Steady-state Compliance Je Research Articles

Comparison of viscoelastic properties of gluten from spelt and common wheat

Rheological properties of gluten from spelt and common wheat were studied. The mechanical spectra of gluten samples were registered over a frequency range of 0.001–200 rad/s. Retardation tests were performed to keep all measurements within a linear regime. The mechanical spectra were fitted with Cole–Cole functions to calculate the viscoelastic plateau modulus GN0, the central frequency of the upper dissipative loss peak ω0, and the spread parameter n. Steady state compliance Je0 and Newtonian viscosity η0 were determined from the retardation tests results. Recovery data were converted from time to frequency domain using the Kaschta method and combined with dynamic data; this enabled the extension of the gluten mechanical spectra down to 10−6 rad/s, revealing the lower dissipative peak loss. The width of the viscoelastic plateau τm0/τ0 was calculated, and substantial qualitative and quantitative differences were found in spelt and common wheat gluten. All differences in gluten rheological properties were related to spelt and common wheat flour baking quality and protein composition.

Fluctuation Effects on Viscoelastic Properties of Diblock Copolymer Solutions in Disordered State

Viscoelastic properties of three poly(styrene-d8-block-isoprene)s in dioctyl phthalate are measured under oscillatory and steady shear flows in the disordered state, to examine the fluctuation effects on zero shear viscosity η0 and steady state compliance Je based on the effective interaction parameter (χN)eff. Flow-induced microphase separation is not observed when (χN)eff is lower than 9.9. Enhancement of η0 and Je due to the fluctuation effects, which is more obvious for Je, are observed in oscillatory flow, while suppression of the fluctuation effects are observed in steady shear flow, which is confirmed by small angle neutron scattering measurements. Comparing these results with those for poly(styrene-block-2-vinylpyridine)s (SP), it is concluded that the viscosity enhancement due to the fluctuation effects slightly depend on component viscosities. When viscosity ratio of components is close to 1 (i.e., SP), the viscosity enhancement is negligible. On the other hand, enhancement of reduced steady state compliance JeR seems to be insensitive to the viscosity ratio of components.

Dependence of zero-shear viscosity and steady-state compliance on molecular weight between entanglements for ethylene–cycloolefin copolymers

Dynamic viscoelastic properties of a series of cyclic olefin copolymers have been investigated. The specimens differ in total molecular weight as well as molecular weight between entanglements. The angular frequency (ω) dependence curves of dynamic storage and loss moduli (G′ and G″, respectively) of the specimens have shown that G′ ∝ω2 and G″ ∝ω in the terminal region, and a plateau region at high ω. On the basis of the experimental results, the dependence of total molecular weight as well as molecular weight between entanglements has been examined for zero-shear viscosity (η0) and steady-state compliance (Je). It is shown that η0∝Me1.5(Mw/Me)3.5 for the melts of the copolymers in the entangled regime, Mw being the weight-average molecular weight and Me the molecular weight between entanglements. The steady-state compliance Je for the melts scales with Me and Mw as Je∝Me0.5(Mw/Me)0.

Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory

The strain hardening of blends of polystyrene (PS) and ultra-high molecular weight polystyrene (UHMW-PS) in elongational flow is modeled by the molecular stress function (MSF) theory. Assuming that the ratios of strain energies stored in polydisperse and monodisperse polymers are identical for linear and nonlinear deformations, the value of the only non-linear parameter of the theory in extensional flows, the maximum molecular stress fmax, can be determined and is shown to be related to steady-state compliance Je0. Using only linear-viscoelastic data, the elongational viscosity of PS/UHMW-PS blends is consistently predicted by the MSF theory.

Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine Oxide Micelles

Marked effects of protonation (ionization) of tetradecyldimethylamine oxide on the viscoelastic properties of the micelle solutions were found. The effect strongly suggests the short-range attractive interaction between the headgroups of the nonionic (deprotonated) and the cationic (protonated) species. The zero shear viscosity reached a maximum at the half-ionized state (the degree of ionization α = 0.5) and the value was larger than that of the nonionic species (α = 0) or the cationic species (α = 1) by more than 2 orders of magnitude. At a surfactant concentration C of 0.1 mol/kg, approximately single Maxwell behavior was observed as α approached 0.5 from either side. For the half-ionized micelles (α = 0.5) in 0.1 mol/kg NaCl solutions, the steady-state compliance Je0 decreased with C with an exponent of 2.1 ± 0.2, suggesting the presence of an entangled network of flexible threadlike micelles. The relaxation time, on the other hand, exhibited a nonlinear dependence on C. It was about 0.1 s and remaine...

Viscoelastic Properties of Poly(2-vinylpyridine) in Bulk and Solution

Viscoelastic properties of poly(2-vinylpyridine) (P2VP) over a wide range of molecular weight (M) were studied in bulk and solution. It was found that the absolute values of zero-shear viscosity η0 of P2VP in bulk and in α-chloronaphtharene (αCN) are practically the same as those of polystyrene (PS) over whole experimental range of M. The temperature dependence of η0 in bulk is also the same. It is concluded that among various polymers so far studied, P2VP and PS have very similar viscoelastic properties in both bulk and a good solvent (αCN), though the plateau modulus GN0 and steady state compliance Je of P2VP are slightly different from those of PS.

Viscoelasticity of CTAB:NaSal/W detergent micelles. Salt and temperature effects

Dynamic viscoelasticity is measured for threadlike micelles from cetyltrimethyl‐ammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at temperatures T=25, 33, 40, and 50 °C. The CTAB concentration of the solutions is fixed at CD=0.01 M and a ratio of NaSal concentration CS to CD, CS/CD, is varied from 1 to 41. Effects of both CS/CD and T on frequency dependence of storage and loss shear moduli, G’(ω) and G‘(ω), are described in this paper in detail. Characteristic features of this micelle system may be summarized as (1) at 25 and 33 °C, the steady viscosity η and the mechanical relaxation time τM both show a minimum at CS/CD∼4 that is followed by a maximum at CS/CD∼10 as CS/CD increases. (2) The η and τM monotonically decrease with increasing T in the range of CS/CD from 1 to 20, but the maximum itself gradually disappears as T increases. (3) The steady state compliance Je is independent of T and decreases at lower CS/CD. A rapid increase in Je is observed at higher T and CS/CD ends. (4) An additional viscoelastic relaxation process is observed at the high frequency side. This mode appears in the same ω range independent of the salt concentration and exhibits the T dependence such as a type of the local friction factor, ηS/T. The discussion is mainly devoted to the applicability of a couple of models proposed so far.

Viscoelastic Properties of Poly(vinyl methyl ether)

Viscoelastic properties of fractionated poly(vinyl methyl ether) in melts were measured in oscillation flow in the molecular weight range of 2.44×104–13.4×104. It was found that the molecular weight dependences of zero-shear viscosity η° and steady-state compliance Je are qualitatively the same as those of other linear polymers, and the Je value in entangled region is about 3×10−6 (cm2 dyn−1), while the plateau modulus GN0 is about 2.6×106 (dyn cm−2).

Viscoelastic Properties of Polymer Solutions at Temperatures Lower than _??_ Points

Zero-shear viscosity η0 and steady-state compliance Je of poly(α-methylstyrenes) in benzyl n-butyl phthalate (_??_=46°C) and polystyrene in dioctyl phthalate (_??_=22°C) were measured at temperatures lower than the _??_ points. Moreover, stress developments after onset of steady shear flow were measured and the strength of entanglement was estimated on the basis of network rupture model.The concentration and the molecular weight dependences of η0 at temperatures lower than the _??_ points are almost the same as those at the _??_ temperatures, but the magnitude of η0 increases with decreasing temperature. This suggests that the strength of entanglement increases with decreasing solvent power.On the other hand, Je values at the temperatures lower than the _??_ points are almost the same as those in good and _??_ solvents. This result indicates that the entangled structure of polymer solution effective to Je is almost independent of solvent power. Therefore, it is concluded that the gel-like behavior of polymer solution at temperatures lower than the _??_ points is caused by the long relaxation times due to the high viscosity.

