Collective behavior in out-of-equilibrium colloidal suspensions

Igor S. Aranson

doi:10.1016/j.crhy.2013.05.002

Living fluids/Fluides vivants

Collective behavior in out-of-equilibrium colloidal suspensions
[Comportement collectif de suspensions colloïdales hors équilibre]

Igor S. Aranson ^1,²

¹ Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA
² Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA

Comptes Rendus. Physique, Volume 14 (2013) no. 6, pp. 518-527.

Résumé
Abstract

Une suspension colloïdale est un liquide hétérogène contenant des particules solides microscopiques. Les colloïdes jouent un rôle important dans notre vie quotidienne, des industries alimentaires et pharmaceutiques à la médecine et aux nanotechnologies. Il est pratique de distinguer deux classes majeures de suspensions colloïdales : à lʼéquilibre, et active, cʼest-à-dire maintenue en dehors de lʼéquilibre thermodynamique par des champs électriques ou magnétiques externes, de la lumière, des réactions chimiques, ou un flux de cisaillement hydrodynamique. Alors que les propriétés des suspensions colloïdales à lʼéquilibre sont assez bien comprises, les colloïdes actifs constituent un formidable défi, et la recherche en est encore à lʼetape exploratoire. Une des propriétés les plus remarquables des colloïdes actifs est la possibilité dʼauto-assemblage dynamique, une tendance naturelle des composants simples à sʼorganiser dans des architectures fonctionnelles complexes. Les exemples sʼétendent des cristaux et membranes colloïdaux modifiables et auto-réparables aux micro-nageurs et robots auto-assemblés. Les suspensions colloïdales actives peuvent montrer des propriétés matérielles qui ne sont pas présentes dans leurs homologues à lʼéquilibre, comme, par exemple, une viscosité réduite, une auto-diffusivité augmentée, etc. Ce travail examine les développements les plus récents dans le domaine de la physique des colloïdes actifs, dans le but dʼélucider les mécanismes de physique fondamentale régissant lʼauto-assemblage et le comportement collectif.

Colloidal suspensions, heterogeneous fluids containing solid microscopic particles, play an important role in our everyday life, from food and pharmaceutical industries to medicine and nanotechnology. Colloidal suspensions can be divided in two major classes: equilibrium, and active, i.e. maintained out of thermodynamic equilibrium by external electric or magnetic fields, light, chemical reactions, or hydrodynamic shear flow. While the properties of equilibrium colloidal suspensions are fairly well understood, out-of-equilibrium colloids pose a formidable challenge and the research is in its early exploratory stage. The possibility of dynamic self-assembly, a natural tendency of simple building blocks to organize into complex functional architectures, is one of the most remarkable properties of out-of-equilibrium colloids. Examples range from tunable, self-healing colloidal crystals and membranes to self-assembled microswimmers and robots. In contrast to their equilibrium counterparts, out-of-equilibrium colloidal suspensions may exhibit novel material properties, e.g. reduced viscosity, enhanced self-diffusivity, etc. This work reviews recent developments in the field of self-assembly and collective behavior of out-of-equilibrium colloids, with the focus on the fundamental physical mechanisms.

Publié le : 2013-05-30

DOI : 10.1016/j.crhy.2013.05.002

Keywords: Colloids, Self-assembly, Collective behavior
Mot clés : Colloïdes, Auto-assemblage, Comportement collectif

Affiliations des auteurs :

Igor S. Aranson ^{1, 2}

¹ Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA
² Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA

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Igor S. Aranson. Collective behavior in out-of-equilibrium colloidal suspensions. Comptes Rendus. Physique, Volume 14 (2013) no. 6, pp. 518-527. doi : 10.1016/j.crhy.2013.05.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.05.002/

Bibliographie
Cité par

[1] R.J. Hunter; L.R. White; D.Y.C. Chan Foundations of Colloid Science, vol. 1, Clarendon Press, Oxford, 1987

[2] W. Norde Colloids and Interfaces in Life Sciences, CRC, 2003

[3] N. Anscombe; F. Craig; S. Harris E-reader revolution? [Technology e-readers], Eng. Technol., Volume 7 (2012), pp. 68-71

