Physical Gelation and Microstructure Formation in Solutions of Associating Polyelectrolytes

Igor I. Potemkin, Roman E. Limberger, Alexei R. Khokhlov

Physics Department, Moscow State University, Moscow 119992, Russia Phone: 007-095-939-4013 Fax: 007-095-939-2988 E-mail: igor@polly.phys.msu.ru

Anomalous gelation. The influence of the number of associating groups

(stickers) on physical gelation in dilute solutions of weakly charged associating polyelectrolytes was studied. Unusual effect of coalescence of optimum-size clusters (or single chains) into the gel at the decrease of the number of stickers per chain was predicted. This so-called anomalous gelation has polyelectrolyte nature and is determined by the presence of mobile counter ions [1,2]. Physical gel occupies small volume of the system in the dilute solution. Counter ions, which are localized within the gel, undergo large losses in entropy. The increase of the number of stickers should require the decrease of the gel volume and stimulate further losses in entropy of counter ions. This situation can become unfavorable and the thermodynamically advantageous option for the gel can be to disintegrate (dissolve) with the formation of finite size clusters and release of part of counter ions to outer solution what is favorable entropically. Therefore, we can say that loose gel can be formed via coalescence of the clusters with the decrease of the number of associating groups. Microphase separation. Strong segregation theory of microphase separation in dilute solutions of associating polyelectrolytes was developed [3]. The driving force of the separation was shown to be a competition between a short-range attraction of associating groups and long-range repulsion of charged groups. We have predicted that with the increase of polymer concentration single chains first aggregate into spherical clusters of optimum size which can be disordered in space or arranged with the symmetry of bcc lattice, Fig. 1. Further increase of polymer concentration can result in the formation of hexagonal and lamellar structures which precede the physical gelation. The hexagonal and lamellar structures are stable at very small fractions of charged groups on the chains. Coexistence of different microphases and the gel phase was predicted.

[1] Potemkin, I.I.; Khokhlov, A.R. Polymer Gels and Networks (Marcel Dekker, New York, 2001), 47. [2] Potemkin, I.I.; Andreenko, S.A.; Khokhlov, A.R. J. Chem. Phys. 2001, 115, 4862. [3] Limberger, R.E.; Potemkin, I.I.; Khokhlov, A.R. J. Chem. Phys., submitted.

2

4

6

8

0,0 5,0x10-4 1,0x10-3 1,5x10 -3

Single chains

Lamellae

Cylinders

Spheres

Gel

φ

τ

N = 104

u = 1λ = 10l = 500

σ = 1000

Figure 1. Phase diagram of dilute solution of associating polyelectrolytes in variables: average polymer volume fraction φ and gain in energy of aggregated stickers τ.

50 100 150 200 2500,0000

0,0002

0,0004

0,01

0,02

0,03

DCBAφmax

φ

l

single chains

spherical clusters

phase separation

physical gelN=1000u=1τ=5σ=20

PHYSICAL GELATION AND MICROSTRUCTURE FORMATION IN SOLUTIONS OF ASSOCIATING

POLYELECTROLYTESI.I. Potemkin 1, R.E. Limberger 1,2, A.R. Khokhlov

1,21 Physics Department, Moscow State University, Moscow 119992, Russia

2 Department of Polymer Science, University of Ulm, D-89069 Ulm, Germany

This work has been done in the frameworkof SFB-569, Project I1. Financial support of

the Deutsche Forschungsgemeinschaft andVolkswagen Stiftung is gratefully acknowledged.

Homogeneous distribution of chargesin the solution of single chains

Macroscopic electricneutrality of the gel phase

Low attraction (concentration)

High attraction (concentration)

Electrostaticrepulsion andtranslationalentropy of

counterionsAttraction ofthe stickers

2

4

6

8

0,0 5,0x10-4 1,0x10-3 1,5x10-3

Single chains

Lamellae

Cylinders

Spheres

Gel

φ

τ

N = 104

u = 1λ = 10l = 500σ = 1000

Gai

n in

ene

rgy

of a

ggre

gate

d st

icke

r

Polymer volume fraction

Phase Diagram of theSolution in the

Strong SegregationRegime

Total free energy:•Energy of stickers•Coulomb energy•Entropy of counterions and chains

•Elastic free energy of the chains•Energy of excluded volumeinteractions

Surface energyper unit of volume

Coulomb energyper unit of volume

Spheres

Cylinders

Rγ3

Rγ2 ( )φφρ /ln~ *22R

22~ Rρ

1*

>φφ

ρ

*φφ

- charge density of the clusters

- polymer volume fraction within the clusters

- average polymer volume fraction

Spheres Cylinders Lamellae Physical gelat the increase of polymer volume fraction

LamellaeRγ ( )φφρ /~ *22R

increase

R - radius (semithickness) of the clusters

2

4

6

8

0,0 5,0x10-4 1,0x10-3

Singlechains

Lamellae

Cylinders

GelSpheres

BCC

φ

τ

N = 104

u = 1λ = 10l = 500σ = 500

2

4

6

8

0,0 5,0x10-4 1,0x10-3

Singlechains

Lamellae

Gel

Spheres

BCC

φ

τ

N = 104

u = 1λ = 10l = 500σ = 250

2

4

6

8

0,0 4,0x10-4 8,0x10-4 1,2x10-3

GelBCC

Single chains

φ

τ

N = 104

u = 1λ = 10l = 500σ = 150

Effect of the Degree of Ionization of the Chains on the Structure of the Solution

Increase ofthe fractionof charged

groups

Disordered Spherical Clusters

BCC Structure

The size of the spherical clusters decreases with the increase of the fraction of charged groups. It is independent of the chain length 2

3 1~ρ

R

Aggregation number of the cluster depends essentially on the chain length N: 2

1ρN

m ≈

For long chains (or high fraction of charged groups): Several clusters can be formed within one chain (m<1) (cf. necklace model by Dobrynin, Rubinstein and Obukhov) Anomalous gelation

- polymer volume fraction

in the solution

φ

- number of monomer units

between two stickersl

Effect ofgel destruction

upon the increase

of the numberof stickers

Large loss in translationalentropy of counter ions

Number of stickers

usual gelationanomalous gelation

CONCLUSIONS

•Microphase separation is a result of the competition between short-range attraction of the stickers and long-range repulsion of the charged groups.

•Cylinders and lamellae can be stable. Reason: (i) gain in the surface energy

(ii) decrease of the Coulomb energy with the increase of polymer concentration

Weakly Charged Associating Polyelectrolytes

Associating groups(stickers)

Charged groups

Counter-ions

All monomer units are modeled to have the same size

•Microphase Separation of Weakly Charged PELs•The Effect of the Degree of Ionization•Normal and Anomalous Physical Gelation

Inhomogeneous distribution of chargesin the solution of spherical clusters

OUTLINED PROBLEMS

•Decrease of the fraction of charged groups is in favor of the cylindrical and lamellar structures.

•Counterions are responsible for anomalous physical gelation.