29.06.2013 Views

a) b - École Polytechnique de Montréal

a) b - École Polytechnique de Montréal

a) b - École Polytechnique de Montréal

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Antonoff’s rule (Equation 2-13) is valid only when phase 1 and phase 2 have a zero contact<br />

angle and two phases are in equilibrium vapor adsorption(Donahue & Bartell, 1952).<br />

γ = γ − γ<br />

Equation 2-13. 12 2 1<br />

γ ≥ γ<br />

Since polymers have negligible vapor pressure, equilibrium vapor adsorption can not occur<br />

within the experiment time. Therefore, this relation is invalid for polymers.<br />

Good and Girifalco(Girifalco & Good, 1957; Good & Girifalco, 1964) introduced an interaction<br />

parameter(φ) based on work of adhesion as follows:<br />

= 1<br />

W − + γ γ<br />

Equation 2-14 12 2<br />

a<br />

Equation 2-15 ( ) 5 . 0<br />

γ = γ + γ − φ γ<br />

γ<br />

12 2 1 2 1γ<br />

2<br />

The calculated φ values for small-molecule organic liquids give reasonable predictions of the<br />

interfacial tensions(Good & Girifalco, 1964).<br />

The harmonic mean equation(Equation 2-16) is a result of the fractional polarity theory in which<br />

various molecular forces are linearly additive(Wu, 1982). It is valid for low energy<br />

materials(Wu, 1971) and represents the combination of the polar component and the dispersion<br />

component of the work of adhesion as,<br />

γ<br />

Equation 2-16 12 2 1 d d p p<br />

1<br />

d<br />

1<br />

d<br />

2<br />

γ γ<br />

= γ + γ − 4<br />

γ + γ<br />

2<br />

1<br />

2<br />

p<br />

1<br />

1<br />

p<br />

2<br />

γ γ<br />

− 4<br />

γ + γ<br />

Interfacial tension between a low-energy material and a high-energy material is obtained by the<br />

geometric mean equation(Wu, 1971) as follows:<br />

Equation 2-17 ( ) ( ) 5 . 0<br />

d d 0.<br />

5 p p<br />

γ = γ + γ − 2 γ γ − 2 γ γ<br />

12<br />

2<br />

1<br />

Due to high molecular weight and viscosity of polymers, several interfacial tension measurement<br />

methods have been suggested. Generally, calculations of interfacial tensions in these methods are<br />

1<br />

2<br />

1<br />

2<br />

2<br />

13

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!