ARTICLESPUBLISHED ONLINE: 15 MARCH 2009 | DOI: 10.1038/NMAT2405

Cloning polymer single crystals through self-seedingJianjun Xu1,2*, YuMa3,4, Wenbing Hu4*, Matthias Rehahn1,2 and Günter Reiter3†

In general, when a crystal is molten, all molecules forget about their mutual correlations and long-range order is lost. Thus,a regrown crystal does not inherit any features from an initially present crystal. Such is true for materials exhibiting awell-defined melting point. However, polymer crystallites have a wide range of melting temperatures, enabling paradoxicalphenomena such as the coexistence of melting and crystallization. Here, we report a self-seeding technique that enables thegeneration of arrays of orientation-correlated polymer crystals of uniform size and shape (‘clones’) with their orientationinherited from an initial single crystal. Moreover, the number density and locations of these cloned crystals can to some extentbe predetermined through the thermal history of the starting crystal. We attribute this unique behaviour of polymers to thecoexistence of variable fold lengths in metastable crystalline lamellae, typical for ordering of complex chain-like molecules.

Owing to the statistical nature of nuclei formation, thereare no orientation correlations between neighbouringcrystals. It is normally not possible to predict when and

where crystals will start to grow. In addition, in macromolecularsystems nucleation often represents a severe problem in polymerprocessing, requiring heterogeneous nucleation (for example,nucleating agents1–3) to start the crystallization. As an alternative, aself-seeding approach1,4–7 enables the problems of nucleation to beavoided. It consists of two steps. First, an already crystalline sample(crystallized at temperature TC) is melted at temperatures (TSS)slightly above the calorimetrically determined nominal meltingpoint to the extent that neither by calorimetry, nuclear magneticresonance nor bymicroscopic techniques are any crystalline regionsdetectable8–10. Then, the sample is cooled to a lower temperature(TRC) where crystals grow from submicroscopic, crystalline remainsresisting the previous melting procedure. However, the underlyingphysics of this self-seeding approach is so far only poorlyunderstood4–10. In particular, it is not clear yet if the seedsrepresent stable crystalline remains or reflect a melt state witha ‘kinetic’ memory of the crystalline state due to non-relaxedconformation of preferentially orientated chains. Here, we establishfor the first time that a correlation between a starting crystaland regenerated crystals (called ‘clones’) exists, expressed by aninheritance of molecular orientation between different generationsof crystals. We demonstrate the suitability of this approach forthe fabrication of arrays of orientation-correlated, nanometre- tomicrometre-sized crystals.

To enable a clear-cut and unambiguous demonstration that suchan orientation correlation between the regenerated polymer crystalsexists, we carried out experiments in quasi-two-dimensional thinfilms11,12. We used lamellar single crystals as the seeding crystalsthat were grown under well-defined isothermal conditions (seethe Methods section).

Single crystals—defined by a unique orientation of all moleculeswithin such a crystal—may have various morphologies, rangingfrom dendritic to faceted shapes11–15, which are mainly controlledby the diffusion field around the growing crystal, as shown byMullins and Sekerka16,17. We identified single crystals on thebasis of the symmetry of the unit cell and the shape of the

1Ernst Berl-Institut für Technische und Makromolekulare Chemie, TU Darmstadt, Petersenstrasse 22, D-64287 Darmstadt, Germany, 2DeutschesKunststoff-Institut, Schlossgartenstrasse 6, D-64289 Darmstadt, Germany, 3Institut de Chimie des Surfaces et Interfaces, ICSI-UHA-CNRS, 15, rue JeanStarcky, B.P. 2488, 68057 Mulhouse Cedex, France, 4State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering,Department of Polymer Science and Engineering, Nanjing University, 210093, Nanjing, China. †Present address: Physikalisches Institut, UniversitätFreiburg, 79104 Freiburg, Germany. *e-mail: jxu@dki.tu-darmstadt.de; wbhu@nju.edu.cn.

