Correlation of nanoscale organizations of polymer and nanocrystals in polymer/inorganic nanocrystal bulk heterojunction hybrid solar cells: insights from multiscale molecular simulations

Energy &Environmental Science

PAPER

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aResearch Center for Applied Sciences, Aca

Taipei 11529, Taiwan. E-mail: cwpao@gatebDepartment of Materials Science and En

Taipei, Taiwan

† Electronic supplementary informa10.1039/c2ee23372j

Cite this: DOI: 10.1039/c2ee23372j

Received 5th September 2012Accepted 13th November 2012

DOI: 10.1039/c2ee23372j

www.rsc.org/ees

This journal is ª The Royal Society of

Correlation of nanoscale organizations of polymer andnanocrystals in polymer/inorganic nanocrystal bulkheterojunction hybrid solar cells: insights frommultiscale molecular simulations†

Cheng-Kuang Lee,a Chun-Wei Pao*a and Chun-Wei Chenb

A comprehensive insight into the correlations of the nanoscale organizations of polymer and nanocrystals

in polymer/inorganic nanocrystal bulk heterojunction (BHJ) hybrid solar cells is the key toward

nanomorphology control for improving device performance. In this study, we investigated the

organizations of both the polymer and nanocrystals in polymer/inorganic nanocrystal hybrid solar cells

by performing multiscale molecular simulations of P3HT:TiO2 nanocrystal BHJs incorporating

nanocrystals with two different dimensionalities, namely, zero-dimensional nanoparticles (NPs), and one-

dimensional nanorods (NRs). We reveal that nanocrystal dimensionality has significant impacts on the

polymer/nanocrystal organizations for polymer/inorganic nanocrystal hybrid blends. One-dimensional

nanocrystals, such as TiO2 NRs, can effectively enhance the polymer degree of crystallinity as a result of

preferential polymer chain alignment along the axial dimension of the NRs, thereby promoting hole

transport; in addition, the elongated, anisotropic NRs significantly reduce the probability of electron

hopping, and maintain a high specific interfacial area for efficient exciton dissociation. Therefore, the

present study demonstrates the possibility of the nanoscale morphology control of polymer/inorganic

nanocrystal BHJ hybrid blends via tuning the nanocrystal shapes, which is potentially helpful for

developing next-generation polymer/inorganic nanocrystal hybrid electronic devices such as solar cells

or thin film transistors.

Broader context

Polymer/inorganic nanocrystal bulk heterojunction (BHJ) hybrid solar cells are one of the promising renewable energy sources due to their low production cost,mechanical exibility, and lightweight compared with their pure inorganic counterparts. One primary feature of polymer/inorganic nanocrystal BHJ hybrid cellsis the tunability of the nanocrystal shapes/sizes. By synthesizing nanocrystals in different shapes [e.g., nanoparticles (NPs), nanorods (NRs), and nanotetrapods]with controllable sizes, the nanocrystal electronic properties can be manipulated to optimize device performance. Nanocrystal shapes/sizes have signicantimpacts on the polymer/nanocrystal organizations in the BHJ layer, which is critical for the solar cell performance. However, the correlations of polymer andnanocrystal organizations in polymer/inorganic nanocrystal BHJ hybrid cells are still unknown since their introduction in 2002. In this work, we developed amultiscale molecular simulation model to investigate polymer/nanocrystal organizations and morphological properties (e.g., specic interfacial area) in P3HT/TiO2 NP/NR blends. Our simulation results indicate that anisotropic NRs can effectively promote polymer crystallinity and eliminate inter-nanocrystal junctions,thereby promoting hole and electron transport. Therefore, the present study provides comprehensive insights into the correlations of polymer/nanocrystalorganizations in polymer/inorganic nanocrystal hybrid solar cells, which is potentially helpful for nanomorphology control in next-generation polymer/inor-ganic nanocrystal solar cells or thin lm transistors.

1 Introduction

Polymer/inorganic nanocrystal hybrid solar cells have drawnconsiderable attention as one of the promising renewable

demia Sinica, 128 Sec. 2 Academia Rd.,

.sinica.edu.tw

gineering, National Taiwan University,

tion (ESI) available. See DOI:

Chemistry 2012

energy sources.1–14 The photoactive layers in polymer/inorganicnanocrystal hybrid solar cells comprise interpenetratingnetworks of electron donor and acceptor phases. The electrondonor materials are usually semiconducting conjugated poly-mers [e.g., regioregular poly(3-hexylthiophene) (P3HT), seeFig. 1a], whereas the electron acceptor materials are usuallysemiconducting inorganic nanocrystals (e.g., CdSe, ZnO, PbS,TiO2). These hybrid solar cells have several advantageousfeatures over their pure inorganic counterparts: lower produc-tion costs through solution processing, greater mechanicalexibility, lighter weight, and additional versatility provided by

Energy Environ. Sci.

