Equation of State of Polystyrene and Polymethylmethacrylate from Ultrasonic Measurements at Moderate Pressures

Abstract

The relationship of ultrasonic velocities to equations of state is addressed for two homogeneous isotropic plastics, polystyrene and polymethylmethacrylate. Ultrasonic velocities were measured at hydrostatic pressures up to 10 kbar and temperatures from ambient to 75°C at an acoustic frequency of 6 MHz. From these data the pressure and temperature dependence of the elastic moduli are calculated. In particular, the bulk modulus is used to compute an equation of state from models proposed by Birch and Murnaghan. The nonlinearity of the bulk modulus at pressures below 10 kbar favors the Birch model. Comparison with shock data shows that the Birch equation of state, determined ultrasonically, agrees quite well with the shock data to pressures well over an order of magnitude in excess of the 10-kbar ultrasonic data for both polystyrene and polymethacrylate.