CHARGED POLYMERS THE STORY SO FAR Andrey V Dobrynin Institute of Materials Science &Department of Physics University of Connecticut What are polyelectrolytes? Poly(styrene sulfonate) CH-CH 2 SO Na Poly(methacrylic acid) CH CH 2 -C COOH DNA + + + + + Dr. Andrei Dobrynin, University Connecticut 1
Half a Century of Polyelectrolytes 40-50 s Fuoss, Katchalsky, Morawetz, Flory.. 60-70 s Oosawa, degennes, Odijk, Manning, Fixman 5000 4000 000 2000 1000 0 '80-'85 '86-'90 '91-'95 '96-'00 '01-'05 Number of publications in scientific journals on topic POLYELECTROLYTES Physical model of polyelectrolyte chain Bead-spring model + - - - - + ε + - - + f=n charg /N fraction of the charged monomers Dr. Andrei Dobrynin, University Connecticut 2
Pearl-Necklace Story of Hydrophobic Polyelectrolytes Dilute solutions Necklace globule Counterion condensation Semidilute solutions Dr. Andrei Dobrynin, University Connecticut
Polymers in poor solvent Uncharged globule R Globule is densely packed by attraction between monomers The average monomer density inside globule is ρ ~ a - Globule size R ~ a N 1/ Instability of a charged liquid droplet Lord Rayleigh 82 + Q < Q crit Q > Q crit For the surface charge larger than the critical value charged liquid droplet splits into two smaller droplets. γ R 2 2 Q ε R crit Dr. Andrei Dobrynin, University Connecticut 4
Charged globule R Rayleigh s stability condition: electrostatic repulsion is balanced by surface energy ( efn) εr 2 γr 2 Critical fraction of charged monomers f crit ~ N -1/2 Chain size vs charge Normalized size R 2 /N 2/ Normalized charge Q/Q crit u=2, ε LJ =1.5 Dr. Andrei Dobrynin, University Connecticut 5
Cascade of transitions Dobrynin,Rubinstein, Obukhov 96 f=0 f=0.1 Charge on the chain increases f=0.2 Necklace globule l str m b D b L nec The length of a string is determined by the balance of the electrostatic repulsion between neighboring beads and the surface tension of string ( efm ) εl b str 2 γl a str Number of monomers in a bead m b ~ f -2 String length l str ~ a fm b ~am b 1/2 Necklace length L nec ~ l str N/m b ~ a fn How can one measure a chain size? Dr. Andrei Dobrynin, University Connecticut 6
ph dependence of the reduced viscosity for poly(methyacrylic acid) Katchalsky& Eisenberg 51 η R L nec Dilute solutions Necklace globule Counterion condensation Semidilute solutions Dr. Andrei Dobrynin, University Connecticut 7
Concentration induced cascade of transitions Number of beads on the chain varies with polymer concentration Polymer concentration increases Chains in dilute solution N=187, f=1/, ε LJ =1.5, u=2, ca = 1.5 10-4 Dr. Andrei Dobrynin, University Connecticut 8
Chains in dilute solution N=187, f=1/, ε LJ =1.5, u=2, ca = 1.5 10-2 Two-zone model Oosawa 68 Zone I Beads with condensed Counterions D b Zone II Volume free of the polymer V ch =N/c Dr. Andrei Dobrynin, University Connecticut 9
Counterion condensation D b m b monomers per bead fm b original charge xfm b effective charge of a bead 1-x fraction of condensed counterions V ch =N/c Bead size D a( uf x ) b 2 2 1/ Rayleigh stability condition l B ( fxm ) D b b 2 2 2 ( ) m uf x b 2 Db 2 a 1 Total free energy of the necklace F kt xfna x fna 2/ 1 Nf εc x + x ln + ( 1 x) ln ( ) Db Vch Db N / mb Electrostatic energy ( ) ε c u / f 1/ Counterion entropy -attraction of counterion to a fully charged bead Effective charge of PSS Williams et al 01 Osmotic pressure measurements in dilute solution π ktc 0.4 0.5 0. 0.25 0.2 0.15 0.1 0.05 0 0.2 0.4 0.6 0.8 1 f Best fit with the parameters ε c =4. and ca =10 - Osmotic coefficient for two-zone model π 2εc = fx + f ( 1 x) exp / ktc x 1 Dr. Andrei Dobrynin, University Connecticut 10
Dilute solutions Necklace globule Counterion condensation Semidilute solutions Overlap concentration L nec N C * N L nec 2 For c < c* - dilute solution of necklaces For c > c* - sedilute solution of necklaces Dr. Andrei Dobrynin, University Connecticut 11
Dependence of overlap concentration on degree of polymerization -2 Semidilute string regime ξ c Correlation length * < c < c str Chain is strongly stretched on the length scales smaller than correlation length de Gennes et al 76 / ξ ~ c 1 2 Chain size: R ~ N c 1/ 2 1/ 4 Dr. Andrei Dobrynin, University Connecticut 12