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Fig. 1 (a) Atomistic structure of a P3HT chain and the CG model employedherein. Red beads represent CG particles of P3HT; the red-dashed line highlightsthe P3HT repeat unit; all CG intramolecular degrees of freedom (CG bond length,rCG,P3HT; CG bond angle, qCG,P3HT; CG dihedral angle, 4CG,P3HT) are displayed inblue. (b) Upper left panel: atomistic structure of anatase TiO2; the blue boxhighlights the anatase unit cell. Lower left panel: atomistic structure and corre-sponding CG model of a TiO2 NP; lower right panel: atomistic structure andcorresponding CG model of a TiO2 NR.

Energy & Environmental Science Paper

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the ability to control the shapes and sizes of the inorganicnanocrystals.9,10,13 Inorganic nanocrystals can be synthesized ina number of forms with controllable sizes, including nano-particles (NPs), nanorods (NRs), or nanotetrapods;11–16 thenature of these nanostructural materials can signicantlyimpact (i) the organization of the electron donor and acceptormaterials and (ii) the electronic properties of the electronacceptor materials, potentially improving the efficiency of thepolymer/inorganic hybrid solar cells.

The nanoscale organization of polymers and inorganicnanocrystals in a polymer/inorganic hybrid cell has a criticaleffect on device performance. When the photoactive layerabsorbs incident photons, excitons are generated within thepolymer domains; these excitons diffuse toward the polymer/nanocrystal interface and dissociate into free electrons andholes, which are transported to their corresponding electrodesto generate the photocurrent. In polymer/inorganic nanocrystalhybrid solar cells, the donor–acceptor morphological organi-zations are critically correlated with the nanocrystal shapes(e.g., NP, NR or nanotetrapod); hence, a comprehensive insightinto the correlations of polymer/nanocrystals organizations iscritical for morphology control to boost device performance.However, experimental characterization of the polymer/nano-crystal organization of polymer/inorganic hybrid cells is nevertrivial. Recently, electron tomography experiments haverevealed the three-dimensional (3D) structures of variousorganized inorganic nanocrystal phases (ZnO nanocrystals;CdSe NPs and NRs; TiO2 NPs and NRs) in hybrid polymer/inorganic hybrid cells.14–16 Nevertheless, little information existsregarding the correlation between a nanocrystal's shape and itspolymer/nanocrystal organization. Moreover, the generalmorphological criteria determining the optimal blending ratiosin polymer/inorganic hybrid cells, regardless of nanocrystalshape or elemental composition, remain unclear.


In this study, we revealed the correlations of nanoscaleorganizations of both the polymers and inorganic nanocrystalsin polymer/inorganic hybrid cells by performing a series ofmultiscale, coarse-grained (CG; mesoscale) molecular simula-tions of the annealing processes of P3HT:TiO2 nanocrystalhybrid blends with two TiO2 nanocrystal dimensionalities:namely, zero-dimensional nanoparticles (NPs), and one-dimensional nanorods (NRs). With the aid of CGMD compu-tational experiments, we were able to simulate a system sizearound 60 � 60 � 60 nm3, which are compatible with experi-ments and are well-beyond those that can be achieved byconventional atomistic molecular simulations. Our simulationsindicated that a nanocrystal's shape has a signicant impact onpolymer/nanocrystal organization. Relative to zero-dimensionalnanocrystals (i.e., NPs), one-dimensional nanocrystals (i.e.,NRs) can enhance the polymer's degree of crystallinity throughpreferential alignment of the polymer along the NRs' axialdirections, thereby promoting hole transport; furthermore,because they are longer in one dimension, NRs can effectivelyminimize electron hopping events between neighboring NRs topromote electron transport, while retaining a sufficiently smallrod diameter to maintain a large specic interfacial area forefficient exciton dissociation. Finally, we found that, regardlessof the nanocrystal's shape, polymer/inorganic hybrid cellsincorporating favorably organized blends (i.e., blends withoptimal performance) must have a high specic interfacial areato maximize exciton dissociation and almost identical electrondonor–acceptor percolation probabilities to balance electronand hole transport—similar to those of polymer/fullereneblends. Our present study therefore provides comprehensiveinsights into the correlation between polymer/nanocrystalorganization and nanocrystal shape for polymer/inorganicnanocrystal hybrid blends, potentially helpful for developingnovel nanostructural materials of next-generation polymer/inorganic nanocrystal hybrid solar cells or thin lm transistors.

