Nonlinear viscoelasticity of polystyrene solutions. III. Stress development at the start of steady shear flow and an experimental check of some constitutive models

The development of the shear stress at the start of shear flow at constant rate of shear κ was measured for polystyrene solutions in diethyl phthalate with a cone-and-plate rheometer. Ranges of molecular weight M and concentration c were 3.10 × 10⁶?7.62 × 10⁶ and 0.112?0.329 g/cm³, respectively. The shear stress as a function of time t exhibited a marked maximum at large κ when either M or c was relatively low. When M and c were high, the maximum was broad and low. In a few extreme cases no maximum was observed in the range of κ studied. The constitutive model of Bernstein, Kearsley, and Zapas could describe approximately the shear stresses at a sudden start and on cessation of steady shear flow with a memory function evaluated from the strain-dependent relaxation modulus. The strain dependence of the memory function for solutions of low M or c was approximately expressed as exp{?α|s|} where α is a constant (ca. 0.37) and |s| is the absolute value of shear strain. When M and c were high, the strain dependence was found to be more diffuse and to require several terms if approximated by exponential functions of |s|. The Lodge model based on a strain-rate dependent relaxation spectrum was not able to describe the strain-dependent relaxation modulus as well as the interrelation between shear stresses at a sudden start and a cessation of steady shear flow.     

Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

Experimental determination of the relationships among various measures of fluid elasticity

The viscoelastic properties of a 4% solution of monodisperse polystyrene (molecular weight 394,000) in Aroclor 1260 were determined by the following techniques: creep recovery, stress relaxation upon cessation of steady flow, dynamic measurements, and normal stress difference and shear stress measurements in steady flow. All measurements were carried out with cone and plate geometry in a Weissenberg rheogoniometer. The modification of this instrument to perform creep and creep recovery experiments by use of an air-bearing suspension and an air-turbine drive is described. A broad range of shear rates and frequencies encompassing both linear and nonlinear behavior was employed. The elastic behavior is described in terms of the recoverable shear strain s or the steady-state compliance J_e°. The first three techniques gave identical results for J_e° in the range of linear viscoelasticity for which it is defined. The normal stress difference measurements confirmed Lodge's relation s = (P₁₁ ? P₂₂)/2σ₂₁. Reasons for previous experimental disagreement with this result are discussed.     

The effect of wall depletion on the rheology of microfibrillated cellulose water suspensions by optical coherence tomography

Rheology of microfibrillated cellulose (MFC) water suspensions was characterized with a rotational rheometer, augmented with optical coherence tomography (OCT). To the best of the authors’ knowledge, this is the first time the behavior of MFC in the rheometer gap was characterized by this real-time imaging method. Two concentrations, 0.5 and 1 wt% were used, the latter also with 10^?3 and 10^?2 M NaCl. The aim was to follow the structure of the suspensions in a rotational rheometer during the measurements and observe wall depletion and other factors that can interfere with the rheological results. The stepped flow measurements were performed using a transparent cylindrical measuring system and combining the optical information to rheological parameters. OCT allows imaging in radial direction from the outer geometry boundary to the inner geometry boundary making both the shear rate profile and the structure of the suspension visible through the rheometer gap. Yield stress and maximum wall stress were determined by start-up of steady shear and logarithmic stress ramp methods and they both reflected in the stepped flow measurements. Above yield stress, floc size was inversely proportional to shear rate. Below the yield stress, flocs adhered to each other and the observed apparent constant shear stress was controlled by flow in the depleted boundary layer. With higher ionic strength (10^?2 M NaCl), the combination of yield stress and wall depletion favored the formation of vertical, cylindrical, rotating floc structures (rollers) coupled with a thicker water layer originating at the suspension—inner cylinder boundary at low shear rates.     

