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 Å3 • 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 Post processing: Collision causes dimerization Detect collisions / formation of dimers (Cut off distance between CG - 5 Å ) Life time of the formed dimer(Cut off time = 1 pico second )

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 • Stable Trimer • Dimer transition state • Life time ~200ps • 30-42 : 380 ps • 4-42 : 210 ps • 4-30 : 190 ps

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 Interaction energy = (Energy of cluster) - (n*Energy of single molecule) E1 = 18.3757 Kcal/mole Min @ 25 ° 3.5 Å

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 -31.1021 Kcal/mole Interaction Energy : -30.5966 Kcal/mole

13. Tetramer to Octomer Tetramer Pentamer Hexamer Heptamer Octamer

14. Trends in cluster formation Bulk Phase Energy of formation ~ -35 Kcal/mole

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 Hard Sphere + Energy Barrier Assumption

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

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 Å ( 278 amu ) • Dimer - 12.29 Å ( 556 amu ) • Trimer - 13.96 Å ( 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