2 Models and methods

The atomistic structures of P3HT and anatase TiO2 NP/NR, andtheir corresponding CG models are depicted in Fig. 1. For theP3HT component, each P3HT repeat unit (region enclosedinside the red dashed line in Fig. 1a) was mapped into a CGbead (colored red in Fig. 1a) centered at the thiophene ring. Ingeneral, there are two approaches for deriving the CG force eldfrom atomistic simulations of smaller system of interest,namely, energy- and structural-based approaches. In the energy-based CG approach, the CG force eld is targeted to reproducethermodynamic properties such as energies or free energies.17,18

On the other hand, the structural-based CG scheme is targetedto reproduce structural properties such as radial distributionfunction (RDF), CG bond length, CG bond angle, and dihedralangles of the CG degrees of freedom.19–30 For the CG model ofP3HT, because the conformations of the P3HT chains are crit-ical for investigating polymer organizations, the CG force eldsbetween the CG particles of P3HT were obtained by employingthe structural-based CG scheme.19–30 It has been demonstratedthat there exists a unique pair function by imposing the same

This journal is ª The Royal Society of Chemistry 2012


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RDF.31 Hence, such a scheme has been demonstrated to be thesafest approach for developing CG models of colloids32,33 orwater molecules.34 The optimized potential parameters arecompiled in Table S1 (ESI).† Detailed procedures for the ttingof the intra- and intermolecular CG potential of P3HT employedin the present study can be found elsewhere.29 The CG forceeld of P3HT tted can successfully reproduce the persistencelength of P3HT,29 guaranteeing that the chain conformationsand associated structural features would be captured well insubsequent CGMD simulations.

For constructing CG models of TiO2 nanocrystals, a differentapproach was employed. TiO2 NPs andNRs with given sizes weremapped into spherical or cylindrical (with hemispherical caps inboth ends) clusters comprising CG beads, see the clusters oforange beads in the lower le and right panels of Fig. 1b, and inthe insets of Fig. S1 in theESI.† Itmust be stressed thatwedidnotcoarse-grain one TiO2 nanocrystal into a single large CG particle(e.g., coarse-graining one TiO2 NR into single ellipsoid). Sincenanocrystals are rigid, in the present study, only inter-nano-crystal interactions between CG beads (i.e., interactions betweenCG beads belonging to different NPs/NRs) were taken intoaccount in tting the CG force elds. The inter-nanocrystal CGforce eld between the CG beads was tted into Lennard-Jonesform, such that the resultant potential energy between two NPs(NRs) from the multisite inter-nanocrystal interaction of CGbeads can reproduce the potential energy surface computedfrom AMD calculations. The diameter of the TiO2 NPs waschosen to be 2.5 nm; the rod diameter and aspect ratio for theTiO2 NRs were set at 2.0 nm and 5, respectively. These sizes forboth the NPs and NRs are comparable with those tested experi-mentally.14 The potential energy surfaces between two TiO2 NPsandNRs fromAMDcalculations are displayed in Fig. S1a andb–e(ESI),† respectively. The uctuations in the potential energybetween the NPs/NRs, due to TiO2 crystal orientations (see errorbars in Fig. S1†), and the TiO2 NR stacking types (e.g., side-by-side, end-to-end, cross and T-shape; inset to Fig. S1b–e†), werealso taken into account. The CG force elds between the CGbeads of the TiO2 NPs and NRs were then tted to reproduce thepotential energy surfaces in Fig. S1† through simplex optimiza-tion35,36 (see blue lines in Fig. S1†). The optimized CG Lennard-Jones parameters for the NPs and NRs are compiled in Table S1(ESI).† Note that there is no orientation-dependent terms in theCG force eld of TiO2 NRs, because we did not coarse-grain a NRinto a single ellipsoid, and the NR orientation dependences wereencapsulated into the simple Lennard-Jones-type CG force eldbetweenCGbeads that takes potential energy surfaces of the fourNR stacking types listed above into account. The CG pairpotential betweenP3HT andTiO2CGbeadswas obtained using amixing rule, due to the compatible CG particle sizes. To examinethe reliability of the CG potential between P3HT and TiO2 CGparticles, two separate simulations were performed to comparethe RDFs of P3HT monomers surrounding a TiO2 NP (see insetsto Fig. S2, ESI†) from the CG model potential and AMD simula-tions. The RDF determined by the CG potential for P3HTmonomers surrounding TiO2 NPs was in excellent agreementwith that from AMD simulations (Fig. S2, ESI†). SubsequentCGMD simulations of P3HT:TiO2 blends employed the MD