Rheological properties of internal viscosity models with stress symmetry

Internal viscosity models (IVM) for dilute-solution polymer dynamics differ in how they define the deformational force F ^d which includes φ, the IV coefficient, and in how they treat polymer rotational velocity Ω. Here, the handling of angular momentum is shown to be crucial. A torque balance in simple shear flow at shear rate G leads to stress symmetry and specification of Ω(G) which differs greatly from the conventional Ω = G/2. This determines the G dependence of viscosity η and normal stress coefficient ζ. There are also implications of a transition in rotational behavior as φ approaches a critical value. Predictions of η(G), ζ(G), and η^*(ω) are presented for two versions of F^d : one derived recently by the authors and one being most commonly used at present. Limiting cases for high and low φ, and for high and low G and ω, are discussed. Some differences exist between predictions of the two F^d models, but these are surprisingly minor.     

Strain stiffening and negative normal stress in alginate hydrogels

Alginate hydrogels are polysaccharide biopolymer networks widely useful in biomedical and food applications. Here, we report nonlinear mechanical responses of ionically crosslinked alginate hydrogels captured using large amplitude oscillatory shear experiments. Gelation was performed in situ in a rheometer and the rheological investigations on these samples captured the strain‐stiffening behavior for these gels as a function of oscillatory strain. In addition, negative normal stress was observed, which has not been reported earlier for any polysaccharide networks. The magnitude of negative normal stress increases with the applied strain amplitude and can exceed that of the shear stress at large‐strain. Fitting a constitutive relationship to the stress‐strain curves reveals that the mode of deformation involves stretching of the alginate chains and bending of both the chains and the junction zones. The contribution of bending increases near saturation of G blocks as Ca²⁺ concentration was increased. The results presented here provide an improved understanding of the deformation behavior of alginate hydrogels and such understanding can be extended to other crosslinked polysaccharide networks. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1767–1775     

Synthesis and Conformational Analysis of Macrocyclic Dilactones Mimicking the Pharmacophore of Aplysiatoxin

A small number of macrocyclic dilactones of type 3 , i.e., 9, 10, 11 , and epi‐ 11 , comprising a 3,4‐dihydroxypentanoic acid unit, the pharmacophore of aplysiatoxin, and a conformationally preorganized ω‐hydroxynonanoic acid unit were synthesized. Conformational analysis – based on ²J and ³J NMR coupling constants – of the dihydroxypentanoyl part of these macro‐dilactones indicates the extent to which a conformation induction across the macro‐dilactone ring occurs from the stereogenic centres implemented in the ω‐hydroxynonanoic acid part.     

Shear-induced β-form crystallization in isotactic polypropylene

Extruded, injection-molded, unoriented crystallized specimens and capillary rheometer efflux strands of commercially stabilized polypropylene without nucleating agents were examined by optical microscopy and x-ray diffraction to determine the conditions for β-form crystallization as a function of the distance from the surface and of the shear rate at commercial processing conditions. Results demonstrate that at all “cooling conditions” ΔT = T_m ? T_b (defined as the melt temperature T_m minus the bath temperature T_b) effects of strain flow initiate nucleation of β-form crystals. The shear rate is demonstrated to be important for β-form crystallization. A critical average threshold value for the shear rate of approximately 3 × 10² sec^?1 has to be exceeded. The β modification is mostly connected with type-III spherulites and partly to row structures, and it is observed at processing conditions in oriented structures only.     

A rotational rheometer with a drag-cup torque transducer

A rotational cone-and-plate rheometer incorporating a drag-cup torque transducer and a frictionless, wire suspension has been designed and constructed. The instrument design provides for a controlled atmosphere for the sample, including anhydrous conditions necessary for studies on solutions of polymers in strong acids. The rheometer can be used to determine the shear deformation in response to an applied stress, including creep, recovery, and the shear stress in response to an applied steady shear. Both transient and steady-state measurements are possible. Illustrative examples of the instrument performance are given.     

