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

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

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

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 Å 3  Temperatures K, 573 K, 623 K, 673 K (experimental ~ 320 C)  NVE ensemble (after NVT Thermalization)  Time - 500,000 1 fs time step)

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 )

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

Trimers and transition states  Dimer transition state  Stable Trimer  Life time ~200ps  : 380 ps  4-42 : 210 ps  4-30 : 190 ps

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?

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

Dimer energetics  2-D configurational space Interaction energy = (Energy of cluster) - (n*Energy of single molecule) E 1 = Kcal/mole 25 ° 3.5 Å

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

Trimer Kcal/mole Interaction Energy : Kcal/mole

Tetramer to Octomer TetramerPentamerHexamer Heptamer Octamer

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

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

Collision Theory Hard Sphere + Energy Barrier Assumption

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

Species and Reactions  Each type of cluster is a species  Monomer -> P 1 ; Dimer -> P 2 ; Trimer -> P 3  Cluster formation / dissociation each is modeled as an independent reaction  P 1 + P 1 ---> P 2 ; P 2 ---> P 1 + P 1  P 2 + P 1 ---> P 3 ;P 3 ---> P 2 + P 1 or 3*P 1  Rate Constant for each reaction is found using modified collision theory equations

Further details  Assume effective diameter of pentacene clusters  Monomer Å( 278 amu )  Dimer Å( 556 amu )  Trimer Å ( 834 amu )  Based on geometry of minimized structures  Calculate  Use E * from energetics to find rate contant

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

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

Test Case  Reactions  P 1 + P 1 --> P 2  P 1 + P 2 --> P 3  Propensity (Rate Constant / Volume )  0.05 (initial # = 300,00 )  (initial # = 30 )

No of P 2 clusters with time

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