Multi-scale modeling of diffusion-controlled reactions in polymers: Renormalisation of reactivity parameters

Everaers, Ralf; Rosa, Angelo

doi:doi:10.1063/1.3673444

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The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

Article Outline

INTRODUCTION
THEORY
1. Mean first-contact times and contact correlation functions
2. Rouse model
RESULTS
1. The origin of the different scaling regimes in the Rouse model
2. Reaction times as a function of chain discretization and spatial dimension
MULTI-SCALE MODELING OF DIFFUSION LIMITED REACTIONS IN POLYMERS
1. Disregarding the model-dependent microscopic dynamics
2. Universal and model-dependent contributions to τ_dc
3. Coupling of contact radius and conversion rate
4. Reactivity parameters for models with different resolution
SUMMARY

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KEYWORDS and PACS

Keywords

chemical reactions, diffusion, polymers, reaction kinetics theory, renormalisation

PACS

82.20.Wt

Computational modeling; simulation
82.35.-x

Polymers: properties; reactions; polymerization
36.20.Fz

Constitution (chains and sequences)

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.3673444

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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