Measurements of Viscoelastic Properties of Linear Polymers in Dilute and Semidilute Solutions with a Flow Birefringence Method

To study viscoelastic properties of flexible macromolecules in dilute and semidilute solutions, a birefringence instrument with high sensitivity was constructed. A circularly polarized laser beam is used as an incident light, and the distortion of the beam by polymer molecules in shear flow was detected by a rotating half wave plate and photomultiplier and compensated with a Babinet–Soleil plate. The birefringence Δn and extinction angle χ of polymer solutions can be measured simultaneously and independently. The steady-shear viscosity η and steady-state compliance Je can be evaluated from observed values of Δn and χ using a stress-optical law. The reliability of these data was confirmed by comparing the data with those determined by a Maron–Krieger–Sisko capillary viscometer and a Weissenberg rheogoniometer. The concentration dependence of reduced steady-state compliance JeR of linear polystyrenes in bromobenzene (a matching solvent) in dilute and semidilute solutions are reported.

Viscosity and Steady-State Compliance of Multi-Branched Star Polystyrenes

Reductions of molecular weight dependences of the zero-shear viscosity η0 and the steady-state compliance Je0 for multi-branched star polystyrenes with different numbers (P=7∼40) and molecular weights (Ms=1.3∼20×104) of branches as well as those of small- number (six or less) branched polystyrenes and linear ones have been investigated. The reduction methods of η0 and Je0 ever established both theoretically and experimentally for small-number branched star polymers could not be applied to multi-branched star polymers. We tried to reduce the data of η0 and Je0 for multi-branched star polymers by corrected molecular weights by considering the expansion of molecules. In the course of discussions we proposed a new method to estimate the unperturbed dimensions of star polymers from the rheological measurements.

Characterization and Rheological Properties of Multi-Branched Star Polystyrenes

The star polymer samples were prepared by coupling narrow-distribution polystyryl anions with divinylbenzene and were characterized in terms of molecular weight, molecular weight distribution and coupling ratio. Dynamic viscoelastic properties of star-shaped polystyrenes having different molecular weights (Ms=1.3∼20×104) and numbers (P=7∼39) of branches have been measured. The zero-shear viscosity η0 depends strongly upon the molecular weight at constant P, while it depends much less at constant Ms. Molecular weight dependence of the steady-state compliance Je° are quite complicated. Je° increases with increasing molecular weight at constant P. When Ms is constant, Je° is independent of molecular weight at P≤7 and increases at P≥7. Values of Je° are higher than those for the corresponding linear polymers. Relaxation spectra for star-shaped polystyrenes having many (P≥15) branches exhibit a two-step change on the long-time side. These two sets of relaxation times are attributed to the relaxation mechanism associated with ordinary intermolecular entanglements and to that peculiar to branched polymers. The difference in the entanglement compliance JeN° for branched and linear polymers is smaller than that in Je°.

Concentration Dependence of Viscoelastic Properties of a Mixture of Three- and Four-Branched Star Polystyrenes

Viscoelastic properties of concentrated solutions of a mixture of three- and four-branched polystyrenes were measured by means of a concentric cylinder type rheometer. The Vogel parameters, αf and T0, were calculated from the temperature dependence of viscosity and the shift factor aT. From the frequency dependence of the storage shear modulus G′ and the loss modulus G″, the characteristic parameters in the terminal zone such as zero-shear viscosity η0 and steady-state compliance Je0 were evaluated. The dependence of these parameters on concentration was compared with that of concentrated solutions of linear polystyrenes. The concentration dependence of η0 for star polymers is very similar to that for linear ones. However, Je0 for the mixture of three-and four-branched polystyrenes showed unusual behavior that was quite different from that of linear polymer and monodisperse star polymer. The entanglement compliance is also discussed.

