Phase Transition Dynamics in Polymer Gels

Transcription

1 Phase Transition Dynamics in Polymer Gels Akira Onuki Department of Physics, Kyoto University, Kyoto 606, Japan Phone: Faximile: We first present dynamic equations based on the basis of the two-fluid dynamics 1 in polymer gels in theta solvent in the presence of electric charges in the network and counterions. The total free energy is the sum of the Flory-Huggins free energy, the gradient free energy, the elastic energy, and the electrostatic energy 2. These dynamic equations are highly nonlinear but can then be solved numerically in the nonlinear regime. 2. Then we examine phase separation which occurs in the bulk region with a decrease of the solvent quality. In real gels opaqueness due to such processes have been observed. A unique feature is that the coarsening of the domain growth is stopped even without breakage of the crosslinkage at a characteristic size. It is of order γ/µ in neutral gels. Here γ is the surface tension between the polymer-rich and solvent-rich regions and µ is the shear modulus due to the network. In the above figure we show such frozen density patterns in neutral gels in our previous simulation 3, where the left figures correspond to the isotropically swollen case and those on the right correspond to the uniaxially stretched case.

2 3. Next we discuss response of a charged gel immersed in a solvent against applied electric field E 0 in parallel capacitor plates separated by L. We assume that the electric charges (minus sign) are attached to the network and the monovalent counterions (plus sign) are distributed in the container (gel+outer solvent) obeying the Poisson-Boltzmann distribution, n c = const.exp(-e φ el /κ Β Τ), where φ el is the electrostatic potential equal to 0 at the top plate and to LE 0 at the bottom plate. In the figure below shrinking is taking place at the lower part of the gel. In this case the network charge density is so high that the counterions are confined in the gel region. The deviation of the counterion density is almost proportional to the polymer density deviation and the charge neutrality is nearly satisfied in the whole space. In the figure of the electric potential (right) we can see that the potential is flat within the gel because the counterions screen the applied field. We can also see that the counterions gradually escape from the gel into the outer solvent region with decreasing the network charge density. As a by-product we clarify the condition under which the counterions are trapped within the gel (the so-called Donnan equilribrium assumption ). 1) Onuki A, Phase Transition Dynamics (Cambridge, 2002) 2) Onuki A, NATO series ARW NATO Nonlinear Dielectric Phenomena in Complex Liquids, Poland, ) Onuki A and Puri S, Phy. Rev. E 59 (1999) R1331

3 Phase Transition in Gels: Ginzburg-Landau Theory and Simulation Akira Onuki

4 Surface patterns of uniaxial gels attached to dish (Tanka et al) Coarsening from (a) to (g) after quench

5 Matsuo, Tanaka (1992) bubbles bamboo (uniaxial ) Various patterns appeared depending on solvent composition and stretching degree

6 Patterns of shrinking gels A.Suzuki (JCP,1999)

7 Gels show three instabilities (similar to metals-hydrogen) Network heterogeneity produces excess scattering

8 Ginzburg-Landau theory

9 GL free energy Osmotic stress tensor Flory-Huggins elastic counterion

10 Two-fluid dynamics Poisson-Boltzman

11 Spinodal decomposition (2D solutions of neutral case) Network (left) (similar patterns appear in viscoelastic case) Lamellar in uniaxial stress (right)

12 Domain size R(t) saturates, leading to pinned domains Pinned states are glassy metastable states g_e : crosslink density ~ shear modulus steady state R ~ surface tension / shear modulus

13 Phase diagram black:polymer-rich white:solvent-rich Domains are pinned. +, x: first-order curves spinodal polymer-rich solvent-rich network

14 First order curves are obtained from free energy calculations

15 Charged gel in 2D: fion=1, τ= 3, <φ>ν 0.5 =1 periodic boundary (volume fixed) polymer-rich network 0.4< φ < 3 N

16 Charged gel in 2D: fion=1, τ= 3, <φ>ν 0.5 periodic boundary (volume fixed) =2 Solvent-rich droplets

17 fion=1, τ= 3, <φ>ν 0.5 =1.5 Electric potential is higher in solvent-rich regions

18 How can we explain the patterns? third shape-dependent, order, shape-dependent 3 rd order! Elastic deformations accumulate in polymer-rich regions! In binary alloys, the same 3 rd order interaction arises with φ being the fraction of soft regions (see Onuki book)

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20 Shrinking gels after temperature change Gel-solvent surface! E.Matsuo and T.Tanaka J.Chem.Phys.89, 1695 (1988) surface skins bubbles

21 Shrunken charged gel in solvent: τ= 3, <φ>ν 0.5 fion=1 =1.5 periodic surface patterns

22 Shrunken charged gel in solvent: τ= 3, <φ>ν 0.5 =2 λ solvent no surface instability with larger <φ>

23 Shrunken charged gel in solvent: τ= 3, <φ>ν 0.5 =2 no internal spinodal decomposition with lower fion

24 Shrunken gel in solvent: τ= 3, <φ> Ν 0.5 =1 bubbles at low fion and <φ>?

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26 Phase Transition Dynamics Cambridge 2002 Akira Onuki