[4] L.M.C. Sagis Dynamic properties of interfaces in soft matter: Experiments and theory, Rev. Mod. Phys., Volume 83 (2011), pp. 1367-1403

[5] D. Frenkel Soft condensed matter, Phys. A, Stat. Mech. Appl., Volume 313 (2002), pp. 1-31

[6] M. Kléman; O.D. Lavrentovich Soft Matter Physics: An Introduction, Springer-Verlag, 2003

[7] T.A. Witten Insights from soft condensed matter, Rev. Mod. Phys., Volume 71 (1999), p. S367-S373

[8] I.S. Aranson; L.S. Tsimring Granular Patterns, Oxford University Press, Oxford, 2009

[9] J.N. Israelachvili Intermolecular and Surface Forces, Academic Press, 2011

[10] F. Ebert; P. Keim; G. Maret Local crystalline order in a 2d colloidal glass former, Eur. Phys. J. B, Volume 26 (2008), pp. 161-168

[11] C.P. Royall; E. Vermolen; A. van Blaaderen; H. Tanaka Controlling competition between crystallization and glass formation in binary colloids with an external field, J. Phys. Condens. Matter, Volume 20 (2008), p. 404225

[12] P.A. Hiltner; I.M. Krieger Diffraction of light by ordered suspensions, J. Phys. Chem., Volume 73 (1969), pp. 2386-2389

[13] G. Subramanian; V.N. Manoharan; J.D. Thorne; D.J. Pine Ordered macroporous materials by colloidal assembly: A possible route to photonic bandgap materials, Adv. Mater., Volume 11 (1999), pp. 1261-1265

[14] A.P. Hynninen; J.H.J. Thijssen; E.C.M. Vermolen; M. Dijkstra; A. Van Blaaderen Self-assembly route for photonic crystals with a bandgap in the visible region, Nat. Mater., Volume 6 (2007), pp. 202-205

[15] K. Miszta; J. de Graaf; G. Bertoni; D. Dorfs; R. Brescia; S. Marras; L. Ceseracciu; R. Cingolani; R. van Roij; M. Dijkstra et al. Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures, Nat. Mater., Volume 10 (2011), pp. 872-876

[16] T. Vissers; A. Wysocki; M. Rex; H. Löwen; C.P. Royall; A. Imhof; A. van Blaaderen Lane formation in driven mixtures of oppositely charged colloids, Soft Matter, Volume 7 (2011), pp. 2352-2356

[17] T. Vissers; A. Imhof; F. Carrique; A.V. Delgado; A. van Blaaderen Electrophoresis of concentrated colloidal dispersions in low-polar solvents, J. Colloid Interface Sci., Volume 361 (2011), pp. 443-455

[18] M.E. Leunissen; C.G. Christova; A.P. Hynninen; C.P. Royall; A.I. Campbell; A. Imhof; M. Dijkstra; R. van Roij; A. van Blaaderen Ionic colloidal crystals of oppositely charged particles, Nature, Volume 437 (2005), pp. 235-240

[19] M.E. Leunissen; H.R. Vutukuri; A. van Blaaderen Directed colloidal self-assembly with biaxial electric fields, Adv. Mater., Volume 21 (2009), pp. 3116-3120

[20] F.J. Martinez-Veracoechea; B.M. Mladek; A.V. Tkachenko; D. Frenkel Design rule for colloidal crystals of dna-functionalized particles, Phys. Rev. Lett., Volume 107 (2011), p. 045902

[21] D. Frenkel; D.J. Wales Colloidal self-assembly: Designed to yield, Nat. Mater., Volume 10 (2011), pp. 410-411

[22] H. Löwen Colloidal dispersions in external fields: Recent developments, J. Phys. Condens. Matter, Volume 20 (2008), p. 404201

[23] S. Sacanna; W.T.M. Irvine; P.M. Chaikin; D.J. Pine Lock and key colloids, Nature, Volume 464 (2010), pp. 575-578

[24] Q. Chen; S.C. Bae; S. Granick Directed self-assembly of a colloidal kagome lattice, Nature, Volume 469 (2011), pp. 381-384

