Supplementary information
Optimal parameters for morphology of BHJ solar cells from
simulations
Junwei Xue, Tingjun Hou, Youyong Lia)
Institute of Functional Nano & Soft Materials (FUNSOM) and Jiangsu
Key Laboratory for Carbon-Based Functional Materials & Devices,
Soochow University, Suzhou, Jiangsu 215123, P. R. China
a)
Email: yyli@suda.edu.cn
This pdf file includes computational details of our simulation approach.
Table of contents
1. The combination of atomistic simulation with mesoscale
simulation
2. Molecular Dynamics(MD) Simulation of Atomistic Model
3. Mesoscopic Dynamics
4. Time evolution of morphology during mesoscopic simulation
1
1. The combination of atomistic simulation with mesoscale
simulation
Molecular dynamics(MD) simulation of atomistic models in
combination with quantum chemical calculations have been employed to
study the microstructure, electronic structure and charge mobility of
organic semiconductors in crystalline or amorphous states.1 However,
atomistic simulation of phase domains on the length scale of a few of
nanometers would be too expensive to perform.
Coarse-grained models in which collection of atoms from an
atomistic model are mapped onto a smaller number of “superatoms”,
decrease the number of force sites and thus reduce computational
requirements and increase the time and distance accessible in molecular
simulation.2 Huang et al3 developed coarse-grained simulation model to
study the structure and dynamic evolution of poly(3-hexylthiophene)
(P3HT)/fullerene-C60 bulk heterojunction(BHJ) at the molecular level for
systems approaching the device scale. On the mesoscopic scale, some
other methods such as dissipative particle dynamics (DPD)4 and dynamic
density functional theory (DDFT)5 have been applied to simulate the
self-assembling behavior of mixtures, typically for dilute or semi-dilute
polymer solutions.6 These mesoscopic models form a bridge between fast
molecular kinetics and the slow thermodynamic relaxation of macroscale
properties.
Here we combine atomistic simulation with mesoscale
2
simulation (dynamic density functional theory) to predict the morphology
of BHJ solar cells.
2. Molecular Dynamics Simulation of Atomistic Model
The cubic boxes of pure P3HT, [6,6] -phenyl C61-butyric acid
methylester (PCBM) and their blends are constructed with the
Amorphous package of Materials Studio 5.0, followed by geometry
optimization with the energy convergence threshold of 110-4 kcal∙mol-1.
An amorphous cell of P3HT/PCBM blend at 50% PCBM by weight is
shown in Figure S1. Preliminary runs of 1.5 nanoseconds(ns) in
Isothermal-Isobaric (NPT) ensemble at a constant pressure of 1 atm are
performed to bring the system to equilibrium stage. Sequentially,
production runs of 200 picoseconds(ps) in the NPT ensemble are
followed, during which trajectories are stored per 2 ps for later analysis.
The interactions are modeled with the COMPASS7 force field. The
initial velocities are generated by Maxwell distribution and the
temperature and pressure are normalized by Nose and Berendsen method
respectively. The Ewald summation is adopted for the Coulomb
interactions with an accuracy of 0.01 kcal·mol-1, and the atom-based
summation is applied for the van der Waals interactions with a cut-off
distance of 9.5 Å, a spline width of 1 Å, and a buffer width of 0.5 Å. For
each configuration, MD simulation is conducted by Forcite package of
3
Materials Studio 5.0. The temperature of all MD simulations is set to
298K, with time step 1 femtosecond. The size of oligomers used in model
calculations is important to calculate thermodynamic parameters. We use
3HT 12-mers to represent the real long-chain P3HT as reported
previously3.
Figure S1. Simulation cell of weight ratio = 1:1 P3HT/PCBM blend
constructed by Amorphous Builder of Materials Studio 5.0. The carbon
and sulfur atoms are colored in brown and blue respectively. The
hydrogen atoms are not displayed for clearness.
Solubility parameter (δ) is a characteristic of a polymer used in predicting
the solubility of that polymer in a given solvent. The solubility parameter
is related to each component’s volumetric cohesive energy density Ecoh/V
of the system via the definition:
4
(1)
For a substance of low molecular weight, the value of the solubility
parameter is often estimated from the enthalpy of vaporization; for a
polymer, it is usually taken to be the value of the solubility parameter of
the solvent producing the solution with maximum intrinsic viscosity or
maximum swelling of a network of the polymer.
Molecular dynamics simulations of the two pure systems are carried
out to estimate the solubility parameters. The solubility parameters for
P3HT and PCBM are estimated to be 16.788 and 20.527 (J∙cm-3)0.5 based
on our simulation results. Similarly, the Hansen solubility parameters for
C60 have been found to be 20.09 MPa1/2 (δD, δP, δH = 19.7, 2.9, 2.7,
respectively)8. MD simulation with COMPASS force field provides us
reasonable solubility parameters.