observedmorphologies. These crystals were heated to a temperatureTSS where morphological features characterizing the crystallinestate disappeared under an optical microscope. Subsequently, thesampleswere brought to a lower temperatureTRC. In Fig. 1, we showtypical results of such a self-seeding procedure for single crystals(Fig. 1a) of a diblock copolymer, poly(2-vinylpyridine-block-polyethyleneoxide) (P2VP-b-PEO), in which P2VP is amorphousand PEO is crystalline. We can clearly observe the generation ofmany small crystals (Fig. 1b–e), which all had nearly the same shapeand orientation (Fig. 1e) as the original starting crystal. Deviationsfrom the square shape (Fig. 1b,d) can be attributed to coalescence ofclones resulting from two or multiple seeds18. The number densityof clones (Fig. 1b,c) depended on TSS. We emphasize that underthese conditions no crystals were ever observed outside the areaor within some distance to the periphery (Fig. 1b,c) of the seedingcrystal. Previous experiments11,12 with this polymer showed that theprobability of homogeneous (‘primary’) nucleation is so low that itis practically impossible to nucleate crystals in thin homogeneousfilms at temperatures above approximately 45 ◦C if there were notany seeds or nucleating agents. Thus, we are confident that all clonesoriginated from the remains aftermelting of the starting crystal. Theanalysis of a multitude of samples showed that more than 95% ofthese clones have their axis pointing in the same direction as theseeding crystal (Fig. 1f).

Generating starting crystals through a two-step growth process(initial growth at a constant temperature TC,1 is continued by asecond period of growth at a higher temperature TC,2), enabled usto produce clones only at the periphery of these starting crystals(Fig. 2). During the second growth step, the thickness of the startingcrystal increased at the periphery19–21. Melting this two-step crystalat TSS high enough to completely melt the interior (the dendriticpattern was lost), but still low enough to keep seeds at the periphery,led to clones (Fig. 2d,e), which again were all oriented in the samedirection as the seeding crystal (Fig. 2f).

To demonstrate the generality of our approach, we have chosenas a second crystallizable polymer an organometallic homopolymer,poly(ferrocenyl dimethyl silane)22–24 (PFS). Under the chosencrystallization conditions, PFS yielded compact single crystals withan almost rectangular but not truly faceted shape (Fig. 3a). Applying

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Figure 1 | Transforming a large compact dendritic single crystal into a plethora of uniquely oriented small crystals. a, The starting crystal ofP2VP-b-PEO, outlined by a dotted red square, after 22 min at 45 ◦C. The inset shows the temperature protocol used for the samples shown in b,c. Thedashed line indicates the nominal melting temperature. b, After an extra 20 s at 62 ◦C plus 5 s at 63 ◦C, and 4 min at 56 ◦C followed by a quench to roomtemperature. The inset shows a magnification of the central area indicated by the dotted square. c, Another crystal analogous to a was annealed for 20 s at62 ◦C before it was recrystallized for 3 min at 56 ◦C and then quenched to room temperature. d,e, AFM images of the selected regions of sample c. The redarrows in e indicate the orientation of the seeding crystal. f, Probability of orientation of the cloned crystals with respect to the seeding crystal.

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Figure 2 | Nucleating crystals at the periphery of the seeding crystal following a two-step crystallization procedure. a, The starting crystal ofP2VP-b-PEO after 8 min at 45 ◦C. The inset shows the temperature protocol used. The dashed line indicates the nominal melting temperature. b, After anextra 10 min at 56 ◦C. c, After subsequent annealing for 10 s at 62 ◦C. d, After recrystallization at 56 ◦C for 4 min and quenching to room temperature.e, AFM image of the area in d indicated by the dotted red square. f, Probability of orientation of the cloned crystals with respect to the seeding crystal.

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Figure 3 | A control experiment using an organometallic homopolymer. a, Typical starting crystal of PFS after 18.5 h at 125 ◦C. The inset shows thetemperature protocol used. The dashed line indicates the nominal melting temperature. b, Cloned crystals after annealing for 14 min at 138 ◦C, plus 10 minat 143 ◦C, plus 2 min at 145 ◦C and 1 min at 146 ◦C, followed by crystallization at 125 ◦C for 13 h and quenching to room temperature. c, AFM image ofcloned crystals taken after annealing for 10 min at 140 ◦C, plus 10 min at 145 ◦C, followed by crystallization at 125 ◦C for 40 min and quenching to roomtemperature. d, Cloned crystals resulting from a seeding crystal (21 h at 130 ◦C), after annealing for 5 min at 137 ◦C, plus 10 min at 142 ◦C, plus 5 min at145 ◦C and finally 2 min at 147 ◦C. This sample was recrystallized at 125 ◦C for 110 min and quenched to room temperature. e, AFM image of the sample ind. f, Probability of orientation of the clones with respect to the seeding crystal.

a similar self-seeding procedure, we could generate a large amountof small crystals (Fig. 3b–e) which reappeared on repeated self-seeding. As for P2VP-b-PEO, the unique size of these clones is dueto the fact that all crystals started to grow simultaneously at the samerate. By systematically increasing the self-seeding temperature TSS,we could reproducibly decrease the average number density (N ) ofclones in an exponential fashion with TSS (see Fig. 4). Interestingly,N did not vary with the time tSS the sample was molten at TSS,given that TSS was high enough (TSS> 140 ◦C in our experiments).This independence of N on tSS clearly demonstrates that the seedsare stable crystalline remains and are not representing a moltenstate of preferentially oriented molecules with a memory of thepreviously crystalline state, as such memory is expected to relax intime. Following the process of regrowing crystals in real time (byoptical microscopy) yielded a constant growth rate for the clones.An extrapolation fromcomparatively large sizes of the clones at laterstages back to the time when the sample temperature was loweredfrom TSS to TRC demonstrated that the size of the seeds was muchless than the resolution limit of opticalmicroscopy,�1 µm.