Concentration dependence of the correlation length -1/2 Semidilute Bead Controlled Regime ξ Dobrynin& Rubinstein 99 D b <ξ c str < c < c b Colloidal fluid of beads Beads on neighboring chains screen electrostatic repulsion of beads on the same chain reducing the length of strings to the distance between beads ξ. Correlation length m cξ ξ m c b 1/ 1/ b ξ ~ c -1/ f -2/ Chain size: R ξ N / m N c b 1/ 2 1/ Dr. Andrei Dobrynin, University Connecticut 1
Correlation Length -0. -0.66 NaPSS, M W (PS)=68 000 Single Chain Form Factor (NaPSS, M W (PS H )=68 000, M W (PS D )=7 000 ) Bead size vs fraction of charged monomers Theory: D b ~ f -2/ Experiment: D b ~ f -0.7 Dr. Andrei Dobrynin, University Connecticut 14
Effect of Added Salt Spitery & Boue 97 For charge fraction f=0.64 at polymer concentration C = 0.4 M R ( c = 0M) = 97 ± 5A g s R ( c = 0. 4 M) = 7 ± 8A g s R ( c = 0. 68M ) = 66 ± 5A g s Correlation length ξ -1/2 l str -1/ D b c str c b c String Controlled Bead Controlled Concentrated Dr. Andrei Dobrynin, University Connecticut 15
Nonmonotonic Dependence of the Chain Size on Polymer Concentration Polymer concentration increases Dependence of the Chain Size on Polymer Concentration R b N 1-1/4 f 1/ -1/ c str c b c Dr. Andrei Dobrynin, University Connecticut 16
Dependence of the Chain Size on Polymer Concentration 100 R e 10 1E-7 1E-6 1E-5 1E-4 1E- 0.01 0.1 1 cσ Chains in concentrated solution N=187, f=1/, ε LJ =1.5, u=2, ca = 10-1 Dr. Andrei Dobrynin, University Connecticut 17
Dynamics of Hydrophobic Polyelectrolytes String Bead Concentrated τ -1/2-1 c * c str c b c τ η ξ ξ τ s τ ξ kt N g ξ 2 Relaxation time of correlation blob N m 2 c c 1/ 2 1 bead,, string bead Transition at the bead overlap concentration c b with a dramatic increase of chain relaxation time and solution viscosity resembles gelation transition. 1/ 2 Dynamics of Hydrophobic Polyelectrolytes L R -1/4-1/ ξ -1/2-1/ D e string bead concentrated c * c str c b c η τ -1/2 string bead -1 concentrated c * c str c b c string bead concentrated 1/2 c * c str c b c Hydrophobic polyelectrolytes in a string- regime are similar to hydrophilic ones. Strong decrease of polymer size in a bead- regime leads to a rapid decrease of relaxation time and to a concentrationindependent viscosity of unentangled solutions. Counterion condensation on beads enhances this phenomenon. Dr. Andrei Dobrynin, University Connecticut 18
Gelation Transition of Hydrophobic Polyelectrolytes Below the bead overlap concentration c b necklace size is much smaller than the ideal chain size. Above the bead overlap concentration c b chains are ideal with much higher relaxation time and solution viscosity. Transition at the bead overlap concentration c b with a dramatic increase of solution viscosity resembles gelation transition. Size increase at bead overlap transition can be accompanied by chain entanglements. η above / η below = (Z N/N e ) 2 Z = m bead /m string The relaxation time vs concentration Boris& Colby 98-1/2-1 Concentrated String Bead Poly(styrene sulfonate), M w =1200K, f=0.85 Dr. Andrei Dobrynin, University Connecticut 19
Diagram of regimes for solutions of hydrophobic polyelectrolytes Dilute Semidilute string Semidilute bead Concentrated solution ξ C* C str C b Polymer concentration increases Conclusions Polyelectrolyte chain with short-range attraction and long-range repulsion forms a necklace globule. With changing charge on the chain or polymer concentration there exists cascade of transitions between necklaces with different number of beads. Conformational transition in solutions of hydrophobic polyelectrolytes leads to a sharp increase of viscosity - an apparent gelation. The predictions of the model are confirmed by recent experiments. Dr. Andrei Dobrynin, University Connecticut 20
Acknowledgments Collaborations Michael Rubinstein Qi Liao (University of North Carolina) Sergei Obukhov (University of Florida) Financial Support National Science Foundation Petroleum Research Fund Eastman Kodak Company Dr. Andrei Dobrynin, University Connecticut 21