrix increased the crystallization temperature and the thermal stability of nanocomposites prepared. Rheological properties such as storage modulus, loss modulus, and relative viscosity have close relationship with the dispersion favorably compatible with the organically modified clay. Comparing with neat nylon‐11, the nanocomposites show much higher dynamic modulus and stronger shear thinning behavior. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2161–2172, 2006     

Morphology and rheology of polystyrene nanocomposites based upon organoclay

A correlation between morphology development and rheology of polystyrene nanocomposites based upon organophilic layered silicates (organoclay) such as fluoromicas was found as a function of the silicate modification. Organoclay was obtained by means of ion exchange of clay with protonated amine‐terminated polystyrenes with molar mass of M_n = 121 and 5 800 g/mol. Only when applying shear forces during melt compounding of organoclay modified with high molar mass polystyrene (PS), individual silicate platelets of 1 nm diameter and 600 nm length were obtained. Dispersions of such in‐situ formed nanoparticles with aspect ratio of 600 accounted for unique elastic properties observed in the low frequency range of the dynamic modulus, whereas organoclay modified with low molecular PS did not exfoliate and exhibited rheological behavior very similar to that of conventional fillers.     

Viscoelastic behavior of epoxy prepolymer/organophilic montmorillonite dispersions

Dispersions of a bisphenol A‐based epoxy resin with an organophilic montmorillonite (Nanofil 919) were studied by X‐ray diffraction and oscillatory shear rheometry. X‐ray studies reveal that the clay is intercalated by the epoxy and forms stable dispersions. The viscoelastic behavior of the nanodispersions was measured as a function of the Nanofil concentration and temperature. An increase in both G′ and G″ moduli was detected as the concentration increases. Furthermore, a transition from a liquid‐like behavior, at low temperatures, to a solid‐like behavior, at higher temperatures, was observed for all the samples. This transition is accounted for the formation of a percolated structure of interconnected tactoids through hydrophobic interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1837–1844, 2008     

Comparison of Critical Exponents Determined by Rheology and Dynamic Light Scattering on Irreversible and Reversible Gelling Systems

Summary: The sol-gel transition of a radical chain cross-linking copoly-merization system [N-vinylcaprolactam/2-hydroxylethyl methacrylate/allyl-methacrylate] and various thermoreversible gelling systems (mixtures made of xanthan gum and locust bean gum as well as gelatin) have been studied using in-situ time-resolved dynamic light scattering (DLS) and in-situ rheology. A critical dynamical behavior was observed near the sol-gel transition, which is characterized by the presence of a power-law spectra in the time-intensity correlation function g₂(t)−1 ∝ t^−µ and in the low-amplitude oscillatory shear experiment G′(ω) ∝ G″(ω) ∝ ωⁿ. A comparison of the obtained critical dynamical exponents µ and n were made according to the theory by Doi and Onuki. This theory predicts a relation between these exponents, but up to now no detailed experimental comparison was done in the past. It was found that for all investigated systems n > µ.     

The superposition of small deformations on large deformations: Measurements of the incremental relaxation modulus for a polyisobutylene solution

The incremental relaxation modulus ΔG(t) for a concentrated solution of polyisobutylene has been determined from step-shear experiments in which a small deformation Δγ was superimposed on a large deformation γ₁; ΔG(t) was found to decrease with increasing γ₁ and to increase with the time t_e after the imposition of the large deformation. It was also observed that the “apparent relaxation specturm” associated with δG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic relaxation modulus G(t). The results are well described by the nonlinear constitutive equation of the BKZ elastic fluid theory.     

