Study of Pentacene clustering

1. Study of Pentacene clustering MAE 715 Project Report By: Krishna Iyengar

2. Motivation Pentacene - new age applications Solar Panels Thin Film Transistors (TFTs) Organic Light Emitting Diodes (OLEDs) Experimental study of pentacene deposition to form thin films Formation of clusters observed

3. Problem outline Study the tendency to form clusters Energetics of clusters Dynamics of cluster formation Stochastic simulation

4. Part I: Tendency to form molecular clusters MD simulations - as proof of concept Simulation parameters MM3 Potential (Tinker) Partial Pressure of pentacene gas (V = nRT/P) Volume - 250 �3 Temperatures - 523 K, 573 K, 623 K, 673 K (experimental ~ 320 C) NVE ensemble (after NVT Thermalization) Time - 500,000 ( @ 1 fs time step)

5. Pentacene Dimers

6. Normalized Histogram Data Normalization of the histograms: 523 K - 50 573 K - 70 623 K - 72 673 K - 47 At lower T, larger proportion of stable dimers At higher T, large # of short life span dimers Correlation with theory?

7. Trimers and transition states Dimer transition state

8. Issues with the MD simulations System size dependence ? Effect of Pressure / Volume of simulation cell ? What characterizes a stable clusters? Formation of N-mers ? (problems with small time scale of simulations) Does this simulation model the experimental set up?

9. Part II: Energetics Why? - Will give an idea of stable structures, energy barriers (if any) How? : Ab-initio calculation ( using Gaussian ) Expensive (limited to ~ 200 atoms ~ 4 mol) Energy minimization using empirical potentials ( MM3 + Tinker) Range: Dimer - Octamer ---> Bulk

10. Dimer energetics 2-D configurational space

11. N-mer structures Take 200 random initial configurations Energy minimization to obtain structure At higher cluster size - compare with crystalline pentance : Herring bone structure

12. Trimer

13. Tetramer to Octomer

14. Trends in cluster formation

15. Part III: Dynamics Why energetics is required Rate constant = Prefactor * Energy barrier -> solve differential equation -> use KMC to stochastically evolve the system Assumptions: Molecules are approximated as spheres Assume hard sphere collisions Assume effective radius based on energetics Ideal gas behavior

16. Collision Theory

17. Change in opacity factor Integral from 0 to E* (interaction energy) Rate Constant based on collision theory Modifications for clustering

18. Species and Reactions Each type of cluster is a species Monomer -> P1 ; Dimer -> P2 ; Trimer -> P3 Cluster formation / dissociation each is modeled as an independent reaction P1 + P1 ---> P2 ; P2 ---> P1 + P1 P2 + P1 ---> P3 ; P3 ---> P2 + P1 or 3*P1 Rate Constant for each reaction is found using modified collision theory equations

19. Further details Assume effective diameter of pentacene clusters Monomer - 11.86 � ( 278 amu ) Dimer - 12.29 � ( 556 amu ) Trimer - 13.96 � ( 834 amu ) Based on geometry of minimized structures Calculate <vab> Use E* from energetics to find rate contant

20. Exact Stochastic Simulation Gillespie algorithm - generates a statistically correct trajectory of a stochastic equation Useful for simulating chemical or biochemical reaction systems It is a variety of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods

21. Summary of the steps to run the Gillespie algorithm Initialization: Initialize the number of molecules in the system, reactions constants, and random number generators. Monte Carlo Step: Generate random numbers to determine the next reaction to occur as well as the time step. Update: Increase the time step by the randomly generated time. Update the molecule count based on the reaction that occurred. Iterate

22. Test Case Reactions P1 + P1 --> P2 P1 + P2 --> P3 Propensity (Rate Constant / Volume ) 0.05 (initial # = 300,00 ) 0.005 (initial # = 30 )

23. No of P2 clusters with time

24. Thank You