REPORTS A selection of results is presented in Fig.3 ery.To address this,we tentatively used a scaling 5.B.Devincre,L Kubin,T.Hoc,Scr.Mater.54,741 (2006) for tensile deformation at 300 K.with emphasis law derived from Escaig's model for cross-slip (4). 6.V.V.Bulatov et al.,Nature 440,1174 (2006). on copper crystals.Although the model does The present results indicate that,paradoxi- 7.V.Bulatov,F.Abraham,L.Kubin,B.Devincre,S.Yip, Nature391,669(1998) not incorporate ad hoc switches,the resolved cally,realistic strain hardening properties in uni- 8.R.Madec.B.Devincre,L Kubin,T.Hoc,D.Rodney, stress/strain curves (Fig.3A)exhibit the tradi- axial deformation are obtained without accounting Science301,18792003). tional stages that characterize fcc single crystals for dislocation pattering (18,19);that is,for 9.P.Franciosi,M.Berveiller,A.Zaoui,Acta Metall.28,273 (16).The low-hardening stage I,during which a the emergence of non-uniform microstructures (1980). 10.U.F.Kocks,H.Mecking,Prog.Mater.Sci.48,171 (2003). single slip system is activated,appears for low- during plastic flow.A possible reason is that the 11.C.Teodosiu,).-L.Raphanel,L Tabourot,in Large Plastic symmetry orientations like [123].The linear wavelength of dislocation patters and the mean Deformations,C.Teodosiu,)L.Raphanel,F.Sidoroff,Eds. stage II is due to forest hardening,and its slope free path values follow the same scaling rela- (A.A Balkema,Rotterdam,Netherlands,1993),p.153. increases with the number of active slip systems. tion,in tension or compression. 12.M.-Carmen Miguel,A.Vespignani,S.Zapperi,]Weiss, 1.-R.Grasso,Nature410,667(2001). The subsequent decrease in strain hardening rate This study shows that the mean free path 13.F.F.Csikor,C.Motz,D.Weygand,M.Zaiser,S.Zapperi, is also orientation-dependent and stems from of dislocations is the missing link connecting Science318,251(2007). dynamic recovery.All of these features are in discrete dislocation interactions and avalanche 14.B.Devincre,L Kubin,T.Hoc,Scr.Moter.57,905 (2007) excellent agreement with published experimen- processes to strain hardening properties in the 15.T.Hoc,C.Rey,1.-L Raphanel,Acto Mater.49.1835 (2001). 16.T.E.Mitchell,Prog.AppL Mater.Res.6,117 (1964). tal results (16,/7).Figure 3B shows the evo- bulk.The present multiscale methodology should 17.T.Takeuchi,Trans.JIM 16,629 (1975) lution of the shear strains and densities on the apply to several areas of practical importance, 18.L Kubin,Science 312,864 (2006). primary and secondary slip systems during a such as the mechanical response of polycrystal- 19.L Kubin,B.Devincre,T.Hoc,Mater.Sci.Eng.A simulated [123]test.It is representative of the line materials or size effects in small dimensions. 483-484,19(2008). 20.The authors acknowledge funding by their host wealth of detailed information that can be ob- institutions:CNRS,ONERA and Ecole Centrale Paris tained at the scale of slip systems.Finally,Fig.3C illustrates a broader aspect of this type of mod- References and Notes 1.]Friedel,Dislocotions (Pergamon,Oxford,1967). Supporting Online Material eling by presenting [123]stress/strain curves for 2.)Hirth,]Lothe,Theory of Dislocations (Krieger www.sciencemag.org/cgi/content/full/320/5884/1745/DC1 several foc crystals at room temperature.In addi- Malabar,FL 1992). SOM Text tion to a rescaling of lattice parameters and elastic 3.A.H.Cottrell,in Dislocations in Solids,vol.11, Fig.S1 constants,shifting from one fcc material to the F.R.N.Nabarro,M.S.Duesbery,Eds.(Elsevier, References Amsterdam,2002),p.vii. other implies changes in the annihilation proper- 4.Simulation methods and additional information are 5 February 2008;accepted 2 May 2008 ties of screw dislocations during dynamic recov- avallable as supporting material on Science Online. 10.1126/cience.1156101 Despite this progress,the conversion of metal- Ordered Mesoporous Materials polymer hybrids into mesoporous materials with ordered and large pores (10 nm)has not been from Metal Nanoparticle-Block accomplished,in part because of the low volume fraction of metals in most hybrids and the wide- Copolymer Self-Assembly spread use of gold,which has a high diffusion coefficient and therefore retains its mesostructure only at low temperatures(7-9).Although a protec- Scott C.Warren,1.2 Lauren C.Messina,2 Liane S.Slaughter,2 Marleen Kamperman,1 Qin Zhou,2 tive organic layer can be added to metal NPs to Sol M.Gruner,3 Francis ]DiSalvo,2 Ulrich Wiesner* prevent uncontrolled aggregation,even a thin or- ganic layer represents a considerable volume of The synthesis of ordered mesoporous metal composites and ordered mesoporous metals is a the overall material:For example,a 1-nm-diameter challenge because metals have high surface energies that favor low surface areas.We metal NP with a relatively thin 1-nm organic shell present results from the self-assembly of block copolymers with ligand-stabilized platinum is just 4%metal by volume.As a result,the typica nanoparticles,leading to lamellar CCM-Pt-4 and inverse hexagonal(CCM-Pt-6)hybrid metal content in most block copolymer-metal NP mesostructures with high nanoparticle loadings.Pyrolysis of the CCM-Pt-6 hybrid produces an hybrids is only a few volume%,and the prospects ordered mesoporous platinum-carbon nanocomposite with open and large pores for converting the hybrid into an ordered meso- (>10 nanometers).Removal of the carbon leads to ordered porous platinum mesostructures. porous material,in which the metal would have a The platinum-carbon nanocomposite has very high electrical conductivity (400 siemens per volume fraction between 60 and 75%for an in- centimeter)for an ordered mesoporous material fabricated from block copolymer self-assembly. verse hexagonal structure,are poor. Mesoporous metals have been synthesized at a espite considerable progress in the field tion of Raney nickel and other metals(3).Dealloy- smaller length scale,with 2-to 4-nm pores,through of porous solids,major challenges re- ing processes provide limited control over structural the coassembly of metal ions with small-molecule main in the synthesis of ordered meso- parameters such as pore geometry and order.In surfactants followed by reduction (10-13).The porous materials with high metal content from contrast,block copolymer self-assembly or tem- small pore size,however,limits the flow of liquids the coassembly of macromolecular surfactants plating with metal species provides access to highly through the material,which is essential for many and inorganic species.Controlling the structure of ordered structures.Synthetic routes to such struc- applications (14,15).Metals have also been de- metals at the mesoscale (2 to 50 nm)is crucial for tures have included adsorbing and then reducing posited onto (/6)or into (/7)thin films of block the development of improved fuel cell electrodes metal ions within a preassembled block copolymer and may also assist in the miniaturization of scaffold (4)and coassembling ligand-stabilized Department of Materials Science and Engineering,Cornell optical and electronic materials for data transmis- nanoparticles (NPs)with block copolymers (5). University,Ithaca,NY 14853,USA.Department of Chemistry sion,storage,and computation (/2). More recently,polymer-coated NPs that behave and Chemical Biology,Cornell University,Ithaca,NY 14853,USA.Department of Physics,Comell University. An early route to preparing mesoporous metals like surfactants have been isolated at the interface Ithaca,NY 14853.USA. involves the dealloying of a less noble metal from a of block copolymer domains,which can create a *To whom correspondence should be addressed.E-mail: bimetallic alloy;this has been used for the prepara- bicontinuous morphology at higher loadings (6). ubw1@cornell.edu 1748 27 JUNE 2008 VOL 320 SCIENCE www.sciencemag.orgA selection of results is presented in Fig. 3 for tensile deformation at 300 K, with emphasis on copper crystals. Although the model does not incorporate ad hoc switches, the resolved stress/strain curves (Fig. 3A) exhibit the tradi￾tional stages that characterize fcc single crystals (16). The low-hardening stage I, during which a single slip system is activated, appears for low￾symmetry orientations like [123]. The linear stage II is due to forest hardening, and its slope increases with the number of active slip systems. The subsequent decrease in strain hardening rate is also orientation-dependent and stems from dynamic recovery. All of these features are in excellent agreement with published experimen￾tal results (16, 17). Figure 3B shows the evo￾lution of the shear strains and densities on the primary and secondary slip systems during a simulated ½123
test. It is representative of the wealth of detailed information that can be ob￾tained at the scale of slip systems. Finally, Fig. 3C illustrates a broader aspect of this type of mod￾eling by presenting [123] stress/strain curves for several fcc crystals at room temperature. In addi￾tion to a rescaling of lattice parameters and elastic constants, shifting from one fcc material to the other implies changes in the annihilation proper￾ties of screw dislocations during dynamic recov￾ery. To address this, we tentatively used a scaling law derived from Escaig’s model for cross-slip (4). The present results indicate that, paradoxi￾cally, realistic strain hardening properties in uni￾axial deformation are obtained without accounting for dislocation patterning (18, 19); that is, for the emergence of non-uniform microstructures during plastic flow. A possible reason is that the wavelength of dislocation patterns and the mean free path values follow the same scaling rela￾tion, in tension or compression. This study shows that the mean free path of dislocations is the missing link connecting discrete dislocation interactions and avalanche processes to strain hardening properties in the bulk. The present multiscale methodology should apply to several areas of practical importance, such as the mechanical response of polycrystal￾line materials or size effects in small dimensions. References and Notes 1. J. Friedel, Dislocations (Pergamon, Oxford, 1967). 2. J. Hirth, J. Lothe, Theory of Dislocations (Krieger, Malabar, FL, 1992). 3. A. H. Cottrell, in Dislocations in Solids, vol. 11, F. R. N. Nabarro, M. S. Duesbery, Eds. (Elsevier, Amsterdam, 2002), p. vii. 4. Simulation methods and additional information are available as supporting material on Science Online. 5. B. Devincre, L. Kubin, T. Hoc, Scr. Mater. 54, 741 (2006). 6. V. V. Bulatov et al., Nature 440, 1174 (2006). 7. V. Bulatov, F. Abraham, L. Kubin, B. Devincre, S. Yip, Nature 391, 669 (1998). 8. R. Madec, B. Devincre, L. Kubin, T. Hoc, D. Rodney, Science 301, 1879 (2003). 9. P. Franciosi, M. Berveiller, A. Zaoui, Acta Metall. 28, 273 (1980). 10. U. F. Kocks, H. Mecking, Prog. Mater. Sci. 48, 171 (2003). 11. C. Teodosiu, J.-L. Raphanel, L. Tabourot, in Large Plastic Deformations, C. Teodosiu, J. L. Raphanel, F. Sidoroff, Eds. (A. A. Balkema, Rotterdam, Netherlands, 1993), p. 153. 12. M.-Carmen Miguel, A. Vespignani, S. Zapperi, J. Weiss, J.-R. Grasso, Nature 410, 667 (2001). 13. F. F. Csikor, C. Motz, D. Weygand, M. Zaiser, S. Zapperi, Science 318, 251 (2007). 14. B. Devincre, L. Kubin, T. Hoc, Scr. Mater. 57, 905 (2007). 15. T. Hoc, C. Rey, J.-L. Raphanel, Acta Mater. 49, 1835 (2001). 16. T. E. Mitchell, Prog. Appl. Mater. Res. 6, 117 (1964). 17. T. Takeuchi, Trans. JIM 16, 629 (1975). 18. L. Kubin, Science 312, 864 (2006). 19. L. Kubin, B. Devincre, T. Hoc, Mater. Sci. Eng. A 483–484, 19 (2008). 