Control of Drug Release from Coatings: Theories and Methodologies - Biological and Biomedical Coatings - page 229

For neutral species [60, 62,63],

2 Av d

b

γ LR

n 1 2 / 1 2 / − 1 1 2 /

ln = 1 + bI − ( 1 + bI ) − 2 ln( 1 + bI )

3

(5.119)

2
1000

AM
b

w 1 2 / 1 2 / − 1 1 2 /

= 1 + bI − ( 1 + bI ) − 2 ln( 1 + bI

3

where v is the molar volume and d is the density of the mixture.
The activity coefficient calculated from the above equation is in the unit of molarity
(mole/kilogram solvent), to convert it to mole fraction used in consistent to previous
equations:

vM m

ln = ln − ln 1 +

W

(5.120)

γ γ

mole-fraction molarity

1000

Free-Volume Contribution
In polymer solution, free-volume effects are not negligible; therefore, an extra term is
introduced [64]

R C FV

ln = ln + ln + ln (5.121) γ γ γ γ

i i i i

The combinatorial part of UNIFAC model is sometimes given in another form [65]:

z q

φ φ

ln

C

ln

i

ln

i

γ

= − 1

φ

+

φ

− 1 − +

i i i i

2 F F

i i

(5.122)

r
r x

q
r x

=

i

, F =

i

φ

∑ ∑

i i

j j j j

j

q i and r i are calculated as in UNIFAC model.
Residual part is given as the same as UNIFAC, and the free-volume contribution is

− 1

− 1 3 /

v
v

−
−

1
1

v
v

1

γ i FV ln = 3 c ln

i

− c

i

− 1 1 −

i i

− 1 3 / − 1 3 /

v

m m i

(5.123)

v v

v =

i

=

i

i

15 17 . br

*

v

i

i

where v i is the molar volume, v i * is the hard core molar volume, b is the proportionality
constant, and c is also a constant depending on the type of molecules involved in the
system.