Rheological study of an aromatic polyamide-hydrazide

Rheological and rheo-optical data are reported for the poly(terephthalamide of p-aminobenzhydrazide), X-500, in dimethyl sulfoxide solutions in the concentration range 0.2 to 6.0 g/100 ml. The objective of these measurements is to seek evidence of shear-induced isotropic → nematic phase transition. Three types of measurement, Couette, cone and plate, and capillary rheometer, all indicate that this system exhibits flow instabilities at high shear rates and concentrations. In this region both the viscosity and the primary normal stress difference decrease with time under shear. In the capillary rheometer the apparent viscosity is smaller for shorter capillaries and, for short capillaries, there is a range of shear rates in which plug flow and a coiled extrudate are observed. These instabilities may arise from the existence of a mixture of isotropic and nematic phases. At lower shear rates, where the flow behavior appears normal, the concentration dependence of the flow birefringence increases at a critical polymer concentration C This value is in reasonable accord with the concentration corresponding to the change of slope of logη (measured at low shear rate) vs. logC_p. Both the latter measurements appear to be sensitive to the onset of the phenomenon, which may be due to a shear-induced transition or the rheological effect of chain entanglements.     

Concentration dependence of the viscoelastic properties of polystyrene-tricresyl phosphate solutions

Based on creep and creep-recovery measurements, the viscoelastic functions [J(t), J_r(t), J′(ω), J″(ω), G′(ω), G″(ω), and L(lnτ)] are presented for solutions of a narrow molecular-weight-distribution polystyrene in tri-m-tolyl phosphate in the concentration range of 1% to 100% polymer. For concentrations of 25% polymer and above, two maxima are exhibited by the retardation spectrum, L(lnτ). In the neighborhood of each of the maxima the retardation spectra of the more concentrated solutions can be superimposed by translations along both the logL and logτ axes. Reflecting the increasing width of the rubbery plateau with increasing polymer concentration, the dependence of the concentration time-scale shift factors is greater for the terminal region of response. The response of the solvent is seen at the lower concentrations and it is a less sensitive function of the concentration than that of the polystyrene. This behavior is associated with the previously reported observation of two glass-transition temperatures in the middle concentration range. For the higher concentrations, both the steady-state and rubbery-plateau compliances are inversely proportional to the square of the concentration.     

Rheological properties of ionic and nonionic polyacrylamide solutions

Non-Newtonian shear viscosities were measured over six decades of strain rate k for 13 solutions of both the ionic and nonionic forms of polyacrylamide. By using the Weissenberg rheogoniometer with both the cone-and-plate and the parallel-plate attachments, the normal stress functions σ₁ (k²) and σ₂(k²) were obtained for four of the solutions. From the measurements of the shear viscosity and the normal stresses at low rates of strain, characteristic times τ and τ_N, respectively, were determined for each solution. The quantity τ was then used to nondimensionalize the strain rate τk, and when plotted versus the reduced shear viscosity, found successfully to correlate the experimental data for all the polyelectrolyte solutions over the entire range of τk and the data for the concentrated solutions of the nonionic polymer over a smaller range of τk. However, in order to correlate the normal stress data for the polyelectrolyte solutions, a second reduced strain rate (τ_Nk) was used. Thus, two different times were required to correlate all the observed data. The shear viscosity data for the dilute solutions of the nonionic polymer were well represented by the two-parameter, non-Newtonian intrinsic viscosity function that has been computed by Fixman.     

Stress relaxation of polybutadiene at large deformation. Measurements of stress and birefringence in shear and elongation

The rheological behavior of an uncrosslinked polybutadiene on sudden application of finite strain was examined. The shear stress σ, two components of birefringence, and the extinction angle were measured in shear (magnitude of shear γ ≤ 3.5) and tensile stress and the birefringence were measured in uniaxial elongation (elongation ratio λ ≤ 3.8). Measurements were performed at 30°C with a tensile tester equipped with appropriate sample holders. The stress-optical coefficient was 3.01 × 10^?9Pa^?1. The first and second normal-stress differences v₁ and v₂ were separately evaluated with the use of stress-optical law. The Lodge—Meissner relation v₁ = γσ held good. The ratio v₂/v₁ was independent of time and varied from about ?0.3 to ?0.2 with increasing γ in the range of measurements. Each of the stress components was factored into a function of strain and one of time, and the latter was common to all the stress components. Simple formulas were proposed to represent stress components in step deformations.     

