Supratelechelics: thermoreversible bonding in difunctional polymer blends

Transcription

1 Supratelechelics: thermoreversible bonding in difunctional polymer blends Richard Elliott Won Bo Lee Glenn Fredrickson Complex Fluids Design Consortium Annual Meeting MRL, UCSB 02/02/09

2 Supramolecular Assembly 1. Some background: the supramolecular diblock. 2. The supramolecular triblock, abridged. 3. Linear supramolecular assembly: homogeneous and heterogeneous telechelics. 4. Mixed bonding telechelics. 5. Extensions: the 3-junction and networks.

3 Some background: the supramolecular diblock Notes and assumptions: A B h Individual, bonding polymers are equivalent, but chemically distinct. h = the affinity the gain in free energy associated with bonding, h~1/kt. N = polymerization of a polymeric segment. AB xn = the distaste blue has for red segments, xn~1/kt. The Grand-Canonical Hamiltonian for the melt: The mass-action law: All three single-chain partition functions evaluated in the standard way:

4 Some background: the supramolecular diblock Model parameters for the isopleth (za=zb=1): 1/xN is a temperature h h/xn is a temperature independent bond strength. N must be independently specified. Mean-field phase behavior with changing bond affinity on the isopleth W. B. Lee et al. Macromolecules, , 2007

5 The supramolecular diblock, phase behavior with changing bond affinity on the isopleth Increasing N, the segment polymerization Concentration of linkers goes as 1/N: -Homogeneous phase is preserved for larger N.

6 The supramolecular triblock. A B Parameters of interest: f = the fraction of species blue to the total. h = the affinity the gain in free energy associated with bonding, h~1/kt. AB ABA N = length of the triblock polymer. xn = the distaste blue has for red segments, xn~1/kt. z or phi, an activity or composition. T (1/xN) z or phi h/xn

7 The supramolecular triblock, mean-field phase behavior with changing bond affinity Asymmetric A, B, AB Symmetric ABA Isopleth plane: equal concentrations of A and B links. NABA=300 W.B. Lee et al. Macromolecules, 40, 8445 (2007)

8 The supramolecular triblock, mean-field phase behavior with concentration and fixed bond affinity 2NA=NB h/xn= Asymmetric A, B, AB Symmetric ABA W.B. Lee et al. Macromolecules, 40, 8445 (2007)

9 New interest: the 'infinite chain'. Bond. In this case, heterogeneous bonding only. Loops are disregarded.

10 New interest: the 'infinite chain'. k=1 The Hamiltonian: k=2 k=3 All activities may be 'bootstrapped': Trouble: how to evaluate an infinite set of partition functions, Qk? The k-link, single chain propagator.

11 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k=1 The Hamiltonian: k=2 k=3 The entropic contributions: A composite, multiple end-segment distribution. With, G s=0 s=n

12 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k=1 The Hamiltonian: k=2 k=3 With, Generally, The entropic contributions: A composite, multiple end-segment distribution. k links +1

13 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k links Summing over the addition of all k possible links, and, with, The Born Scattering Equation. No approximations have been made, this is exact. k=1 k=2 k=3 Solving the Born Scattering equation immediately yields the entropic contribution, +1

14 The infinite homogeneous bonding chain. k=1 The bonding affinities are haa and hbb. haa haa k=2 k=3 haa k=4 Phase diagram on the symmetry axis, with h=haa=hbb? 1/xN 1/2 hbb hbb? k=1 h/xn k=2 k=3 hbb k=4

15 The infinite homogeneous bonding chain. k=1 The bonding affinities are haa and hbb. haa haa k=2 k=3 haa hbb hbb Phase diagram on the symmetry axis, with haa=hbb. k=4 DIS k=1 k=2 2 phase k=3 hbb k=4 NA=NB=300

16 The infinite homogeneous bonding chain. DIS Average characteristic length of the chains, <na> and <nb>, along cut 1: 2 phase Cut 1. 2 phase DIS

17 The infinite homogeneous bonding chain. DIS Average characteristic length of the chains, <na> and <nb>, along cut 2: 2 phase Cut 2. DIS 2 phase

18 New interest: the 'infinite chain', continued. The polychromatic chain. k=1 k=2 Here only reds (A) and blues (B) bond, with affinity hab k=3 Generally, As could also bond with other As, Bs... Chain initiates with A. A-block contributions with a 2nd A-block attached. Contributions from an A-block attached to a B-block.

19 New interest: the 'infinite chain', continued. The polychromatic chain. k=1 k=2 Here only reds (A) and blues (B) bond, with affinity hab k=3 Generally, As could also bond with other As, Bs... Simple polymers: Simple chain propagation Infinite chain telechelics: G Solve coupled Born Scattering equations

20 The supramolecular infinite chain, phase behavior with changing bond affinity, on the isopleth The infinite chain supramolecular melt: A's only bond with B's. The supramolecular diblock blend: A's with only one other B. xna=2 NA=300 Theoretical limit. xna~7.55* *T. Kavassalis and M. Whitmore, Macromolecules , 1991

21 The supramolecular infinite chain, some statistics with changing bond affinity, on the isopleth The average number of blocks linked together, the characteristic length, <NA>. A cut at xna=7.00. (for chains that initiate with A-links.)

22 The mixed, infinite bonding chain. AB Bond. AA Bond. BB Bond. A full set of affinities: {haa,hab,hbb} No loops.

23 The mixed, infinite bonding chain. The heterogeneous bonding chain from before: First order line. Set affinities haa/xn=hbb/xn=1.50, vary hab/xn.

24 The mixed, infinite bonding chain. The heterogeneous bonding chain from before: First order line. Set affinities haa/xn=hbb/xn=1.50, vary hab/xn. The mixed bonding chain with set homogeneous affinities. Unbinding line.