package DL_POLY_4 (ref. 37) using the Nose–Hoover thermostatand barostat. The system temperature and pressure were set at423 K and 1 atm; a large time step (5–10 fs) was used in the CGsimulations (cf. 1–2 fs in AMD), and all the boundaries wereperiodic.

3 Results and discussionsThree-dimensional morphologies of the polymer andnanocrystals

Fig. 2a displays the 3D morphologies of P3HT:TiO2 NP (upperpanel) and NR (lower panel) blends prepared at a blending ratioof 1 : 1 aer CG molecular dynamics (CGMD) simulation of thethermal annealing at 423 K for 20 ns; Fig. S3 (ESI)† presents themorphologies obtained at other blending ratios. We observe theformation of interpenetrating networks between the polymerand nanocrystal phases, a critical feature for polymer/inorganicnanocrystal hybrid cells if they are to generate a photocurrent.Fig. 2b and c display the organization of the polymer (Fig. 2b)and nanocrystal (Fig. 2c) units in P3HT:TiO2 NP (upper panel)and NR (lower panel) blends prepared at a blending ratio of1 : 1. In Fig. 2b, the self-alignment of polymer chains is evidentfor both the P3HT:TiO2 NP and NR blends. For mesoscalesimulations, such polymer self-alignment can be viewed aspolymer crystallization. Close examination of Fig. 2b revealsthat the self-alignment (i.e., the degree of crystallinity) of thepolymer units in the P3HT:TiO2 NR blend was greater than thatin the P3HT:TiO2 NP blend. Hence, our simulations indicatethat the nanocrystal's shape can have a signicant impact onthe polymer's organization. Fig. 2c displays the organization ofthe TiO2 NPs (upper panel) and NRs (lower panel); we observenanocrystal aggregation and the existence of percolation path-ways through the simulation cells in both NP and NR blends.Notably, the nanocrystal organization determined from ourCGMD simulations resemble those from electron tomographyexperiments of polymer/TiO2, polymer/CdSe and polymer/ZnOnanocrystal hybrid cells;14–16 therefore, the nanocrystal organi-zation revealed in the present study appears to be generic for allnanocrystals in polymer/inorganic nanocrystal hybrid cells.

Nanocrystal shapes and polymer crystallinity

To quantitatively analyze the polymer organization inP3HT:TiO2 nanocrystal hybrid cells, we employed a spatial-discretization (SD) scheme that we had developed earlier forstudying polymer/fullerene blends.29,30 In this scheme, theentire simulation cell was discretized into cubes (or “pixels”)having sizes (0.7 nm) comparable with those of the CG particlesof P3HT and TiO2. Fig. S4 (ESI)† displays the simulation cellaer SD processing. Next, we coarsed several P3HT “pixels”displayed in Fig. S4† into one sub-domain and computed thelocal orientational order parameter Sj for P3HT monomerswithin the jth sub-domain, using the equation

Sj ¼ 3

2

��uij$nj

�2� 1

3

�; (1)

where uij is the bond vector of the ith bond in the jth sub-domainand nj is the averaged bond vector of the jth sub-domain. Note



Fig. 2 (a) 3D Morphologies of P3HT:TiO2 NP (upper panel) and NR (lower panel) blends; P3HT chains and nanocrystals are colored red and blue, respectively.Organization of (b) P3HT chains and (c) nanocrystals in P3HT:TiO2 NP (upper panel) and NR (lower panel) blends with blending ratio 1 : 1.


