Download - Grozdana Bogdanić INA-Industrija nafte, d.d., Technology Development and Project Management
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Grozdana Bogdanić
INA-Industrija nafte, d.d., Technology Development and Project ManagementDepartment, Zagreb, Croatia
Additive Group Contribution Methods for Predicting Properties of Polymer Systems
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1. VLE
1.1. Group contribution methods for predicting the properties of polymer–solvent mixtures
Activity coefficient models
Equations of state
2. LLE
2.1. Group contribution methods for predicting the properties of polymer–solvent mixtures
Activity coefficient models
Equations of state
2. 2. Group contribution methods for predicting the properties of polymer–polymer mixtures (polymer blends)
3. Conclusions
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jjj
ii
jj
ii Mx
Mxm
mw
iiiii w = x = a
Group Contribution Methods for Predicting Properties of Polymer – Solvent Mixtures (VLE)
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The UNIFAC-FV model
i
FV
i
resid
i
comb
i ln + ln + ln = ln
combinatorial residual free-volume
1
v~i1/31
-11-v~M
v~iCi - 1-v~M
1/31-v~i
1/3lnCi3 = i
FVln
T. Oishi, J.M. Prausnitz, 1978.
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The Entropic-FV model
i
attr
i
entr
i ln + ln = ln
x - 1 +
x ln = ln
i
i
FV
i
i
FV
i
entr
The free-volume definition:
v - v = v *iiif, v = v iw,
*i
H.S. Elbro, Aa. Fredenslund, P. Rasmussen, 1990.G.M. Kontogeorgis, Aa. Fredenslund, D.P. Tassios, 1993.
)UNIFAC( ln i
attr
i
attr
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The GC-Flory EOS
combinatorial FV attractive
VE+
1-v~C+v~
V
RTn = P
attr
1/3
1/3
i
attr
i
FV
i
comb
i ln + ln + ln = ln
F. Chen, Aa. Fredenslund, P. Rasmussen, 1990.G. Bogdanić, Aa. Fredenslund, 1994.
N. Muro-Suñé, R. Gani, G. Bell, I. Shirley, 2005.
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x - 1 +
x ln = ln
i
i
i
ii
comb
j
jijiiiiiiattri )RT/(exp ln - 1 + )]v~(-)v~([
RT
1 qz1/2 = ln
k
kik
jij
j /RT)(-exp
/RT)(-exp -
v~v~ ln C -
1 - v~1 - v~ln )C + 3(1 = ln i
i1/3
1/3i
iFVi
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The GC-lattice-fluid EOS
T~ -
v~1-q/r+v~
ln2
z +
1-v~v~
ln = T~P~ 2
T~ -
T~
2q +
v~1)-v~(
1)-v~(
v~ln q +
v~v~ ln + wln - ln= ln
i
pi,i
i
ii
iiii ii
i ln2
qz +
M.S. High, R.P. Danner, 1989; 1990.
B.C. Lee, R.P. Danner, 1996.
T~ -
T~
2q +
v~1)-v~(
1)-v~(
v~ln q +
v~v~ ln + wln - ln= ln
i
pi,i
i
ii
iiii ii
i ln2
qz +
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Prediction of infinite dilution activity coefficients versus experimental values for polymer solutions (more than 120 systems)
UNIFAC-FV Entropic-FV
GC-Flory GC-LF (1990)
G. Bogdanić, Aa. Fredenslund, 1995.
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Prediction of infinite dilution activity coefficients versus experimental values for systems containing nonpolar solvents (215-246 systems)
B.C. Lee, R.P. Danner, 1997.
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Predictions of infinite dilution activity coefficients versus experimental values for systems containing weakly polar solvents (cca 60 systems)
B.C. Lee, R.P. Danner, 1997.
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Predictions of infinite dilution activity coefficients versus experimental values for systems containing strongly polar solvents (cca 30 systems)
B.C. Lee, R.P. Danner, 1997.
