Super Tg Relaxation and Entanglement Effect PDF

25. Super Tg relaxation and entanglement effect 25.1. Super Tg relaxation Super Tg relaxation of a polymer is a prolonged thermal relaxation process that occurs at temperatures above the glass transition temperature (Tg). For a polymer near the rubbery state, a small perturbative stress σ is appli...

25. Super Tg relaxation and entanglement effect 25.1. Super Tg relaxation Super Tg relaxation of a polymer is a prolonged thermal relaxation process that occurs at temperatures above the glass transition temperature (Tg). For a polymer near the rubbery state, a small perturbative stress σ is applied and we look at the strain e(t) induced by this step increase in stress. For small σ, the strain is a linear function of the stress 𝑒(𝑡) = 𝜎𝑱(𝑡) J(t) is the creep compliance of the polymers. J = 1/E. At short times, the conformations in all the chains do not adjust, and the mechanical response is similar to what one measures in a polymeric glass (Conformations are permanently frozen). At longer times, the conformations do change, and the strain becomes more important. However, there is a large span of time (t 𝜏𝑡 ) 𝑑𝑡 𝜏𝑡 is called terminal relaxation time. It is the longest relaxation time observed in mechanical measurements. (Super Tg relaxation) If we compare the latter form with the viscous flow equation, we are led to 𝜂 ≅ 𝐸𝜏𝑡 25.2. Elastic modulus of the transient network For long chains, the plateau modulus E is independent of chain length. When the chains are fully flexible, E essentially measures the number of entanglement points per unit volume in the transient network. 𝑐𝑇 𝐸= 𝑁𝑒 Where c (~1/a3) is the concentration in the melt, and Ne is the average interval between entanglement points along one chain. Ne is typically of order 100. Our discussion here is restricted to long chains 𝑁 ≫ 𝑁𝑒. 25.3. Viscosity and terminal time The viscosity η is very sensitive to chain length. Both η and 𝜏𝑡 increase as a power of N. 𝜂~𝜏𝑡 ~𝑁 𝑚𝜂 (𝑁 ≫ 𝑁𝑒 ) Where 𝑚𝜂 is of order 3.3 to 3.4. 𝑚𝜂 represents one of the major unsolved problems of polymer physics. 2 25.4 Molar mass dependence 3