師:林金福

2003. 6.18

1.Please derive the theory of rubber elasticity, where the retractive force f
  of rubber under extension to l length can be expressed by
  f≒(δU/δl)T,V + T*(δf/δT)l,P    (15%)

2.Please show that for a single polymer chain, the retractive force f for an
  extension of magnitude r can be expressed by f=2kT(β^2)r     (10%)
  Hint:Gaussian distribution of the end-to-end distance of a polymer chain is
       given follows, W(x,y,z)=w(x)w(y)w(z)=(β/√π)^3 * exp(-(β^2)(r^2))

3.Please show that the stretch stress s on an elastomer per unit volume is
  s = (δΔFel/δr)T,V = νe*kT*((ri^2)bar/(r0^2)bar)*(γ-(1/γ^2))
  where νe is the number of sub-chains per unit volume; γ is the strain of
  the elastomer; (ri^2)bar is the initial mean-square of end-to-end distance
  of sub-chains; and (r0^2)bar = 3/(2β^2)       (10%)

4.From the Doolittle equation η = η0 * exp(βstarυstar/υf), please derive
  the WLF equation as following,
  ln(ηT/ηTg) = (-βstarυstar/υfg)(T-Tg)/((υfg/αυg)+T-Tg)     (15%)

5.The famous WLF equation to predict the viscosity of polymer as a function of
  temperature can be shown as following,
  ln(ηTg/η2) = 40(T2-Tg)/(52+T2+Tg)
  If the equation has been changed to
  ln(ηTg+30/η2) = C1(T2-Tg-30)/(C2+T2-Tg-30)
  Where ηTg+30 is the viscosity of polymer at Tg+30度C. What are C1 and C2?
  (10%)

6.What are the chian conformation and configuration? Please show three
  possible configurations of polypropylene.      (10%)

7.Please define the following terms:      (2%*15=30%)
  (1)Solubility parameter         (2)Excluded volume
  (3)θ-temperature               (4)Zimm plot
  (5)Elastic scattering           (6)Intrinsic viscosity
  (7)GPC                          (8)Lamellae
  (9)Spherulite                   (10)Avrami equation
  (11)Shish kebab morphology      (12)Crazing
  (13)Stress relaxation master curve
  (14)Creep experiment            (15)Voigt model