A recording, air‐bearing torsion pendulum

Abstract

SynopsisA recording torsion pendulum has been designed which allows the measurement of storage modulus and loss modulus for weak gels. The gel is held in a cone-plate geometry. The 5" cone, along with the inertial elements of the pendulum, is supported by an air-lubricated bearing. The decay of oscillations is sensed by a Proximeter which does not touch the moving apparatus and which converts the amplitude of oscillation into a dc signal of several volts. Storage moduli as low as 40 dyn/cm2 and log decrements as low as 0.0054 have been measured.The dynamic mechanical properties of weak, fragile gels are not easily measured in conventional instruments. With self-healing gels such as those formed by soaps in lubricating oil, many kinds of penetrometers and consistometers are available which measure gel strength, rigidity, and recovery. However, with gels of covalently crosslinked polymers in water, only small strains and stresses can be imposed without irreversibly disrupting the network structure. The torsion pendulum, properly designed and operated, can yield useful results within the limits of a shear strain less than 0.5 and with shear moduli down to 40 dyn/cm2.When a sample of a material is used as the restoring element in a torsion pendulum, the dynamic modulus and loss for the material can be estimated from the geometry of the sample together with the frequency and the decay rate of the oscillations. If the experiment can be confined to the region of linear viscoelasticity and if the damping of the oscillations is not excessive, the frequency of oscillation f (in radians per second) will be a function only of the moment of inertia of the system 1 (in g-cm2) and the stiffness of the sample as torque k per unit of twist (in dyne-centimeters per radian) :A useful measure of the damping properties of the material is t,he log decrement A, which is the decay rate of maximum amplitude em with cycle number n :