A Model of the Chemical Kinetics Exhibited by a Telechelic Polymer

1. A Model of the Chemical Kinetics Exhibited by a Telechelic Polymer Mark Wilson Acknowledgements: Dr. Arlette Baljon Department of Physics, San Diego State University Dr. Avinoam Rabinovitch Department of Physics, Ben Gurion University of the Negev, Israel Joris Billen PhD. Candidate, Department of Computational Science, SDSU

2. Overview • System of interest • Chemical kinetic model • Analytic solution • Stochastic simulation • Conclusions

3. General Polymeric Properties System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Fluid-like Micelle forming Transient network Concentration Temperature

4. Telechelic Polymer Simulation System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions • Implementation: Dr. Arlette Baljon, Department of Physics, Computational Biophysics group, SDSU • Polymeric chains • Functionalized end groups • Define aggregates • MD/MC simulation • Rich dynamics in equilibrium • Units of temperature

5. Aggregate Distribution System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions

6. Chemical Kinetic Model System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Assume simple reactions occur: Association Disassociation + Master equation:

7. Chemical Kinetic Model System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Track frequency of reactions occurring Using the master equation, solve for time averaged rates

8. Analytic Solution System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions System of coupled ODE’s Multiple solutions

9. Stochastic Simulation System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions • Gillespie stochastic algorithm • Probabilistic MC model • Based upon the given state of the system Aggregation probability density function – derived by Gillespie Aggregation probability frequency Probability at time that species and will aggregate/disassociate inside volume within Probability an aggregation event will take place in the interval regardless of its type

10. Stochastic Simulation System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Gillespie Algorithm • Calculate probabilities of each specific reaction occurring • Choose 2 random numbers: • Compute • integer satisfying • Update distribution and time

11. Stochastic Simulation Results System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Performed 10,000 reactions, averaged 500 simulations

12. Conclusions System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Development of kinetic model resulting in master equation Found solutions to master equation one physically real equilibrium solution spiraling, attractive eigenvalues Stochastic simulation Achieve known polymer distribution Simulation appears to be independent of initial conditions

14. Chemical Kinetic Model System of Interest Kinetic Model Analytic Solution Stochastic Simulation Conclusions Assume simple reactions occur: + Disassociation Association Master equation: