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Controllable Bulk Heterojunction Morphology by Self-Assembly of Oppositely Charged Nanoparticles Kulveer Singh, Prateek K. Jha, and Soumitra Satapathi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06168 • Publication Date (Web): 02 Jul 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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The Journal of Physical Chemistry

Controllable Bulk Heterojunction Morphology by Self-Assembly of Oppositely Charged Nanoparticles Kulveer Singh,† Prateek K. Jha,∗,‡ and Soumitra Satapathi∗,¶ †Centre of Nanotechnology, IIT Roorkee ‡Department of Chemical Engineering, IIT Roorkee ¶Department of Physics, IIT Roorkee E-mail: [email protected]; [email protected]

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Abstract Using kinetic Monte Carlo simulations of a simple coarse-grained model, we demonstrate that the self-assembly of oppositely charged nanoparticles is a promising approach to design efficient bulk heterojunction (BHJ) solar cells. Simulations are performed starting from a random configuration of oppositely charged nanoparticles in solution for a range of concentrations. Interconnected percolated morphologies form at high nanoparticle concentrations, when the aggregate growth ceases after certain time. If only Coulombic interactions are present, the observed morphologies have very high interfacial area but too small domain size, whereas optimum values of both the interfacial area and domain size are desired for BHJ. We therefore propose and establish that an additional hydrophobic attraction between nanoparticles of same type is desired to obtain the ideal BHJ morphology. We also discuss the effects of solvent dielectric constant and the size- and charge-asymmetry of nanoparticles, which may provide additional means to control the BHJ morphology.

Introduction Organic solar cells have high commercialization prospects due to their low cost, ease of fabrication and flexibility. 1,2 Continuous effort in designing novel low band gap materials with higher photon absorption and improved device architectures have led to power conversion efficiency(PCE) of OSCs as high as 10.6%. 3 In addition to broad absorption spectrum, another desired attribute for a high efficiency in OSCs is an optimal BHJ morphology that facilitate efficient charge separation and charge transport. 4–6 In an ideal BHJ (Fig. 1), both electron- and hole-conducting materials interpenetrate to form a bi-continuous network, such that the interfacial area (active layer) is maximum and the average domain size of both the donor and acceptor materials is comparable to the exciton diffusion length. The interpenetration of the two domains must have an optimum value for high efficiency of OSCs, as too much interpenetration inhibits the charge transfer to the electrodes and too 2


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little interpenetration hinders the exciton diffusion to the interfaces. To achieve this optimal morphology, various experimental stratigies 7,8 such as controlling the solvent removal rate or the ratio of the donor and acceptor components, thermal/solvent annealing have been used. These ensure that the donor and acceptor phases are bicontinuous and length scale of the phases is similar to exciton diffusion length. In some recent studies, adding a third component in blend system have shown improvement in PCE of OSCs. 9,10 Nevertheless, achieving an optimal architecture in blend system is a challenge due to interplay of various kinetic processes occurring during fabrication like crystallization, phase separation, solvent evaporation etc. 11 Further, the organic solvents used in fabrication of blend system are toxic and volatile results in environmental and safety issues for large-scale commercialization. 12 Due to these concerns, recently a lot of attention have been gained by solar cells made of polymer NPs system. 13,14 In very short duration of time PCE of 4% has been achieved in polymer NP OSCs. 15 Beside having an environmental and industrial advantage over blend system, a controllable morphology with proper domain size can also be achieved by self assembly of spherical NPs. 16–19 In principle, tailored ordering of assembly can be achieved by changing the NPs radii, their composition, surface charge, their number ratio and other interactions. However synthesizing NP of diameter comparable to the exciton diffusion length (∼ 10nm) was very difficult using existing experimental method. The size and charge of the NP can be controlled by surfactant concentration 18,20 during NP synthesis and using reprecipitation method Nagai et al. 21 have developed NPs in the range of 10nm − 65nm. Thus there is a possibility that the self assembly of pre-tailored NPs of different size and charge could facilitate the control of interfacial area and domain size of BHJ devices. Theoretical and computational studies may assist in developing the design rules for “bottom-up" assembly of NPs into BHJ morphology and thus guide future experiments. In earlier studies, charge transport within BHJ was studied using kinetic Monte Carlo (kMC) simulations on an artificially generated morphology developed on a cubic lattice. 22–24 However, to the best of our knowledge, a systematic study of the formation of BHJ by NP self-