The Flory-Huggins χ parameter could be estimated from:
(2)
where Vmono is a monomer unit volume. Here we use the average molar
volume of 3HT and PC60BM as the volume, and Flory-Huggins
interaction parameters between P3HT and PCBM is calculated to be
2.155.
3. Mesoscopic Dynamics
5
The phase behavior of the P3HT/PCBM blends at the mesoscopic
level is simulated by using dynamic density functional theory (DDFT)
with MesoDyn of Materials Studio 5.0. MesoDyn is based on a dynamic
variant of mean-field density functional theory,5 in which there is a one to
one mapping between the distribution functions of the system, the
densities and an external potential field. In dynamic density functional
theory, the optimal distribution function  is such that the free energy
F[] is minimized. Hence  is independent of the history of the system,
and is fully characterized by the constraints that it represents the density
distribution and minimizes the free energy functional. This constraint on
the density fields is realized by means of an external potential UI.
The molecule is defined as a string (Gaussian chain) of beads which
represent groups of atoms such as one or a few monomers of a polymer
chain. Chemically specific information can be used to define the
properties of the bead type such as the self-diffusion coefficients of the
bead components, the Flory-Huggins interaction parameters, the bead
sizes and the molecular architecture (chain length, branching, etc).
The dynamic process of the system is the Langevin equation of
motion, which describes the evolution of the bead density field. In
Mesodyn, the method used to model the time evolution of a mesoscopic
system is the time-dependent Ginzburg-Landau model.
The polymer chains are mapped to Gaussian chains by demanding
6
the mean square end-to-end distance and the length of a fully extended
chain. Thus, the number (Nb) and the length (αb) of the Gaussian chain
segments are estimated by the following formulas:
(3)
(4)
where Nmon is the polymerization degree of the polymer molecule, and
is the characteristic ratio. Empirical methods implemented in Synthia,
Materials Studio 5.0, provide a value of 3.49 for P3HT. In this study,
Mn(P3HT) is assumed to be 50000 g∙mol-1, the polymerization degree is
equal to 300. A P3HT chain is represented by A85. B bead represents
PCBM molecule. αb is equal to 1.4 nm.
The dimensions of the simulation lattice are 323232, and the cell
size (h) has an optimal value of α/1.1543. The diffusion coefficients of all
beads are assumed to be equal to 1.010-7cm2∙s-1. The time step is set to
20 ns for numerical stability. The noise scaling parameter is 75 and the
compressibility is 10.
4. Time evolution of morphology during mesoscopic simulation
After setting up the initial configurations, the systems are subjected
to 10000 time steps, i.e. 200microseconds(μs),
run to approach the
equilibrium. The isosurface of the density fields for P3HT at θP3HT= 0.56
with time evolution at T = 298K for 1:1 P3HT/PCBM blend is shown in
7
Figure S2. In order to show the microstructure more clearly, only the
P3HT domains are colored with red and PCBM is not shown. The green
curved surface stands for the interface between P3HT and PCBM.
Unlike molecular dynamics simulation, which provides details of
small-scale fluctuating motion of atoms, mesoscale modeling focuses on
physical processes in microsecond and is able to simulate the system with
a large size (e.g. 39.8nm × 39.8 nm × 39.8 nm as shown in Figure
S2).
Figure S2. The isosurface of the density fields for P3HT at θP3HT=0.56 at
different time stages from simulation. (T = 298K for 1:1 vol%
P3HT/PCBM blend)
8
(a)
(b)
Figure S3 Time evolution of (a) free energy density and (b) order
parameters of P3HT and PCBM for 1:1 vol% P3HT/PCBM blend at T =
298K
Over the course of a simulation, the free energy asymptotically
approaches a stable value. Phase separation is characterized by the order
parameters for each of the beads. The order parameter, Pi, is defined as
the volume average of the difference between the local density squared
and the overall density squared,
( 5 )
where ηI is a dimensionless density volume fraction for species I, defined
as ηI(r) = ν ρ(r).
Large order parameter indicates strong phase
segregation. Small value indicates a relatively homogenous system.
The time evolution of the free energy and order parameters for the
9
1:1 vol% P3HT/PCBM system at T = 298K are shown in Figure S3. The
dynamic process can be divided into two stages. During the first 2000
time steps, free energy of the system decreases rapidly and the order
parameters surge, which shows that the microphase separation is
performed mainly during this stage. After the first 2000 time steps, the
free energy fluctuates and approaches to the equilibrium slowly. The
density profiles in Figure S2 show that the domains grow coarsely by
phase transfer as well as by coalescence.
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