Proceeding of the 6th National Seminar on Neutron and X-Ray Scattering, ISSN 1410-76

CHARGE ORDERING IN SPHERICAL POLYELECTROLYTE BRUSHES

Johan R. C. Van der Maarel Department of Physics

National University of Singapore, Singapore Email: phyjrcvd@nus.edu.sg

ABSTRACT CHARGE ORDERING IN SPHERICAL POLYELECTROLYTE BRUSHES. Polyelectrolyte brushes consist of charged polymer chains (polyelectrolytes) attached to a substrate. They have vast technological potential due to providing control of, e.g., gelation, lubrication, and flow behavior, so have found wide-spread applications from the stabilization of colloidal suspensions in cosmetics and food products to encapsulation and delivery of bioactive agents to living cells. Polyelectrolyte diblock copolymers comprise two linearly attached polymer chains - a polyelectrolyte, which is hydrophilic, and a neutral, hydrophobic polymer. In aqueous solution, the copolymers arrange themselves into micelles so that the hydrophobic attachments are shielded from the water. These nanometer-sized micelles thus comprise a neutral core of self-assembled neutral chains (typically about 100), surrounded by a polyelectrolyte coronal brush. In my talk, I will describe the structure of spherical micelles of the diblock poly(styrene-block-acrylic acid) [PS-b-PA] copolymer in water. We obtained the partial structure factors pertaining to the core and corona density correlations with small angle neutron scattering (SANS) and contrast matching in the water. The counterion structure factor was obtained with small angle X-ray scattering (SAXS) with a synchrotron radiation source as well as SANS with contrast matching in the counterion. We have also measured the flow curves and dynamic visco-elastic moduli. The dimension of the micelles and the radial scaling of the corona charge density are discussed in terms of a balance of the elastic, conformational, stretching forces and the osmotic pressure exerted by the co- and counterions trapped in the coronal layer. The fluid rheology is interpreted in terms of interpenetration of the coronal at high packing fractions. Keywords: polyelectrolyte, SAXS, SANS, synchrotron

INTRODUCTION Small Angle Scattering Estimates of Charge Ordering in the Coronal Layer Amphiphilic Diblock Copolymers:

Two linearly attached polymer chains One part is hydrophobic Second part is hydrophilic (e.g., acid) Solvent can be selective (e.g., water) In selective solvent they “self-assemble” into nano-

structures Spontaneous process (Meta) stable equilibrium Pathway controlled

-b-COOH

-b-COOH

Asymmetric amphiphilic block copolymers in solution: A morphological wonderland N.S. Cameron, M.K. Corbierre, and A. Eisenberg Can. J. Chem.77: 1311-1326 (1999)

Spheres Rods Vesicles Hollow loopsSpheresSpheres RodsRods VesiclesVesicles Hollow loops Spherical Polyelectrolyte Brushes

Stabilization of colloidal suspensions Control of flow, gelation and lubrication Host of enzymes Model for cell recognition

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Charge Ordering in Spherical Polyelectrolyte Brushes Johan R. C. Van der Maarel

PolyStyrene-b-PolyAcrylate PS(20)-b-PA(85)

Aggregation number Core size Corona expansion Ion distribution Interaction among

micelles

-b-COOH

-b-COOH

+

+

+

++

+

+

+

+

+ ++

+

+

+

+

+

-

+

+

+

-

-

-

-

--

-

++

++

++

++++

++

++

++

++

++ ++++

++

++

++

++

++

--

++

++

++

--

--

--

--

----

--

Transmission Electron Microscopy

(a)

DN = 1

(full charge)

(a)(a)

DN = 1

(full charge)

(b)(b)

DN = 0

(almost no charge) The bar corresponds to 100 nm. Infra-Red Spectroscopy

COOHCOO-

COOHCOO-

Flow Behaviour

4.5 (circles), 17 (squares), 30 (diamonds), 44 (triangles) g/l 1000 fold increase in viscosity Low shear rate Newtonian behavior Shear thinning at higher rates Transition from liquid to gel

X-ray scattering (SAXS)

ESRF, France Energy: 6 GeV Maximum Current: 200 mA DUBBLE (BM26) operational energy: 5-30 keV

Neutron Scattering (SANS)

D11, D22 ILL and PAXY LLB

- 45 -

Charge Ordering in Spherical Polyelectrolyte Brushes Johan R.C. Van der Maarel

( ) ( ) ( )4 sin 2i j ijij

I q b b S q q π θλ

=∑Intensity:

Contrast: ( )2 2

1i i i s s s D O H Ob b v v b b X b X b= − = + −

Partial Structure Factor (PSF):

•Solute bi and/or solvent bs contrast variation gives PSF’s.