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that the jth sub-domain is considered to be a crystalline phase ifSj > 0.3.38 Aer computing local order parameters Sj for all P3HTsub-domains, we determined the probability distribution of Sj.Fig. 3a displays the probability distributions of Sj for P3HTphases featuring different TiO2 blending ratios and nanocrystalshapes; the fractions of crystalline P3HT phases of theP3HT:TiO2 NR blends were in general greater (i.e., a higherproportion of the histogram with Sj > 0.3) than those of theP3HT:TiO2 NP blends; we veried this behavior quantitativelyby computing the degree of crystallinity through integration ofthe histogram from values of Sj ranging from 0.3 to 1.0. Theinset to Fig. 3a displays the degree of crystallinity of P3HT inP3HT:TiO2 NP (upper panel of the inset) and P3HT:TiO2 NR(lower panel of the inset) blends prepared at a blending ratio of1 : 1; we found that the degree of crystallinity of the P3HT:TiO2

NR blend was substantially higher than that of the P3HT:TiO2

NP blend. Therefore, our study reveals that the nanocrystal'sshape can signicantly affect the polymer's organization; withsuitable design of the nanocrystal's shape and size, it should bepossible to enhance the degree of crystallinity of the polymerphase, thereby improving hole transport.

Next, we computed the radial distribution of the degree ofcrystallinity of P3HT—that is, the degree of crystallinity ofP3HT within a shell (spherical for NP; cylindrical for NR)between r and r + Dr, where r is the distance from the TiO2

NP/NR center and Dr is the thickness of the shell (here, we set


Dr at 5 A). Fig. 3b displays the radial distributions of thedegree of crystallinity of P3HT for both TiO2 NPs and NRs.Note that in the horizontal axis of Fig. 3b and c, we used r � a

instead of r, where a denotes the radius of NP/NR. Hence, r �a refers to the distance from the NP/NR surface. It is clear thatP3HT chains tend to crystallize close to the nanocrystalsurface, with the degrees of crystallinity of the polymer in theP3HT:TiO2 NR blends being generally higher than those in theP3HT:TiO2 NP blends. Such a distribution of polymer crys-tallinity can be explained by considering heterogeneousnucleation—namely, the polymer–nanocrystal interfaceproviding heterogeneous nucleation sites for polymercrystallization.

We attribute the higher degrees of crystallinity of P3HT inP3HT:TiO2 NR blends to the alignment of P3HT chains alongthe axial direction of the NRs. For verication, we dened theradial NR axial orientational order parameter sk(r) for P3HTchains as

skðrÞ ¼ 3

2

��uijðrÞ$Nk

�2� 1

3

�; (2)

where uij(r) is the bond vector of the ith bond in the jth chains atdistance r from the kth NR center and Nk is the axial orientationvector of the kth TiO2 NR. If sk(r)$ 0.3, we considered the P3HTbond vectors positioned at a distance r from the kth NR to bealigned with the axial vector of the kth NR. We further dened



Fig. 3 (a) Probability distributions of the local order parameter Sj for the P3HT:TiO2 NP/NR blends; inset: degrees of crystallinity of the P3HT:TiO2 NP (upper panel) andP3HT:TiO2 NR (lower panel) blends prepared at blending ratios of 1 : 1. (b) Radial distributions of the degrees of crystallinity of P3HTnear TiO2 NPs andNRs; a: radius of TiO2

NP or NR. (c) Time lapse of the distribution of the degree of axial alignment of P3HT chains with a TiO2 NR. (d) Schematic depiction of NR-assisted polymer crystallization.


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U(r), the degree of axial alignment of P3HT chains with a TiO2

NR at a distance r from the NR surface, as

UðrÞ ¼

� ÐrþDr

r

H�skðrÞ � 0:3

�2prdr

�kÐrþDr

r

2prdr

� 100%; (3)

where H is the Heaviside step function. Fig. 3c displays the timelapse of U(r) of the 1 : 1 P3HT:TiO2 NR blend. Clearly, as theannealing process continued, U(r) became increasingly large—particularly in the region near the NR surface. The inset ofFig. 3c provides a schematic representation of this phenom-enon, with the polymer units beginning to align themselveswith the axial direction of the NRs. Similar phenomena areunlikely for NPs because of their spherical symmetry. Further-more, by comparing U(r), at a t value of 20 ns (blue line inFig. 3c), with the radial distribution of the degree of crystallinityof P3HT (Fig. 3b, also computed at t ¼ 20 ns), we nd that thecrystallization of P3HT was correlated directly to the alignmentof polymer chains along the NR's axial direction. Fig. 3d pres-ents a schematic representation of the roles played by the TiO2


