Processes that can produce states of broken chiral symmetry are of particular
interest to physics, chemistry and biology. Chiral symmetry breaking during
crystallization of sodium chlorate occurs via the production of secondary
crystals of the same handedness from a single "mother crystal" that seeds the
solution. Here we report that a large and "symmetric" population of D- and
L-crystals moves into complete chiral purity disappearing one of the
enantiomers. This result shows: (i) a new symmetry breaking process
incompatible with the hypothesis of a single "mother crystal"; (ii) that
complete symmetry breaking and chiral purity can be achieved from an initial
system with both enantiomers. These findings demand a new explanation to the
process of total symmetry breaking in crystallization without the intervention
of a "mother crystal" and open the debate on this fascinating phenomenon. We
present arguments to show that our experimental data can been explained with a
new model of "complete chiral purity induced by nonlinear autocatalysis and
recycling".Comment: 5 pages, 4 figures, Added reference

Cristobal Viedma

D. K. Kondepudi

F. S. Kipping

K. Soai

R. L. Joesten

R. W. G. Wyckoff

W. A. Bonner

English

arXiv

Crossref

Chiral Symmetry Breaking During Crystallization: Complete Chiral Purity Induced by Nonlinear Autocatalysis and Recycling

We report experimental results that show a large and symmetric population of D and L crystals moving
into complete chiral purity, with one of the enantiomers completely disappearing. The results indicate (i) a
new symmetry breaking process incompatible with the hypothesis of an initial single chiral phase or
‘‘mother crystal,’’ (ii) that total symmetry breaking and complete chiral purity can be achieved from a
system that initially includes both enantiomers, and (iii) that this is achieved through a nonlinear
autocatalytic-recycling process.Depto. de Mineralogía y PetrologíaFac. de Ciencias GeológicasTRUEpu