25 Possible extensions: supramolecular networks A network-forming supramolecular assembling system. The integral equation for supramolecular 3-point chain contacts: Networks and heterogeneous networks are likely possible in this formalism.

26 An extension: the 3-junction homogeneous bonding melt ry a in m eli r P 2-junction to 3junction change in the critical line. Lengths for h/xn=2 across the critical line.

27 Acknowledgements Thanks to, The Fredrickson group Dow Chemical

28 Possible extensions: supramolecular networks Simple polymers: s=0 G s=n Supramolecular chains: +1 k links For all lengths, one solves a scattering (integral) equation. with, Simple chain propagation

29 The infinite homogeneous bonding chain. Bond. In this case, homogeneous bonding only. Loops are neglected.

30 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k=1 The Hamiltonian: k=2 k=3 The entropic contributions: A composite, multiple end-segment distribution. With, G s=0 s=n

31 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k=1 The Hamiltonian: k=2 k=3 With, Generally, The entropic contributions: A composite, multiple end-segment distribution. k links +1

32 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k links Summing over the addition of all k possible links, and, with, The Born Scattering Equation. No approximations have been made, this is exact. k=1 k=2 k=3 Solving the Born Scattering equation immediately yields the entropic contribution, +1

33 New interest: the 'infinite chain', continued. The polychromatic chain. k=1 k=2 Here only reds (A) and blues (B) bond, with affinity hab k=3 Generally, As could also bond with other As, Bs... Chain initiates with A. A-block contributions with a 2nd A-block attached. Contributions from an A-block attached to a B-block.

34 New interest: the 'infinite chain', continued. The polychromatic chain. k=1 k=2 Here only reds (A) and blues (B) bond, with affinity hab k=3 Generally, As could also bond with other As, Bs... Simple polymers: Simple chain propagation Infinite chain telechelics: G Solve coupled Born Scattering equations

35 Part 2. Van der Waal forces in thin films 1. A polymer thin film experiment. 2. Background: the Hamaker thin film. 3. What the field theoretic model has to offer this system. 4. An investigation of mode instability.

36 A thin, trilayer polymer film heated slowly from room temperature. Polystyrene T=90C Polyisoprene Polystyrene Upon heating, holes will form, via two mechanisms: T=100C 1. Nucleation about defects or density inhomogeneities. 2. Amplification of fluctuations driven by the interaction between the film surfaces. 127 mm T>100C Dalnoki-Veress, K. Phys. Rev. Lett. 82, 1486 (1999) Murray, C. A. et al. Phys. Rev E. 69, (2004) h=50nm, L=60nm

37 Surface dispersion interactions: the Hamaker constant. A careful summation over all contributions, one can show, H. Hamaker, Physica , 1937

38 A field-theoretic approach the Van der Waals thin film. Benefits: 1. Get an an actual, static (mean-field) calculation of the film: -complete with partitioned densities in the phases. -interfacial properties well-characterized in the mean-field. 2. The interaction can be tailored: -the long-range 1/r^6 tail can be included or neglected for a xn-like contact potential. 3. Can use a simple fluid or polymers (or several or both) in the blend.

39 Some foreshadowing? A varicose instability from a static, analytic calculation. The varicose mode for a thin film. The zigzag mode of a thin film. In a simple Landau-like free energy expansion.. The zigzag mode is stable to perturbations. The varicose mode is unstable to longwavelenth perturbations. It is favorable for the strip to break up into circular domains. A. Frischknecht, Phys Rev. E. 56, 6970, 1997

40 Surface dispersion interactions: the Hamaker constant.

41 New interest: the 'infinite chain', continued. An easier case first, the monochromatic chain. k=1 The Hamiltonian: k=2 k=3 The entropic contributions: A composite, multiple end-segment distribution. With, The Born Scattering Equation.

42 Correspondence with the SCF calculations, h/xn= f=1/2 f=2/3

43 Architectural effects at constant bond strength h/xn= N=300

44 Architectural effects at constant bond strength h/xn= N=300 Unusal symmetry architecture: f=

45 Effects of Bond Strength for f=0.50 h/xn= N=300 Decrease h/xn The eutectic fades away. Decreasing more...

46 Effects of Bond Strength for f=0.50 Decrease h/xn Decrease h/xn Decrease h/xn h/xn= N=300

47 Cause of re-entrance? re-entrance!

48 Snapshots of the RPA spinodal topology.

49 General trends in the topology. Architecture, determined by f, determines lobe structure at high h/xn Length N enhances re-entrance. Bonding strength h/xn determines the envelope shape

50 Acknowledgements. Thanks to, Kirill Katsov Ludwig Leibler Valeriy Ginsburg for helpful discussions and insight.

51 New Tools: A pseudo-analytic theory. The inhomogeneous RPA method. The Free Energy expansion Simple Homogeneous Landau Theory Threshold for mechanical stability: the spinodal for The Correlation Function Correlation function behavior at the spinodal The bottom line Landau Theory with the RPA extension. There is no memory of a perturbation at any distance.

52 New Tools: A pseudo-analytic theory. The inhomogeneous RPA method. The Free Energy expansion Simple Homogeneous Landau Theory Threshold for mechanical stability: the spinodal for The Correlation Function This is calculated directly based on a microscopic model of the chains and some simple assumptions. Correlation function behavior at the spinodal The bottom line Landau Theory with the RPA extension. There is no reaction in the bulk of a perturbation at any distance. There is a spatial, local response as a result of chain connectivity and their interactions. NO BINODAL CALCULATIONS HERE...

53 New Tools, continued. The (mostly) analytic RPA theory. This is calculated directly based on a microscopic model of the chains and some simple assumptions.