NRs during the organization of the P3HT polymer units: here,the NRs serve as “templates” for P3HT crystallization. The P3HTchains close to the NR surface tended to align along the NR axialdirection; therefore, highly crystallized regions (cylindricalvolume highlighted in yellow in Fig. 3d) of P3HT were formedsurrounding the NRs, with the P3HT chains aligned along theNR axis. A recent experimental study has revealed P3HT chainalignment with TiO2 rod axis;39 therefore, our observations arein excellent agreement with recent experiments. Hence, byselecting a one-dimensional, anisotropic nanostructural mate-rial (e.g., a nanowire or NR), having a suitable size, as theelectron acceptor material, the polymer's degree of crystallinitycan be enhanced substantially, thereby improving the holemobility of the polymer/inorganic nanocrystal hybrid cell.

Nanocrystal shape and nanocrystal organization

The organization of nanocrystals has a critical effect on electrontransport aer exciton dissociation and subsequent chargeseparation at the polymer–nanocrystal interface. The bottleneckfor electron transport within the nanocrystal phase is electronhopping between neighboring nanocrystals; therefore, the




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number of hopping events required for electron transportwithin a nanocrystal domain is positively correlated with theelectron mobility within the nanocrystal phase. Hence, we canuse the number of inter-nanocrystal junctions per nanocrystaldomain to estimate the number of hopping events required forelectron transport. The number of inter-nanocrystal junctionsper domain readily correlates with the number of nanocrystalsper domain, which can be estimated by dividing the totalnumber of nanocrystals by the number of nanocrystal domains.Fig. 4a displays a time lapse of the number of TiO2 NP/NRdomains obtained at different P3HT:TiO2 blending ratios. Weobserve that all of the blends reached equilibrium aer 20 ns ofannealing simulation. Aggregation of the TiO2 NPs and NRs wasevident because the number of NP/NR domains underwent asignicant decrease during the annealing process. At thebeginning of each of our simulations, none of the TiO2 NPs/NRswere in contact; therefore, the number of TiO2 NP/NR domainsat t¼ 0 ns was equal to the total number of TiO2 NPs/NRs in theblends. Therefore, we could estimate the average number ofnanocrystals per nanocrystal domain at the end of each simu-lation. At a blending ratio of 1 : 1, Fig. 4a reveals that 46.7 and15.7 TiO2 NPs and NRs, respectively, were present per domain.Therefore, there were many more inter-nanocrystal junctions inthe polymer/NP blends than in the polymer/NR blends. As dis-played schematically in Fig. 4b, the number of electron hoppingevents required for electron transport among the NPs wasgreater than that for the NRs; hence, our study reveals that, dueto their long length in one dimension, NRs can effectivelyminimize the number of electron hopping events required fortransporting electrons, thereby promoting electron transport inpolymer/inorganic nanocrystal hybrid cells.

Domain characteristic width and specic interfacial area

Our simulations have revealed that polymer/NR blends havesuperior polymer crystallinity and fewer inter-nanocrystaljunctions than those of polymer/NP blends; as a result, wewould predict that electron and hole transport in polymer/NR

Fig. 4 (a) Time lapse of the number of NP/NR domains. (b) Schematic representat


blends should be superior to that in polymer/NP blends. Inaddition to polymer/nanocrystal organizations and theirimplication in charge carrier transport, mesoscale, morpho-logical properties correlated with domain sizes and donor–acceptor interfacial area are also critical for charge carriertransport, exciton dissociation, and subsequent photocurrentgeneration in polymer/nanocrystal hybrid cells. Recent device-oriented, theoretical studies have indicated that large domainsize leads to high charge mobilities,40 high current density, andlow exciton dissociation efficiencies.41 However, the initialcongurations for these mesoscale theoretical calculations werenot derived from experiments or from direct molecular simu-lations. Hence, based on the morphologies directly obtainedfrom CGMD simulations, we wished to investigate the effects ofnanocrystal shape on the morphological properties that arecorrelated with exciton dissociation rates and charge separationprobabilities—namely, (i) the characteristic length-scale thatexcitons must travel in the polymer phase to reach the polymer–nanocrystal interface and (ii) the specic interfacial area of thepolymer–nanocrystal interface. The characteristic length-scalefor exciton diffusion can be evaluated by computing the char-acteristic pathway width (w) of polymer/nanocrystal phasesthrough autocorrelation length (ACR) analysis of the polymerphase.42 The details of the ACR analysis employed in the presentstudy are provided in the ESI.†

