Measurement of Viscoelastic Properties of Polymer Solutions by Torsional Crystals

Abstract

ABSTRACT:The network analyzer was used for measurement of the viscoelastic properties of dilute polymer solutions. It is a sensitive instrument to measure resonance resistance and resonant frequency of crystals by the admittance circle diagrams shown on the digital oscilloscope. Measurements can be conducted more correctly and rapidly compared to the previous measuring system. Its validity was verified by measuring the complex shear modulus of dilute polymer solutions and comparing the results with the Rouse theory. The complex shear modulus was determined by measuring changes in the properties of a torsionally vibrating crystal. Frequency dependence of complex shear modulus is investigated in the frequency range from 3 to 252 kHz and temperature range from -60 to 23°C. The samples are several kinds of dilute solutions of polystyrene in toluene. The use of polystyrene is limited in narrow molecular weight fractions ranging in number-average molecular weight from 2.1 x 10 3 to 1.60 x 10 5 . The results agreed with the theory by Rouse.KEY WORDS Network Analyzer / Torsional Crystal / Polymer Solution / Polystyrene / Rouse Theory / In order to investigate the viscoelastic properties of polymer solutions, it is necessary to measure the complex shear modulus at various frequencies. If liquids are sheared sufficiently rapidly, they exhibit a shear elastic effect as well as viscous effect. 1 It is the purpose of this paper to describe a method for measuring viscoelastic properties of polymer solutions at ultrasonic frequencies using torsionally vibrating crystals and a new measuring system, the network analyzer.Measurement of viscoelastic properties of dilute polymer solutions requires very sensitive instruments. The first technique suitable for work in this field was introduced by Mason. 1 • 2 Mason et al. measured the resistance and reactance of a torsional crystal by a bridge circuit. This method has been extended by McSkimin and his coworkers. 3 • 4 They made improvement so that small change in phaseshift can be determined using AT-cut quartz unit. Birnboim and Ferry 5 measured over a continuous frequency range from 0.01 to 5 Hz by amplitude-phase shift measurements. Wada and his coworkers 6 measured amplitudes and phase-shift in the frequency range from 20 to 300kHz.In the present paper, a simple technique is presented for measuring accurately and directly the equivalent circuit elements of a crystal. The network analyzer used in this experiment is a fully automatic instrument designed to measure several impedance parameters of electronic devices. The procedure of measurement has been more simplified compared to that by using the previous electrical measurement systems.The longitudinal relaxation is complicated even in a dilute solution due to the presence of excess absorption originated from a compressional mode motion. The merit of the shear measurement lies in the fact that relaxation behavior in a normal state is well 553

Viscoelasticity of Poly(ethylene glycol) Solutions on Supported Lipid Bilayers via Quartz Crystal Microbalance with Dissipation

“…Diffusing wave spectroscopy can measure the viscoelasticity of polymer solutions up to frequencies of about 100 kHz but is not applicable, in general, to dilute polymer solutions. Instruments based on the torsional resonator, which was pioneered by Mason, have been used to study the viscoelasticity of polymer solutions up to hundreds of kilohertz. − Another potential technique to probe the viscoelasticity of polymer solution at high frequency is the quartz crystal microbalance with dissipation (QCM-D). QCM was initially employed in air to measure the mass deposited on a piezoelectric resonator according to the decrease of the oscillation frequency and was later applied in liquid environments. − Similar to torsional resonators which are working in the kilohertz range, QCM-D measures both resonance frequency and bandwidth (or energy dissipation factor) of the resonator in contact with the fluids, from which one can deduce the viscosity of Newtonian fluids in the megahertz frequency range .…”

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

“…The use of a piezoelectric quartz tuning fork with wide, thin oscillating arms was pioneered by Mason [Mason (1947)] and has been employed by Yoshizaki [Yoshizaki (1993)]. For every frequency measured, a separate tuning fork is employed.…”