of Factors Affecting the Precision of Viscosity Measurements with the Torsion
Crystal.l--P. E. RousE, JR., ~ E. D. BAILEY, 2 and JEAN A. MISKIN. ~ This paper gives the results of a study whose objective was the refinement of a technique which promises to be of great value in the study of complex liquids. As a result of this work it is now possible to measure the high frequency viscosity of liquids with almost as high a precision as can be attained with steady-state flow instruments.
The torsion crystal method of studying the complex high frequency shear reaction of liquids was introduced by W. P. Mason s of the Bell Telephone Laboratories in 1946. This method makes it possible to measure the component of the liquid reaction in phase with the velocity of the crystal surface and the component 90 Β° out of phase with this velocity. When the high frequency reaction of a liquid can be entirely described by the steady-flow viscosity and density of the liquid, the magnitudes of the in-phase and out-phase components of the high frequency reaction are equal. In the case of liquid polymers, polymer solutions and other multi-component systems the component in phase with the velocity of surface is larger than the out-phase at frequencies which can be attained experimentally. A knowledge of the values of the components of the reaction as a function of frequency over a wide frequency range makes it possible to draw important conclusions concerning the structure of a liquid system.
The usefulness of the information which can be supplied by a torsion crystal study is very dependent on the precision with which the measurements can be carried out. This is a consequence of the fact that it is essential to know when the in-phase and out-of-phase components of the liquid reaction do differ and to know the magnitude of their differences. The study of very dilute polymer solution is an important application of the method, and since the reaction of such systems differs very little from the pure solvent, the measured values must be known very accurately if the contribution of the polymer to the total reaction is to be studied. It is equally important that the behavior of the crystal be very reproducible.
In this technique a cylindrical crystal of quartz is oscillated in a liquid medium. The resonant amplitude, which is inversely proportional to the in-phase component of the reaction, and the resonant frequency, which changes linearly with the out-phase component, are deter mined. Since the crystal system may be represented as a series resonant circuit (Fig. 1), the resonant amplitude is determined from the value of the resonant resistance measured with a conductance-capacitance budge. The resonant frequency is measured with an electronic counter used in conjunction with a precision tuning fork. The resonant resistance can be measured to 0.2 per cent for liquids whose viscosities fall in the range from 1 centipoise to 1 poise. For liquids in this viscosity range the resonant frequency can be measured to one part in 200,000. This means that the uncertainty in the change in resonant frequency produced by the reaction of the liquid is 4 per cent when the liquid viscosity is 0.5 centipoise and 0.2 per cent when the liquid viscosity is one poise. These values compare with a precision of 10-15 per cent reported in early work. 8 Figure 2 shows graphically the agreement between the measured values found in the recent study and the theoretical relationships derived by Mason. This figure illustrates the difference in behavior of a simple liquid and a liquid in which the reaction depends on processes whose relaxation times are of the same order as the period of oscillation of the crystal. The linear plots shown were obtained from the measured reaction of solvents and low molecular