John L. Schrag

Deviation of Velocity Gradient Profiles from the “Gap Loading” and “Surface Loading” Limits in Dynamic Simple Shear Experiments

The shear‐wave field generated in a linear viscoelastic medium confined between parallel plates (one fixed, the other oscillating sinusoidally in its own plane) has been evaluated and presented in a graphical form convenient for determination of the role of wave propagation effects in dynamic rheological measurements. The transition from closely spaced planes (“gap loading”) to the freely propagating plane wave (“surface loading”) limit is examined; the importance of deviations in magnitude and phase of the gradient profile from the gap loading limit is discussed in terms of high precision dynamic rheological experiments; significant deviations occur for shear wavelength to gap width ratios of 30 or less.

Application of the Birnboim Multiple Lumped Resonator Principle to Viscoelastic Measurements of Dilute Macromolecular Solutions

A new multiple lumped resonator apparatus for the measurement of the viscoelastic properties of very dilute macromolecular solutions is described. The instrument may be used to study the viscoelastic behavior appropriate to infinite dilution for comparison with current theories. It has a frequency range from 100 to 8300 Hz (discrete frequencies) and may be used with solution viscosities from 0.005 to 0.5 P. Values of G′ less than 0.5 dyne/cm2 have been measured with reasonable accuracy when used in conjunction with a computerized data acquisition system.

Theoretical predictions for the mechanical response of a model quartz crystal microbalance to two viscoelastic media: A thin sample layer and surrounding bath medium

Theoretical predictions are presented for the operating characteristics of a quartz crystal microbalance (QCM) system consisting of the crystal, an attached viscoelastic sample layer, and a surrounding viscoelastic bath medium. Predictions are given for the spatial variation of “particle” velocity and velocity gradient throughout the sample layer, for the characteristic mechanical impedance acting on the crystal surface due to the viscoelastic sample layer plus surrounding bath medium, and for the resultant changes, Δfr, in the resonance frequency of the QCM. Errors introduced by employing the usual simple Sauerbrey-type Δfr/sample-layer–mass relationship, together with a constant frequency offset to approximate the effect of the viscoelastic bath medium, are explored. In general, the viscoelastic properties of both the sample and bath media can substantially affect the apparent thickness (mass) of the sample layer if it is obtained by employing the typical Sauerbrey-type approximation noted above.

An instrument for precise measurement of viscoelastic properties of low viscosity dilute macromolecular solutions at frequencies from 20 to 500 kHz

A high‐frequency torsional rod apparatus (HFTRA) has been developed for measurements of moderately high‐frequency viscoelastic properties of dilute, low viscosity polymer solutions. It employs a long cylindrically shaped resonating element driven by an X‐cut (torsional mode) quartz piezoelectric crystal. Up to 11 different normal modes are employed, resulting in 11 discrete frequencies, ranging from approximately 20 to 500 kHz. Measurements are made in free decay; a key feature of the apparatus is the method for high precision measurements of damping coefficients and eigenfrequencies. The instrument is suitable for liquids with 0.003P<‖η*‖<5P and η’≥1.33η‘. Typically, η’ has a relative uncertainty of ±2% or less, with the relative uncertainty for η‘ being about 4% for liquids with η‘ greater than 0.01P. Values of η’ obtained in the HFTRA for low viscosity liquids with small η‘ show excellent agreement with the known steady flow viscosities. Measurements of the viscoelastic properties of polymer solutions ...

Dilute‐solution dynamic viscoelastic properties of xanthan polysaccharide

The frequency dependences of the storage and loss shear moduli, G’ and G‘, of dilute solutions of highly purified xanthan polysaccharide were measured at 20.0 °C using the Birnboim–Schrag multiple‐lumped resonator. The frequency range was 150–8000 Hz and the concentration range was 0.1–0.4 g/l. Three solvents were used, one of which contained 75% by weight glycerol to increase the solution viscosity. Measurements of oscillatory flow birefringence were also made in one solvent over the frequency range from 1–630 Hz and agreed well with the viscoelastic data in the range of overlap. The intrinsic viscosity in both water and 25%/75% water/glycerol (with 0.085 mol/l sodium chloride) was determined as 5200 ml/g. The frequency dependences of G’ and G‘, extrapolated to infinite dilution, could be fitted to a hybrid model for semiflexible rods which was modified to take into account a moderate degree of molecular weight distribution (Mw/Mn=1.4). From the experimental data the persistence length of the native xant...