Fig. 5a displays the characteristic widths w of both the P3HTpolymer and the TiO2 nanocrystals phases at different blendingratios and various nanocrystal shapes. We observe that thevalues of wP3HT in the P3HT:TiO2 NR blends were always largerthan those in the P3HT:TiO2 NP blends. Therefore, the chanceof charge recombination in P3HT:TiO2 NR blends was greaterthan that in NP blends. We note, however, that the maximumvalue of wP3HT in the NR blend was 21 nm (blending ratio: 1 : 1);therefore, the distance one exciton must travel to meet thenearest polymer–nanocrystal interface was approximately11 nm—within the typical diffusion length of an exciton inP3HT. In addition, we also found that the values of wTiO2

inP3HT:TiO2 NR blends were larger than those in P3HT:TiO2 NP

ion of electron transport in NP (upper panel) and NR (lower panel) domains.



Fig. 5 Morphological properties of P3HT:TiO2NP/NRblends at various blending ratios, determined fromthe SD scheme: (a) characteristicwidthw; (b) specific interfacialarea g; (c) percolation probability r. The optimal blending ratios for P3HT:TiO2 NP/NR blends, determined experimentally,14 are highlighted with gold dashed lines.


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blends; hence, the microstructures in the NR blends were, ingeneral, coarser than those in NP blends.

Next, we examined the specic interfacial areas (g) of thepolymer/nanocrystal interfaces. Fig. 5b displays the values of gplotted with respect to the blending ratio and the nanocrystal'sshape. We found that the specic interfacial areas of theP3HT:TiO2 NP blends were, in general, greater than those in theNR blends, suggesting that the microstructures in theP3HT:TiO2 NR blends are “coarser” than those in the P3HT:TiO2

NP blends—in agreement with our characteristic width anal-yses. Because NRs are long in one dimension and rigid, theycannot form NR domains with domain shapes that meander,such as those of NPs with similar diameters, as displayedschematically in Fig. 4b. Hence, our results indicate that theanisotropy of NRs leads to less meandering domains andcoarser polymer/nanocrystal microstructures in comparisonwith those obtained with NPs. Therefore, we reveal that forsimilar particle/rod diameters, polymer/NP blends should haveslightly superior exciton dissociation and charge separationrates, and lower charge carrier mobilities than those of polymer/NR blends; these observations are in good agreement withrecent photocarrier dynamics experiments.14

Based on our analyses, we believe that, when used as electronacceptor materials in polymer/inorganic nanocrystal hybridcells, one-dimensional nanocrystals, such as NRs, have severaladvantages over zero-dimensional nanocrystals, such as NPs.The long cylindrical shape of a NR can effectively promotepolymer crystallinity and, thereby, facilitate hole transport. Inaddition, because the specic interfacial area is inverselyproportional to the rod diameter, NRs can minimize electronhopping events between neighboring NRs by increasing the rodlength, thereby promoting electron transport, while maintain-ing a rod diameter sufficiently small to maintain a high specicinterfacial area for efficient exciton dissociation. For zero-dimensional nanocrystals, such as NPs, the specic interfacialarea is inversely proportional to the particle diameter; therefore,it is impossible to increase the particle size (to minimize thenumber of inter-nanocrystal junctions) while maintaining ahigh specic interfacial area. For example, to eliminate the NPinter-nanocrystal junctions displayed schematically in Fig. 4b,the particle diameter should be four times larger; this change


will, however, result in the specic interfacial area of the NPblend becoming four times smaller. On the other hand, byusing the NRs displayed in Fig. 4b, it should be possible toeliminate electron hopping while maintaining a high specicinterfacial area. Hence, relative to zero-dimensional NPs, one-dimensional NRs provide a better balance between electrontransport and exciton dissociation by promoting polymer crys-tallinity and minimizing the number of inter-nanocrystaljunctions, while maintaining a reasonably high specic inter-facial area.