[25] R.M. Erb; H.S. Son; B. Samanta; V.M. Rotello; B.B. Yellen Magnetic assembly of colloidal superstructures with multipole symmetry, Nature, Volume 457 (2009), pp. 999-1002

[26] D. Nykypanchuk; M. Maye; D. Van Der Lelie; O. Gang Dna-guided crystallization of colloidal nanoparticles, Nature, Volume 451 (2008), pp. 549-552

[27] D.J. Kraft; R. Ni; F. Smallenburg; M. Hermes; K. Yoon; D.A. Weitz; A. van Blaaderen; J. Groenewold; M. Dijkstra; W.K. Kegel Surface roughness directed self-assembly of patchy particles into colloidal micelles, Proc. Natl. Acad. Sci. USA, Volume 109 (2012), pp. 10787-10792

[28] R. Dreyfus; J. Baudry; M.L. Roper; M. Fermigier; H.A. Stone; J. Bibette Microscopic artificial swimmers, Nature, Volume 437 (2005), pp. 862-865

[29] P. Tierno; R. Golestanian; I. Pagonabarraga; F. Sagués Magnetically actuated colloidal microswimmers, J. Phys. Chem. B, Volume 112 (2008), pp. 16525-16528

[30] A. Snezhko; M. Belkin; I.S. Aranson; W.-K. Kwok et al. Self-assembled magnetic surface swimmers, Phys. Rev. Lett., Volume 102 (2009), p. 118103

[31] E. Kumacheva; P. Garstecki; H. Wu; G.M. Whitesides Two-dimensional colloid crystals obtained by coupling of flow and confinement, Phys. Rev. Lett., Volume 91 (2003), p. 128301

[32] N. Osterman; I. Poberaj; J. Dobnikar; D. Frenkel; P. Ziherl; D. Babić Field-induced self-assembly of suspended colloidal membranes, Phys. Rev. Lett., Volume 103 (2009), p. 228301

[33] A. Snezhko; I.S. Aranson Magnetic manipulation of self-assembled colloidal asters, Nat. Mater., Volume 10 (2011), pp. 698-703

[34] C. Sanchez; H. Arribart; M.M.G. Guille Biomimetism and bioinspiration as tools for the design of innovative materials and systems, Nat. Mater., Volume 4 (2005), pp. 277-288

[35] B.A. Grzybowski; C.E. Wilmer; J. Kim; K.P. Browne; K.J.M. Bishop Self-assembly: From crystals to cells, Soft Matter, Volume 5 (2009), pp. 1110-1128

[36] F. Li; D.P. Josephson; A. Stein Colloidal assembly: The road from particles to colloidal molecules and crystals, Angew. Chem., Int. Ed. Engl., Volume 50 (2011), pp. 360-388

[37] A. Snezhko Non-equilibrium magnetic colloidal dispersions at liquid–air interfaces: Dynamic patterns, magnetic order and self-assembled swimmers, J. Phys. Condens. Matter, Volume 23 (2011), p. 153101

[38] J. Dobnikar; A. Snezhko; A. Yethiraj Emergent colloidal dynamics in electromagnetic fields, Soft Matter, Volume 9 (2013), pp. 3693-3704 | DOI

[39] S.J. Ebbens; J.R. Howse In pursuit of propulsion at the nanoscale, Soft Matter, Volume 6 (2010), pp. 726-738

[40] E. Lauga; T.R. Powers The hydrodynamics of swimming microorganisms, Rep. Prog. Phys., Volume 72 (2009), p. 09601

[41] S. Gangwal; O.J. Cayre; M.Z. Bazant; O.D. Velev Induced-charge electrophoresis of metallodielectric particles, Phys. Rev. Lett., Volume 100 (2008), p. 58302

[42] A. Sokolov; I.S. Aranson Reduction of viscosity in suspension of swimming bacteria, Phys. Rev. Lett., Volume 103 (2009), p. 148101

[43] S. Rafaï; L. Jibuti; P. Peyla Effective viscosity of microswimmer suspensions, Phys. Rev. Lett., Volume 104 (2010), p. 098102