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Anode

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Anode

Anode

A

B

Cathode

C

Cathode

Cathode

Figure 1: Working principle of BHJ organic solar cells. (A) Formation of exciton by photon absorption and diffusion to the interface, (B) generation of charges by dissociation of exciton at the interface, (C) propagation of charges to the anode and cathode. assembly has not been performed. In this paper, we do not attempt to mimic the equilibrium phase diagram of oppositely charged nanoparticles, which may result in crystal formation. 25 Instead, we are interested in out-of-equilibrium gel-like, percolated structures that form when the self-assembly is dynamically arrested. 26,27 Here, we discuss our study of the self-assembly of charged NPs into BHJ morphology using a recently developed kMC scheme 28 for nonequilibrium simulations. This scheme offers several advantages over conventional Brownian dynamics simulations for short to intermediate time evolution for a range of systems 28–30 and therefore particularly suitable for the study of non-equilibrium self-assembly of NPs into thin films used in BHJ where the NP assemblies are far-from-equilibrium states.

Model and methods We have performed implicit-solvent simulations of solutions containing two NP types, type A (+) and type B (−), with opposite and dissimilar valence zA and zB and different diameters σA and σB , respectively. Number of particles of type A and type B are nA and nB respectively, such that nA zA + nB zB = 0 (global electroneutrality) and nA + nB = NT , where NT is the total number of NPs. NPs interact via a Coulombic interaction and a Lennard Jones (LJ) interaction, where the latter is used to characterize the soft-core repulsion between NPs and an additional, solvent-mediated hydrophobic interaction (if present). The Coulombic

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interaction between NPs is modelled using a pair-wise screened Coulomb potential 25 Uij (r) z i z j λB σ 0 = kB T (1 + κσ2 i )(1 +

eκσij e−κr . κσj ) r 2

(1)

where i = A, B and σij = (σi + σj )/2 is the average of diameters of NPs of type i and type j. λB = e2 /4πεǫo kB T σ0 is the dimensionless Bjerrum length and κ−1 = (8πλB cs )−1/2 is the Debye screening length of monovalent electrolyte, where σ0 = (σA + σB )/2, ε is the relative dielectric constant of the solvent, ε0 is vacuum permittivity, kB is Boltzmann constant, T is absolute temperature, and cs is the salt concentration. In order to improve computational efficiency, we use a truncated and shifted form of the potential in eq. 1, that is,

Uijc (r) =

   Uij (r) − Uij (rcut ) r ≤ rij,cut   0

(2)

,

r > rij,cut

where rij,cut = 2.5σij is the cutoff distance for Coulombic interactions. The LJ interaction between NPs are of the form h σ 12 σ 6 i UijLJ (r) ij ij , = 4ǫLJ − ij kB T r r

(3)

where ǫLJ ij characterizes the strength of the LJ potential between type i and type j NPs. This is also truncated and shifted to result in a modified potential,

UijLJ,c (r)

=

   U LJ (r) − U LJ (r ij

ij

  0

cut )

LJ r ≤ rij,cut

r>

.

(4)

LJ rij,cut

Here, the cutoff distance for LJ interaction rij,cut is 21/6 σij when only soft core LJ repulsion is present and 2.5σij when an additional hydrophobic attraction is also present. Simulations start with a random distribution of NPs inside a cubic box of length L =

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h

π 6η

σA3 nA

+

σB3 nB

i1/3

, where η is the packing fraction i.e. the fraction of volume occupied

by the NPs. One kMC step consists of randomly picking one NP and attempting to move its center to the surface of a sphere of radius a with the NP center being the origin. In order to ensure uniform probability density of choosing points on the sphere surface, the attempted move is performed by choosing an azimuthal angle θ = 2πu and a polar angle φ = cos−1 (2v − 1), where u and v are random variables in (0, 1). Energy change of the attempted move ∆E is calculated and the move is accepted/rejected with a Glauber transition probability p = [1 + exp(∆E/KB T )]−1 for accepting moves. NT such steps constitute one kMC sweep. Time step of a sweep is related to the step size (a) of the move as ∆t = a2 /12D = (τ0 /12)(a/σ0 )2 , where D is the diffusion coefficient of a free NP of diameter σ0 in solution and τ0 = σ02 /D is the diffusion time scale. ∆t in theory is derived 28 assuming that the energy change associated with each move is small, and therefore small value of a is desired. In simulations, we have used a = .02σ0 , which was observed to be a proper step size in a previous kMC study of electrolytes in solution. 30