To shed light on the origin of self-seeding and to understandthe mechanism for generating aligned arrays of cloned crystals,we first have to identify why such a cloning process throughself-seeding is possible for polymers but cannot be observed forsmall molecules15,25. In contrast to small molecules, polymersencounter a tremendous difficulty (Fig. 5) when crystallizing21,26:instead of attaching individual ‘blocks’ independently, a polymeralways arrives as a ‘chain of blocks’. Owing to the connectivityof the blocks, they can be integrated into the crystal at only alimited number of nearby sites. If crystallization proceeds quickly,no optimization of the block arrangement can be achieved. Someof these blocks may stay excluded from the crystal if all accessiblenearby sites on the crystal were already occupied by other blocks.Consequently, polymers form lamellar crystals bound by surfacescontaining chain folds27,28. The thickness of such lamellae, thatis, the length of the crystalline stems and thus the degree ofchain order, increases with the time available for the polymerchains to integrate into the crystal27,28. If long chains have to berapidly integrated into the crystal, they can do so only at the

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140 142

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Figure 4 | Average number density N of baby crystals after annealing atdifferent self-seeding temperatures (TSS). The samples were kept forvarying times (tSS) at TSS: 10 s (squares) and 2 min (diamonds) for all TSS

and 80 min at 141 ◦C, 200 min at 143 ◦C and 130 min at 145 ◦C (stars),respectively. The samples were quenched from TSS to 125 ◦C for isothermalcrystallization for about 1 h. Starting crystals were obtained aftercrystallization at 128.5 ◦C for 920 min. The insets are optical microscopyimages of crystals annealed for 2 min at 141 ◦C, 143 ◦C and 146 ◦C ,respectively, followed by isothermal crystallization at 125 ◦C forabout 70 min.

expense of lower perfection, that is, a larger number of chain folds.Then, even after growth, some reorganization in the crystallinestate19–21 may take place, leading to (local) improvement of order byremoving some folds29–31. Reorganization is typically much slowerthan growth. The degree of chain order (chain folding) within apolymer crystal depends on the rate it was grown (characterizedby the crystallization temperature), the time the crystal spent attemperatures below the melting point (its age) and, in general, alltemperature variations during its existence (its thermal history).Consequently, polymer crystals unavoidably consist of regionsof differing degrees of chain order and conformational entropy,which thus have different melting temperatures27,28,32. This is incontrast to small molecules such as, for example, water15, wheremelting is characterized by a well-defined temperature. Increasingtemperature by a fraction of a degree can switch water from thecrystalline (ice) to the liquid state. In polymer systems, however,a small increase in temperature typically leads to melting of only a(small) part of the sample. Continuously increasing the temperaturein an annealing experiment will thus lead to successive melting andreorganization events, leaving eventually only a few small clusterscontaining molecules in the least-folded crystalline state. Whendecreasing the temperature again, these clusters will act as nucleifor clones that now all have the same orientation because all of thesenuclei belonged to the same initial single crystal.

Molecular reorganization and lamellar thickening can occur atany point during the ‘lifetime’ of a polymer crystal. Reorganizationis typically more pronounced and often faster at high temperaturesand if the reorganizing crystalline region is not surrounded byalready highly organized polymers. Consequently, most significantchanges occur at the crystal growth front during growth and duringannealing of highly imperfect crystals.

