Polyelectrolyte
Solution Rheology

Institute of Solid State Physics SOFT Workshop August 9, 2010

1976 de Gennes model
for semidilute polyelectrolytesr > ξ: SCREENEDELECTROSTATICS
A random walk ofcorrelation blobs

ξD < r < ξ: STRONGξELECTROSTATIC
STRETCHING
A directed random walkof electrostatic blobs
r < D: WEAK
ELECTROSTATICS
Conformation is similar toa neutral polymer,
Dswollen in good solvent,collapsed in poor solvent

Semidilute polyelectrolytes have apeak in their scattering function
Neutral polymers
overlap correlation
volumes easily andhave lots of scattering
at low wavevector.

neutralpolymer
log S(q)polyelectrolyte2π/ξlog q

The osmotic pressureof their counterions
prevents overlap ofcorrelation volumes
for polyelectrolytes.
Moreover, charge
repulsion between
neighboring chainsfavors a regularinter-chain spacing.

Semidilute polyelectrolytes have apeak in their scattering function
NaPSS
SANS

M. Nierlich, et al., J. de Phys. (Paris) 40, 701 (1979).

Small-angle X-ray scattering fromsemidilute polyelectrolyte solutions
DSAXS dominated by I- counterions
Quaternized poly(2-vinyl pyridine)in N-methyl formamide

Correlation volumes do not overlap and electrostatic interactions between the
directed random walk chains forces them near the correlation volume centers
S. Dou and RHC, Macromolecules, 41, 6505 (2008).

Polyelectrolyte Solution Correlation
Length from SAXS of QP2VP-I in NMF

SAXS determinationof correlation length

Semidilute unentangled viscosity
determination of correlation length

P. G. deGennes, P. Pincus, R. M. Velasco, F. Brochard, J. Phys. (Paris) 37, 1461 (1976).
A. V. Dobrynin, RHC and M. Rubinstein, Macromolecules 28, 1859 (1995).

Semidilute Unentangled Solutions‘Phase Diagram’ of W. W. Graessley, Polymer 21, 258 (1980).

106

What happens with
polyelectrolytes?
105
M
c* ~ N-2 forpolyelectrolytes
104

103
0.001

0.01

c*ce

Comparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no salt

next few slides from RHC, Rheol. Acta 49, 425 (2010) and references thereinComparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no salt
Red circles are entanglement
concentration ce and red stars
are overlap concentration c* ofpolystyrene in toluene(neutral good solvent) ce ~ c*Blue circles are entanglement
concentration ce, blue stars
are overlap concentration c*from SAXS and circled bluestars are c* from viscosity of
sodium poly(styrene sulfonate)in water(polyelectrolyte with no salt)
Lines have slopes of -2 and -0.74

Scaling expects ce ~ c*not observed for polyelectrolytes

Comparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no salt

Osmotic Pressure
Polyelectrolyte kT per counterionNeutral dilute kT per chain
Neutral semidilute kT per correlation volumeCorrelation Length
PE no salt ξ ~ c-1/2
neutral-good ξ ~ c-0.76
neutral-θ ξ ~ c-1

Semidilute Unentangled Dynamics
Zimm time of a correlation volume
Rouse time of a chain
Polyelectrolytes

Neutral Polymers

A. V. Dobrynin, RHC and M. Rubinstein, Macromolecules 28, 1859 (1995).

Semidilute Unentangled Dynamics
Zimm time of a correlation volume
Rouse time of a chain
Polyelectrolytes

with neutral polymers
dilute solution~

Neutral Polymers

A. V. Dobrynin, RHC and M. Rubinstein, Macromolecules 28, 1859 (1995).

Semidilute Unentangled Dynamics
Zimm time of a correlation volume
Rouse time of a chain
Polyelectrolytes

empirical Fuoss law firstpredicted by de Gennes

Neutral Polymers

A. V. Dobrynin, RHC and M. Rubinstein, Macromolecules 28, 1859 (1995).

Semidilute Unentangled Dynamics
Zimm time of a correlation volume
Rouse time of a chain
Polyelectrolytes

even stranger prediction,
expects polyelectrolytes
to be rheologically unique

Neutral Polymers

A. V. Dobrynin, RHC and M. Rubinstein, Macromolecules 28, 1859 (1995).

Quaternized P2VP in ethylene glycol• ethylene glycol does not react with air• ethylene glycol has extremely low salt
• ethylene glycol is good solvent for neutral
P2VP (the unquaternized parent polymer)

Polyelectrolyte Solution Rheology
Partially quaternized poly(2-vinyl pyridine) in ethylene glycol

c/c* reduces all polyelectrolyte specific viscosity data on dilute andsemidilute unentangled solutions to a common functional form withforandwith~forS. Dou and R. H. Colby, J. Polym. Sci., Polym. Phys. 44, 2001 (2006).

Comparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no saltpoly(2-vinyl pyridine)in ethylene glycol(neutral-good solvent)partially quaternizedpoly(2-vinyl pyridine)in ethylene glycol(polyelectrolyte with no salt)
same chain length
ethylene glycol is unusual
as it dissolves both neutral
and polyelectrolyte andhas no residual salt
S. Dou and R. H. Colby, J. Polym. Sci., Polym. Phys. 44, 2001 (2006).

