Storage and Loss Modulus

In class we considered the mechanical response of an elastomer as it depends on chemistry (happy and sad balls), temperature (liquid nitrogen cooled rubber ball) and time (speed of impact for rubber ball, shear rate (frequency) dependent viscosity). We can consider that if the total energy of the falling ball were converted into recoil the ball would bounce to as high as possible. The actual bounce is always less than this. The distance of the actual bounce is proportional to the storage modulus, G', or the energy stored in the ball on impact and released in the bounce. The remaining distane to the initial point is lost in heat to the environment. This distance is proportional to the loss modulus, G".

If we consider a plot of G" versus G' or of i G" versus G', where i is the square root of -1, the angle of a line to the point in complex space is d. tan(d) = G"/G' .

A plot of tan(d) versus tempearture of time shows a peak that occurs at the glass transition temperature, T_g. T_g is related to the chemical composition of the polymer as it effects the barrier energies between rotational isomeric states for the long chain molecule.