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Activity of ethyl benzene in PBD (Mn = 250000)
T = 373 K
Activity of MEK in PS (Mn = 103000)
T = 322 K
Activity of 2-methyl heptane in PVC (Mn = 30000; Mn = 105000)
T = 383 K
G. Bogdanić, Aa. Fredenslund, 1995.
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0G
P,T
21
2
0GG32
3
22
2
0lnln
2
12
2
1
LLE
Polymer solutions Polymer blends
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The segmental interaction UNIQUAC-FV model(s)
G. Bogdanić, J. Vidal, 2000.G.D. Pappa, E.C. Voutsas, D.P. Tassios, 2001.
i
resid
i
entr
i ln + ln = ln
x - 1 +
x ln = ln
i
i
FV
i
i
FV
i
entr
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)i(kk
k
)i(k
residi lnlnln
nseg
mnseg
nnmn
kmmnseg
mmkmkk ln1Qln
ncomp
j
nseg
m
)j(mj
ncomp
i
)i(ki
k
x
xX
02,mn1,mnmn TTaaa
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Correlation ( ) of LLE PEG/water system by the UNIQUAC–FV model
J. Vidal, G. Bogdanić, 1998.
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Correlation and prediction of LLE for PBD/1-octane by the UNIQUAC-FV model
Mv=65000 g/mol, correlation Mv=135000 g/mol, prediction Mw=44500 g/mol, - - - - prediction
Correlation and prediction of LLE for poly(S-co-BMA)/MEK by the UNIQUAC-FV model
poly(S0.54-co-BMA0.46), Mw=40000 g/mol, correlation
poly(S0.80-co-BMA0.20), Mw=250000 g/mol, - - - - prediction
G. Bogdanić, J. Vidal, 2000.
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The GC-Flory EOS
LLE parameters
G. Bogdanić, Aa. Fredenslund, 1994. G. Bogdanić, 2002.
εnn , Δεnm
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0.00 0.02 0.04 0.06 0.08 0.10390
400
410
420
Mn=60400, Mw=82600
Mn=97700, Mw=135900
Mw=180000
T/K
Mass fraction of polymer
Coexistence curves for HDPE/n-hexane systems as correlated by the GC-Flory EOS ( )
0.00 0.05 0.10 0.15 0.20 0.25250
275
300
325
350
375
400
Mv=98000
Mv=191000
Mv=380000
T/K
Mass fraction of polymer
Coexistence curves for PIB/n-hexane systems as correlated
by the GC-Flory EOS ( )
G. Bogdanić, 2002.
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The mean-field theory
21blend22
21
1
1M
+ ln N
+ ln N
= TR
G
BDBCADACblend yx + ) y - 1 (x + y )x - 1 ( + ) y - 1 ( )x - 1 ( =
CDAB ) y - 1 ( y - )x - 1 (x -
combinatorial residual
R.P. Kambour, J.T. Bendler, R.C. Bopp, 1983.G. ten Brinke, F.E. Karasz, W.J. MacKnight, 1983.
(A1-xBx)N1/(C1-yDy)N2:
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Miscibility of poly(S-co-oClS)/SPPO Miscibility of poly(S-co-pClS)/SPPO () one phase; () two phases; ( ) predicted miscibility/immiscibility boundary by the mean-field model
G. Bogdanić, R. Vuković, et. al., 1997.
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Miscibility behavior PPO/poly(oFS-co-pClS) Miscibility of SPPO/poly(oBrS-co-pBrS) system system
( ------ ) correlated by the UNIQUAC-FV model ( ) correlated by the UNIQUAC-FV model
G. Bogdanić, 2006.
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Why so many different models have been developed for polymer systems?
The choice of a suitable model depends on:
the actual problem and on the type of mixture type of phase equilibrium (VLE, LLE, SLE) conditions (temperature, pressure, concentration) type of calculation (accuracy, speed, yes/no
answer, or complete design)
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Many databases and reliable GC-methods are available for estimating:
pure polymer properties phase equilibrium of polymer solutions
VLE: GC - models based on UNIFAC + FV GC - EOS
LLE simple FV expression + local composition
energetic term (UNIQUAC)