1 1 Chapter 2. Thermophysical Properties of Polymers Thermophysical properties include: 1. Volumetric properties 2. Calorimetric properties 3. Transition temperatures 4. Cohesive properties and solubility 5. Interfacial energy properties 6. Transport properties (diffusion et al.) 2 2 3 4 3 5 6 • Physical aging of glassing polymers 4 7 I. Volumetric properties 1. Specific volume (=volume per unit weight) 2. Molar volume 8 5 9 10 • Enthalpy relaxation 6 11 )/()( ∞∞ −−= υυυυδ iLet τδδ // −=dtd So, [ ]τδ /)(exp itt −−= 12 7 13 PT ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ = υ υ α 1 14 8 15 16 II. Calorimetric properties 1. Heat capacity 9 17 18 10 19 20 11 21 22 m m m T HS ∆=∆ , ∑ ∆=∆ iim snS 12 23 24 13 25 26 III. Transition Temperature 14 27 28 15 29 M IYY M Y T i xiggi g g ∑ + == )( where Ix is 5.0 22 2 = + =I 30 16 31 32 M ODDYIYY M YT i mxmmi m m ∑ ∑ ∑++ == )()( 17 33 34 18 35 IV. Cohesive properties and solubility 36 Cohesive energy density of polymers can be determined by swelling or dissociation experiments. 19 37 38 20 39 • The solubility parameter 40 21 41 42 V. Interfacial energy properties 22 43 44 where κ is the compressibility 1. 2. 23 45 46 • Interfacial tension between a solid and a liquid Young’s equation svsllv γγθγ =+cos 24 47 48 • How to estimate the surface tension of solid polymers 1. Measure the contact angle with the liquid with known surface tension. 2. , where γ expressed in mJ/m2 and ecoh in mJ/m3. 3. Using group contribution to Parachor for estimation 3/275.0 cohe≈γ 25 49 50 26 51 52 27 53 54 28 55 56 29 57 VI. Transport properties (Diffusion) 58 J J+ㅿJΔx the flux x cDJ ∂ ∂ −= t c x JJJ x ∂ ∂ = ∆ ∆−− →∆ 0 lim So, x cD xt c ∂ ∂ ∂ ∂ = ∂ ∂ If D is independent of c and x, 2 2 x cD t c ∂ ∂ = ∂ ∂ R=nl 6 2 2 nlS = lu oφ=If , 6 2lD oφ= where Φo is the jump frequency From the Fick’s first law (Fick’s second law) 30 59 B.C. C=Ci for 0 31 61 • For the specimens with an infinitive thickness 2 2 x cD t c ∂ ∂ = ∂ ∂ B. C. C=Ci for 0 32 63 DT DLFor the unidirectional composites, ffmfL DVDVD +−= )1( 0 ( ) ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − − −+−= − π π π ππ /1 )/(1 tan /1 4/21 2 1 2 fD fD fDD m mfT VB VB VBB DDVD where ⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= 12 f m D D DB . When Df 0, ( ) mfT DVD π/21−≅ Since yxT DDD == , zL DD = 2 /21 1 1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − ++= πf f T V V n h l hDD From the slope of experimental data, we can obtain D, DT,, Dm.and DL.