[44] B.M. Haines; A. Sokolov; I.S. Aranson; L. Berlyand; D.A. Karpeev Three-dimensional model for the effective viscosity of bacterial suspensions, Phys. Rev. E, Volume 80 (2009), p. 041922

[45] D. Saintillan The dilute rheology of swimming suspensions: A simple kinetic model, Exp. Mech., Volume 50 (2010), pp. 1275-1281

[46] X.L. Wu; A. Libchaber Particle diffusion in a quasi-two-dimensional bacterial bath, Phys. Rev. Lett., Volume 84 (2000), pp. 3017-3020

[47] A. Sokolov; R.E. Goldstein; F.I. Feldchtein; I.S. Aranson Enhanced mixing and spatial instability in concentrated bacterial suspensions, Phys. Rev. E, Volume 80 (2009), p. 031903

[48] T. Vissers; A. van Blaaderen; A. Imhof Band formation in mixtures of oppositely charged colloids driven by an ac electric field, Phys. Rev. Lett., Volume 106 (2011), p. 228303

[49] M.V. Sapozhnikov; Y.V. Tolmachev; I.S. Aranson; W.-K. Kwok Dynamic self-assembly and patterns in electrostatically driven granular media, Phys. Rev. Lett., Volume 90 (2003), p. 114301

[50] H. Löwen Particle-resolved instabilities in colloidal dispersions, Soft Matter, Volume 6 (2010), pp. 3133-3142

[51] S. Yeh; M. Seul; B.I. Shraiman Assembly of ordered colloidal aggregrates by electric-field-induced fluid flow, Nature, Volume 386 (1997), pp. 57-59

[52] I.S. Aranson; M.V. Sapozhnikov Theory of pattern formation of metallic microparticles in poorly conducting liquids, Phys. Rev. Lett., Volume 92 (2004), p. 234301

[53] M.V. Sapozhnikov; I.S. Aranson; W.K. Kwok; Y.V. Tolmachev Self-assembly and vortices formed by microparticles in weak electrolytes, Phys. Rev. Lett., Volume 93 (2004), p. 84502

[54] A. Yethiraj; A. van Blaaderen A colloidal model system with an interaction tunable from hard sphere to soft and dipolar, Nature, Volume 421 (2003), pp. 513-517

[55] A. Snezhko; I.S. Aranson; W.-K. Kwok Structure formation in electromagnetically driven granular media, Phys. Rev. Lett., Volume 94 (2005), p. 108002

[56] J. Martin; E. Venturini; G. Gulley; J. Williamson Using triaxial magnetic fields to create high susceptibility particle composites, Phys. Rev. E, Volume 69 (2004), p. 021508

[57] N. Elsner; C.P. Royall; B. Vincent; D.R.E. Snoswell Simple models for two-dimensional tunable colloidal crystals in rotating ac electric fields, J. Chem. Phys., Volume 130 (2009), p. 154901

[58] J.E. Martin; R.A. Anderson; R.L. Williamson Generating strange magnetic and dielectric interactions: Classical molecules and particle foams, J. Chem. Phys., Volume 118 (2003), p. 1557

[59] B.A. Grzybowski; H.A. Stone; G.M. Whitesides Dynamics of self assembly of magnetized disks rotating at the liquid–air interface, Proc. Natl. Acad. Sci. USA, Volume 99 (2002), p. 4147

[60] K.J. Solis; R.C. Bell; J.E. Martin Vortex magnetic field mixing with anisometric particles, J. Appl. Phys., Volume 107 (2010), p. 114911

[61] Y. Nagaoka; H. Morimoto; T. Maekawa Ordered complex structures formed by paramagnetic particles via self-assembly under an ac/dc combined magnetic field, Langmuir, Volume 27 (2011), pp. 9160-9164

[62] S.K. Smoukov; S. Gangwal; M. Marquez; O.D. Velev Reconfigurable responsive structures assembled from magnetic Janus particles, Soft Matter, Volume 5 (2009), pp. 1285-1292

[63] J. Yan; M. Bloom; S.C. Bae; E. Luijten; S. Granick Linking synchronization to self-assembly using magnetic Janus colloids, Nature, Volume 491 (2012), pp. 578-581

