Programming colloidal phase transitions with DNA strand displacement · ization reaction, known as toehold exchange or strand displacement, is widely used in the DNA nanotechnology

plane. The net result is expected to be a pinningof the dislocation core near the oxygen intersti-tials as shown in Fig. 1B, resulting in strongstrengthening effects. The local cross-slippingdue to oxygen interstitials is consistent with thetomograms of the dislocation arrays in Ti-0.3 wt% O samples in Fig. 3B. The classical solid solu-tion strengtheningmodel that neglects these twoeffects may not provide an accurate descriptionof oxygen strengthening in a-Ti (details are pro-vided in the supplementary materials).The present work establishes a direct connec-

tion between the pronounced strengthening ef-fect of oxygen in hcp-structured a-Ti and thestrong interactions between these solute atomswith screw dislocation cores. The strongly re-pulsive solute-dislocation interaction energies,the large barriers for the “mechanical shuffle”of oxygen atoms in the core, and the local cross-slip induced by oxygen interstitials combine toresult in a strong pinning effect on screw dis-locations. We suggest that these results providea well-documented, prototypic example of solidsolution strengthening by solute interactionwith screw dislocations. This type of crystallo-graphically induced strengthening mechanism

should also exist for other types of dislocations,depending on the corresponding dislocation corestructures and themobility of solid solute atoms.

REFERENCES AND NOTES

1. J. P. Hirth, J. Lothe, Theory of Dislocations (McGraw-Hill,New York, 1982).

2. H. Neuhäuser, Phys. Scr. T49B, 412–419 (1993).3. G. P. M. Leyson, W. A. Curtin, L. G. Hector Jr., C. F. Woodward,

Nat. Mater. 9, 750–755 (2010).4. J. A. Yasi, L. G. Hector Jr., D. R. Trinkle, Acta Mater. 58,

5704–5713 (2010).5. Metals Handbook (ASM International, Metals Park, OH, ed. 10,

1990), vol. 2.6. H. Conrad, Prog. Mater. Sci. 26, 123–403 (1981).7. G. Lutjering, J. C. Williams, Titanium (Springer‐Verlag, Berlin,

ed. 2, 2007).8. W. R. Tyson, Scr. Metall. 3, 917–921 (1969).9. M. L. Wasz, F. R. Brotzen, R. B. McLellan, A. J. Griffin,

Int. Mater. Rev. 41, 1–12 (1996).10. F. D. Rosi, C. A. Dube, B. H. Alexander, Trans. Am. Inst.

Mining Metall. Eng. 197, 257 (1953).11. C. Kisielowski et al., Microsc. Microanal. 14, 469–477 (2008).12. S. Kibey, J. B. Liu, M. J. Curtis, D. D. Johnson, H. Sehitoglu,

Acta Mater. 54, 2991–3001 (2006).13. G. Lu, N. Kioussis, V. Bulatov, E. Kaxiras, Phys. Rev. B 62,

3099–3108 (2000).14. V. Vítek, Philos. Mag. 18, 773–786 (1968).15. G. Kresse, J. Furthmüller, Phys. Rev. B Condens. Matter 54,

11169–11186 (1996).16. M. Ghazisaeidi, D. R. Trinkle, Acta Mater. 76, 82–86 (2014).

17. H. H. Wu, D. R. Trinkle, Phys. Rev. Lett. 107, 045504 (2011).18. B. Joós, M. S. Duesbery, Phys. Rev. Lett. 78, 266–269

(1997).19. M. Ghazisaeidi, D. R. Trinkle, Acta Mater. 60, 1287–1292

(2012).20. X. Z. Wu, R. Wang, S. F. Wang, Appl. Surf. Sci. 256, 3409–3412

(2010).