Optimal polymer/nanocrystal blending ratios

We have found a correlation between the morphological prop-erties and the donor–acceptor blending ratio. Fig. 5b reveal that,regardless of the nanocrystal's shape, the blending ratio with amaximum specic interfacial area (1 : 1) overlaps with theoptimal blending ratio found experimentally. Because thespecic interfacial area correlates positively with the degrees ofexciton dissociation and charge separation, our results indicatethat, for polymer/inorganic nanocrystal hybrid cells, blendswith the optimal blending ratio must have a maximum specicinterfacial area to facilitate the generation of free electrons andholes. It must be noted that electron–hole recombination alsotakes place at donor–acceptor interface;43 therefore, largespecic interfacial area also increases the charge carrierrecombination probability. Since our simulation results showthat blends with the highest specic interfacial area correspondto the blending ratio giving the optimal device performance, itis highly likely that charge carrier generation prevails chargecarrier recombination. Hence, a mesoscale charge carriertransport simulation such as random walk numerical simula-tion (RWNS)44 based on the morphologies generated fromCGMD in the present study would be helpful in clarifying thecomplicated interplay between charge carrier generation/recombination.

In addition to specic interfacial area, percolation pathwaysfor the electron donor–acceptor phases are also necessary forsubsequent electron–hole transport to electrodes. To quantifythe percolation quality of each phase, we dened the percola-tion probability r as the volume fraction of each phase that




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could percolate through the simulation cell. Fig. 5c plots thepercolation probabilities r of the P3HT and TiO2 nanocrystalphases with respect to the blending ratio and the nanocrystal'sshape. We observed that the value of rP3HT decreased signi-cantly upon increasing the TiO2 blending ratio, indicating thatmore isolated P3HT domains existed and poorer hole transportoccurred at higher TiO2 blending ratios. On the other hand,increasing the P3HT blending ratio led to more isolated TiO2

domains and poorer electron transport. Fig. 5c reveals that thevalues of rP3HT and rTiO2

were most similar at the optimalblending ratio reported from previous experiments (i.e., aP3HT:TiO2 blending ratio of 1 : 1). This result can be explainedby considering the balance between charge carrier trapping andtransport: at blending ratios that lead to high values of rP3HT

(rTiO2) and low values of rTiO2

(rP3HT), despite improved hole(electron) transport, the electron (hole) transport would behindered as a result of the existence of numerous isolated TiO2

(P3HT) domains. Therefore, our study reveals that, for polymer/inorganic nanocrystal hybrid cells, regardless of the nano-crystal's shape, blends featuring the optimal blending ratiomust have the maximum specic interfacial areas and themost-similar donor–acceptor percolation probabilities; these criteriaare similar to those of the polymer/fullerene blends that we hadinvestigated previously.29,30

4 Conclusion

Based on structural properties and potential energy surfacesdetermined from AMD simulations of smaller systems, we haveconstructed CG models for P3HT:TiO2 nanocrystal hybridblends featuring nanocrystals with two types of shapes: NPs andNRs. With such a CG model, we could simulate the thermalannealing processes of blends at various P3HT:TiO2 nanocrystalblending ratios, with system sizes comparable with those foundexperimentally. We investigated the effect of the nanocrystalshape on the polymer/nanocrystal organization and polymer–nanocrystal interfaces—and, therefore, on hole–electron trans-port and exciton dissociation/charge separation, respectively.Our results indicate that one-dimensional nanocrystals, such asNRs, can promote polymer crystallinity as a result of preferen-tial polymer alignment along the NR axis, thereby enhancinghole transport. Hence, the present study reveals the possibilityof morphology control by ne-tuning nanocrystal shapes. Inaddition, the one-dimensional features of NRs make it possibleto minimize the number of inter-nanocrystal junctions topromote electron transport, while retaining a reasonably highspecic interfacial area for efficient exciton dissociation.Finally, we determined the morphological criteria inuencingthe optimal blending ratios in polymer/inorganic hybrid cells—namely, the highest specic interfacial area to maximize excitondissociation and the most-similar donor–acceptor percolationprobabilities to balance electron–hole transport. This studydemonstrates that multiscale molecular simulations andsubsequent morphological evaluations can provide compre-hensive insight into the mesoscale morphologies of polymer/inorganic blends—features that are difficult to characterizeexperimentally—and, therefore, it has the potential to aid the


development of more-efficient polymer/inorganic nanocrystalhybrid cells.

Acknowledgements

We thank for the Research Center for Applied Science,Academia Sinica, and the National Science Council of Taiwan(project no. NSC 99-2112-M-001-004-MY3) for nancial supportand the National Center for High Performance Computing forcomputational support.

Notes and references

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