(53b) Modeling of Solution Thermodynamics: A Method for Tuning the Properties of Blend Polymeric Membranes

Thermodynamics
of polymer blends are modeled using Flory-Huggins theory for polymer solutions
and ternary phase diagrams are plotted for various blend compositions.
Equations of spinodal curve and plait point for the quaternary systems are
derived based on solution thermodynamics. For quaternary systems, the plot of
free energy against composition is not a curve but a surface plot, having a
distinct number of minimum points, which will be equal to the number of
coexisting phases in equilibrium with each other [1,2].
Locus of minimum free energy on phase diagram represents the location of
binodal curve [3].
In between two minima, the free energy curve passes through local maxima, which
represents the plait point [3].

The
spinodal curve is a locus of point of inflexion of free energy curve for
various polymer volume fractions. So, the equation representing the spinodal
curve is obtained by equating the determinant of the Hessian matrix of free
energy to zero, |H=0|,
where H is the Hessian matrix. The locus of the line joining the two minimum
points of the free energy curve gives the equation of binodal curve [3–6].
At the binodal curve, the two separating phases are in equilibrium with each
other and follow the condition of chemical equilibrium. Chemical potential for
any component can be calculated from the first derivative of free energy and
the expression for chemical potential is derived based on the above definition [7].
Binodal curves are calculated by minimizing Gibb’s free energy for blend
system, poly(acrylonitrile) (PAN) and poly(urethane) (PU).

Effects
of polymer molecular weight and interaction parameters on the phase diagram are
quantified. The published data of membrane transport characteristics are
correlated with the modeled phase diagram and validated using FESEM micrographs
and pore-diameter analysis [8].
The reason for increase in the permeability of blend membranes is established
with respect to structural changes with the possible formation of hydrogen bond
and justified by the infrared spectra analysis of the blend membranes. The
shifting of the phase diagram towards solvent axis for the blend compositions
are explained using possible formation of hydrogen bond between PAN and PU.
Formation of the hydrogen bond is supported by the shifting of –CN absorbance
peaks in FTIR of the membrane surface. Variation of spinodal curve with varying
molecular weight is studied and it is observed that increasing the molecular
weight shifts the spinodal curve towards polymer axis thereby making it denser.
However, the influence of molecular weight is effective for values of M_w 100
kDa or below. The role of various interaction parameters in locating the
spinodal curve on ternary plot is studied in details and it is observed that
even after blending, individual polymers interact separately with the solvent
and nonsolvent. The influence of polymer solvent interaction parameter on
modeled phase diagram is found to be more prominent in case of weak solvents as
compared to strong solvents. This work is very useful in predicting the
relative characteristics of polymer blend membranes and also acts as a tool in
selecting proper components for blending to prepare membranes of tailor made
properties.

Figure
1:
Thermodynamic model as a tool to predict membrane characteristics

Reference

[1]         R.M. Boom, T. van den Boomgaard, C. a.
Smolders, Mass transfer and thermodynamics during immersion precipitation for a
two-polymer system. Evaluation with the system PES-PVP-NMP-water, J. Memb. Sci.
90 (1994) 231–249. doi:10.1016/0376-7388(94)80074-X.

[2]         R.M. Boom, T. van den Boomgaard, C.A.
Smolders, Equilibrium Thermodynamics of a Quaternary\rMembrane-Forming System
with Two Polymers. 1. Calculations, Macromolecules. 27 (1994) 2034–2040.
doi:10.1021/ma00086a009.

[3]         L. Yilmaz,  a J. Mchugh, Analysis of
Nonsolvent -Solvent -Polymer Phase Diagrams and Their Relevance to Membrane
Formation Modeling, J. Appl. Polym. Sci. 31 (1986) 997–1018.
doi:10.1002/app.1986.070310404.

[4]         F.W. Altena, C.A. Smolders, Calculation
of liquid-liquid phase separation in a ternary system of a polymer in a mixture
of a solvent and a nonsolvent, Macromolecules. 15 (1982) 1491–1497.
doi:10.1021/ma00234a008.

[5]         C.C. Hsu, Prausnitz J. M.,
Thermodynamics of Polymer Compatibility in Ternary Systems, Macromolecules.
(1973) 320–324. doi:10.1021/ma60039a012.

[6]         H. Tompa, Phase relationships in
polymer solutions, Trans. Faraday Soc. 45 (1949) 1142.
doi:10.1039/tf9494501142.

[7]         Y.M. Wei, Z.L. Xu, X.T. Yang, H.L. Liu,
Mathematical calculation of binodal curves of a polymer/solvent/nonsolvent
system in the phase inversion process, Desalination. 192 (2006) 91–104.
doi:10.1016/j.desal.2005.07.035.

[8]         S.R. Panda, S. De, Preparation,
characterization and antifouling properties of polyacrylonitrile/polyurethane
blend membranes for water purification, RSC Adv. 5 (2015) 23599–23612.
doi:10.1039/C5RA00736D.