20. The authors acknowledge funding by their host institutions: CNRS, ONERA, and Ecole Centrale Paris. Supporting Online Material www.sciencemag.org/cgi/content/full/320/5884/1745/DC1 SOM Text Fig. S1 References 5 February 2008; accepted 2 May 2008 10.1126/science.1156101 Ordered Mesoporous Materials from Metal Nanoparticle–Block Copolymer Self-Assembly Scott C. Warren,1,2 Lauren C. Messina,2 Liane S. Slaughter,2 Marleen Kamperman,1 Qin Zhou,2 Sol M. Gruner,3 Francis J. DiSalvo,2 Ulrich Wiesner1 * The synthesis of ordered mesoporous metal composites and ordered mesoporous metals is a challenge because metals have high surface energies that favor low surface areas. We present results from the self-assembly of block copolymers with ligand-stabilized platinum nanoparticles, leading to lamellar CCM-Pt-4 and inverse hexagonal (CCM-Pt-6) hybrid mesostructures with high nanoparticle loadings. Pyrolysis of the CCM-Pt-6 hybrid produces an ordered mesoporous platinum-carbon nanocomposite with open and large pores (≥10 nanometers). Removal of the carbon leads to ordered porous platinum mesostructures. The platinum-carbon nanocomposite has very high electrical conductivity (400 siemens per centimeter) for an ordered mesoporous material fabricated from block copolymer self-assembly. Despite considerable progress in the field of porous solids, major challenges re￾main in the synthesis of ordered meso￾porous materials with high metal content from the coassembly of macromolecular surfactants and inorganic species. Controlling the structure of metals at the mesoscale (2 to 50 nm) is crucial for the development of improved fuel cell electrodes and may also assist in the miniaturization of optical and electronic materials for data transmis￾sion, storage, and computation (1, 2). An early route to preparing mesoporous metals involves the dealloying of a less noble metal from a bimetallic alloy; this has been used for the prepara￾tion of Raney nickel and other metals (3). Dealloy￾ing processes provide limited control over structural parameters such as pore geometry and order. In contrast, block copolymer self-assembly or tem￾plating with metal species provides access to highly ordered structures. Synthetic routes to such struc￾tures have included adsorbing and then reducing metal ions within a preassembled block copolymer scaffold (4) and coassembling ligand-stabilized nanoparticles (NPs) with block copolymers (5). More recently, polymer-coated NPs that behave like surfactants have been isolated at the interface of block copolymer domains, which can create a bicontinuous morphology at higher loadings (6). Despite this progress, the conversion of metal￾polymer hybrids into mesoporous materials with ordered and large pores (≥10 nm) has not been accomplished, in part because of the low volume fraction of metals in most hybrids and the wide￾spread use of gold, which has a high diffusion coefficient and therefore retains its mesostructure only at low temperatures (7–9). Although a protec￾tive organic layer can be added to metal NPs to prevent uncontrolled aggregation, even a thin or￾ganic layer represents a considerable volume of the overall material: For example, a 1-nm-diameter metal NP with a relatively thin 1-nm organic shell is just 4% metal by volume. As a result, the typical metal content in most block copolymer–metal NP hybrids is only a few volume %, and the prospects for converting the hybrid into an ordered meso￾porous material, in which the metal would have a volume fraction between 60 and 75% for an in￾verse hexagonal structure, are poor. Mesoporous metals have been synthesized at a smaller length scale, with 2- to 4-nm pores, through the coassembly of metal ions with small-molecule surfactants followed by reduction (10–13). The small pore size, however, limits the flow of liquids through the material, which is essential for many applications (14, 15). Metals have also been de￾posited onto (16) or into (17) thin films of block 1 Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA. 2 Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA. 3 Department of Physics, Cornell University, Ithaca, NY 14853, USA. *To whom correspondence should be addressed. E-mail: ubw1@cornell.edu 1748 27 JUNE 2008 VOL 320 SCIENCE www.sciencemag.org REPORTS