ACKNOWLEDGMENTS

We gratefully acknowledge funding from the U.S. Office of NavalResearch under grant N00014-12-1-0413. Work at the MolecularFoundry was supported by the Office of Science, Office of BasicEnergy Sciences, of the U.S. Department of Energy undercontract DE-AC02-05CH11231. T.T. acknowledges the financialsupport of the Japanese Ministry of Education, Culture, Sports,Science and Technology (MEXT), Grant-in-Aid for ScientificResearch in Innovative Areas “Bulk Nanostructured Materials.”We thank J. Kacher for dislocation tomography training and Timet(Exton, PA) for the production of the high-purity model alloysused in this study.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/347/6222/635/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S6Tables S1References (21–39)Movies S1 to S7

27 August 2014; accepted 8 January 201510.1126/science.1260485

DNA NANOTECHNOLOGY

Programming colloidal phase transitionswith DNA strand displacementW. Benjamin Rogers1 and Vinothan N. Manoharan1,2*

DNA-grafted nanoparticles have been called “programmable atom-equivalents”: Likeatoms, they form three-dimensional crystals, but unlike atoms, the particles themselvescarry information (the sequences of the grafted strands) that can be used to “program”the equilibrium crystal structures. We show that the programmability of these colloids canbe generalized to the full temperature-dependent phase diagram, not just the crystalstructures themselves.We add information to the buffer in the form of soluble DNA strandsdesigned to compete with the grafted strands through strand displacement. Using onlytwo displacement reactions, we program phase behavior not found in atomic systems orother DNA-grafted colloids, including arbitrarily wide gas-solid coexistence, reentrantmelting, and even reversible transitions between distinct crystal phases.

Like atoms, colloidal particles suspendedin a fluid can form bulk phases such asgases and crystals. These particles can alsobe directed to form new states of matter(1) through careful tuning of their inter-

particle interactions—for example, by graftingDNA strands onto the particles to create specificattractions (2, 3). SuchDNA-grafted particles havebeen called “programmable atom-equivalents”(4), a moniker that highlights the experimenter’sability to dictate, or “program,” the self-assembledstructures through the DNA sequences. The im-plied analogy to computer programming is a

useful way to conceptualize how informationin the sequences is translated to structure: Muchas one can program a computer to perform com-plex tasks by writing statements that are com-piled tomachine code, one can “program” a colloidto form a complex structure by designing nucleo-tide sequences (statements) that are “compiled”into specific interparticle interactions (machinecode). Recent advances in our understandingof this compilation process, in the form of de-sign rules (5) or mean-field models (6–8) relatingthe effective interactions directly to the nucleo-tide sequences (9), have enabled the assemblyof crystal phases not found in ordinary colloids(5, 10–13) and could be extended, in principle,to the assembly of prescribed nonperiodic struc-tures (14, 15).

Structure, however, is just one aspect of self-assembly; more generally, self-assembly describesa phase transition between a disordered and anordered state, or a pathway on a phase diagram.Thus far, only a subset of the full colloidal phasediagram has been programmed: the equilibriumstructure of the ordered state as a function ofdensity and composition. Programmatic controlover the phase behavior in the orthogonal ther-modynamic dimension—the temperature—remainselusive. Typically, the attraction between twoDNA-grafted particles decreases steeply and mono-tonically with increasing temperature (16, 17). Asa result, the suspension displays phase behaviorresembling that of simple atoms rather thanprogrammable ones: It is fluid at high temper-ature and solid at low temperature (Fig. 1A). Ourgoal here is to develop a comprehensive ap-proach to programming the full phase diagramof colloidal suspensions: We seek to design aset of interaction “primitives” that can be com-bined to program both the structure of equilib-rium phases and their temperature-dependenttransitions. In other words, we aim to programthe equilibrium self-assembly pathways, not justtheir end points.We achieve this goal by adding information

to the buffer in the form of free DNA strands.We refer to these as displacing strands becausetheir sequences are designed to be complemen-tary to subunits of the grafted strands; they cantherefore react with a double-stranded bridge,displacing one of the grafted strands and form-ing a nonbridging duplex (Fig. 1B). This hybrid-ization reaction, known as toehold exchange orstrand displacement, is widely used in the DNAnanotechnology field to construct dynamic assem-blies and devices (18, 19). Strand displacement has