( ) ( ) ( )1 e 0iq rij i jV

S q dr rV

ρ ρ−= ∫r rr r

SANS Contrast Matching

+

+

+

++

+

+

+

+

+ ++

+ ++

+

+

++

+

+

+ ++

Core Corona

Ions

+

+

+

++

+

+

+

+

+ ++

++

++

++

++++

++

++

++

++

++ ++++

+ ++

+

+

++

+

+

+ ++

+ ++

+

+

++

+

+

+ ++

++ +++

+

+

++

+

+

+ ++

++

++

++

++++

++

++

++ ++++

Core Corona

Ions SANS Partial Structure Factors

Core Corona Composition

Coro

na C

harg

e

10-1

100

100

102

104

106

108

1010

1012

q (nm-1)

Cor

ePS

F(P

S-PS

)

0

0.04

0.35

0.1

0.6

1

10-1

100

100

102

104

106

108

1010

1012

q (nm-1)

Cor

ePS

F(P

S-PS

)

0

0.04

0.35

0.1

0.6

1

0

0.04

0.35

0.1

0.6

1

10

-110

0-2

0

2

4

6

8

10

12

0 0.2 0.4 0.6

0

100

200

300

400

500

600

0 0.2 0.4 0.60

100

200

300

400

500

600

Core – Corona Model

( ) ( ) ( )2sin4i i

qrF q dr r r

qrπ ρ= ∫( ) ( ) ( ) ( )1

ij i j cmag

S q F q F q S qN

=

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

r (nm )

ρ (

r)

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

r (nm )

ρ(r

)

34 3cPS agr Nρ π = ( )cr

PA PA cr r αρ ρ −=

( )cmS q Percus-Yevic hard sphere model

Exponent alpha (micelle radius ro) Core radius rc Distance of closest approach Dhs Aggregation number Nag

Core Structure

• Core radius rc = 5 nm • Aggregation number Nag

= 110 • Densely packed • No dependence on

charge, salt, and concentration

Center of Mass Structure

Co

po

lym

er

Co

nce

ntr

ati

on

44 g/l

30 g/l

17 g/l

100% charge

Open boxes: distance of closestapproach

Solid line: average distance SAXS Counterion Structure

SAXS (counterions) vsSANS (corona, symbols)

- 46 -

Charge Ordering in Spherical Polyelectrolyte Brushes Johan R. C. Van der Maarel

SANS Counterion vs Corona Structure

10-1 10010-2

10-1

100

101

102

q (nm-1)

Cor

ona/

Cou

nter

ion

PSF

CoronaCounterion

0 10 200

0.01

0.02

r (nm)

ρ

10-1 10010-2

10-1

100

101

102

q (nm-1)

Cor

ona/

Cou

nter

ion

PSF

CoronaCounterion

0 10 200

0.01

0.02

r (nm)

ρ

CoronaCounterion

0 10 200

0.01

0.02

r (nm)

ρ

0 0.1 0.2 0.3 0.40

20

40

60

80

q (nm-1)

Cou

nter

ion/

Cor

ona

-Cor

e C

ompo

sitio

n SF

0 0.1 0.2 0.3 0.40

20

40

60

80

q (nm-1)

Cou

nter

ion/

Cor

ona

-Cor

e C

ompo

sitio

n SF

0 0.1 0.2 0.3 0.40

20

40

60

80

q (nm-1)

Cou

nter

ion/

Cor

ona

-Cor

e C

ompo

sitio

n SF

Similar counterion and corona segment radial profiles

Within a 10 % margin, all counterions are trapped in the corona

Salt-Free Polyelectrolyte Stars

Borisov and Zhulina Eur. Phys. J. B 1998, 4, 205.

++

++

++

++++

++

++

++

++

++ ++++

3agN Nf R∆Π

( )3logosmo ag agF N Nf N Nf R

( )1 1

conf agF N R N aυυ −

( )1 2/5 0.6R Naf Nafυ υ− =

( ) ( ) 2,r ag af r rυ υξ ρ− −

High charge + +

+High charge + +

+

++ ++

++

( ) 1r g a f υξ −

( ) ( ) ( )1/ 2 1f r r fρ −

( )( )( )( ) ( )