Local modification of solvent dynamics by polymeric solutes

Abstract Extensive oscillatory flow birefringence and dynamic viscoelastic measurements on a variety of polymer-solvent systems indicate that the solvent contributions to the measured solution properties are not given by the neat solvent birefringence or viscosity, respectively, by contrast with the predictions of chain dynamics theory. Rather, the high frequency limiting plateaus observed in the loss components of both the dynamic birefringence and dynamic viscosity, designated S′∞ and η′∞, respectively, represent the appropriate solvent contributions. Measurements of solvent rotational and translational friction in some of the same polymer-solvent systems provide direct support for the postulate that the values of S′∞ and η′∞ reflect predominantly polymer-induced modifications to the dynamics of the solvent surrounding the chains.

Measurements of N1 — N2 and η in steady shear flow and η′, η″, and birefringence in small-strain oscillatory shear for the polyisobutylene solution M1

Steady shear flow Stressmeter data for N1 — N2 and shear stress σ near 20 ° C for increasing and decreasing values of shear rate γ. in the range 14–427 s−1 exhibit hysteresis and evidence of polymer degradation; N1 and N2 denote the first and second normal stress differences in steady shear flow. Comparison with BASF cone-plate data for N1 shows that N2/N1 lies in the range from −0.1 to −0.2. Values of η′ at temperatures in the range 0–40 ° C and values of angular frequency ω in the range 1–3600 s−1, obtained with a coaxial cylinder rheometer in which the inner cylinder oscillates along its axis, give satisfactory time-temperature superposition; values of η″, however, show small but significant deviations from time-temperature superposition. The curves ηr(γ.r) and η′r(ωr) intersect; the limiting value of (N1 - N2)r/(2γ.2r) obtained by extrapolation to low γ.r equals the value of G′r/ω2r at low ωr. Oscillatory shear birefringence data (0–40 ° C, 5 s−1 < ω < 6280 s−1), obtained with a parallel plate apparatus in which one plate oscillates in its plane, show small but significant deviations from the equation n = AI + Cp, where n and p denote the solution refractive index and stress tensors and A, C are ω-independent scalars. Solvent contributions were not subtracted from n or p.

Bead-spring chain model for the dynamics of dilute polymer solutions: Part 2. Comparisons with experimental data

Abstract Comparisons are made between experimental rheological data and theoretical predictions obtained from a recently developed algorithm which incorporates three major molecular concepts in a theory for dilute polymer solutions (hydrodynamic interaction, excluded volume and nonlinear springs). These predictions include the radius expansion factor, the apparent chain expansion factor, the molecular weight dependence of the intrinsic viscosity, the frequency dependence of oscillatory flow birefringence, and the shear rate dependence of the intrinsic viscosity. This paper shows that a bead-spring chain model quantitatively predicts these quantities when the relevant molecular concepts are incorporated, suggesting that the rheological properties of dilute polymer solutions can be explained and predicted in terms of these molecular parameters.

An improved system for data acquisition and analysis for viscoelastic measurements of dilute macromolecular solutions with the modified birnboim-schrag multiple lumped resonator

Abstract A new system of data acquisition and analysis has been developed for the modified Birnboim-Schrag multiple lumped resonator apparatus which is used to measure the viscoelastic properties of long-chain macromolecules in dilute solution. The modifications to the original apparatus include improved temperature control and vibration isolation. The original theory has been reworked so that each resonance mode can be characterized by a greater number of data points. The entire data acquistion/processing system is automated and placed under computer control; a correlation for mode coupling is derived. The modifications result in improved precision in the measured viscoelastic moduli and increased instrumental reliability.

Studies of the concentration dependence of the conformational dynamics of solutions containing linear, star or comb homopolymers

The concentration dependence of the conformational dynamics of polymer solutions as revealed by measurements of oscillatory flow birefringence (o.f.b.) has been obtained for narrow-distribution linear, comb and regular-star molecules for concentrations in the range c[η]≲ 11. The data obtained show that the relaxation-time spectrum is affected markedly by concentration. The longest relaxation time is affected most; for the linear, comb or 3-armed star polystyrenes studied to date, τ1 exhibits an exponential dependence on concentration for c[η] < 3. The Muthukumar theory correctly predicts the dependence of τ1 on concentration for solutions containing linear molecules for which c[η]⩽ 5. There is some indication that τ1 as a function of concentration exhibits two different concentration regimes, one above and one below the onset of significant entanglement effects. The shortest relaxation times are almost unaffected by concentration. The measured frequency dependences of o.f.b. properties for finite concentrations have also been compared with the predictions of the Muthukumar and Freed and the Muthukumar theories for the concentration dependence of the relaxation times for the bead–spring model.