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1School of Engineering and Applied Sciences, HarvardUniversity, Cambridge, MA 02138, USA. 2Department ofPhysics, Harvard University, Cambridge, MA 02138, USA.*Corresponding author. E-mail: [email protected]

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also been used to melt or change the lattice con-stants of nanoparticle-based materials (20–23).Here, rather than modifying the structure ofan already assembled material, we use strand-displacement reactions to control the equilib-rium assembly process. The additional degrees offreedom that we introduce allow us to designtemperature-dependent interaction potentialswith tunable shape, steepness, and specificity(Fig. 1, B and C). Returning to the computer pro-gramming analogy, the free DNA sequences actas the language for programming the transitionsbetween phases, much as the grafted sequencesprogram the structure of the phases. Because weseparate the functions of the grafted and freestrands, the two mechanisms can be controlledindependently.To understand how displacing strands affect

the interparticle potential, consider the hybrid-ization reactions shown in Fig. 1. Given that hy-bridization of complementary strands happenson time scales much shorter than that of particlemotion, we can assume that interacting DNAstrands are in chemical equilibrium (6–8). Moreprecisely, the DNA-induced colloidal attractionis determined by the spatially varying hybrid-ization yield of DNA bridges, whose tempera-ture dependence comes from the free energychange DG/RT [for details, see (7, 24, 25)]. Inthe absence of displacement, the free energychange of the hybridization reaction A þ B⇌AB,given by DG/RT = DHAB/RT – DSAB/R, is mono-tonic with a steepness set by DHAB, because theenthalpy change DHAB and entropy change DSABare largely independent of temperature (Fig. 1A).With displacing strands, the free energy dif-

ference between bridged and unbridged statescan bemodified owing to the additional reactionpathways ABþ D1⇌AD1 þ B and ABþ D2⇌A þBD2. Because the enthalpic changes of displace-ment reactions can be tuned through the basesequences of the displacing strands, the freeenergy change DG′/RT can be designed to havevarious nonlinear dependences on temperature(figs. S1 andS2). Furthermore, the entropic changesof the displacement reactions can be adjustedby changing the molar concentrations of thedisplacing strands, providing a way to tune themagnitude of DG′/RT independently of its de-pendence on temperature.A single displacement reaction (Fig. 2A) al-

lows precise control over the thermodynamicsof the fluid-solid transition. We control the tem-perature dependence of the free energy changeDG′/RT, and thus of the interaction potential, bychanging the displacing strand sequence. Using thenearest-neighbor model, which relates DNA se-quences to hybridization free energies (9), we pre-dict the enthalpic changes of displacement andbridge formation. If we choose the appropriate se-quences such that these enthalpic changes are thesame ðDHAB ¼ DHAD1 Þ, we can eliminate the tem-perature dependence entirely over a range of tem-peratures (fig. S1). We thereby establish a dynamicequilibrium in which the bridging and nonbridg-ing duplexes exchange freely by toehold-exchangehybridization, without an enthalpic barrier.

This single-displacement scheme, where DHAB ¼DHAD1 , eliminates the boundary between the co-existence region and the solid phase, resulting incoexistence between fluid and solid that persistseven at low temperatures (Fig. 2B). In the ab-sence of the displacing strand, we find a single,steep melting curve with an approximate widthof 1°C, consistent with earlier reports (16). Themelting transition softens with increasing con-centration of the free strand (Fig. 2C), wideningby 10°C or more. Furthermore, the singlet frac-tion remains nonzero and constant down to roomtemperature. Because the entropy of the freestrands can be adjusted by changing their molarconcentration, the singlet fraction, and thus theinteraction strength, can still be tuned.This single-displacement scheme solves a long-

standing problem in DNA-directed self-assembly:the steep dependence of the interparticle attrac-tion on temperature (17), which frustrates equi-librium self-assembly. Previous experiments andsimulations have shown that crystal nucleationand growth occur over a range of interactionstrengths only 1 to 2 kBT wide, corresponding toa temperature window roughly 1°C wide (6, 26).In contrast, with a single displacement reaction,we find that nucleation and growth of binarycrystals occurs over a range of temperatureswider than 10°C—an improvement of at least an

order of magnitude relative to displacement-freeschemes. Expanding the temperature window ofequilibrium assembly makes it easier to growcrystals and obviates the need for precision tem-perature control, temperature gradients, or com-plex annealing schemes (10, 11, 13).Our model of DNA-mediated attractions in

the presence of strand displacement quantita-tively reproduces these measurements (Fig. 2C).Taking the grafting density, free-strand concen-tration, ionic strength, and DNA sequences as in-puts, we reproduce themeasured singlet fractionsto within the inherent uncertainty associatedwith the nearest-neighbor model (25). This levelof agreement supports our physical picture—thatthe changes in the temperature dependence re-sult directly from molecular-scale displacementreactions—and demonstrates that the emergentphase behavior can be predicted and thereforeprogrammed.With two-displacement reactions (Fig. 3A),

we canmake the free energy not only a nonlinearfunction of temperature but also a nonmono-tonic one, with interesting consequences for thephase behavior: The resulting suspensions displaymultiple fluid-solid transitions and inverted phasebehavior, in which the stable, low-temperaturephase is a fluid that freezes upon heating be-fore melting again at higher temperatures. Such

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fluid

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Fig. 1. Strand-displacement reactions program phase behavior by modifying the local chemicalequilibrium between DNA-grafted particles. (A) In the absence of displacing strands, the strength oftheDNA-induced attraction (DFa) decreasesmonotonicallywith increasing temperatureT, resulting in simplephase behavior in the f-Tspace, where f is the particle volume fraction.The fluid-solid coexistence region isshown in gray. (B) A single displacement reaction eliminates the temperature dependence of DFa/kBTover arange of temperatures, thereby widening the fluid-solid coexistence region. (C) Adding a second strand-displacement reaction allows DFa/kBT to vary nonmonotonically with T, inverting the colloidal phase behaviorand creating a reentrant fluid phase.The elementary reaction steps in orange are drawn schematically.

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reentrant behavior results from a competi-tion between entropy and enthalpy. The low-temperature fluid is stabilized enthalpically:Because each bridge can be replaced by two non-bridging duplexes of the same length, the mostfavorable state contains few or no bridges be-tween particles, thus maximizing the total num-ber of base pairs. At higher temperatures, entropyfavors the solid phase, because formation of asingle bridge liberates two displacing strands.At even higher temperatures, the solid phasemelts again, owing to thermal dissociation ofDNA bridges.Our experiments (Fig. 3B) show that the re-

sulting reentrant melting transition is tunableand can be programmed independently of thesolid-phase symmetry. By adjusting the concen-trations of the displacing strands, we control thetemperature window in which the solid phase isstable (Fig. 3C). Higher concentrations of dis-placing strands shift the local chemical equilib-rium toward nonbridging duplexes, leading to anarrower window (Fig. 3D). Strand concentra-tions exceeding a critical limit prevent freezingentirely. The crystals that we assemble have theexpected cesium chloride (CsCl) symmetry (fig. S3).

Because energetic arguments suggest that intra-species attractions as weak as ~1 kBT would leadto formation of Cu-Au crystals instead of the ob-served CsCl crystals (13, 27), we conclude that ourapproach does not result in undesired cross-talkbetween intra- and interspecies attractions.Of course, the principal feature of DNA-grafted

particles is the ability to create multiple particlespecies that interact with each other in specificways. Strand displacement allows us to modifyeach interaction and thereby program path-ways between different self-assembled structures.To demonstrate this feature of our approach,we combine the displacement-free and two-displacement schemes to program a reversiblepathway between two compositionally distinctequilibrium ordered phases. Specifically, we de-sign a system containing three different particlespecies with a temperature-dependent interac-tion matrix, implemented through six DNA se-quences (table S5), four of which are grafted toparticles and two of which are displacing strandsthat modulate interactions between species 2(green in Fig. 4A) and the other two species. Atlow temperatures, the interaction matrix favorscocrystallization of species 2 and 3, as confirmed

