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Micellization of diblock copolymer in selective solvent

Lecture 1 : Neutral brushes. Scaling model of a neutral planar polymer brush (mushroom and brush regimes). Effect of solvent . Strong stretching approximation : chain trajectory and parabolic potential.

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Micellization of diblock copolymer in selective solvent

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  1. Lecture 1: Neutral brushes. Scaling model of a neutral planar polymer brush (mushroom and brush regimes). Effect of solvent. Strong stretching approximation: chain trajectory and parabolic potential. Internal structure of a planar brush. Response of polymer brush to compression. Curved polymer brushes. Scaling model of star-like and comb-like molecular brushes (stars and combs in solution). Lecture 2: Charged brushes. Strong and weak polyelectrolytes. Scaling model of strong PE planar brush. Main regimes of PE brush (counterion and salt dominated). Local electroneutrality approximation. Parabolic potential and internal structure of planar PE brush. Interactions between planar PE brushes. Curved PE brushes (scaling model). Corona of neurofilament(NF) as a cylindrical PE brush. Lecture 3: Polymer micelles. Micellization of neutral diblock copolymers in dilute solution in selective solvent. CMC. Strong segregation limit and narrow interface approximation. Starlike and crew-cut spherical micelles. Cylindrical and lamellar aggregates. Morphological transitions sphere-cylinder-lamella. Micelles with charged coronae. Diblock copolymer aggregates in semi-dilute solutions and melts. Strong and weak segregation limits. Multi-compartment micelles (MCMs).

  2. Micellization of diblock copolymer in selective solvent Unimer Micelle A c, T, pH,cs B corona boundary layer core Nomenclature Star-like micelle: H >> R; Rtotal= H H H Rcorona Rcorona R R Crew-cut micelle: H << R; Rtotal= R

  3. Critical micelle concentration (CMC) Micelle Unimer NB NA corona boundary layer PS PI core La Rue et al, 2008 La Rue et al, 2008 PI – 94kD PS – 39kD PI – 99kD PS – 19kD

  4. Critical micelle concentration (theory) free energy per molecule in micelle with aggregation number p

  5. Critical micelle concentration (theory cont’d) “Practical” equations: Aggregation number p0 in equilibrium micelle (does not depend on concentration of amphiphilesc) Concentratonc1of unimers Concentratoncmicof micelles

  6. Scaling model of spherical block copolymer micelle Zhulina & Birshtein 1985; Halperin 1987 p p Core j - volume fraction of B in the core Rcorona Interface x Rcore g – surface tension Corona (spherical brush) Star-like, Rcorona> > Rcore Crew-cut, Rcorona<< Rcore Minimization of Fpwith respect to p gives equilibrium aggregation number p0 Important note: in stable spherical micelles Fcoronar Finterface >> Fcore

  7. Star-like spherical block copolymer micelle (Rcorona>> Rcore) Equilibrium aggregation number 0 La Rue et al, 2008 Different length of soluble block A Fp(p0)/kBT= -F1 Fp(p0) CMC depends most strongly on length of insoluble block B, but also on temperature T and length of soluble block A

  8. Crew-cut spherical block copolymer micelle (Rcorona<< Rcore) Corona is planar-like brush with Dominant terms in the free energy per chain are the same for all morphologies of micelle (lamella, cylinder, sphere), Fp/kBT = gs+ NA(s/a2)-1/2v Minimization with respect to s gives: 0 Crew-cut asymptote Full solution Star-like asymptote La Rue et al, 2008

  9. Polymorphism in non-ionic micelles In aggregates with Rcorona>> Rcore, spherical micelle is always most stable: at the same area per chain s, spherical corona has more space and is less extended due to intra-chain repulsions. In crew-cut aggregates, dominant contributions to Fp = F1(planar corona ) + gsare the same for all morphologies i=1,2,3, but morphology-dependent corrections (DFA and FB) are different. FcoronarFAdecreases in the row:lamella, cylinder, sphere On the contrary, Fcoreincreases in the row lamella, cylinder, sphere Fcore /kBT = bi Rcore2/a2NB with b1 = p2/8, b2 = p2/16 and b3=3p2/80 Semenov JTEP 1985 Balancing DFA + Fcorein morphologies, i and (i+1) we find binodals for morphological transitionsito (i+1)

  10. Diagram of states PS PI in n-heptane Zhulina et al, 2005 NA Spheres ( ) 240 Cylinders 200 ( ) 160 Lamellas ( ) 120 (Sediment) NB 300 400

  11. Micelles with charged corona In experimentally relevant cases , coronal charge is compensated Low salt : ac >> cs High salt : ac << cs Novel micelle – to - micelle transition in annealing PEs Xu et al 2007 Morphological transitions . Same physics as in neutral aggregates

  12. Dilute solution of neutral star-like micelles, j < j* j* j** Rcorona R xlast

  13. Semi-dilute solution of star-like micelles with j*< j < j ** Non-uniformly stretched segment of blobs Micelles remain segregated (quasi-globular regime) Rcorona = (pNAa3/j)1/3 Aggregation number increases logarithmically with solution concentration p = p0 ln((j/j*) r Rcorona = (pNAa3/j)1/3 correlation blob x

  14. Semi-dilute solution of star-like micelles with j > j ** Micelles remain segregated (quasi-globular regime) due to retained stretching of coronal block, Rcorona = (pNAa3/j)1/3 BUT aggregation number increases with solution concentration as p = gNBj3/4 Rcorona correlation blob x(j)

  15. Diagram of states of concentrated solution of neutral block copolymer Strong segregation limit (narrow interface, well defined domains) Transitions between morphologies are characterized by si+1 = si Rcore,i+1= Rcore,i(i+1)/i L C A Polyisoprene – polymethylstyrene – polyisoprene (ABA) in decalin B Volkova et al 1982 C’ 2 S jB/jA C melt, nonselective solvent Rcore s s 1 cylinder lamella L Rcore S’ C’ S’ NA/NB Polymer concentration j~jA

  16. Theoretical phase diagram of diblock copolymer melt Leibler 1980, Semenov 1985, Fredrickson, Helfand 1987, Matsen 1996 Strong segregation limit Intermediate range Weak segregation limit

  17. Recent advances: multi-compartment micelles (MCM) with well controlled morphology Terpolymer ABC in selective solvent Step I: Step II: A B C Groschel et al, Nature Communications 2012

  18. Recent advances: scaling model of MCM VC = NC aC3 VB = NB aB3 VA= NA aA3 VA/VB A B C q Conservation of material in B and A domains, ignore curvature of A domain,,etc VA/VB >>1 Star-like corona of MCM is split into n coronas around B-patches and peripheral (laterally uniform) part modified surface tension at BS boundary (like for diblock AC) Minimization with respect to p and m: Number of patches

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