Grozdana Bogdanić

INA-Industrija nafte, d.d., Technology Development and Project ManagementDepartment, Zagreb, Croatia

Additive Group Contribution Methods for Predicting Properties of Polymer Systems

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

jjj

ii

jj

ii Mx

Mxm

mw

iiiii w = x = a

Group Contribution Methods for Predicting Properties of Polymer – Solvent Mixtures (VLE)

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.

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

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.

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

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 +

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.

Prediction of infinite dilution activity coefficients versus experimental values for systems containing nonpolar solvents (215-246 systems)

B.C. Lee, R.P. Danner, 1997.

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.

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.

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.

0G

P,T

21

2

0GG32

3

22

2

0lnln

2

12

2

1

LLE

Polymer solutions Polymer blends

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

)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

Correlation ( ) of LLE PEG/water system by the UNIQUAC–FV model

J. Vidal, G. Bogdanić, 1998.

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.

The GC-Flory EOS

LLE parameters

G. Bogdanić, Aa. Fredenslund, 1994. G. Bogdanić, 2002.

εnn , Δεnm

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.

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:

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.

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.

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)

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)