Results and discussion Aggregation kinetics We first studied the aggregation kinetics of oppositely charged NPs in order to understand the aggregation regimes, threshold concentrations and the time scales to obtain percolated structures. Additional hydrophobic attractions are not considered in these simulations; only the Coulombic interactions and the soft-core LJ repulsions are considered. Aggregate size distribution of NPs is computed at different times from which the weight-averaged aggregate P P size Mw = j nj j 2 / j nj j is calculated, where nj is the number of aggregates having j NPs. Two NPs are considered to be a part of the same aggregate if the distance between them is less than 1.5σ0 . Mw evolution for three different packing fractions (η = 0.005, 0.025, 0.060) are shown in Fig. 2. As evident from the figure, aggregate size increases with an increase in 6


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η=.005 η=.025 η=.060

100

Mw

1.06

10

0.69

0.49

0.45 1

0.20 0.1

1

t/τ0 10

100

Figure 2: Mw as a function of t/τ0 for three different values of η. Markers(η = 0.005(⊙), 0.025(•), 0.060(△)) indicate simulation data and lines indicate power-law fits for different time windows; exponents of these fits are shown on the plot. Typical snapshots at different times for different η are also shown. Mw data in the plot is averaged over 50 different simulations starting with different initial configurations. Model parameters are NT = 100, LJ 1/6 σA = σB , zA = −zB , λB = 80, κ−1 = σ0 , ǫLJ σij . ij = 1 and rij,cut = 2 η and a single aggregate spans whole simulation box for η = 0.060, indicating the formation of percolated structures. In general, Mw evolves as Mw ∼ tα1 for short times and ∼ tα2 at intermediate times, where α2 > α1 . As η increases, the crossover time from ∼ tα1 regime to ∼ tα2 regime decreases. Also, since α1 < α2 , NPs aggregate at slower rate at short times but aggregation rate increases after the crossover time. This increase in aggregation rate is due to the fusion of small NP aggregates that are formed in the first power-law regime. As η increases, average separation between NPs decreases, which results in strong Coulombic force and therefore both exponents α1 and α2 increases. We have also investigated (not shown) the 7



effect of λB (= 40, 10), asymmetric size (σA = 1.5σB ), asymmetric charge (zA = −2zB ), and system size (NT = 200, 500), but did not find any qualitative difference on the aggregation kinetics.

Formation of BHJ structure 9

λB =1 λB =2 λB =4 λB =6 λB =10

8 7

λB =1

g+-(r)

6

λB =10

5 4 3 2

λB =2

D

1

λB =4

λB =6

0

9

λB =1 λB =2 λB =4 λB =6 λB= 10

8 7

g++(r)

6

A

5 4 3 2

λ =1 B

type A

type B

E

1 0

+

=

B λ =10 B

type A

type B

+

g--(r)

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=

C

9 8 7 6 5 4 3 2 1 0

λB =1 λB =2 λB =4 λB =6 λB =10

F 0

1

2

3

4

5

6

r/σav

Figure 3: (A) Snapshots of morphology after evolving a random configuration for time t = 10τ0 with different λB and keeping other parameters constant. (B) and (C) shows domains of positive and negative NPs separately for λB = 1 and λB = 10 cases. (D), (E), and (F) are the radial distribution functions for AB, AA, and BB pairs, respectively. Other LJ LJ model parameters are σA = σB , rAA,cut = 2.5σA , rBB,cut = 2.5σB , NT = 5000, zA = −zB , −1 LJ κ = σ0 , ǫij = 5 and η = 0.3. Based on aggregation kinetics results discussed above, it was decided to use high η values to study the percolated structures desired for BHJ. Simulations of large number of NPs (NT = 5000) is feasible for these simulations, since we are interested in short-time evolution without ensemble averaging. While percolated structures do form at high η in fig. 2, contacts 8