Viedma Molero, Cristóbal

Docta Complutense

PRL 94, 065504 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending18 FEBRUARY 2005Chiral Symmetry Breaking During Crystallization: Complete Chiral PurityInduced by Nonlinear Autocatalysis and RecyclingCristobal Viedma*Departamento de Cristalografia y Mineralogia, Facultad de Geologia, Universidad Complutense, Madrid, Spain(Received 30 July 2004; published 17 February 2005)0031-9007=We report experimental results that show a large and symmetric population of D and L crystals movinginto complete chiral purity, with one of the enantiomers completely disappearing. The results indicate (i) anew symmetry breaking process incompatible with the hypothesis of an initial single chiral phase or‘‘mother crystal,’’ (ii) that total symmetry breaking and complete chiral purity can be achieved from asystem that initially includes both enantiomers, and (iii) that this is achieved through a nonlinearautocatalytic-recycling process.DOI: 10.1103/PhysRevLett.94.065504 PACS numbers: 61.50.–f, 82.65.+rIntroduction.—Chiral symmetry breaking occurs when aphysical or chemical process that does not have preferencefor the production of one or other enantiomer spontane-ously generates a large excess of one of the two enantiom-ers: left-handed (L) or right-handed (D). From theenergetic point of view, these two enantiomers can existwith an equal probability and inorganic processes involv-ing chiral products commonly yield a racemic mixture ofboth (L) and (D) enantiomers [1]. However, life on earthutilizes only one type of amino acids and only one type ofnatural sugars: (L)-amino acids and (D)-sugars. The factthat biologically relevant molecules exist only as one of thetwo enantiomers is a fascinating example of completesymmetry breaking in chirality and has long intriguedmany scientists.With a few exceptions, the symmetry breaking producedby different natural mechanisms has proved giving smallenantiomeric excess (EE) [2], ranging from the 20% foundexperimentally for asymmetric photolysis to the 1017alleged theoretically for parity violating energy differencebetween enantiomers. This means that to reach total chiralpurity, mechanisms to enhance any initial imbalance inchirality are absolutely essential [3].In 1953, Frank [4] suggested that a form of autocatalysisin which each enantiomer catalyses its own production,while suppressing that of its mirror image, might havenonlinear dynamics leading to the amplification of smallinitial fluctuations in the concentrations of the enantiom-ers. Many theoretical models are proposed afterwards, butthey are often criticized as lacking any experimental sup-port [5]. Recently, asymmetric autocatalysis of pyrimidylalkanol has been studied intensively [6–9]. The enhance-ment of EE was confirmed [7], and its temporal evolutionwas explained by the second-order autocatalytic reaction[8,9]. But only with the nonlinear autocatalysis, chiralityselection is not complete; the value of EE stays less than100% and total chiral symmetry breaking is not achieved.In a recent theoretical model Saito [10] shows that in aclosed system the nonlinear autocatalysis amplifies the05=94(6)=065504(4)$23.00 06550initial small enantiomeric excess, but eventually the simplebackreaction can promote the decomposition of less abun-dant enantiomer to the reactant, which is recycled to pro-duce the more abundant type. Through this recyclingprocess, the complete chiral purity would be achieved.In this Letter we show the first experimental case wheretotal symmetry breaking and complete chiral purity isachieved from a system where both enantiomers arepresent since the beginning.First, we show with laboratory experiments how anisothermal saturated solution of sodium chlorate(NaClO3) with a large population of D and L crystalsmoves into complete chiral purity: (i) any small initialcrystal enantiomeric excess (CEE) eventually gives riseto total crystal purity disappearing the less abundant enan-tiomer (100% CEE); (ii) ‘‘symmetric’’ proportion of bothenantiomeric crystals gives rise to total symmetry breakingand crystal purity disappearing randomly one of the twoenantiomers. We study the key factors that promote thisbehavior.Second, up to now it was believed that any case of totalsymmetry breaking during crystallization occurs via pro-duction of secondary crystals of the same handedness froma single ‘‘mother crystal’’ that seeds the solution. However,our results show a case of total symmetry breaking incom-patible with the latter idea; i.e., we are dealing with anentirely different process. Furthermore, the experimentalresults show that complete symmetry breaking and chiralpurity can be achieved from an initial system with bothenantiomers. Therefore, the findings demand a new expla-nation for this process of total symmetry breaking and openthe debate on this fascinating phenomenon.Finally, we present arguments indicating that our experi-mental data can been explained by the model of ‘‘completechiral purity induced by nonlinear autocatalysis andrecycling.’’Sodium chlorate crystallization.