NATUREIVol 439 5 January 2006 LETTERS ligands. Although these additives are effective in adjusting the particle example, ABA, ABS, AB6, AB13)might form when both charged and charge states, the specific interactions by which this charge tuning neutral nanoparticles of type B are incorporated into the structures. occurs will require further study( Supplementary Discussion 1 The presence of differently charged nanoparticles in the colloidal In the presence of oleic acid, PbSe and Au nanoparticles are solutions(Fig. 2a and Supplementary Fig. 5)could also contribute to oppositely charged(Fig. 2e). The Coulomb potential between two the simultaneous formation of different BNSLs Intentional addition oppositely charged nanoparticles(Z==1)separated by 10 nm of a of a large concentration of charged species into a solution of solvent like chloroform is comparable with kTat room temperature, nanoparticles might reduce the Debye screening length down to and solutions of mixed PbSe and metal nanoparticles retain stability Ro, relaxing the strict rules for BNSL charge neutrality and allowing a for several weeks. The relatively small interparticle potential range of new structures to be formedto. favours annealing of the BNSLs as they grow. For a NaCl-type Tuning the charge state of the nanoparticles allows us to direct the BNSL with Z+=1, Z-=-l and the nearest-neighbour distance self-assembly process. Reproducible switching between different Ro=11.5nm(Fig 1a), the Coulomb binding energy per unit cell is BNSL structures has been achieved by adding small amounts of estimated to be UCoul mz 4tEEORo)N-0 1ev (or about carboxylic acids, TOPO or dodecylamine to colloidal solutions of 4kT at the superlattice growth temperature, 50C), where PbSe(PbS, Fe203, and so on) and metal(Au, Ag, Pd)nanocrystal M=-17476 is the Madelung constant. The Coulomb binding Figure 3 demonstrates how these additives direct the formation of energy is comparable to the van der Waals attractive energy expected specific BNSL structures Combining native solutions of 6.2 nm PbSe forces(1/R)can rival long-range Coulomb energy(1/R)only at results in the formation of several BNSL structures with MgZn2 and the nanometre scale. In BNSLs, we can neglect screening of the cuboctahedral ABi3 lattices dominating. However, the same nano- Coulomb potential by charged species in solution because the Debye particles assemble into orthorhombic AB- and AlBz-type super screening length(-10"cm)is much larger than Ro(refs 10, 11). In lattices after adding oleic acid(Fig. 3a),and into NaZn13-or an ABx BNSL where A and B hold opposite charges, the Coulom potential per ABx molecule' is UCoul = -a+B(xZ-+Z+N2/3 here a and B are positive constants and N is the number of TOPO assembled nanoparticles( Supplementary Discussion 2) Coulomb energy determines the stoichiometry of the growing BNSL.An extended three-dimensional BNSL can form only if the positive and negative charges compensate each other. If during E growth the BNSL accumulates non-compensated charge, eventually m UCoul changes sign from negative to positive and the growth is self limiting. The superlattice nucleation stage should be less sensitive to 8 the Coulomb interactions. Indeed, we observed that many small domains with different BNSL structures can simultaneously nucleate E one or two structures grow to larger length scales 6 on the same substrate, but their size does not exceed -10- nano- (-106-10 particles). BNSLs with many particles per unit cell (for o1 dig nm d 0.8-0.40 0.4 Figure 2 I Electrophoretic mobility of PbSe and Au nanocrystals in 20m chloroform. a-d, Distribution of electrophoretic mobility for 7. 2nm PbSe tals a, PbSe nanocrystals washed to remove excess of cappin Figure 3 TEM images of binary superlattices self-assembled in the inds. The grey bars show mobilities predicted for nanocrystals with ence of 4 mM oleic acid (left column) and 6 mM tri-n-octylphosphi arges of-1, 0, I and 2(in units of e). b-d, Electrophoretic mobility of oxide, TOPo (right column). a, 6.2 nm PbSe and 3.0 nm Pd PbSe nanocrystals in the presence of b, 0.02 M oleic acid, c, 0.06 M oleic acid anopartides self-assembled into orthorhombic AB- and AlB,type BNSls, and d, 0.05 M tri-n-octylphosphine oxide. e, f, Comparison of nd b, into NaZn3-type BNSL. c, d, 7.2 nm PbSe and 4.2 nm Ag electrophoretic mobilities of 7. 