Viscoelastic Properties of Concentrated Solutions of Mixtures of Three- and Four-Branched Star Polystyrenes

Viscoelastic properties of concentrated solutions of mixtures of three- and four-branched polystyrenes were measured by a concentric cyclinder type rheometer and compared with those of undiluted star-shaped polymers having the same type of branching and linear polystyrenes studied previously. The viscoelastic parameters, zero-shear viscosity η0, steady-state compliance Je0, and entanglement compliance JeN0, have been evaluated from the frequency dependences of storage shear modulus G′(ω) and loss modulus G″(ω). η0 for 50 and 90 wt% solutions are proportional to Mw4.5 at high molecular weight. Je0 for 90 wt% solution is independent of molecular weight, while Je0 for 50 wt% solution depends on molecular weight. The unusual behavior found is that the Je0 value for 50 wt% solution of star polystyrenes is lower than those for a 90 wt% solution and an undiluted polymer at the same molecular weight.

Viscoelastic Properties of Branched Polymers. II. In Concentrated Solutions

Rheological parameters, i.e., the zero-shear viscosity η0 and the steady-state compliance Je of solutions of four-armed, star-shaped and also of highly branched, comb-shaped polystyrenes were determined with a Weissenberg rheogoniometer. The molecular weight and concentration dependences of the parameters of the samples were compared with those of linear polystyrenes and also those of three-armed, star-shaped polymers, published previously. Emphasis is placed on the discussion of the difference between Je of linear polymers and that of branched polymers.

Viscoelastic Properties of Star-Shaped Polystyrenes Having Six Branches and Their Concentrated Solutions

The viscoelastic properties of star-shaped polystyrenes having six branches and their solutions were measured and compared with those of four-branch and linear polystyrenes. The dependence of the rheological parameters, such as zero-shear viscosity η0 and steady-state compliance Je0, on the molecular weight and concentration were discussed. At a constant molecular weight, η0 decreases with increasing number of branches in the polymer molecule. Molecular weight dependence of η0 for branched polystyrenes having a constant molecular weight of branch, is very similar to that for comb-shaped and randomly branched polystyrenes. Je0 clearly depends on the molecular weight even in the entanglement region, and the critical concentration evaluated from Je0 is two times higher than that from η0 for branched polystyrenes.

Viscoelastic Properties of Concentrated Solutions of Poly(methyl methacrylate) in Diethyl Phthalate

The viscoelastic properties of concentrated solutions of poly(methyl methacrylate) in diethyl phthalate were measured by means of a concentric cylinder type rheometer and capillary viscometer.The Vogel parameters, αf and T0 were calculated from the temperature dependence of viscosity and the shift factor aT obtained from the time-temperature superposition. Moreover, the viscoelastic parameters characteristic of polymer liquids such as the zero-shear viscosity η0, steady-state compliance Je0, and entanglement compliance JeN0 were evaluated from the frequency dependence of the storage shear modulus G′ and the loss modulus G″.With decreasing concentration, the Vogel temperature T0 decreases at higher concentrations, but increases at lower concentrations after passing through a minimum at about 20 wt%. The temperature coefficient of the fractional free volume, αf however, is almost constant at and above 20 wt%, and then rapidly increases with decreasing concentration. This particular concentration of 20 wt% is very near the critical concentration of entanglement coupling.η0 is proportional to w24.0, where w2 is the weight fraction of polymer, in the iso-free-volume state, and this exponent 4.0 is equal to that for molecular weight, which was obtained from the molecular weight dependence of η0. Both Je0 and JeN0 are proportional to w−22, and Je0 is six times higher than JeN0 over the entire range of concentration where JeN0 can be evaluated.