To visualize the consequences of metastability and reorganiza-tion at a molecular scale, that is, to show that the thickness of alamellar single crystal is fluctuating around some mean value andincreases with time and with distance to the growth front, we havecarried out dynamic Monte Carlo simulations33,34 (see the Methods

Small molecules

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Polymers

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Figure 5 | Schematic presentation of essential steps in polymercrystallization enabling cloning. a, Small molecules, represented by cubes,arrive randomly and independently at the crystal growth front where theymay undergo extra steps of reorganization. b, Polymers, represented bychains of connected cubes, attach only sequentially to the crystal, imposingsevere constraints on the attachment possibilities of subsequent chainsegments, leading to chain folding and the formation of lamellar crystals.c, The kinetically selected thickness of a lamellar crystal may increase intime or in response to a temperature jump by removing progressively morechain folds in the course of reorganization within the crystal.

section). As can be seen in Fig. 6, the thickness of the lamellarcrystal is never constant. It increased continuously during crystalgrowth owing to internal reorganization in the crystalline state. Thelamella was always thicker in the centre region than at the growthfront. The most frequently observed length of the crystalline stemshifted to higher values in the course of time. Importantly, whileconcentrated close to the centre of the crystal, long stems were notdistributed in a regular fashion. Simulations were not intended toreproduce our experiments but demonstrated that the thickness ofa polymer single crystal is highly heterogeneous, in accordance withprevious simulations20,21,30,31. Heterogeneities in thickness are notdisappearing in time or with the age of the crystal.

We would like to emphasize that in our experiments theorientation of the clones is neither due to epitaxy on an inorganic35or organic3 crystalline substrate (our substrate is amorphous),nor due to nano-confinement36. Orientation is also not controlledby external triggers such as an electric field37 or atomic forcemicroscopy (AFM) tips38. The mechanism presented here of crystalcloning through self-seeding does not rely on any foreign nucleating

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Figure 6 | Distribution of local lamellar thickness (stem length L) within a polymer crystal obtained by dynamic Monte Carlo simulation. a,b, A crystalgrown on a cubic lattice for 1 (a) and 100 (b) kMCC (kMCC: thousand Monte Carlo cycles). The local stem length (in lattice units) is represented bycolours. Typical cross-sections, as indicated by white lines, are shown in the insets. c, Distribution frequency of stem length (L) for the crystals shown ina,b. The melting temperature (Tm) is related to the stem length (Tm∼ Tm,∞(1−α/L), with α being a constant).

agents that may act as templates like in a seeded supersaturatedsolution39. Of course, a seed of the samematerial can also be createdby other ways than self-seeding, for example, by locally coolingpart of the sample. However, we did not use any temperaturegradient for defining a melt–crystal interface like in the growthof single semiconductor crystals40. We simply took advantage ofthe fact that the degree of order of a crystalline polymer chain isa kinetically determined parameter that varies with crystallizationtemperature, depends on the age and thermal history of the sampleand evolves in time.

Our experiments enable us to clearly distinguish between ‘meltmemory’ and ‘self-seeding’. The term ‘melt memory’ implies thatthe crystal is completely molten. Only owing to the slownessof conformational relaxations of the already molten polymer,correlated chain orientations of the previous crystalline state couldsurvive for a certain time. The term ‘self-seeding’ reflects thepossibility that some seeds survive the melting process and remaincrystalline. As a consequence, the seeds will not disappear evenif the time at the seeding temperature (the seeding time) isincreased, as shown in Fig. 4.

We re-emphasize that it is crucial that the starting points forcrystal growth (the ‘seeds’) are derived from a previously formedsingle crystal. Consequently, the seeds all have the same orientation.However, if a crystal of small molecules (such as a snow flake)were to be melted, no seeds would ever form as such a crystalwould always melt completely (given that the time allowed for themelting process is sufficiently long). Crystals of small moleculeshave a well-defined melting temperature TM (sharp melting point)and thus either will melt completely (T >TM) or do not melt at all(T <TM). In contrast, a polymer crystal can consist simultaneouslyof regions that melt and regions that stay crystalline, independentof how long the sample is kept at TSS. Thus, the cloning processpresented here is a feature that is possible only for polymercrystals with simultaneously existing metastable states of differentmelting temperatures.

In summary, we have demonstrated a method for preparing amultitude of uniquely oriented polymer single crystals of uniformsize and shape. The number density and spatial distribution of thesecrystals can be influenced by the thermal history of the startingcrystals, in particular by TSS (see Fig. 4). Successfully applying thisprocess for two different polymers, a homopolymer and a diblockcopolymer, we are confident that the inheritance of molecularorientation between different generations of crystals represents ageneral aspect of all crystallizable macromolecules. In addition,our work demonstrates that non-equilibrated, metastable states,which are frequently the result of molecular ordering in complexmacromolecular systems, can be at the origin of phenomena

that are not observable if these systems were equilibrated. Theorder and size of crystals represent crucial parameters affectingmany properties of polymer crystals. For example, optoelectroniceffects in semicrystalline conjugated polymers depend sensitivelyon (local) chain order and the way crystalline domains areinterconnected and oriented. Thus, having a handle on nucleationmay enable optimization of these properties. Besides potential usein applications demanding oriented crystals, this cloning approachgenerates model systems of identical crystals for investigating basicquestions ofmolecular ordering inmacromolecular systems.

