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4. At very small values of j 1 , ln j 1 is so deeply negative that DGm is negative, independent of the values of V 1 , V2, c etc. The same holds for j2 . g. as indicated in the figure. 26. 4. 5. When there is a UCST (upper critical solution temperature), then above that temperature the components are fully mixable. 6. 3). If we blend below this temperature, we can obtain a homogeneous mixture. Subsequent heating to above the LCST can result in segregation; the rapid cooling in an injection moulding machine does not allow to undo this.
A. a. The curve p is typical for an amorphous, not cross-linked polymer; q for a cross-linked polymer, b. For both curves the maximum lies at the glass-rubber transition temperature Tg, c. For p the polymer gradually shifts into the liquid condition; d increases up to p2 and tan d to infinity, d. In a network (q) the loose chain ends (not held between two cross-links) do not contribute to the network elasticity, but they behave more or less as a fluid. Therefore, with increasing T, tan d approaches to a finite value, dependent on the network structure.
17) looks as follows: s = E·v·t·(1 – exp(–t/t) = h·v·(1 – exp(–t(t)). 17. 9. 10. Again: e = v·t. Now the stress on the spring is s1 = E· e = E·v·t, and on the dashpot: s 2 = h ·v. The total stress is s = v ·(E · t + h ) = (e/t)·(E·t + h ) = e·(E + h/t) = e·E + h·v. 18. 10. 11. Apparently the stress relaxation proceeds in two phases, each with a stress decrease of 1 MPa at a strain e = 1. It seems logical to think of a parallel arrangement of two Maxwell elements, both with a spring constant E = 1 MPa, but with relaxation times which differ by a factor 10,000 .