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between NPs of same type are missing due to Coulombic repulsion between NPs of same type. We therefore introduce additional hydrophobic attraction between NPs of same type (ǫLJ AA = LJ ǫLJ BB = 5), by increasing the LJ cutoff distances for AA and BB interactions (rAA,cut = 2.5σA , LJ rBB,cut = 2.5σB ). The LJ cutoff distance of AB interaction is unchanged (rAB,cut = 21/6 σAB ),

as they do not have an additional hydrophobic attraction. Fig 3A shows how an initial random configuration evolves to configurations with different domain sizes after time t = 10τ0 for different values of λB . The relative importance of additional hydrophobic attraction compared to the Coulombic repulsion between NPs of same type decreases with an increase LJ in λB , since the strength of LJ interaction (ǫLJ AA , ǫBB ) is fixed. Therefore, the domain sizes

of positive and negative NPs decrease and the interfacial area increases with an increase in λB . This can be easily visible in Fig. 3B and Fig. 3C, where the domains of type A and type B NPs are separately shown for λB = 1 and λB = 10 cases. For λB = 1, domain size of both acceptor and donor are large but the interfacial area is small. On changing λB to 10, domain sizes decrease but the interfacial area increases. To further characterize the resulting BHJ morphology, we computed radial distribution functions (RDFs), g+− (r), g++ (r) and g−− (r) (see Fig. 3D, Fig. 3E, and Fig. 3F). Intensity of first RDF peak at r/σav ∼ 1 refers to the probability of contacts of NPs of given types (normalized with reference to that in an ideal gas of same η). For example, g+− (r) represents probability of contacts of positive and negative NPs; g+− (1) ≈ 8.4, 5.7, 2.6, 0.9 for λB = 10, 6, 4, 2, implying the formation of more AB contacts (larger interfacial area) for larger values of λB . First peak intensity of g++ , g−− decreases and g+− increases as λB increases, which confirms that the number of AA and BB contacts decrease and AB contacts increase with an increase in λB . These correspond to an increase in interfacial area and decrease in domain size of donor and acceptor materials. In fact, for λB = 1, g+− peak vanishes, which indicates the formation of a big single percolated cluster of acceptor and donor materials. This kind of morphology is not suited for BHJ solar cells, as the probability of exciton to reach the interface is less when the domain size is very large and the interfacial area is

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very small, which results in fewer exciton dissociations and lower PCE. At another extreme (λB = 10 in Fig. 3), domain size is least and the interfacial area is maximum, which is also not an efficient BHJ morphology because of the hindrance created by non-percolated small clusters on the charge transport to respective electrode. Efficient morphology corresponds to intermediate values of λB , where both domain sizes and interfacial area are sufficiently large for exciton migration and dissociation.

Effect of asymmetry on BHJ Finally, we investigated the effect of size- and charge-asymmetry of NPs on BHJ morphology. Snapshots in Fig. 4 show the comparison of obtained morphologies of size-asymmetric NPs (σA = 1.5σB , zA = −zB ) and charge-asymmetric NPs (zA = −2zB , σA = σB = σ0 ) with symmetric NPs (σA = σB , zA = −zB ) for two different values of λB . In the size-asymmetric

symmetric

λΒ = 1

+

λ Β = 10

=

size asymmtery

=

+

=

+

=

+

=

E

B =

+

C

+

D

A

charge asymmetry

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type A

type B

F

type A

type B

Figure 4: Comparison of morphology between asymmetric size/charge with symmetric case for two different λB . (A) and (D) shows typical snapshots of morphology formed by selfassembly of size- and charge-symmetric NPs (η = 0.3, σA = σB = σ0 , zA = −zB ) for λB = 1 and 10 respectively. (B), (E) and (C), (F) shows the typical snapshot of morphology formed by self-assembly of size-asymmetric (σA = 1.5σ0 , σB = σ0 ) and charge-asymmetric NPs LJ LJ (zA = −2zB ), respectively. Other model parameters are rAA,cut = 2.5σA , rBB,cut = 2.5σB , −1 LJ NT = 5000, κ = σ0 , ǫij = 5 and η = 0.3. case (Fig. 4B, Fig. 4E), domain size of type A (larger diameter) NPs do not change appre10


