Structure and Properties of Polymers Essay

Structure and Properties of Polymers Essay Structure and Properties of Polymers Essay C 10 Lecture Notes Freely jointed chain, a â€Å"phantom† chain n links of same length, ak Joints permit completely free rotation Mean squared end to end length = nkak2 Contour (stretched out) length Lc=nkak Persistence length aq=ak/2 What is the size of the blob? For an ideal Kuhn chain RG2 = RL2/6 (approx.) RG: Characteristic radius of blob 3. Non-crystalline Polymer (Physical States of Matter) 3.1 Glass transition temperature Specific volume a) Tg occur in all materials where crystallinity doesn’t get in the way b) Because it is not an equilibrium phase, glass transition is not a thermodynamic transition Melt/Rubber Glass Equilibrium line T 0 Specific volume Specific volume 1. Cool slowly 2. Heat quickly Tg depends on time scale of observation Slow cool Fast heat Anneal 0 T 0 T 3.2 Polymeric states Molecular weight Increase molecular weight to infinity (chemically linked) → All RUBBER in this region Tg Glass Rubber Viscous melt T 1 GPa Glass log E Rubber 1 MPa ~ 10 MPa Viscous creep Temperature Spring: purely elastic, ÏÆ' = EÃŽ µ Dashpot: purely viscous, ÏÆ' = ÃŽ ·ÃŽ µ stiff spring model elasticity of glass (Eg) dashpot controls short relaxation time processes (frees upon reaching Tg) Eg-Er Er ÃŽ ·1(T) ÃŽ ·2(T) weak spring model elasticity of glass (Er) dashpot for longest relaxation time processes (frees for rubber-melt transition) ÃŽ ·1 and ÃŽ ·2 solid → glass: Eg ÃŽ ·2 solid, ÃŽ ·1 free → rubber: Er viscosity, ÃŽ · = ÏÆ'/ÃŽ µ 4.1 Behavior of spring/dashpot models ÏÆ' ÃŽ µ Maxwell element Time tot = E + − CON. EQN ÏÆ' ÏÆ'0 at time t = Ï„, ÏÆ' = ÏÆ'0/e 0 t ÏÆ' ÃŽ µ = ÏÆ'0/E t Voigt element Add stresses, ÏÆ'tot = EÃŽ µ + ÃŽ ·ÃŽ µ − CON. EQN â‘ ¢ Constant ÃŽ µ, ÃŽ µ = 0 ÏÆ' = EÃŽ µ Constant ÏÆ', ÏÆ' = 0 4.2 How realistic? Assumptions: (i) Viscosity Newtonian ÃŽ · ≠  f (ÃŽ µ) Not very good assumption at high strain rate (ii) Only two relaxation processes Ï„1 Ï„2 LHS controls Tg Relaxation of molecular chain segments RHS longest Ï„ Unraveling of entangled chain N (Ï„) Relaxation Time Spectrum Ï„ Note: N (Ï„): number of elements with Ï„ between Ï„ and Ï„ + d Ï„, like ‘density of state† 5.1 Modulus of glass Eg ~ E of van der Waals solid (held together by VdW forces), approx. 1 GPa Einorganic glass ~ 65 GPa → combinations of ionic bonding and Si – Si Emetal : steel ~ 210 GPa Al ~ 70 GPa Epolymer chain pulled out ~ 250 GPa 5.2 Viscosity of ÃŽ ·1 dashpot In region of Tg, (a) Time-temperature superposition (Fig 5.1) (b) Superimposed curve, made by shifting data by log aT (Fig 5.2 b) (c) Plot of shift factor aT vs. temperature (Fig 5.2 c) Williams-Landel-Ferry (WLF) found empirical equation to describe (c) Ts ~ reference temperature, works well if Ts = Tg With C1 = 17.4 , C2 = 51.6 K Implication: log aT (i.e. ÃŽ ·1) turns to ∞ when T = Tg – C2 → (Tg – 51.6) K ∠´Creep of polymer glass turns to zero at temperature (Tg – 51.6) K or lower Justification of WLF in terms of free volume Specific volume Occupied volume 0 T Second Input: Doolittle Equation 5.3 Elasticity of Rubber Spring 5.4 Viscosity of dashpot Rubber ⇄ viscous melt? Viscous flow ~ relative motion of centers of masses of molecules A. Reptation Model Molecules effectively confined in tube by entangling neighbours Constraints physical cross-linked points Reptation - Molecule can only escape lengthwise Parameters: Need two other equations: B Above critical molecular weight for