Conclusions: 60PMVP-I in EG• EG has very little residual salt with ε = 37
• EG is a good solvent for neutral P2VP• Lack of salt contaminants allows full test
and elegant demonstration of scaling fordilute and semidilute unentangled solutions• Entangled solutions show the expectedconcentration dependences but ce is not
simply proportional to c*, so scaling fails forc > ceS. Dou and R. H. Colby, J. Polym. Sci., Polym. Phys. 44, 2001 (2006).

Polyelectrolyte Solution SpecificViscosity of QP2VP-I in NMF
Residual salt concentration:

Crossover at
Low salt limit:

High salt limit:~for

S. Dou and RHC, Macromolecules 41, 6505 (2008).

(high-salt polyelectrolyte is thesame as neutral good solvent)
NMF self-dissociates

Polyelectrolyte Solution Modulus
and Relaxation Time QP2VP-I-NMF
high-salt

low-salt

Terminal modulus
G = ckT/N (dashed)insensitive to salt

Relaxation time(solid)~increases withdilution in the
low-salt limit
S. Dou and RHC, Macromolecules 41, 6505 (2008).

Conclusions: 60PMVP-I in NMF• NMF has high ε = 182 and large f = 0.27
• NMF has cs =1.4 mM residual salt
• NMF is a good solvent for neutral P2VP• The Dobrynin 1995 scaling model
describes viscosity ηsp(c)• The correlation length from SAXS andviscosity agree quantitatively and have theconcentration dependence expected by
the deGennes 1976 scaling model.
S. Dou and RHC, Macromolecules 41, 6505 (2008).

The Rouse Model Describes
Linear Viscoelasticity
1/2

QP2VP-Cl of various
molecular weights
in ethylene glycolc = 0.02 M

D. F. Hodgson and E. J. Amis, J. Chem. Phys. 94, 4581 (1991).

Shear Thinning Enhanced by Dilution
Gravitydriven
capillaryviscometer
shear rate
range

NaPAMS = sodium poly(2-acrylamido-2-methylpropane sulfonate)
M = 1.7 × 106 with no added salt (2.2 × 10-4 M ≤ c ≤ 8.0 × 10-2 M)
W. E. Krause, J. S. Tan and RHC, J. Polym. Sci.: Polym. Phys. 37, 3429 (1999).

Unentangled – Rouse Model• The Rouse Model describes linear
viscoelasticity of unentangled
polyelectrolyte solutions• The Rouse Model qualitatively describes
η(c), τ(c), G(c), and D(c) for unentangled
semidilute solutions• Shear thinning starts at lower rates aspolyelectrolytes are diluted

Unentangled – Rouse Model• The Rouse Model describes linear
viscoelasticity of unentangled
polyelectrolyte solutions• The Rouse Model qualitatively describes
η(c), τ(c), G(c), and D(c) for unentangled
semidilute solutions• Shear thinning starts at lower rates aspolyelectrolytes are diluted
This makes polyelectrolyte solutions
rheologically unique!

Open Questions in Polyelectrolytes
•
••

•
•

for: What is the form factor for the
directed random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformationdetermined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist atultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Open Questions in Polyelectrolytes•
•
•

•
•

for: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist at
ultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Open Questions in Polyelectrolytes•

for: What is the form factor for the
directed random walk inside the correlation blob?
Experimental way toaccess the form factor ofa dilute polyelectrolyte?
Sulfonated polystyrene with
deuterated TMA+ counterions
that are contrast-matched
inside the correlation
blob shows universal formwith~Directed random walk?
Bending on the scale ofJ. R. C. van der Maarel, et al., Macromolecules 26, 7295 (1993).

?

Open Questions in Polyelectrolytes•••••for: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist atultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Open Questions in Polyelectrolytes•

for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
Huge forward scattering (at low q)
suggests structures on scalesconsiderably larger than the chain size!
Electrostatic attractions?
Possibly related to the slow mode in
dynamic light scattering?
If they exist, these large structures seemto have no effect on macroscopic rheology
or thermodynamics (osmotic pressure).
Inconsistent with the strong correlations
on the scale of the correlation volumes!

B. D. Ermi and E. J. Amis, Macromolecules 31, 7378 (1998).

Open Questions in Polyelectrolytes•••••for: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist atultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Open Questions in Polyelectrolytes• How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?

Phases of Ion-Containing Polymers
Polyelectrolyte: Many ions dissociate from the chain in ahigh-dielectric medium – dominated by charge repulsion
Ionomer: All counterions are paired with the ions attachedto the chain in a low-dielectric medium and ion pairs cluster– dominated by dipolar attraction

Open Questions in Polyelectrolytes• How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?