2 / 3 3/ 4

4 / 3 5/ 4

8 / 3 5 / 2

,

,

,

0.5 0.6

r a r a r

f r r r

r r r

ξ

ρ

υ υ

− −

− −

= =

Weak charge ( )2 1K f fρ= −

Corona Scaling

( ) ( )8/ 3 8 /3r rρ α− =Weak charge,

salt free

( ) 2 ( 2)r rρ α− =High charge,

salt free

Salt dominated

( ) ( )4/ 3 4 / 3r rρ α− =

Neutral ( ) ( )4/ 3 4 / 3r rρ α− =

( ) ( )8/ 3 8 /3r rρ α− =Weak charge,

salt free

( ) 2 ( 2)r rρ α− =High charge,

salt free

Salt dominated

( ) ( )4/ 3 4 / 3r rρ α− =

Neutral ( ) ( )4/ 3 4 / 3r rρ α− =

Corona Structure

Co

ron

a C

harg

e

0

0.04

0.35

0.1

0.6

1

10-1

100-2

0

2

4

6

8

10

12

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

Co

ron

a C

harg

e

0

0.04

0.35

0.1

0.6

1

0

0.04

0.35

0.1

0.6

1

10-1

100-2

0

2

4

6

8

10

12

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

12

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

DN2/5

Mic

elle

Rad

ius(

nm)

2/5R Naf

Charge Annealing

Cs = 0 M

Cs = 0.05 M Cs = 0.05 M

Cs = 0 M

0 0.2 0.4 0.6 0.80

50

100

150

q (nm-1)

Com

posi

tion

PSF

(PS-

PA)(

PS-P

A)

10-1

100

10-2

100

102

104

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

Cs = 0 M

Cs = 0.05 M Cs = 0.05 M

Cs = 0 M

0 0.2 0.4 0.6 0.80

50

100

150

q (nm-1)

Com

posi

tion

PSF

(PS-

PA)(

PS-P

A)

10-1

100

10-2

100

102

104

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

10-1

100

10-2

100

102

104

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

10% charge

alpha = 8/3

alpha = 4/3

( )crPA P cr rA

αρ ρ −=

- 47 -

Charge Ordering in Spherical Polyelectrolyte Brushes Johan R.C. Van der Maarel Do the brushes interdigitate? PA Salt Corona Structure Factor

Filled circles: outer diameterOpen boxes: distance of closest

approachSolid line: average distance

Ion

ic S

tren

gth

2

4/3

2-4/3

2-4/3

0 M

0.05 M

0.2 M

1M

10

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

1 1.2 1.4 1.6 1.8

15

20

25

ρs-1/5(mole-1/5dm3/5)

Out

er R

adiu

s (nm

)

1 2 3 4 55

10

Cro

ssov

er (n

m)

ρs-1/2 (mole-1/2dm3/2)

Ion

ic S

tren

gth

10

2

4/3

2-4/3

2-4/3

2

4/3

2-4/3

2-4/3

0 M

0.05 M

0.2 M

1M

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

10

q (nm-1)

Cor

ona

PSF

(PA

-PA

)

1 1.2 1.4 1.6 1.8

15

20

25

ρs-1/5(mole-1/5dm3/5)

Out

er R

adiu

s (nm

)

1 2 3 4 55

10

Cro

ssov

er (n

m)

ρs-1/2 (mole-1/2dm3/2)

CONCLUSIONS • Fixed core structure • Osmotic star polyelectrolyte behavior

• Full corona stretching at high charge and minimal screening conditions

Osmotic Polyelectrolyte Salt Stars • The counterion distribution follows the one for the corona-forming blocks

• Within a 10 % margin, all counterions are trapped in the corona

( )2 2 2 6ag sN N f R ρ∆Π

( )( ) ( )( ) ( )

1/ 53 2 2 1/ 5

1/ 32 2 1 2 / 3

1/ 32 8 2 4 / 3

ag s

ag s

ag s

R N N a f

r N a f r

r N a f r

ρ

ξ ρ

ρ ρ

−

−−

− − −

Salt dominance

+

+

+

++

+

+

+

+

+ ++

+

+

+

+

+

-

+

+

+

-

-

-

-

--

-

++

++

++

++++

++

++

++

++

++ ++++

++

++

++

++

++

--

++

++

++

--

--

--

--

----

--

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

r (nm)

α=2

α=4/3

ρs

rs ρ

( )1/ 21 1/ 2 1/ 2s ag sr N a f ρ− −

Intermediate ionic strength

• Charge annealing toward the outer corona region for low charge

• Corona shrinks before overlap • Corona interdigitate at high packing fraction • Transition from viscous liquid to elastic gel ACKNOWLEDGEMENTS • Wendy Groenewegen, Leiden University. • Sasha Korobko, Leiden University. • Wim Jesse, Leiden University. • Stefan Egelhaaf, University of Duesseldorf.

• Alain Lapp, Laboratoire Léon Brillouin.

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