Grozdana Bogdanić

Institute of Chemical Process Fundamentals ASCR, Prague

Group Contribution Methods for Predicting Properties of Systems Containing Polymers

POLY − MER

many units

−M−M−M−M−M−M−M−M−M−M−

or

−(M)n−

Modeling

description of thermophysical properties (vapor pressures, viscosities, caloric data, etc.) of pure components and mixtures

properties of different apparatuses like reactors, distillation columns, pumps, etc.

chemical reactions and kinetics

environmental and safety-related data

Two main different types of models can be distinguished:

Rather simple equations and correlations where parameters are fitted to experimental data

Predictive methods where properties are estimated

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

 G. Bogdanić:

Additive Group Contribution Methods for Predicting the Properties of Polymer systems

In: Polymeric Materials, Chapter 7

Transworld Reserach Signpost, Trivandrum, India (2009).

G. Bogdanić, I. Wichterle, A. Erceg Kuzmić:

Collection of Miscibility Data and Phase Behavior of Binary Polymer Blends based on Styrene, 2,6-Dimethyl-1,4-Phenylene Oxide and of Their Derivatives

Transworld Research Signpost, Trivandrum, India (2010).

jjj

ii

jj

ii Mx

Mxm

mw

iiiii w = x = a

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

Calculation of Free Volumes

Component T[°C]

d[g cm-3]

V[cm3 mol-1]

V*

[cm3 mol-1]

Vf

[cm3 mol-1]

Benzene 25 0.8735 89.3 91.9 27.4

Acetone 25 0.7846 73.9 50.0 23.9

Toluene 25 0.8616 106.9 76.2 30.6

Cyclohexane 25 0.7749 108.4 78.6 29.8

Dioxane 20 1.0337 85.1 61.9 23.3

Poly(isobutylene) 25 0.9169 61.1 52.4 8.7

Poly(ethylene oxide) 25 1.126 39.1 30.9 8.2

Poly(vinyl acetate) 25 1.19 60.7 58.7 2.0

Polystyrene 25 1.05 99.0 80.4 18.6

Poly(vinyl alcohol) 25 1.27 34.6 32.1 2.5

Poly(vinyl pyrrolidone) 25 1.215 34.6 32.1 2.5

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.

i

attr

i

attr lnln (UNIFAC)

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)

[G. Bogdanić, Aa. Fredenslund, 1995]

UNIFAC-FV Entropic-FV

GC-Flory GC-LF (1990)

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

22

12

2

1

LLE

Polymer solutions Polymer blends

GM/RT versus molar fraction (GM/RT – se) versus molar fraction of the polymer of the polymer

PVAL–water binary mixture at 420 K x 1

04

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/n-octane by the UNIQUAC-FV model [G. Bogdanić, J. Vidal, 2000]

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 [G. Bogdanić, J. Vidal, 2000]

poly(S0.54-co-BMA0.46), Mw = 40000 g/mol, correlation poly(S0.80-co-BMA0.20), Mw = 250000 g/mol, - - - - prediction

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 correlatedby the GC-Flory EOS ( ) [G. Bogdanić, 2002]

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]

T = 473 K

Miscibility behavior of PPO/poly(oFS-co-pClS) system ( ------ ) correlated by the UNIQUAC-FV model [G. Bogdanić, 2006]

Miscibility of SPPO/poly(oBrS-co-pBrS) system ( ) correlated by the UNIQUAC-FV model [G. Bogdanić, 2006]

T = 473 K

Thermodynamic Databases for Polymer Systems

H. Wen, H.S. Elbro, P. Alessi, Polymer Solution Data Collection, Dechema Chemistry Series, Frankfurt, 1992.

M.S. High, R.P. Danner, Polymer Solution Handbook; DIPPR 881 Project. Design Institute for Physical Property Data, 1992.

C. Wohlfarth, Vapor-Liquid Equilibrium Data of Binary Polymer Solutions, Elsevier, Amsterdam, 1994.

P.Zoller, D.J. Walsh, Standard Pressure-Volume- Temperature Data for Polymers, Technomics Publishing Co., Lancaster, 1995.

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)