Control of relaxation properties in oligomer curing

Theoretical investigations show that there is only one signal that satisfies the condition of equal amplitudes in a Fourier expansion this input signal is written as 

The FTMS method allows us to follow changes in several parameters that carry information on the role of different mechanisms during formation of an end-product by reactive molding. Specifically, the development of fluctuating entanglements of long-chain macromolecules can be distinguished from the appearance of rubber-like three-dimensional networks of chemical bonds. 

The results of measurements of the dependencies G (w,t) for three circular frequencies w0 = 27tf0, wi= 4rcwo, and w2 = 16jtwo are shown in Fig. 3.1. The lack of coincidence in the shapes of die time dependencies of the dynamic modulus components for different frequencies is obvious. This phenomenon is especially true for G , because the position of the maximum differs substantially along the time axis. In the most general sense, this reflects the contributions of the main relaxation mechanisms of the material to its measured viscoelastic properties. 

The relaxation spectrum H(0) completely characterizes the viscoelastic properties of a material. H(0) can be found from the measured frequency dependence of the dynamic modulus of elasticity G (co) by means of the following integral equation  

A Cole-Cole diagram is shown in Fig. 3.2. The experimental points in the G - vs - G coordinate system fall lie closely on a half-circle, with the exception of a narrow time interval very close to the transition (gelation) time, t. This curve corresponds to simplest model of a linear viscoelastic body with one relaxation time. In this case, G ( ) is expressed as follows  

---