Molecular orientational motion in discotic liquid crystals

Abstract

The spectral densities of motion for the aromatic and chain deuterons of the discotic mesogen hexahexyoxytriphenylene (THE6) have been reported in the literature for a frequency of 46 MHz. Most spectral densities J_p (pω₀, 90°) have been obtained from samples consisting of a planar distribution of domains in which the directors were perpendicular to the magnetic field Limited data J_p (pω₀) have also been available from single-domain samples with the director aligned parallel to the magnetic field. We have applied the small-step rotational diffusion model of Nordio et al. to the data from the aromatic deuterons of THE6-ard in its uniaxial columnar D_ho phase, to describe the spinning (D _∥, rotational diffusion constant about the planar normal to the disc) and the tumbling (D?, rotational diffusion constant of the planar normal) motions of the molecular core. Although this model has been successfully used for rod-like nematic liquid crystals, its use has not been attempted for discotic liquid crystals. The model seems to indicate that molecular reorientation has slowed down in the D_ho phase, giving frequency dependence to the spectral densities. This can be explained by the high orientational order of the molecules. We are able to account for the four spectral densities J ₁ (ω₀), J ₁ (ω₀, 90°), J ₂ (2ω₀) and J ₂(2ω₀, 90°) with a calculated ratio D∥/D? of about 1. This is quite different from that of rodlike liquid crystals.     

聚合物熔体壁面滑移的流变研究

用平行板流变仪研究了聚二甲基硅氧烷(PDMS)、聚甲基乙烯基硅氧烷(PMVS)、 高密度聚乙烯(HDPE)及聚丙烯(PP)的壁面滑移, 考察了应力/应变数据对平行板的间距依赖性. 稳态剪切流实验结果表明, 相对于HDPE, PMVS的滑移似乎没有临界剪切应力. 动态剪切实验结果表明, 在不同的间距下, 随着应变增大, 剪切应力数据在小振幅和非线性区前期重合, 然后在某一应变处发生分叉, 即剪切应力依赖于间距, 说明发生了壁面滑移或应变不均匀. 按照Cho等提出的应力分解方法, 在分叉点将剪切应力分解为弹性应力和粘性应力后, 考察了影响壁面滑移发生的可能因素. 发现对于4种聚合物熔体, 当发生壁面滑移或应变不均匀现象时, 存在一个无量纲参数τ'max/|G*|, 即最大弹性应力与线性区复数模量的比值在0.26~0.49范围内变化. 在此范围内, 该参数随角频率的增加而缓慢下降, 而且在较大的温度范围内几乎不依赖于温度. 因而弹性应力是导致聚合物熔体壁面滑移或应变不均匀的关键因素.     

Viscoelastic behavior of low molecular weight polystyrene

The shear creep and creep recovery behavior of narrow molecular weight distribution polystyrene samples of low molecular weight, 1.1 × 10³, 3.4 × 10³, and 1.57 × 10⁴ are reported as a function of temperature, near and above the glass temperature. Time-temperature equivalence for the total creep compliance is found to be nonapplicable, and in fact the steady-state recoverable compliance, J_e, is a strong function of temperature. The time-scale shift factors for the recoverable compliance are analyzed in the light of free volume theory. Viscosity data are presented for samples with molecular weights between 1.1 × 10³ and 6.0 × 10⁵. The temperature dependence of the characteristic time constant ηJ_e can be explained in terms of free volume concepts whereas that of viscosity η cannot. Effects of residual molecular weight heterogeneity are demonstrated.     

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from −6 to −132 cm⁻¹, our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm⁻¹). For the tetranuclear SMMs, the computed J constants are within 6 cm⁻¹ from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.     