Viscoelastic Properties of Concentrated Solutions of Randomly Branched Polystyrenes

The viscoelastic properties of concentrated solutions of linear and randomly branched polystyrenes were measured and compared with each other. From the frequency dependence of the storage shear modulus G′ and the loss modulus G″, the characteristic parameters in the terminal zone, such as zero-shear viscosity η0 and steady-state compliance Je0, were evaluated. The dependence of these parameters on the molecular weight and concentration were discussed. The zero-shear viscosity and its dependence on molecular weight for the solution of randomly branched polystyrene are lower than those of linear polystyrene. The steady-state compliance is proportional to Mw0.84 for the branched samples, while it does not depend on molecular weight for the linear polymer. These results lead to the suggestion that the maximum relaxation time is proportional to Mw2.3 and Mw3.5 for branched and linear polystyrene solutions, respectively. The concentration dependence of the steady-state compliance for the branched polymers is also much less than that of the linear ones. Comparing the frequency dependence curves of G′ for the randomly branched and linear polystyrenes, there seems to be a significant difference in the shape of the relaxation spectra in the region associated with entanglement coupling. This behavior is considered to be due to the difference in the two chain structures.

Viscoelastic Properties of Concentrated Solutions of Star-Shaped Polystyrenes

Hereunder a report is presented of measurement made of the viscoelastic properties of concentrated solutions of star-shaped polystyrenes. From the frequency dependence of the storage shear modulus G' and loss modulus G" the characteristic parameters in terminal zone, such as zero-shear viscosity η0 and steady-state compliance Je0, have been evaluated. The dependence of these parameters on the concentration have been discussed and compared with those of concentrated solutions of linear polystyrenes.For the star polymers, the zero-shear viscosity reduced to the iso-free volume state, f=0.0608, is proportional to (w2ρ)6 and (w2ρ)1 at higher and lower concentrations, respectively, than the critical concentration, where w2ρ is the concentration in g/ml. The critical concentration for entanglement was evaluated to be 0.23g/ml for the star-shaped polystyrene having the molecular weight of 407000. The concentration dependence of steady-state compliance of the solutions of star polymer can be divided into three parts. The steady-state compliance is proportional to (w2ρ)-1 at low concentrations below 30wt%and to (w2ρ)-2 in the concentration range from 30 to 70wt%. In both the regions, Je0 is proportional to the molecular weight. At higher concentrations, Je0 increases rapidly passing through the minimum at about 70wt% but is independent of molecular weight. The molecular weight dependece of Je0 in the entanglement region and its rapid increase at extremely higher concentrations for the star polymers are quite different from those for linear polymers described in our recent papers. The entanglement compliance JeN0 of the solution of star polymers is proportional to (w2ρ)-2 above the critical concentration, which is similar to that of linear polymer.

The Concentration Dependence of Steady-State Compliance for Polymer Solutions

The steady-state compliance Je as a function of the molecular weight M and the concentration c for polymer solution can be expressed as:Je=αM/cRT for smaller values of c or M=βM0/c2∼3 for larger values of c and MHere α and β are constants and RT is used in its usual meaning. The second behavior of Je is characteristic of highly entangled system. In the concentration range where the transition from the first to the second behavior occurs, the Je displays the maximum.Either of the two relaxation spectra, A and B, are found to be compatible with these observed behaviors of Je. These are:(A) HW(τ)=1/2cRT/Me(τc/τ)1/2 0<τ<τcHI(τ)=1/2(1-gN)cRT/Me(τc/τ)1/2 τc<τ<τ1HB(τ)=1/hgNcRT/Me τl<τ<τmτc=τ1E-2, τm=τcE3.5, τl=τmeh(1/E-1)(B) HW(τ)=1.75/3cRT/Me(τc/τ)2/3 0<τ<τcHZ(τ)=1.75/3(1-gN)cRT/Me(τc/τ)2/3 τc<τ<τ1HB(τ)=1/hgNcRT/Me τl<τ<τmτc=τ1E-1.5, τm=τcE3.5, τl=τme1.75h(1/E-1)/2The former corresponds to the Rouse theory, while the latter to the Zimm theory. Here, τ1 represents the maximum relaxation time of the original Rouse or Zimm theory, Me is entanglement spacing, E is the number of entanglement point in a molecule, hence E=M/Me, and gN and h are parameters representing the intensities of HI and HB, respectively.The viscosity η, storage modulus G' and loss modulus G are also calculated on the basis of these spectra. These results are qualitatively in agreement with the observed one, particularly in the case of high value of h and low value of gN.