Handbook of Solvents - George Wypych - ChemTech - Ventech!

204 Christian Wohlfarth
( wq M) ( w q M )
θi = i i / i / k k / k
and the l i-parameter is given by
( )( ) ( )
Σ [4.4.85b]
l = z /2 r −q − r −1
[4.4.85c]
i i i i
where:
i,j components in the solution
z lattice coordination number (usually = 10)
qi surface area of component i based on Bondi’s van-der-Waals surfaces
Mi molar mass of component i (for polymers the number average is recommended)
wi mass fraction of component i
ri segment number of component i based on Bondi’s van-der-Waals volumes
The molecules must be divided into groups as defined by the UNIFAC method. The
segment surface areas and the segment volumes are calculated from Bondi’s tables 264 according
to
ri () i
= ∑νκ Rk and q i
() i =∑ν
Q k k
[4.4.86]
k
k
where:
k number of groups of type k in the solution
νk number of groups of type k in the molecule i
Rk Van-der-Waals group volume parameter for group k
Qk Van-der-Waals group surface parameter for group k
The residual activity coefficient contribution for each component is given by
i [ k k ]
res
() i
()
lnΩi = ∑ν lnΓ −lnΓ
[4.4.87]
k
k
where:
Γk the residual activity coefficient of group k in the defined solution
(i)
Γk the residual activity coefficient of group k in a reference solution containing pure
component i only
The residual activity coefficient of group k in the given solution is defined by
where:
⎡
⎢
⎢ ⎛ ⎧ a
lnΓk = Qk
−ln⎜ ⎢
1 ⎜∑
Λm
exp⎨−
⎝ m ⎩ T
⎢
⎣⎢
mk
⎫⎞
⎬ ⎟
⎭⎠
−
⎛
⎜
⎜
⎜
⎜
⎜
⎝
Λ
m
∑
m
∑ Λp
p
⎧ akm
⎫ ⎞⎤
exp⎨−
⎬
⎟⎥
⎩ T ⎭ ⎟⎥
⎟
⎧ ⎫ ⎥
[4.4.88]
apm
exp⎨−
⎟
⎬ ⎥
⎟
⎩ T ⎭ ⎠⎦⎥
amn and anm group interaction parameter pair between groups m and n
Λm group surface area fraction for group m
The group surface area fraction Λm for group m in the solution is given by
Λm =
QmX m
QX
∑
p
p p
[4.4.89a]