Rheology of (±)‐camphor‐10‐sulfonic acid doped polyaniline‐m‐cresol conducting gel nanocomposites

The rheological behavior of polyaniline‐(±champhor‐10‐sulfonic acid)_0.5‐m‐cresol [PANI‐CSA_0.5‐m‐cresol] gel nanocomposites (GNCs) with Na‐montmorillonite clay (intercalated tactoids) is studied. The shear viscosity exhibits Newtonian behavior for low shear rate (<2 × 10^?4 s^?1) and power law variation for higher shear rate. The zero shear viscosity (η₀) and the characteristic time (λ) increase but the power law index (n) decrease with increase in clay concentration. In the GNCs storage modulus (G′) and loss modulus (G″) are invariant with frequency in contrast to the pure gel. The G′ and G′ exhibit the gel behavior of the GNCs up to 105 °C in contrast to the melting for the pure gel at 75.7 °C. The percent increase of G′ of GNCs increases dramatically (619% in GNC‐5) with increasing clay concentration. The conductivity values are 10.5, 5.65, 5.51, and 4.75 S/cm for pure gel, GNC‐1, GNC‐3, and GNC‐5, respectively, promising their possible use in soft sensing devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 28–40, 2008     

Gelation Studies on a Radical Chain Cross‐Linking Copolymerization Process: Comparison of the Critical Exponents Obtained by Dynamic Light Scattering and Rheology

Summary: The sol–gel transition of a radical chain cross‐linking copolymerization system [N‐vinylcaprolactam/2‐hydroxylethyl methacrylate/allyl methacrylate] has been studied using in situ time‐resolved dynamic light scattering (DLS) and in situ rheology. A critical dynamic behavior was observed near the sol–gel transition, which was characterized by the presence of a power‐law spectra over three decades in the time–intensity correlation function g₂(t) − 1 ∼ t^−μ and over two decades in the oscillatory shear experiment G′(ω) ∼ G″(ω) ∼ ωⁿ. A comparison of the obtained critical exponents μ ≈ 0.62 and n ≈ 0.75 was made. The theory predicts a relationship between these exponents, but up to now no experimental comparison has been done. The experimental results favor the percolation model, with a fractal dimension d_f of the gel clusters of 1.67.

Double‐logarithmic plot of time–intensity correlation functions g₂(t) − 1 versus the delay time t.     

Approximate relations among compliance functions of linear viscoelasticity for amorphous polymers

In the glass–rubber transition region of viscoelastic behavior of amorphous polymers, it is found that is a good first approximation. Here J(t) is the value of the shear creep compliance at time t and J″(1/t) is the value of the shear loss compliance at an angular frequency of 1/t. Previous approximations related the creep compliance to the storage compliance. When J(t) is proportional to t^m, where m is a positive constant, J″(1/t) is within 30% of J(t) for m > 0.6. Over the entire range, is a better approximation than either of the other two. The relaxation modulus G(t) is hardly ever a good approximation for the loss modulus G″(1/t).     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

Gelation Studies: Comparison of the Critical Exponents Obtained by Dynamic Light Scattering and Rheology, 2

Summary: The sol–gel transition of two thermoreversible gelling mixtures made of xanthan gum and locust‐bean gum has been studied by using in situ, time‐resolved dynamic light scattering (DLS) and in situ rheology. A critical dynamical behavior was observed near the sol–gel transition, which was characterized by the presence of power‐law spectra over three and four decades in the time‐intensity correlation function g₂(t) − 1 ∼ t^−μ and over four and three decades in the oscillatory shear experiment G′(ω) ∼ G″(ω) ∼ ωⁿ. A comparison of the critical exponents obtained (μ₁ ≈ 0.36, μ₂ ≈ 0.32 and n₁ ≈ 0.62, n₂ ≈ 0.67) was made as a function of the dependence of the two mixing ratios according to the theory by Doi and Onuki. New experiments were also performed to compare the critical exponents on such a thermoreversible system.

Double‐logarithmic plot of the time‐intensity correlation functions g₂(t) − 1 versus the delay time, t, at a 90° scattering angle and at several temperatures of the mixture 1.     

