No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

End-growth/evaporation living polymerization kinetics revisited

Rent:

Rent this article for

USD

10.1063/1.3560661

### Abstract

End-growth/evaporation kinetics in living polymer systems with “association-ready” free unimers (no initiator) is considered theoretically. The study is focused on the systems with long chains (typical aggregation number *N* ≫ 1) at long times. A closed system of continuous equations is derived and is applied to study the kinetics of the chain length distribution (CLD) following a jump of a parameter (*T*-jump) inducing a change of the equilibrium mean chain length from *N* _{0} to *N*. The continuous approach is asymptotically exact for *t* ≫ *t* _{1}, where *t* _{1} is the dimer dissociation time. It yields a number of essentially new analytical results concerning the CLD kinetics in some representative regimes. In particular, we obtained the asymptotically exact CLD response (for *N* ≫ 1) to a weak *T*-jump (ε = *N* _{0}/*N* − 1 ≪ 1). For arbitrary *T*-jumps we found that the longest relaxation time*t* _{max } = 1/γ is always quadratic in *N* (γ is the relaxation rate of the slowest normal mode). More precisely *t* _{max }∝4*N* ^{2} for *N* _{0} < 2*N* and *t* _{max }∝*NN* _{0}/(1 − *N*/*N* _{0}) for *N* _{0} > 2*N*. The mean chain length *N* _{ n } is shown to change significantly during the intermediate slow relaxation stage *t* _{1} ≪ *t* ≪ *t* _{max }. We predict that in the intermediate regime for weak (or moderate) *T*-jumps. For a deep *T*-quench inducing strong increase of the equilibrium *N* _{ n } (*N* ≫ *N* _{0} ≫ 1), the mean chain length follows a similar law, , while an opposite *T*-jump (inducing chain shortening, *N* _{0} ≫ *N* ≫ 1) leads to a power-law decrease of *N* _{ n }: *N* _{ n }(*t*)∝*t* ^{−1/3}. It is also shown that a living polymer system gets strongly polydisperse in the latter regime, the maximum polydispersity index *r* = *N* _{ w }/*N* _{ n } being *r** ≈ 0.77*N* _{0}/*N* ≫ 1. The concentration of free unimers relaxes mainly during the fast process with the characteristic time *t* _{ f } ∼ *t* _{1} *N* _{0}/*N* ^{2}. A nonexponential CLD dominated by short chains develops as a result of the fast stage in the case of *N* _{0} = 1 and *N* ≫ 1. The obtained analytical results are supported, in part, by comparison with numerical results found both previously and in the present paper.

© 2011 American Institute of Physics

Received 21 December 2010
Accepted 08 February 2011
Published online 15 March 2011

Acknowledgments: This work was partially supported by the French ANR Grant No. “DYNABLOCKs” (ANR-09-BLAN-0034-01).

Article outline:

I. INTRODUCTION

II. OVERVIEW OF THE END-GROWTH KINETICS

A. The kinetic equations

B. Equilibrium state; parameter jumps

C. The fast relaxation stage

D. The slow stages

III. THE CONTINUOUS APPROXIMATION FOR KINETIC EQUATIONS FOR *N* ≫ 1

IV. RELAXATION AFTER A SMALL PARAMETER JUMP

A. The CLD perturbation analysis

B. Relaxation of the mean lengths *N* _{ n }, *N* _{ w }

C. The fast stage

V. NONLINEAR RELAXATION

A. Relaxation to much longer chains, α = *N*/*N* _{0} ≫ 1

B. Terminal relaxation for α < 0.5 (*N* < *N* _{0}/2)

C. Relaxation to much shorter chains: *N* ≪ *N* _{0} (α ≪ 1)

VI. DISCUSSION

VII. SUMMARY AND CONCLUSIONS

/content/aip/journal/jcp/134/11/10.1063/1.3560661

http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/11/10.1063/1.3560661

Article metrics loading...

/content/aip/journal/jcp/134/11/10.1063/1.3560661

2011-03-15

2014-04-16

Full text loading...

### Most read this month

Article

content/aip/journal/jcp

Journal

5

3

Commenting has been disabled for this content