by confocal fluorescence microscopy (Fig. 4B).At high temperatures, it favors cocrystallizationof species 1 and 2. At intermediate temperatures,we program an intervening fluid phase by tuningthe displacing strand concentrations, which al-lows us to easily nucleate and grow either crystalby lowering or raising the temperature. Becausethe system is in equilibrium at each temperature,the observed phase transitions are completelyreversible.These last experiments demonstrate that the

specificity afforded byWatson-Crick base pairing,which is used to program the structure of equi-librium self-assembled phases, can itself be pro-grammed to depend on temperature, enablingreconfigurablematerials inwhich particles changetheir interactions and reconfigure their struc-ture in response to temperature. The approachis limited only by the freezing and boiling pointsof the buffer: Because the transition illustratedin Fig. 4 is roughly 10°C wide, one could con-ceivably design transitions between at least10 distinct solid phases in the 0° to 100°C tem-perature range, which could each be directed toself-assemble independently andon cue simply bychanging the temperature. Moreover, incorpora-tion of thermally driven solid-solid transitionscould also enable the sequential self-assemblyof other crystal phases not accessible by directnucleation from the fluid, but which have thelowest free energy at a given temperature (13).These systems represent an additional directionin self-assembly, in which information suppliedto the buffer can program equilibrium pathwaysbetween many different target structures withina closed system.The zero-, one-, and two-displacement reaction

schemes constitute a set of primitives that can becombined to further program thermal pathwaysto self-assembly.We have demonstratedone suchcombination—a zero-displacement reaction com-bined with a two-displacement reaction—butmany others are possible, owing to the speci-ficity of DNA hybridization. A key feature ofour approach is that it separates the functionsof the grafted strands, which encode the inter-action matrix, and the free displacing strands,which control the temperature dependence ofthe interactionmatrix. Other competitive bindingschemes have been proposed (28–30), but noneresults in independent control of the temperature-dependent phase transitions and the symmetryof the equilibrium phases. This independent con-trol, which is crucial to fully program self-assembly,could make it possible to assemble complex ma-terials in multiple stages. For example, particlesmight first self-assemble into a scaffold that woulddisassemble after helping the final, prescribedstructure to assemble. Similar strategies are usedin biological systems such as bacteriophages (31)and could prove to be more robust than currentone-step approaches to assembly. More gener-ally, our demonstration that strand displacementalters the local chemical equilibrium betweenDNA-grafted particles opens the door to the inclu-sion of more complex strand displacement–baseddevices into colloidal assembly. For example,

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Fig. 2. A single displacement reaction eliminates the temperature dependence of binding. (A)Competition between bridge formation and strand displacement results in stable coexistence betweenfluid and solid phases that persists over a wide range of temperatures. (B) Representative confocalfluorescence micrographs of a binary suspension of DNA-grafted particles at various temperatures. (C)Experimentally measured particle singlet fraction (symbols) shows the broadening of the meltingtransition with increasing concentration of free strand D1 (indicated on plot) (25). Error bars denote SDof three measurements. A model based on local chemical equilibrium (curves), together with a separatemodel of the singlet fraction (16), reproduces our results to within the inherent uncertainty of the nearest-neighbor model (9, 25, 32). DNA sequences and predicted free energies are given in tables S1 and S2.

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incorporation of DNA-based logic gates, cas-caded circuits, or catalytic amplifiers (19) couldmake it possible to program nonequilibrium self-assembly pathways in colloidal matter.

REFERENCES AND NOTES

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(1998).10. D. Nykypanchuk, M. M. Maye, D. van der Lelie, O. Gang,

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(2013).15. Z. Zeravcic, V. N. Manoharan, M. P. Brenner, Proc. Natl. Acad.

