A Multi-Fluid Model of Membrane Formation by Phase-Inversion

Transcription

1 A Multi-Fluid Model of Membrane Formation by Phase-Inversion Douglas R. Tree 1 and Glenn Fredrickson 1,2 1 Materials Research Laboratory 2 Departments of Chemical Engineering and Materials University of California, Santa Barbara Society of Rheology Annual Meeting February 13, 2017

2 Acknowledgements Jan Garcia Dr. Kris T. Delaney Prof. Hector D. Ceniceros Lucas Francisco dos Santos Dr. Tatsuhiro Iwama (Asahi Kasei) Dr. Jeffrey Weinhold (Dow) 2

3 Can we predict the microstructure of polymers? I Microstructure dictates properties I Microstructure depends on process history Polymer Blends Polymer membranes I clean water I medical filters I commodity plastics (e.g. HIPS) I block polymer thin films Saedi et al. Can. J. Chem. Eng. (2014) Polymer composites I bulk heterojunctions I nanocomposites Hoppe and Sariciftci J. Mater. Chem. (2006) A very general problem! Biological patterning I Eurasian jay feathers Parnell et al. Sci. Rep. (2015) 3

4 Can we predict the microstructure of polymers? I Microstructure dictates properties I Microstructure depends on process history Polymer Blends Polymer membranes I clean water I medical filters I commodity plastics (e.g. HIPS) I block polymer thin films Saedi et al. Can. J. Chem. Eng. (2014) Polymer composites I bulk heterojunctions I nanocomposites Hoppe and Sariciftci J. Mater. Chem. (2006) A very general problem! Biological patterning I Eurasian jay feathers Parnell et al. Sci. Rep. (2015) 3

5 Clean water is a present and growing concern U.S. Drought Monitor July 7, 2015 Author: Brian Fuchs National Drought Mitigation Center Intensity: D0 Abnormally Dry D1 Moderate Drought D2 Severe Drought D3 Extreme Drought D4 Exceptional Drought Why membranes? Water is projected to become increasingly scarce. Filtration is a key technology for water purification. Center/Configurations/What-are-Hollow-Fiber-Membranes.aspx 4

6 Polymer membrane synthesis by immersion precipitation polymer solution nonsolvent membrane substrate solvent non-solvent bath Figure inspired by: 5

7 Polymer membrane synthesis by immersion precipitation polymer solution nonsolvent membrane substrate solvent solvent non-solvent bath H G Figure inspired by: L-L L-G polymer non-solvent 5

8 Microstructural variety in membranes Asymmetric Sponge Uniform Sponge Skin Layer Fingers or Macro-voids Strathmann et al. Desalination. (1975) 6

9 Model Development Model Characterization run NIPS quench process

10 Model Development Model Characterization run NIPS quench process

11 How can we model microstructure formation? A difficult challenge Complex thermodynamics out of equilibrium Spatially inhomogeneous (multi-phase) Multiple modes of transport (diffusion & convection) Large separation of length/time scales Continuum fluid dynamics Self-consistent field theory (SCFT) Fredrickson. J. Chem. Phys (2002) Hall et al. Phys. Rev. Lett (2006) Teran et al. Phys. Fluid. (2008) Key idea cheaper models Classical density functional theory (CDFT)/ phase field models 8

12 Multi-fluid models Two-fluid model Momentum equation for each species Large drag enforces cons. of momentum The Rayleighian A Lagrangian expression of least energy dissipation for overdamped systems (Re = 0). R[{v i }] = F [{v i }] free energy + Φ[{v i }] dissipation λg[{v i }] constraints δr δv i & φ i t = (φ iv i ) Transport equations de Gennes. J. Chem Phys. (1980) Doi and Onuki. J Phys (Paris)

13 Multi-fluid models Two-fluid model Momentum equation for each species Large drag enforces cons. of momentum The Rayleighian A Lagrangian expression of least energy dissipation for overdamped systems (Re = 0). R[{v i }] = F [{v i }] free energy + Φ[{v i }] dissipation λg[{v i }] constraints δr δv i & φ i t = (φ iv i ) Transport equations de Gennes. J. Chem Phys. (1980) Doi and Onuki. J Phys (Paris)

14 A ternary solution model F [{v i }] Φ[{v i }] λg[{v i }] free energy dissipation constraints Transport Equations Diffusion & Momentum Coupled, Non-lin. PDEs Solve numerically Pseudo-spectral on GPUs Semi-implicit stabilization Ternary polymer solution (Flory Huggins de Gennes) [ ] F = dr f({φ i }) + 1 κ i φ i 2 2 Φ = 1 2 Newtonian fluid with φ-dependent viscosity [ dr ζ i (v i v) 2 i +2η({φ i })D : D Incompressibility λg = p v i ] 10