—The achiral moleculesof NaClO3 crystallize as two enantiomeric chiral crystalsin the cubic space group P213 [11]. Hence sodium chlorate4-1  2005 The American Physical SocietyPRL 94, 065504 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending18 FEBRUARY 2005is achiral before crystallization, as it exists in solution asmore or less dissociated ions or clusters without a fixedchirality but forms a chiral crystal. About 100 years agoKipping and Pope [12] demonstrated that solutions ofNaClO3 by seeding can produce total CEE. More recentlyKondepudi and others [13] showed that simply stirringduring the crystallization of sodium chlorate from solutionwas sufficient to produce a yield approaching 100% of justone enantiomer. Whereas under normal conditions a dis-tribution of the proportion of one or other enantiomerobtained in a series of experiments falls on a typicalGaussian curve, with the peak yield at 50% of each enan-tiomer, in the stirred experiments the distribution is bimo-dal, with the peak yield close to 100% of one or the otherenantiomer. Kondepudi suggested that the most importantfactor in this chiral symmetry breaking is secondary nu-cleation by which a seed crystal or randomly generated‘‘mother crystal’’ triggers the production of a large numberof secondary crystals at a fast rate if the solution is stirredthat are enantiomerically identical to itself. The result ofthis crystallization process is the generation of crystalswith the same handedness (total chiral symmetry break-ing). Nevertheless, the hypothesis of an initial single chiralcrystal to explain spontaneous chiral symmetry breakinghas been disputed recently [14].Experimental.—Chiral L and D crystals were ob-tained separately by literature procedures via seedingwith the appropriate chiral crystal a supersaturatedsolution [15]. We prepared samples (12 g) with mix-tures of L and D NaClO3 chiral crystals with5% CEE (L crystals:D crystals  5:7000 g:6:3000 gor 6:3000 g:5:7000 g), and samples with symmetricmixtures of both crystals (L crystals:D crystals 6:0000 g:6:0000 g). Every sample was ground using anagate pestle and a mortar and was placed in a set of25 mL round-bottom flasks with 10 mL of water.Because of the solubility of NaClO3 [16], an excess ofmore than 2 g of crystals remains without dissolving at24 C. We added to some solution flasks, 8 g, 6 g, 4 g, or2 g of small glass balls (3 mm of diameter), that continu-ously crushed the crystals that were being subjected tostirring by a magnetic bar (3–20 mm) at 600 rpm. Flaskswith only solutions and crystals and flasks with solutions,crystals, and glass balls were hermetically closed andmaintained at 24 C with constant agitation. Every solu-tion contains a population of more than a million of crys-tals. The continuous mechanical abrasion-grinding ofcrystals by glass balls imposes to crystals a maximumsize of about 200 m that is kept during all the experimentalthough they grow (it depends fundamentally on the sizeof the glass balls because the system works like a mill). Aparallel experiment was performed: four solution flaskswith crystals and 4 g of glass balls were agitated to 200,400, 600, and 800 rpm, respectively. Samples of solutionwith crystals (0.1 mL with more than 10 000 crystals) were06550removed from the flasks every 2 h and left to grow during afew hours. The experiments are considered finished whenchiral crystal purity is achieved. Chiral crystal evolutionwas determined by their optical activity using a petro-graphic microscope [13]. The ease with which the L andD crystals could be identified enables us to know whenchiral crystal purity has been reached. All experimentshave been performed and repeated more than 20 times insuccessive weeks. The reported results are average values.Results and discussion.—Crystals in the stirred solutions(no glass balls involved) maintain indefinably (severaldays) the initial enantiomeric excess or the initial ‘‘sym-metry’’ between both populations of L and D crystals.However, all stirred crystals-solution systems where glassballs (abrasion-grinding process) intervene show a con-tinuous enhancement of CEE, and eventually, total sym-metry breaking and complete chiral crystal purity achievedat different times. The time required to achieve chiralpurity depends on the number of glass balls present inthe system (Fig. 1), and when the number of glass ballsis the same, it depends on the speed of agitation (rpm)(Fig. 2). After 8 h, solutions with initial 5% L-CEE show100% L-CEE, and solutions with initial 5% D-CEE show100% D-CEE (Fig. 3). Solutions with initial symmetricmixtures of L and D crystals and 4 g of glass balls showtotal symmetry breaking and chiral purity after 24 h(Fig. 4). The handedness in this last case is L or D (ran-domly). Nevertheless, any small difference between L andD crystals induces the preferred production of one of them,for example, small differences in the quality of the crystalsbias the progressive