[64] A. Snezhko; I.S. Aranson; W.-K. Kwok Surface wave assisted self-assembly of multidomain magnetic structures, Phys. Rev. Lett., Volume 96 (2006), p. 078701

[65] M. Belkin; A. Snezhko; I.S. Aranson; W.K. Kwok Driven magnetic particles on a fluid surface: Pattern assisted surface flows, Phys. Rev. Lett., Volume 99 (2007), p. 158301

[66] N. Riley Acoustic streaming, Theor. Comput. Fluid Dyn., Volume 10 (1998), pp. 349-356

[67] M. Belkin; A. Glatz; A. Snezhko; I.S. Aranson Model for dynamic self-assembled magnetic surface structures, Phys. Rev. E, Volume 82 (2010), p. 015301

[68] W.F. Paxton; P.T. Baker; T.R. Kline; Y. Wang; T.E. Mallouk; A. Sen Catalytically induced electrokinetics for motors and micropumps, J. Am. Chem. Soc., Volume 128 (2006), pp. 14881-14888

[69] J.R. Howse; R.A.L. Jones; A.J. Ryan; T. Gough; R. Vafabakhsh; R. Golestanian Self-motile colloidal particles: From directed propulsion to random walk, Phys. Rev. Lett., Volume 99 (2007), p. 048102

[70] W. Gao; S. Sattayasamitsathit; J. Orozco; J. Wang Highly efficient catalytic microengines: Template electrosynthesis of polyaniline/platinum microtubes, J. Am. Chem. Soc., Volume 133 (2011), pp. 11862-11864

[71] A. Ghosh; P. Fischer Controlled propulsion of artificial magnetic nanostructured propellers, Nano Lett., Volume 9 (2009), pp. 2243-2245

[72] W.F. Paxton; K.C. Kistler; C.C. Olmeda; A. Sen; S.K.S. Angelo; Y. Cao; T.E. Mallouk; P.E. Lammert; V.H. Crespi Catalytic nanomotors: Autonomous movement of striped nanorods, J. Am. Chem. Soc., Volume 126 (2004), pp. 13424-13431

[73] S. Sanchez; A.A. Solovev; S.M. Harazim; O.G. Schmidt Microbots swimming in the flowing streams of microfluidic channels, J. Am. Chem. Soc., Volume 133 (2011), p. 701

[74] R. Golestanian; T.B. Liverpool; A. Ajdari Propulsion of a molecular machine by asymmetric distribution of reaction products, Phys. Rev. Lett., Volume 94 (2005), p. 220801

[75] J.L. Moran; J.D. Posner Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis, J. Fluid Mech., Volume 680 (2011), pp. 31-66

[76] M.Z. Bazant; T.M. Squires Induced-charge electrokinetic phenomena: Theory and microfluidic applications, Phys. Rev. Lett., Volume 92 (2004), p. 66101

[77] D. Takagi; A.B. Braunschweig; J. Zhang; M.J. Shelley Dispersion of self-propelled rods undergoing fluctuation-driven flips, Phys. Rev. Lett., Volume 110 (2013), p. 038301

[78] H.C. Berg E. coli in Motion, Springer-Verlag, 2004

[79] R. Stocker Reverse and flick: Hybrid locomotion in bacteria, Proc. Natl. Acad. Sci. USA, Volume 108 (2011), pp. 2635-2636

[80] M. Cates; J. Tailleur When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation, Europhys. Lett., Volume 101 (2013), p. 20010

[81] C. Dombrowski; L. Cisneros; S. Chatkaew; R.E. Goldstein; J.O. Kessler Self-concentration and large-scale coherence in bacterial dynamics, Phys. Rev. Lett., Volume 93 (2004), p. 98103

[82] A. Sokolov; I.S. Aranson; J.O. Kessler; R.E. Goldstein Concentration dependence of the collective dynamics of swimming bacteria, Phys. Rev. Lett., Volume 98 (2007), p. 158102

