TY - JOUR
T1 - Formation of polyethersulfone membranes via nonsolvent induced phase separation process from dissipative particle dynamics simulations
AU - Tang, Yuan hui
AU - Ledieu, Eric
AU - Cervellere, M. Rosario
AU - Millett, Paul C.
AU - Ford, David M.
AU - Qian, Xianghong
N1 - Funding Information:
Funding for this work was provided by the National Science Foundation Industry/University Cooperative Research Center for Membrane Science, Engineering and Technology (MAST) (NSF IIP 1361809 and IIP 1822101 ) and industrial sponsors. Helpful discussions with Drs. Lucas McIntosh and Derek Dehn from 3 M and Christina Carbrello from MilliporeSigma are gratefully acknowledged. This research is also supported by University of Arkansas and the Arkansas High Performance Computing Center (AHPCC). Appendix Based on Flory-Huggins theory, the Gibbs free energy of mixing, Δ G m for the PES system is given by the following formula: (16) Δ G m R T = n c ln φ c + n s ln φ s + n p ln φ p + χ c s n c φ s + χ c p n c φ p + χ s p n s φ p where n i and φ i are the number of moles and volume fraction of component i respectively. R is the gas constant and T is the absolute temperature. χ i j is a binary interaction parameter between components i and j . Herein it is assumed that all the binary interactions are significant and constant. When component i is distributed between two phases at equilibrium, the thermodynamic chemical potential of the component should satisfy the following equation: (17) Δ μ i R R T = Δ μ i L R T , i = c , s , p where Δμ i is the difference between the chemical potential of component i in the mixture and the pure state. The superscripts R and L refer to the polymer-rich and polymer-lean phases respectively. By definition, the chemical potential of component i is the derivative of the Gibbs free energy of mixing with respect to the number of moles of each component [ 1 ]: (18) Δ μ i R T = ∂ ∂ n i ( Δ G m R T ) According to equations (16) and (18 ), the chemical potential of each component in the mixture can be derived as follows: (19) Δ μ c R T = ln φ c + 1 − φ c − V c V s φ s − V c V p φ p + ( χ c s φ s + χ c p φ p ) ( φ s + φ p ) − V c V s χ s p φ s φ p (20) Δ μ s R T = ln φ s + 1 − φ s − V s V c φ c − V s V p φ p + ( V s V c χ c s φ c + χ s p φ p ) ( φ c + φ p ) − V s V c χ c p φ c φ p (21) Δ μ p R T = ln φ p + 1 − φ p − V p V c φ c − V p V s φ s + ( V p V c χ c p φ c + V p V s χ s p φ s ) ( φ c + φ s ) − χ c s V p V c φ c φ s where V i is the molar volume of component i . As a phase separation occurs, the polymer solution should demix into a polymer-rich and a polymer-lean phase, which are in thermodynamic equilibrium. To specify the phase diagram, six unknown compositions need to be determined. Firstly, the polymer composition of the polymer-lean phase, φ p L , was chosen as a free variable. In addition to the three relations given by substituting Eqs. (19)–(21) into Eq. (18) , two remaining relations are the material balance relations in the polymer-rich (R) and polymer-lean (L) phases: (22) ∑ i = c , s , p φ i R = ∑ i = c , s , p φ i L = 1 As a result, the five equations were solved to depict the binodal curve of the phase diagram. In addition, the boundary dividing the unstable and metastable regions is the so-called spinodal curve, which is thermodynamically defined as: (23) G 22 G 33 = G 23 2 , G i j = ( ∂ 2 Δ G m ‾ / ∂ φ i ∂ φ j ) v r e f Δ G m ‾ is the Gibbs free energy of mixing on a unit volume basis and v r e f is the molar volume of a reference component that is water here. Therefore, the following expressions can be derived: (24) G 22 = V c V s φ s + 1 φ c − 2 χ c s (25) G 23 = 1 φ c − g c s − χ c p + V c χ s p V s (26) G 33 = V c V p φ p + 1 φ c − 2 χ c p Thus, by choosing φ p R as a free variable, substituting Eqs. (24)–(26) to Eq. (23) , along with Eq. (22) , three variables can be solved numerically to depict the spinodal curve.
Funding Information:
Funding for this work was provided by the National Science Foundation Industry/University Cooperative Research Center for Membrane Science, Engineering and Technology (MAST) (NSF IIP 1361809 and IIP 1822101) and industrial sponsors. Helpful discussions with Drs. Lucas McIntosh and Derek Dehn from 3 M and Christina Carbrello from MilliporeSigma are gratefully acknowledged. This research is also supported by University of Arkansas and the Arkansas High Performance Computing Center (AHPCC).
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - Dissipative particle dynamics (DPD), a coarse-grained simulation method, was used to investigate the formation of polyethersulfone (PES) membranes via the nonsolvent induced phase separation (NIPS) process with N-methyl-2-pyrrolidone (NMP) as the solvent and water as the nonsolvent coagulant. The effects of PES polymer concentration (8–16% (v/v)) and molecular weight (chain length with degree of polymerization of 60, 90, 135) on the membrane structure and morphology were investigated. The formation of asymmetric nanostructures with polymer-lean (liquid-rich) and polymer-rich domains was observed. A thin but dense polymer top layer at the liquid-polymer interface, with a more porous sub-layer, evolved over time. The effect of polymer concentration on membrane structure is more significant than that of the molecular weight of the PES polymer. As the polymer concentration increases from 8 to 16% (v/v), the surface layer becomes significantly denser, which is in agreement with experimental observations. Furthermore, high molecular weight PES leads to a slightly more porous membrane structure.
AB - Dissipative particle dynamics (DPD), a coarse-grained simulation method, was used to investigate the formation of polyethersulfone (PES) membranes via the nonsolvent induced phase separation (NIPS) process with N-methyl-2-pyrrolidone (NMP) as the solvent and water as the nonsolvent coagulant. The effects of PES polymer concentration (8–16% (v/v)) and molecular weight (chain length with degree of polymerization of 60, 90, 135) on the membrane structure and morphology were investigated. The formation of asymmetric nanostructures with polymer-lean (liquid-rich) and polymer-rich domains was observed. A thin but dense polymer top layer at the liquid-polymer interface, with a more porous sub-layer, evolved over time. The effect of polymer concentration on membrane structure is more significant than that of the molecular weight of the PES polymer. As the polymer concentration increases from 8 to 16% (v/v), the surface layer becomes significantly denser, which is in agreement with experimental observations. Furthermore, high molecular weight PES leads to a slightly more porous membrane structure.
KW - Dissipative particle dynamics
KW - Membrane formation
KW - Nonsolvent induced phase separation
KW - Polyethersulfone
UR - http://www.scopus.com/inward/record.url?scp=85078033312&partnerID=8YFLogxK
U2 - 10.1016/j.memsci.2020.117826
DO - 10.1016/j.memsci.2020.117826
M3 - Article
AN - SCOPUS:85078033312
SN - 0376-7388
VL - 599
JO - Journal of Membrane Science
JF - Journal of Membrane Science
M1 - 117826
ER -