Dynamics of living polymers |
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Authors: | Email author" target="_blank">B?O’ShaughnessyEmail author D?Vavylonis |
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Institution: | (1) Department of Chemical Engineering, Columbia University, 500 West 120th Street, NY 10027 New York, USA;(2) Department of Physics, Columbia University, 538 West 120th Street, NY 10027 New York, USA |
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Abstract: | We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate ( velocity ) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean
. After a small perturbation of relative amplitude
, e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For
the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time
, the MWD s first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after
. The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after
. By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables (
) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbation s linearity, the response is non-linear until the late episode (3). For very small perturbations,
, response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system,
-methylstyrene.Received: 23 September 2003PACS:
82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization |
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