Stress relaxation and dynamic viscoelastic properties of end-linked poly(dimethyl siloxane) networks containing unattached poly(dimethyl siloxane)

Stress relaxation in uniaxial extension and dynamic shear moduli G′ and G″ have been studied in networks of vinyl-terminated poly(dimethyl siloxane) (PDMS) of five different molecular weights (M _n from 1800 to 29,200) crosslinked with cis-dichlorobis (diethyl sulfide) platinum (II) and containing 10 and 15 wt % of two samples of high-molecular-weight unattached linear hydroxyl-terminated PDMS (M _w 700,000 and 950,000). The M _w/M _n ratio of both the network prepolymers and the unattached linear species was approximately 2. In stress relaxation the stretch ratio was 1.25 or less and the shear relaxation modulus was calculated from the neo-Hookean stress-strain relation. In the dynamic measurements, the strain amplitude was 15% or less; after conversion to the timedependent shear relaxation modulus G(t) the two sets of measurements were combined and the contribution of the unattached species G₁(t) was calculated by difference. After multiplication by (1 − v)⁻¹G/G_e, where v₂ is the volume fraction of network, G is the plateau modulus of the uncrosslinked polymer, and G_e is the equilibrium modulus of the network containing unattached molecules, G₁(t) was compared with G₁₁(t), the relaxation modulus was essentially the same in both environments. The relaxation was slower in the networks than in the uncrosslinked polymer by 1 to 2 orders of magnitude, and it increased gradually with increasing G_e, which is a measure of total to pological obstacles represented by crosslinks plus trapped entanglements. A similar but less striking difference between relaxation in a network and in the homologous environment of a linear polymer was previously observed in end-linked polybutadiene networks and the butadiene phase of a styrene-butadiene-styrene block copolymer. It appears that, in these systems where the topology of the obstacles is fixed, the reptation is severely restricted or else alternative modes of configurational rearrangement which contribute to relaxation in the uncrosslinked polymer are suppressed.     

Poly(ether ether ketone)/poly(aryl ether sulfone) blends: Melt rheological behavior

Dynamic rheological measurements were carried out on blends of poly(ether ether ketone) (PEEK)/poly(aryl ether sulfone) (PES) in the melt state in the oscillatory shear mode. The data were analyzed for the fundamental rheological behavior to yield insight into the microstructure of PEEK/PES blends. A variation of complex viscosity with composition exhibited positive–negative deviations from the log‐additivity rule and was typical for a continuous‐discrete type of morphology with weak interaction among droplets. The point of transition showed that phase inversion takes place at composition with a 0.6 weight fraction of PEEK, which agreed with the actual morphology of these blends observed by scanning electron microscopy. Activation energy for flow, for blend compositions followed additive behavior, which indicated that PEEK/PES blends may have had some compatibility in the melt. Variation of the elastic modulus (G′) with composition showed a trend similar to that observed for complex viscosity. A three‐zone model used for understanding the dynamic moduli behavior of polymers demonstrated that PEEK follows plateau‐zone behavior, whereas PES exhibits only terminal‐zone behavior in the frequency range studied. The blends of these two polymers showed an intermediate behavior, and the crossover frequency shifted to the low‐frequency region as the PEEK content in PES increased. This revealed the shift of terminal‐zone behavior to low frequency with an increased PEEK percentage in the blend. Variation of relaxation time with composition suggested that slow relaxation of PEEK retards the relaxation process of PES as the PEEK concentration in the blend is increased because of the partial miscibility of the blend, which affects the constraint release process of pure components in the blend. A temperature‐independent correlation observed in the log–log plots of G′ versus loss modulus (G″) for different blend systems fulfilled the necessary condition for their rheological simplicity. Further, the composition‐dependent correlations of PEEK/PES blends observed in a log–log plot of G′ versus G″ showed that the blends are either partially miscible or immiscible and form a discrete‐continuous phase morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1548–1563, 2004     

Network parameters of poly(N‐isopropylacrylamide)/montmorillonite hydrogels: effects of accelerator and clay content