enantiomeric amplification of a certainhandedness.It is evident from these results that under these condi-tions complete chiral purity cannot be explained by themodel of an initial single chiral crystal, and therefore, anew explanation is required.The crystal enantiomeric excess can be measuredby CEE  NL  ND=NL  ND, where NL and NDare the number of each enantiomer, that is, a meansto quantify the symmetry breaking. Recently Cartwright[17] established with theoretical argument that mechanicalcrushing of crystals is on the microscale the same mecha-nism that secondary nucleation. In fact, collisions betweenone crystal an another or between a crystal and the fluidboundaries (container walls, stirring bar, etc.) break piecesoff the surface, and fluid shears, which may also detachfragments from the crystal surface, have each been putforward as responsible for homochiral secondary nuclea-tion [18,19]. The detached fragment will possess the samechirality as the crystal of which they previously formeda part. Thus we can consider that the abrasion-grindingprocess by the glass balls of our experiments is a sortof ‘‘induced’’ secondary nucleation that generates newfragments of crystals with the same chirality as that ofthe mother crystal.4-2FIG. 2. Solutions with initial symmetric mixtures of L and Dcrystals and glass balls show total symmetry breaking and chiralcrystal purity. The data show the necessary time to achieve chiralpurity depending on the speed of agitation of the system (4 g ofballs).FIG. 1. Solutions with initial symmetric mixtures of L and Dcrystals and glass balls show total symmetry breaking and chiralcrystal purity. The data show the necessary time to achieve chiralpurity depending on the number of balls in the system (600 rpm).PRL 94, 065504 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending18 FEBRUARY 2005Following the ideas of Frank [4], indicating that a non-linear autocatalysis amplifies the small initial fluctuationsin the concentrations of the enantiomers, Cartwright andco-workers [17] showed with numerical simulations thatsecondary nucleation can act as just such a nonlinearautocatalytic process. As in the case of chiral crystalliza-tion, secondary nuclei possess the same chirality as themother crystal, so the presence of a crystal of a givenchirality catalyzes the production of further crystals withthe same chirality. However, in their simulation we canobserve that only with the nonlinear autocatalysis chiralityselection is not complete and the value of CEE stays lessthan unity. They assume that to obtain chiral purity weneed ‘‘a single mother crystal: an ancestral Eve for thewhole population.’’Similar results were achieved by Saito and Hyuga [10]with a mathematical model in which substances A and Breact to form substance C. Though reactants A and B areachiral, the product C happened to be chiral in two enan- FIG. 3. Solutions with initial 5% L-CEE show 100% L-CEE,and solutions with initial 5% D-CEE show 100% D-CEE in 8 h(600 rpm).06550tiometric forms; R isomer R-C and S isomer S-C.A B  R-CA B  S-CThey found that the EE amplification takes place with anonlinear autocatalytic chemical reaction. However, thefinal chirality is not complete: the EE is smaller than100%. However, the inclusion of the backreaction fromthe products R-C and S-C to A and B brings about thedrastic change in the results. The component which has aslight advantage starts to dominate, and the other chiraltype extinguishes gradually. Eventually, the complete ho-mochirality or chiral purity is achieved.Because of the combined abrasion-grinding (glass balls)and stirring in our experiments, the left- and right-handedcrystals continuously lose tiny fragments of left- and right- FIG. 4. Initial symmetric mixtures of D and L crystals and 4 gof balls show total symmetry breaking and chiral purity after24 h (600 rpm). The handedness in this case is L or D randomly.4-3PRL 94, 065504 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending18 FEBRUARY 2005hand microcrystallites or clusters; it is to say that weare dealing with an induced secondary nucleation, andbecause of this, with a nonlinear autocatalytic phenome-non. On the other hand, we are dealing with a population ofcrystals in contact with its solution, and therefore, thesurface of crystals is subjected a continuous dissolution-crystallization process. Since the abrasion-grinding pro-cess results in the continuous generation of microcrystalsthe effective surface area of crystalline phase continuouslyincreases. Additionally, the thermodynamic prediction ofGibbs-Thompson equation states that solubility of thecrystalline phase in a solution is dependent on particlesize [20]. Given that solubility of smaller particles isgreater than that of the larger ones, a slight concentrationgradient exists between particles of different size even nearchemical equilibrium. Thus, in the abrasion-grinding pro-cess of our system, the finest fraction of microcrystallitesor clusters easily dissolves, feeding the