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Chapter 2. Thermophysical Properties of oecomposites/notes/527 U3040/ch2.pdf · PDF file Chapter 2. Thermophysical Properties of Polymers Thermophysical properties include: 1. Volumetric

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Text of Chapter 2. Thermophysical Properties of oecomposites/notes/527 U3040/ch2.pdf · PDF file...

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    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.)

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    • Physical aging of glassing polymers

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    I. Volumetric properties

    1. Specific volume (=volume per unit weight) 2. Molar volume

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    • Enthalpy relaxation

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    )/()( ∞∞ −−= υυυυδ iLet

    τδδ // −=dtd So, [ ]τδ /)(exp itt −−=

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    PT ⎟ ⎠ ⎞

    ⎜ ⎝ ⎛ ∂ ∂

    = υ

    υ α 1

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    II. Calorimetric properties

    1. Heat capacity

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    m

    m m T

    HS ∆=∆ , ∑ ∆=∆ iim snS

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    III. Transition Temperature

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    M

    IYY

    M Y

    T i xiggi

    g g

    ∑ + ==

    )(

    where Ix is

    5.0 22

    2 =

    + =I

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    M

    ODDYIYY

    M YT i

    mxmmi m

    m

    ∑ ∑ ∑++ ==

    )()(

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    IV. Cohesive properties and solubility

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    Cohesive energy density of polymers can be determined by swelling or dissociation experiments.

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    • The solubility parameter

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    V. Interfacial energy properties

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    where κ is the compressibility

    1.

    2.

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    • Interfacial tension between a solid and a liquid

    Young’s equation svsllv γγθγ =+cos

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    • 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

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    VI. Transport properties (Diffusion)

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    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)

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    B.C. C=Ci for 0

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    • For the specimens with an infinitive thickness

    2

    2

    x cD

    t c

    ∂ ∂

    = ∂ ∂ B. C. C=Ci for 0

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    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.

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