2 nm PbSe and 4.8 nm Au nanocrystals in the nanoparticles self-assembled into orthorhombic AB and cuboctahedral presence of e, 0.02 M oleic acid and f, 0.05 M tri-n-octylphosphine oxide, AB13 BNSLs, respectively. e, f, 6.2 nm PbSe and 5.0 nm Au nanoparticles self respectively. a u, arbitrary units assembled into CuAu-type and Ca Cus-type BNSLs, respectivel 2006 Nature Publishing Group© 2006 Nature Publishing Group ligands. Although these additives are effective in adjusting the particle charge states, the specific interactions by which this charge tuning occurs will require further study (Supplementary Discussion 1). In the presence of oleic acid, PbSe and Au nanoparticles are oppositely charged (Fig. 2e). The Coulomb potential between two oppositely charged nanoparticles (Z ¼ ^1) separated by 10 nm of a solvent like chloroform is comparable with kTat room temperature, and solutions of mixed PbSe and metal nanoparticles retain stability for several weeks. The relatively small interparticle potential favours annealing of the BNSLs as they grow. For a NaCl-type BNSL with Zþ ¼ 1, Z 2 ¼ 21 and the nearest-neighbour distance R0 ¼ 11.5 nm (Fig. 1a), the Coulomb binding energy per unit cell is estimated to be UCoul < MZþZ2e2=ð4p110R0Þ < 20:1 eV (or about 24kT at the superlattice growth temperature, 50 8C), where M ¼ 21.7476 is the Madelung constant. The Coulomb binding energy is comparable to the van der Waals attractive energy expected for a NaCl-type BNSL. The energy of short-range van der Waals forces (,1/R6 ) can rival long-range Coulomb energy (,1/R) only at the nanometre scale. In BNSLs, we can neglect screening of the Coulomb potential by charged species in solution because the Debye screening length (,1024 cm) is much larger than R0 (refs 10, 11). In an ABx BNSL where A and B hold opposite charges, the Coulomb potential per ABx ‘molecule’ is UCoul < 2a þ bðxZ2 þ ZþÞ 2 N2=3; where a and b are positive constants and N is the number of assembled nanoparticles (Supplementary Discussion 2). Coulomb energy determines the stoichiometry of the growing BNSL. An extended three-dimensional BNSL can form only if the positive and negative charges compensate each other. If during growth the BNSL accumulates non-compensated charge, eventually UCoul changes sign from negative to positive and the growth is self￾limiting. The superlattice nucleation stage should be less sensitive to the Coulomb interactions. Indeed, we observed that many small domains with different BNSL structures can simultaneously nucleate on the same substrate, but their size does not exceed ,102 nano￾particles. Only one or two structures grow to larger length scales (,106 –108 particles). BNSLs with many particles per unit cell (for example, AB4, AB5, AB6, AB13) might form when both charged and neutral nanoparticles of type B are incorporated into the structures. The presence of differently charged nanoparticles in the colloidal solutions (Fig. 2a and Supplementary Fig. 5) could also contribute to the simultaneous formation of different BNSLs. Intentional addition of a large concentration of charged species into a solution of nanoparticles might reduce the Debye screening length down to R0, relaxing the strict rules for BNSL charge neutrality and allowing a range of new structures to be formed10. Tuning the charge state of the nanoparticles allows us to direct the self-assembly process. Reproducible switching between different BNSL structures has been achieved by adding small amounts of carboxylic acids, TOPO or dodecylamine to colloidal solutions of PbSe (PbS, Fe2O3, and so on) and metal (Au, Ag, Pd) nanocrystals. Figure 3 demonstrates how these additives direct the formation of specific BNSL structures. Combining native solutions of 6.2 nm PbSe and 3.0 nm Pd nanoparticles (particle concentration ratio ,1:5) results in the formation of several BNSL structures with MgZn2 and cuboctahedral AB13 lattices dominating. However, the same nano￾particles assemble into orthorhombic AB- and AlB2-type super￾lattices after adding oleic acid (Fig. 3a), and into NaZn13- or Figure 2 | Electrophoretic mobility of PbSe and Au nanocrystals in chloroform. a–d, Distribution of electrophoretic mobility for 7.2 nm PbSe nanocrystals. a, PbSe nanocrystals washed to remove excess of capping ligands. The grey bars show mobilities predicted for nanocrystals with charges of 21, 0, 1 and 2 (in units of e). b–d, Electrophoretic mobility of PbSe nanocrystals in the presence of b, 0.02 M oleic acid, c, 0.06 M oleic acid and d, 0.05 M tri-n-octylphosphine oxide. e, f, Comparison of electrophoretic mobilities of 7.2 nm PbSe and 4.8 nm Au nanocrystals in the presence of e, 0.02 M oleic acid and f, 0.05 M tri-n-octylphosphine oxide, respectively. a.u., arbitrary units. Figure 3 | TEM images of binary superlattices self-assembled in the presence of 4 mM oleic acid (left column) and 6 mM tri-n-octylphosphine oxide, TOPO (right column). a, 6.2 nm PbSe and 3.0 nm Pd nanoparticles self-assembled into orthorhombic AB- and AlB2-type BNSLs, and b, into NaZn13-type BNSL. c, d, 7.2 nm PbSe and 4.2 nm Ag nanoparticles self-assembled into orthorhombic AB and cuboctahedral AB13 BNSLs, respectively. e,f, 6.2 nm PbSe and 5.0 nm Au nanoparticles self￾assembled into CuAu-type and CaCu5-type BNSLs, respectively. NATURE|Vol 439|5 January 2006 LETTERS 57