[83] A. Sokolov; M.M. Apodaca; B.A. Grzybowski; I.S. Aranson Swimming bacteria power microscopic gears, Proc. Natl. Acad. Sci. USA, Volume 107 (2010), pp. 969-974

[84] I. Theurkauff; C. Cottin-Bizonne; J. Palacci; C. Ybert; L. Bocquet Dynamic clustering in active colloidal suspensions with chemical signaling, Phys. Rev. Lett., Volume 108 (2012), p. 268303

[85] J. Palacci; C. Cottin-Bizonne; C. Ybert; L. Bocquet Sedimentation and effective temperature of active colloidal suspensions, Phys. Rev. Lett., Volume 105 (2010), p. 088304

[86] J. Tailleur; M. Cates Sedimentation, trapping, and rectification of dilute bacteria, Europhys. Lett., Volume 86 (2009), p. 60002

[87] J. Schwarz-Linek; C. Valeriani; A. Cacciuto; M. Cates; D. Marenduzzo; A. Morozov; W. Poon Phase separation and rotor self-assembly in active particle suspensions, Proc. Natl. Acad. Sci. USA, Volume 109 (2012), pp. 4052-4057

[88] A. Sen; M. Ibele; Y. Hong; D. Velegol Chemo and phototactic nano/microbots, Faraday Discuss., Volume 143 (2009), pp. 15-27

[89] M. Ibele; T.E. Mallouk; A. Sen Schooling behavior of light-powered autonomous micromotors in water, Angew. Chem., Int. Ed. Engl., Volume 48 (2009), pp. 3308-3312

[90] M.E. Ibele; P.E. Lammert; V.H. Crespi; A. Sen Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions, ACS Nano, Volume 4 (2010), pp. 4845-4851

[91] J. Palacci; S. Sacanna; A.P. Steinberg; D.J. Pine; P.M. Chaikin Living crystals of light-activated colloidal surfers, Science, Volume 339 (2013), pp. 936-940

[92] S.K.Y. Tang; R. Derda; A.D. Mazzeo; G.M. Whitesides Reconfigurable self-assembly of mesoscale optical components at a liquid–liquid interface, Adv. Mater., Volume 23 (2011), pp. 2413-2418

[93] F. Ilievski; A.D. Mazzeo; R.F. Shepherd; X. Chen; G.M. Whitesides Soft robotics for chemists, Angew. Chem., Volume 123 (2011), pp. 1930-1935

[94] M. Rex; H. Löwen Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids, Eur. Phys. J. E, Volume 26 (2008), pp. 143-150

[95] J.E. Martin Theory of strong intrinsic mixing of particle suspensions in vortex magnetic fields, Phys. Rev. E, Volume 79 (2009), p. 011503

[96] K. Kruse; J.F. Joanny; F. Jülicher; J. Prost; K. Sekimoto Asters, vortices, and rotating spirals in active gels of polar filaments, Phys. Rev. Lett., Volume 92 (2004), p. 078101

[97] S. Ramaswamy The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys., Volume 1 (2010), pp. 323-345

[98] G. Grégoire; H. Chaté Onset of collective and cohesive motion, Phys. Rev. Lett., Volume 92 (2004), p. 025702

[99] F. Ginelli; F. Peruani; M. Bär; H. Chaté Large-scale collective properties of self-propelled rods, Phys. Rev. Lett., Volume 104 (2010), p. 184502

[100] M. Ripoll; P. Holmqvist; R. Winkler; G. Gompper; J.K.G. Dhont; M.P. Lettinga Attractive colloidal rods in shear flow, Phys. Rev. Lett., Volume 101 (2008), p. 168302

[101] J. Bialké; T. Speck; H. Löwen Crystallization in a dense suspension of self-propelled particles, Phys. Rev. Lett., Volume 108 (2012), p. 168301

[102] D. Saintillan; M.J. Shelley Orientational order and instabilities in suspensions of self-locomoting rods, Phys. Rev. Lett., Volume 99 (2007), p. 58102

[103] A. Peshkov; I.S. Aranson; E. Bertin; H. Chaté; F. Ginelli Nonlinear field equations for aligning self-propelled rods, Phys. Rev. Lett., Volume 109 (2012), p. 268701

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