larger ones. That isto say, we are dealing with a continuous dissolution-crystallization phenomenon (as expected in any real sys-tem), only that in this case the process is highly enhancedby the abrasion-grinding process.Since the chirality of sodium chlorate is a propertyof its crystal structure, any molecular arrangementgreater than the unit cell is chiral. For NaClO3Znumber of molecules in unit cell  4 [21]. Thus anymolecular group of less than four molecules has not crystalstructure, reaching the achiral molecular level. During thedissolution process the final stage of any crystallite orchiral cluster is at this achiral molecular level and thereforecan feed other crystals independently of its chirality (themajority enantiomer has more advantage). Thus, in thisprocess the chiral crystals are continuously recycled andcomplete chiral purity can be achieved.Very recently Uwaha [22], knowing these experimentalresults, constructed a simple mathematical model based ona few physical assumptions that mimic our experimentalsystem. The development of this model shows completechiral symmetry breaking in a dissolution-crystallizationprocess.Finally, we may speculate that a solution of sodiumchlorate, strongly agitated in an isothermal slow evapora-tion process, can undergo similar pathways at the micro-scopic scale (microcrystals). At this level the effectivesurface of solid phase is maximum, resulting in totalsymmetry breaking that is manifested at the macroscopiclevel. Additionally, chiral clusters smaller than the criticalnucleus size may also be subjected to this symmetry break-ing process. In turn, when these clusters reach the criticalnucleus size, a chiral symmetry breaking in crystallizationfrom primary nucleation will ‘‘inherit’’ the chiral conditionachieved during the prenucleation stage. These hypothesesmust be regarded as complementary explanations to thephenomenon of symmetry breaking described in otherworks [13,14].06550Conclusion.—We show experimental data indicating forthe first time that complete homochirality and chiral puritycan be achieved from an initial system where both enan-tiomers are present. We suggest that in our system thisprocess becomes possible by the combination of (i) non-linear autocatalytic dynamic of secondary nucleation and(ii) the recycling of crystallites when they reach the achiralmolecular level in the dissolution-crystallization process.In this respect, we propose that chiral purity and totalsymmetry breaking during crystallization can be achievedwithout the necessary intervention of an initial single chiralphase. Beyond the specific aspects of these experiments, asignificant fact can be established with far reaching impli-cations: final and total chiral purity seems to be an inexo-rable exigency in the course of some physical processes.4-4*E-mail: viedma@geo.ucm.es[1] M. Avalos, R. Babiano, P. Cintas, J. L. Jimenez, and J. C.Palacios, Tetrahedron: Asymmetry 11, 2845 (2000).[2] W. A. Bonner, Origin of Life and Evolution of theBiosphere 21, 59 (1991).[3] J. G. P. Schmidt, E. Nielsen, and L. E. Orgel, J. Am. Chem.Soc. 119, 1494 (1997).[4] F. C. Frank, Biochim. Biophys. Acta 11, 459 (1953).[5] W. A. Bonner, Top. Stereochem. 18, 1 (1988).[6] K. Soai, S. Niwa, and H. Hori, J. Chem. Soc. Chem.Commun. 14, 982 (1990).[7] K. Soai, T. Shibata, H. Morioka, and K. Choji, Nature(London) 378, 767 (1995).[8] I. Sato, D. Omiya, K. Tsukiyama, Y. Ogi, and K. Soai,Tetrahedron Asymmetry 12, 1965 (2001).[9] I. Sato, D. Omiya, H. Igarashi, K. Kato, Y. Ogi, K.Tsukiyama, and K. Soai, Tetrahedron Asymmetry 14,975 (2003).[10] Y. Saito and H. Hyuga, J. Phys. Soc. Jpn. 73, 33 (2004).[11] S. C. Abrahams and J. L. Bernstein, Acta Crystallogr. B33, 3601 (1977).[12] F. S. Kipping and W. J. Pope, Nature (London) 59, 53(1898).[13] D. K. Kondepudi, R. J. Kaufman, and N. Singh, Science250, 975 (1990).[14] C. Viedma, J. Cryst. Growth 261, 118 (2004).[15] W. C. Chen, D. D. Liu, W. Y. Ma, A. Y. Xile, and J. Fang, J.Cryst. Growth 236, 413 (2001).[16] W. C. Chen, D. D. Liu, W. Y. Ma, A. Y. Xile, and J. Fang, J.Cryst. Growth 236, 413 (2001)[17] J. H. E. Cartwright, J. M. Garcia-Ruiz, O. Piro, C. I. Sainz-Diaz, and I. Tuval, Phys. Rev. Lett. 93, 035502 (2004).[18] B. Martin, A. Tharrington, and X.-I. Wu, Phys. Rev. Lett.77, 2826 (1996).[19] T. Buhse, D. Durand, D. Kondepudi, J. Laudadio, and S.Spilker, Phys. Rev. Lett. 84, 4405 (2000).[20] R. L. Joesten, Mineralogical Society of America ShortCourse Notes 26, 507 (1991).[21] R. W. G. Wyckoff, Crystal Structure (Wiley, New York,1964).[22] M. Uwaha, J. Phys. Soc. Jpn. 73, 2601 (2004).

Physical Review Letters

Chiral Symmetry Breaking During Crystallization: Complete Chiral Purity
Induced by Nonlinear Autocatalysis and Recycling

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Total Chiral Symmetry Breaking during Crystallization: Who needs a
  "Mother Crystal"?

Total Chiral Symmetry Breaking during Crystallization: Who needs a "Mother Crystal"?

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