15 Transport equations φ i t + v φ i = j µ i = δf [{φ i}] δφ i Model H Model B M ij ({φ}) µ j Convection-Diffusion Chemical Potential 0 = p + [η({φ})( v + v T ) ] N 1 φ i µ i i=0 Momentum 0 = v Incompressibility 11

16 Model Development Model Characterization run NIPS quench process 12

17 Characterization of model thermodynamics (a) N = 50 κ = 12 χ = (b) φp 0.4 φn x/r (c) 1.0 (d) x/r φ s φs x/r φ p φ n 13

18 Calculated interface width for many parameters 10 2 l = 1 2 ( ) κ 1/2 χ χ = (χ χ c )/χ c l/l N = 1 N = 20 N = 2 N = 50 N = 5 N = N = 10 N = χ 14

19 What explains the interface width data? 10 2 l/l We are near the critical point, χ c We recover the mean-field critical exponent, ( ) χ 1/2 χc l = l χ c N = 1 N = 20 N = 2 N = 50 N = 5 N = N = 10 N = χ 15

20 Characterization of phase separation dynamics 16

21 There are two dynamic regimes 10 2 domain size simulation time 17

22 Early-time regime initiation of spinodal decomposition λ λ+ 10 λ k Linear stability analysis Exponential growth of the fastest growing mode, δψ = exp[λ + (q)t] - 20 Two key parameters q m fastest growing mode λ m rate of spinodal decomposition φ s q m φ p φ n

23 Long-time regime coarsening surface diffusion bulk diffusion hydrodynamics domain size slope=1/4 domain size slope=1/3 domain size slope=1 time time time 19

24 Comparing simulations to the LSA 10 2 domain size, 2π/ q 10 1 φ s φ p simulation time, t φ n 20

25 Comparing simulations to the LSA 10 1 scaled domain size, qm/ q scaled simulation time, λ m t 20

26 Model Development Model Characterization run NIPS quench process 21

27 How does a quench happen by mass transfer? Qualitative features of NIPS (mass-transfer) v. TIPS (temp.) 1. Inherent anisotropy and inhomogeneities 2. Driving force (solvent exchange) and phase separation inseparably linked by mass transfer film bath Important questions 1. What is the effect of the initial bath/film concentration? 2. What role does film thickness play? 3. How does mass transfer path affect microstructure? 22

28 Anisotropic quench The bath interface gives rise to: Surface-directed spinodal decomposition Surface hydrodynamic instabilities Ball and Essery. J. Phys.-Condens. Mat. 2, (1990) 23

29 Early-time behavior the infinite film limit Key concept time scales Phase separation is faster than solvent exchange At short times we can neglect the role of film thickness. Pego. P. Roy. Soc. A-Math. Phy. 422, 261 (1989) Simple diffusion from a initial step 24

30 Early-time behavior the infinite film limit Key concept time scales Phase separation is faster than solvent exchange At short times we can neglect the role of film thickness. Pego. P. Roy. Soc. A-Math. Phy. 422, 261 (1989) Three possible cases 1. No phase separation, just diffusion (steady) Simple diffusion from a initial step 24

31 Early-time behavior the infinite film limit Key concept time scales Phase separation is faster than solvent exchange At short times we can neglect the role of film thickness. Pego. P. Roy. Soc. A-Math. Phy. 422, 261 (1989) Three possible cases 1. No phase separation, just diffusion (steady) 2. Phase separation, single domain film (steady) Simple diffusion from a initial step 24

32 Early-time behavior the infinite film limit Key concept time scales Phase separation is faster than solvent exchange At short times we can neglect the role of film thickness. Pego. P. Roy. Soc. A-Math. Phy. 422, 261 (1989) Simple diffusion from a initial step Three possible cases 1. No phase separation, just diffusion (steady) 2. Phase separation, single domain film (steady) 3. Phase separation, multiple domain film (unsteady) 24

33 Immediate spinodal decomposition into multi-domain films 25

34 A finite-sized film can exhibit delayed phase-separation φ s polymer film nonsolvent bath φ p φ n Depending on parameters and initial conditions, a delayed phase separation produces either single domain films (shown) multiple domain films 26

35 Finite-film data collapse with a similarity variable φ s f = f = φn φ p ξ φ n 27

36 Conclusions (1D) 1. Inherent anisotropy? SDSD-like wave 2. Film thickness? Short v. long-time Scales with xt 1/2 3. Initial conditions? No PS, single/multiple domains Instantaneous v. delayed PS Future: microstructure (2D) Pore gradients φ s φ p φ n Macrovoids q m Saedi et al. Can. J. Chem. Eng. (2014) Sternling and Scriven. AICHE J. (1959) 28