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ciably when λB value is varied from 1 to 10 but the interfaces become more rugged, whereas domain size of type B NPs (smaller diameter) shows significant change with change in λB . This can be understood by noting that although the repulsive force between both AA and BB pairs increases with an increase in λB , the effect of repulsive force on BB pair is much greater than AA due to lesser center-to-center separation compared to AA. In the chargeasymmetric case (Fig. 4C, Fig. 4F), domain size of NPs of type A (higher charge) decreases as λB increases, whereas domain size of type B remains almost same but the interfaces become rugged. Here, the repulsive force strength on AA pair is much greater than BB, due to higher valence of type A NP compared to type B. These asymmetric size/charge effect results in net energy change of AA, BB and AB pairs. This readjustment of energy makes AB pairs more favorable than AA(BB) as compared to BB(AA) pairs in case of size(charge) asymmetric NP system. These effects are more precisely visible in radial distribution plots

6

λB =1 λB =2 λB =4 λB =6 λB =10

A1

14

λB =1 λB =2 λB =4 λB =6 λB =10

A2

5 4

10

3

8 6

2

4

1

2

0 1

2

3

4

5

0 0

6

1

2

3

0

1

2

3

r/σav

4

g++(r)

λB =1 λB =2 λB =4 λB =6 λB =10

B1

5

6

0

1

2

r/σav

r/σav

18 16 14 12 10 8 6 4 2 0

4

5

6

10 9 8 7 6 5 4 3 2 1 0

7

λB =1 λB =2 λB =4 λB =6 λB =10

B2

3

4

5

6

5

6

r/σav

6

λB =1 λB =2 λB =4 λB =6 λB =10

B3

5

g--(r)

0

λB =1 λB =2 λB =4 λB =6 λB =10

A3

12

g--(r)

10 9 8 7 6 5 4 3 2 1 0

g++(r)

g+-(r)

in Fig. 5.

g+-(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4 3 2 1

0

1

2

3

4

5

6

r/σav

0 0

1

2

3

4

r/σav

Figure 5: Asymmetric size distribution: (A1), (A2), (A3) shows plot of g+− , g++ and g−− for η = 0.3, σA = 1.5, σB = 1, zA = −zB for different λB . Asymmetric charge distribution: (B1), (B2), (B3) shows plot of g+− , g++ and g−− for η = 0.3, σA = 1 = σB = 1, zA = −2zB for different λB . Peak intensities of g++ and g−− are different for asymmetric size/charge case with same value of λB , which was not the case for symmetric size/charge case. Change in peak intensities as λB changes is not similar for g++ and g−− and this can be used to separately control the domain sizes of acceptor and donor materials. Other model LJ LJ parameters are rAA,cut = 2.5σA , rBB,cut = 2.5σB , NT = 5000, κ−1 = σ0 , ǫLJ ij = 5 and η = 0.3 11



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Conclusion In summary, we have performed a systematic study of the formation of BHJ morphology by self-assembly of oppositely charged NPs using kMC simulations. The weight-averaged aggregate size Mw evolves in two power-law regimes - initial clustering of NPs is slow but becomes faster at longer times due to the fusion of small aggregates. With an increase in NP concentration (quantified by the packing fraction η), the aggregate size increases and the number of aggregates decreases, eventually giving rise to a single big, percolated structure at high packing densities. Using these results and introducing additional hydrophobic attraction for NPs of same type, various functional BHJ morphologies are achieved by changing the Coulombic strength between NPs. In experiments, Coulombic strength can be easily controlled either by changing the surface charge on NPs (e.g., using surfactants) or by using solvents of different dielectric constants. Indeed, in blend systems, it has been found that changing the solvent can drastically change the efficiency of the solar cells, 31 which has been attributed to a change in morphology at molecular level. The additional hydrophobic attraction introduced in our model is also dependent on the solvent and the constituents of NPs. Moreover, we demonstrate that the domain sizes and interfacial area of acceptor and donor materials may also be controlled by varying the size- and charge-asymmetry of NPs. Our simulation results can therefore be used to develop the design rules for the formation of BHJ structure by experimentally controllable parameters like dielectric constant, salt concentration, hydrophobicity, 32 and size 21,33,34 /surface charge 20 of NPs. Work in this direction is currently underway.

Acknowledgement KS acknowledge Science and Engineering Research Board (SERB), India (File no. PDF/2016/000442) for financial support. PKJ is supported by the INSPIRE award from the Department of Science and Technology (DST), India (no. IFA14/ENG-72) 12


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Graphical TOC Entry hν

_ + +_

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Controllable Bulk Heterojunction Morphology by ... - ACS Publications

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