Phases of Ion-Containing Polymers
Polyelectrolyte: Many ions dissociate from the chain in ahigh-dielectric medium – dominated by charge repulsion
Chain of Dipoles Phase: Ions are mostly paired but
do not aggregate to form ion domains
Ionomer: All counterions are paired with the ions attachedto the chain in a low-dielectric medium and ion pairs cluster– dominated by dipolar attraction
Change dielectric constant, temperature or concentration

Open Questions in Polyelectrolytes• How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
The ‘polyelectrolyte effect’always has the charges
increase the viscosity
relative to neutral polymer
Chain of Dipoles Phase:
Ions are mostly paired but
do not aggregate
Polyelectrolytes have lower viscosity than the neutral polymer
at high concentrations owing to dipolar attraction of condensed
counterions. H. Schiessel & P. Pincus, Macromolecules 31, 7953 (1998).

Open Questions in Polyelectrolytes•••••

for: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist at
ultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Open Questions in Polyelectrolytes• Does the ordered phase predicted by de Gennes
exist at ultra-low concentrations?
log rD-1/2-1/3

log Rcmlog R

log cc*At sufficiently low c,
the distance between~
chainsis much smaller thanthe Debye screening
length~The chains should
strongly interact andorder onto a lattice(dilute crystal).

P. G. de Gennes, P. Pincus, R. M. Velasco, F. Brochard, Remarks onpolyelectrolyte conformation J. de Phys. (Paris) 37, 1461-73 (1976).
P. G. de Gennes, Global molecular shapes in polyelectrolyte solutions,in Colston Papers No. 29: Ions in Macromolecular and Biological Systems (1978).

Open Questions in Polyelectrolytes
••••
•

for
: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist at
ultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Comparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no salt
Red circles are entanglement
concentration ce and red stars
are overlap concentration c* ofpolystyrene in toluene(neutral good solvent) ce ~ c*Blue circles are entanglement
concentration ce, blue stars
are overlap concentration c*from SAXS and circled bluestars are c* from viscosity ofsodium poly(styrene sulfonate)in water(polyelectrolyte with no salt)
Lines have slopes of -2 and -0.74

Scaling expects ce ~ c*not observed for polyelectrolytes

Comparison of the 3 universality classesof polymer solutions: neutral-θ, neutral-goodand polyelectrolyte with no salt
Red circles PS in benzene (neutral good)Black circles PS in cyclohexane (neutral θ)
Red squares PB in phenyloctane (good)Black squares PB in dioctylphthalate (θ)
Blue various polyelectrolytes

aTerminal Modulus (lines are predicted slopes)
Polyelectrolyte with no salt kT per chainNeutral good solvent G ~ c2.31
Neutral θ-solvent G ~ c7/3
G=kT
a 2ξ

Tube Diameter (open)
Correlation Length (filled)a ~ c-1/2 ξ ~ c-1/2
a ~ c-0.76 ξ ~ c-0.76
a ~ c-2/3 ξ ~ c-1

Open Questions in Polyelectrolytes• What does entanglement mean in a polyelectrolyte solution?

NaPSS
NaPAMSNaIBMANaDIBMAClP2VP in EG

Theory expectsce ≈ 103c* ~ N-2
Entanglement concentration is nearly independent of chain length!

Open Questions in Polyelectrolytes• What does entanglement mean in a polyelectrolyte solution?
NaPSS in water with no salt Specific Viscosity and Diffusion Coefficient
Entanglement concentration is clearly evident in both data sets, with slopes ofsolid lines above and below ce those predicted by the scaling theory. However,scaling expects
with n the (constant?) number of strands sharing
an entanglement volume and expects

The dashed lines both suggest n ~ ce-0.9 ~ N-0.4
D.C. Boris and RHC, Macromolecules 31, 5746 (1998). M.G.Oostwal, M.H. Blees,
J. De Bleijser and J.C.Leyte, Macromolecules 26, 7300 (1993).

Open Questions in Polyelectrolytes•••••for: What is the form factor for thedirected random walk inside the correlation blob?
for: What is the origin of the enormous
scattering at very low wavevectors? Related to slow mode?
How do polyelectrolytes (with conformation dominated bycharge repulsion) crossover to ionomers (with conformation
determined by dipolar attraction of ion pairs) at very highconcentrations?
Does the ordered phase predicted by de Gennes exist atultra-low concentrations?
What does entanglement mean in a polyelectrolyte solution?

Acknowledgments
ACS Petroleum Research Fund (1996-2005)
NSF-DMR-0705745 (2007-2010)
Brian Antalek (Kodak)Federico Bordi (U. of Rome)David Boris (U. of Rochester Ph.D. 1998, now at Kodak)
U Hyeok Choi (current PSU Ph.D. student)
Emanuela DiCola (U. of Leeds Ph.D. 2004, now in Grenoble)
Andrey Dobrynin (U. of Rochester post-doc, now at UConn)
Shichen Dou (PSU Ph.D. 2006, now at Toray Plastics)
Wendy Krause (PSU Ph.D. 2000, now at NC State U.)
Nop Plucktaveesak (PSU Ph.D. 2003, now at Thammasat U.)
Michael Rubinstein (U. of North Carolina)
Julia Tan (Kodak, now retired)
Tom Waigh (U. of Leeds, now at U. of Manchester)