The results of network parameters of poly(N‐isopropylacrylamide)/montmorillonite (PNIPAAm/MMT) hydrogels prepared with two different types and concentrations of accelerators (tetramethylethylenediamine, TEMED and quaternary TEMED containing decyl bromide, QTEMED) using three different clay contents (1.0, 3.0, and 5.0 wt% of total monomer concentration) at two different polymerization temperatures (10 and 32°C) were presented and discussed. It was observed that when the reaction temperature of PNIPAAm crosslinked with MMT was chosen as 10°C both volume swelling ratios (i.e., thermodynamic interaction) and shear moduli, G increased. In hydrogels, thermodynamic interaction is reflected by polymer–water interaction parameter (χ). The lower is the value of χ, the stronger is the interaction between polymer and water, and the lower is the interaction between hydrophobic groups or between polymer chains. In addition, increase in MMT content was slightly affected on these intermolecular interactions. Therefore, this effect that combines high‐shear modulus with lower value of χ in the same molecular structure was defined as clay content‐independent diffusion behavior. On the other hand, in the case of the hydrogels synthesized with the higher concentration of TEMED and MMT, the values of χ and G decreased. These facts were interpreted that increase in both accelerator concentration and clay content, for fixed NIPAAm concentration made the number of effective crosslinks between MMT layers smaller. Copyright © 2010 John Wiley & Sons, Ltd.     

Notes on asymptotic series by H0-strictly singular perturbations

Let two strongly continuous one-parameter semigroups of contraction operators, {Z(t); t≧ 0} and {Z₀(t); t ≧ 0}, determine physical evolutions realized in the Hilbert spaces ? and ?₀, respectively. We consider the mappings under Z(t) and Z₀(t), when the infinitesimal generators G and G₀ belong to a product class, properly defined with respect to an H⁰-norm. The inversed transform of each side in the identity R(λ, G) = R(λ, –iH⁰)–iR(λ, –iH⁰)VR(λ, G), which represents a simple algebraic decomposition of the resolvent of G, converges on Ψ if and only if Ψ ∈ ??(G). By iteration an asymptotic series emerges, when t → 0. Numerical considerations of this approximation in its first order may support the form of a deviation from the pure exponential decay when the semigroup is compared with a integral transform corresponding to a certain self-adjoint H₀ in ?₀. The deviation may hardly ever be observed and it is therefore most fruitful to discuss the results inside the framework of the enveloping algebra of the semigroups.     

SBR composites reinforced with <Emphasis Type="Italic">N</Emphasis>-isopropyl-<Emphasis Type="Italic">N</Emphasis>′-phenyl-<Emphasis Type="Italic">P</Emphasis>-phenylenediamine-modified clay

SBR compounds including the N-isopropyl-N’-phenyl-p-phenylenediamine-modified clay(organoclay) were prepared.Effects of modified clay and antioxidant(IPPD) contents on mechanical and rheological properties of SBR composites were studied.FTIR results confirmed that the clay was chemically modified by IPPD and changed into an organoclay.X-ray diffraction(XRD) results confirmed the increase in interlayer distance of the clay due to the insertion of IPPD.Rheological and cure characteristics of SBR compounds were determined using RPA(Rubber Process Analyzer) and rheometer.Scorch time and cure time of SBR compounds decreased with introduction of the organoclay.Mechanical properties and heat aging resistance of the SBR composites were improved significantly by incorporation of the organoclay.     

Effect of matrix viscosity on the extent of exfoliation in EVA/organoclay nanocomposites

The influence of matrix viscosity and polarity on ethylene‐vinyl acetate copolymer (EVA) nanocomposites was studied. Five different EVA grades, with different melt flow indexes (MFIs) and/or vinyl acetate (VA) contents, were mixed with two montmorillonite (MMT) nanoclays: pristine and modified with a polar surfactant, producing 75/25 w/w% masterbatches which were subsequently diluted in the EVA matrix to obtain 5 wt% MMT nanocomposites. Although the same VA content, WAXS results, rheological measurements and TEM analysis showed that the lower the EVA viscosity, the greater the tendency to obtain exfoliated and well dispersed nanocomposites with the organically modified clay. On the other hand, the high viscosity EVA nanocomposites showed that the (001) organoclay diffraction peak was shifted to higher values of 2θ, suggesting lamellae collapsing. TGA and FTIR measurements were used to probe the thermal degradation of organoclay; furthermore, it was not possible to identify, by the techniques used, any reaction between the VA groups and hydroxyl surfactant groups. Thus, it was inferred that the organic surfactant was removed (or ejected) from the clay galleries as a consequence of huge shear tensions developed during processing of the masterbatches/nanocomposites with high viscosity EVA matrices. Copyright © 2009 John Wiley & Sons, Ltd.