Melt flow behavior in capillary extrusion of nanometer calcium carbonate filled PCL bio-composites

Nanosized calcium carbonate (nano-CaCO₃) filled polycaprolactone (PCL) bio-composites were prepared by using a twin-screw extruder. The melt flow behavior of the composites, including the entry pressure drop, melt shear flow curves and melt shear viscosity, were measured through a capillary rheometer operated in a temperature range of 170∼200 °C and shear rates varying from 50 to 10³ s⁻¹. The entry pressure drop showed a non-linear increase with increasing shear stress when the filler weight fraction was less than 3%, while it decreased slightly with an increase of shear stress at a filler weight fraction of 4%. The melt shear flow roughly followed a power law, while the effect of temperature on the melt shear viscosity was estimated by using the Arrhenius equation. Moreover, the influence of the nano-CaCO₃ on the melt shear viscosity of the PCL composite was not significant at low filler levels.     

Effect of shear history on the steady shear flow behavior of a thermotropic liquid-crystalline polymer

The steady shear stress (σ) and first normal stress difference (N₁) of a thermotropic liquid-crystalline polyester, poly[(phenylsulfonyl)-p-phenylene 1,10-decamethylene-bis(4-oxybenzoate)] (PSHQ10), in both the isotropic and nematic regions were measured as a function of shear rate (γ), using a cone-and-plate rheometer. For the study, PSHQ10 was synthesized via solution polymerization in our laboratory. The PSHQ10 was found to have (a) the weight-average molecular weight of 45,000 relative to polystyrene standards and a polydispersity index of 2, (b) a glass transition temperature of 88°C, (c) a melting point of 115°C, and (d) a nematic-to-isotropic transition temperature of 175°C. For the measurements of σ and N₁ in the nematic region of PSHQ10, its initial conditions for the startup of shear flow was controlled by (a) first heating an as-cast specimen to 190°C, (b) shearing there at γ = 0.085 s^?1 for about 5 min, and then (c) cooling slowly down to a predetermined temperature (130, 140, 150, 160, or 171°C) in the nematic region. For each γ chosen, after start-up of shear flow, we waited for a sufficiently long time until both the shear stress and first normal stress difference leveled off, giving rise to steady-state values of σ and N₁. Emphasis was placed on investigating the effect of shear history on σ and N₁ of PSHQ10 in the nematic region. For this, the following experiments were conducted: (a) a fresh specimen was sheared continuously by increasing the γ stepwise, and (b) a presheared specimen was further sheared continuously by increasing the γ stepwise. We have found that fresh specimens exhibited ‘shear-thinning’ behavior over the entire range of γ (0.008?0.27 s^?1) tested, whereas the presheared specimens exhibited both zero-shear viscosities and shear-thinning behavior. When using fresh specimens, we found that N₁ was positive over the entire range of γ (0.008–0.27 s^?1) tested. However, when using presheared specimens we found that (a) at very low γ, N₁ initially was negative and then became positive as shearing continued, and (b) at higher γ, N₁ was positive over the entire duration of shearing. © 1994 John Wiley & Sons, Inc.     

The physical properties of bisphenol-a-based epoxy resins during and after curing. II. Creep behavior above and below the glass transition temperature

The creep behavior of a series of fully cured epoxy resins with different crosslink densities was determined from the glassy compliance level to the equilibrium compliance J_e at temperatures above T_g and at the glassy level below T_g during spontaneous densification at four aging temperatures, 4,4-diamino diphenyl sulfone DDS was used to crosslink the epoxy resins. The shear creep compliance curves J(t) obtained with materials at equilibrium densities near and above T_g were compared at their respective T_gs. T_gs from 101 to 205°C were observed for the epoxies which were based on the diglycidyl ether of bisphenol A. Creep rates were found to be the same at short times, and equilibrium compliances J_e were close to the predictions of the kinetic theory of rubberlike elasticity. Time scale shift factors determined during physical aging were reduced to T_g. At compliances below 2 × 10^?10 cm²/dyn, Andrade creep, where J(t) is a linear function of the cube root of creep time, was observed. The time to reach an equilibrium volume at T_g was found to be longer for the epoxy resin with lower crosslink densities. The increase of density during curing is illustrated for the epoxy resin with the highest crosslink density.