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(2009).17. L. Di Michele, E. Eiser, Phys. Chem. Chem. Phys. 15, 3115–3129

(2013).18. B. Yurke, A. J. Turberfield, A. P. Mills Jr., F. C. Simmel,

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(2011).20. C. K. Tison, V. T. Milam, Langmuir 23, 9728–9736

(2007).21. M. M. Maye, M. T. Kumara, D. Nykypanchuk, W. B. Sherman,

O. Gang, Nat. Nanotechnol. 5, 116–120 (2010).22. J. T. McGinley, I. Jenkins, T. Sinno, J. C. Crocker, Soft Matter 9,

9119 (2013).23. B. A. Baker, G. Mahmoudabadi, V. T. Milam, Soft Matter 9,

11160 (2013).24. W. B. Rogers, J. C. Crocker, Proc. Natl. Acad. Sci. U.S.A. 109,

E380 (2012).25. See supplementary materials on Science Online.26. T. I. Li, R. Sknepnek, M. Olvera de la Cruz, J. Am. Chem. Soc.

135, 8535–8541 (2013).27. R. Scarlett, M. Ung, J. Crocker, T. Sinno, Soft Matter 7, 1912

(2011).28. S. Angioletti-Uberti, B. M. Mognetti, D. Frenkel, Nat. Mater. 11,

518–522 (2012).29. B. Mognetti, M. Leunissen, D. Frenkel, Soft Matter 8, 2213

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ACKNOWLEDGMENTS

We thank S. Magkiriadou, J. Collins, Z. Zeravcic, and M. Brenner forhelpful discussions. Supported by the Harvard MRSEC through NSFgrant DMR-0820484, NSF grant DMR-1435964, and anAlfred P. Sloan Research Fellowship. See the supplementarymaterials for additional data.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/347/6222/639/suppl/DC1Materials and MethodsFigs. S1 to S3Tables S1 to S6References (33–40)

7 August 2014; accepted 29 December 201410.1126/science.1259762

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Fig. 3. Two strand-displacement reactions program a tunable reentrant melting transition. (A)Hybridization of free displacing strands induces a second melting transition. (B) Representative confocalfluorescence micrographs show reentrant melting of a binary suspension of DNA-grafted particles. (C)Singlet fraction f measurements (symbols) show that the reentrant melting transition can be tuned bychanging the displacing strand concentrationsCD0 for equimolar mixtures of D1 and D2 (indicated on plot)(25). Error bars denote SD of three measurements. Our local chemical equilibrium model (curves)reproduces our results to within the inherent uncertainty of nearest-neighbor predictions (9, 25, 32). (D) Thedisplacing strand concentration–temperature coexistence envelope is delimited by the temperature andCD0 where 0.15 < f < 0.85 (gray). Symbols show experimental data: orange for f>0.85, blue for f <0.15.Weachieve coexistence over roughly 10°C when CD0 = 250 mM. DNA sequences and hybridization freeenergies are shown in tables S3 and S4.

Fig. 4. The zero- and two-displacement reaction schemes are combined to program a pathwaybetween two colloidal crystals. (A) Strand displacement yields a temperature-dependent specificitymatrix defining favorable (gray) and unfavorable (white) interactions in a ternary suspension. Measuredpair interactions (symbols) in this experimental system agree quantitatively with our model calculations(curves). Error bars denote SD of threemeasurements. (B) Confocal fluorescence experiments (25) showCsCl binary crystals of species 2 (green) and 3 (blue) in coexistence with a fluid of species 1 (red) at lowtemperature (left), andCsCl crystals of species 1 (red) and 2 (green) in coexistencewith a fluid of species 3(blue) at high temperature (right), separated by a homogeneous fluid phase of all three species at in-termediate temperature (middle), as predicted.The two crystals have the same symmetry, as determinedby the lattice distance x ¼ ½4=

ffiffiffi

3p

�D in the {110} plane, but different compositions; D is the particlediameter. Hybridization free energies are shown in table S6.

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Programming colloidal phase transitions with DNA strand displacementW. Benjamin Rogers and Vinothan N. Manoharan

DOI: 10.1126/science.1259762 (6222), 639-642.347Science 

, this issue p. 639Sciencedifferent particles to control the temperature dependence of the equilibrium state.displacement reactions. They capitalized on the reversible chemical equilibrium between the DNA strands connectingstrands. Rogers and Manoharan controlled the strength of the colloidal ''bond'' by using a set of competing strand

Colloidal particles have been used as atom mimics and are often connected together using complementary DNADNA control of bonding interactions

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