The characteristic relaxation timetof the mobile units corresponds to a character-
istic frequency 1/t. If the external frequencyo>>1/t, the motion unit cannot catch
up the stimulation, no loss,E"0; ifo<<1/t, it completely synchronizes with the
stimulation, no loss either,E"0; while ifo1/t, the mobile unit wants to catch
but with difficulty (makes resonance), loss happens. In the last case,E"exhibits a
maximum, which reflects a strong internal dissipation, as shown in Fig.6.12. One may
measure the dynamic mechanical spectroscopy under various temperatures to obtain a
series of peaks for hierarchical internal dissipation with characteristic relaxationtimes,
according to the time-temperature superposition principle. They reflect the hierar-
chical features of molecular motions at various time scales. For non-crystalline bulk
polymers, thearelaxation conventionally corresponds to the glass transition, and the
other relaxation peaks correspond to the secondary relaxation modes that freeze
sequentially the chemical repeat units and the side groups. For crystalline polymers,
thearelaxation conventionally corresponds to block-slip motions in the lamellar
crystals (Takayanagi 1978 ; Men and Strobl 2002 ). For PE and PEO, thearelaxation
splits into two, with additional one corresponding to the chain-slip motions in the
crystalline region (Schmidt-Rohr and Spiess 1991 ; Men et al.2003a).
The dielectric relaxation spectroscopy can effectively measure the relaxation
processes of dipoles in the polymers. Like the dynamic mechanical spectroscopy,
the sinusoidal electric field is the imposing stimulation, and again in a complex form,
E^ ¼EexpðiotÞ (6.33)and the polarizability is the detected response, as
D^ ¼DexpðiotidÞ (6.34)Fig. 6.12Illustration of (a) the storage modulus, the loss modulus and the loss factor as a function
of frequency across the glass transition temperature of amorphous polymers; (b) the loss factor as a
function of temperature according to the time-temperature superposition principle. Below the
apeak for glass transition, there are secondary relaxation peaks
106 6 Polymer Deformation