MethodsPolymers. The P2VP-b-PEO copolymer (Mn = 16.4+ 46.6 kgmol−1,Mw/Mn < 1.14, with Mw and Mn being the weight- and number-averagedmolecular masses, respectively) was synthesized by the group of Martin Möller,Aachen, Germany. The equilibrium melting temperature has been extrapolated tobe about 70 ◦C (ref. 41).

The organometallic homopolymer PFS (Mn = 60.7 kgmol−1,Mw/Mn < 1.05)was synthesized by living anionic polymerization in Darmstadt, Germany.The equilibrium melting temperature Tm,∞ derived from linear extrapolationof the melting temperature versus inverse lamellar thickness (assuming aGibbs–Thomason relation, given in ref. 42) yields:Tm,∞≈215 ◦C (ref. 42).

Filmpreparation and crystallization. Films (about 40–50 nm thick) were preparedby spin-coating at 2,000 r.p.m. for 30 s a toluene solution (concentration about10mgml−1) at ambient conditions onto ultraviolet–ozone cleaned siliconwafers.

To prepare the P2VP-b-PEO seeding single crystals, a spin-coated film wasfirst heated rapidly from room temperature to 59 ◦C, kept there for 1min andthen cooled down to 45 ◦C for isothermal crystallization (for 8min or 22min). Attemperatures above about 45 ◦C, no nucleation events were observed for manyhours (after cooling down from higher temperatures). The relation betweencrystal habit and PEO unit cell (crystals are bounded by (120) faces) has beenestablished previously12,18.

PFS seeding crystals were prepared by heating a spin-coated film to 170 ◦Cin a vacuum oven, and cooling it down slowly within 40min to either 125 ◦C or130 ◦C where it isothermal crystallized (which is slow) for around 20 h, before itwas quenched to room temperature.

We have cycled the self-seeding procedure and found that for constant TSS theclones reappeared at the same locations. Even when TSS was increased slightly, theclones reappeared at the same locations. This indicates that some reorganizationalso took place during seeding. Thus, during cycling the stability of the seedsincreased, that is, they exhibited a highermelting temperature.

Washing procedure. Some films containing crystals were washed for shorttimes (5 s up to 1min) in a toluene bath, which was at about 30 ◦C or 5 ◦C forP2VP-b-PEO and PFS, respectively. After removing the samples from the bath,most of the solvent drained off the sample by keeping the sample vertical. Theremaining solvent evaporated at ambient conditions.

Observation techniques. Both initial crystal growth (for P2VP-b-PEO)and subsequent self-seeding (for both samples) were carried out under anoptical microscope. Information with higher spatial resolution was obtainedafterwards by AFM.

For optical microscopy, the samples were placed onto an enclosed hotplate, purged with nitrogen, under a Leitz-Metallux 3 optical microscope. The

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crystallization temperature at the hot stage was controlled to within 0.1◦C. ForP2VP-b-PEO, we have followed the progression of the crystal growth front in realtime by capturing images by a video camera.

AFM measurements were carried out with a Nanoscope IIIa/ Dimension3000 (Digital Instruments) in the tapping mode at ambient conditions. We usedsilicon tips with a resonant frequency of about 160–190 kHz. Scan rates werebetween 0.2 and 4Hz.

Computer simulations. We used an approach of dynamic Monte Carlosimulations33,34 using a three-dimensional 64×64×64 cubic lattice containing 1,920chains each with length 128 (all lengths and distances are given in lattice units). Eachmonomer occupied one site on the lattice. The total volume fraction of polymeris 0.9375, and the unoccupied sites serve as free volume allowing the polymers tomove. In our model, crystallization is driven by the interaction between parallelbonds connectingmonomers, noted as EP. Owing to the semiflexibility of chains, weintroducedEC, the energy gainedwhen the length of the crystalline stem increased byonemonomer.Metropolis sampling was used with the potential energy barrier con-stituted by EP and EC in each step of micro-relaxation, where EP/EC= 1 and kT/EC

(abbreviated byT )measures the temperature (here k is Boltzmann’s constant).The probability for homogeneous nucleation was extremely low at

temperatures T > 4.5. Thus, a seed is generated by first crystallizing the systemat T = 3.9 for 10,000Monte Carlo cycles. Time is measured in Monte Carlocycles, defined by the time needed for trying to move once each monomer andvacancy site of the whole system. Then, the temperature is raised to TSS = 4.7for isothermal melting.

We note that, limited by the computer power, the polymer crystals formed inour Monte Carlo simulations were much smaller and grew faster in comparisonwith the ones studied in our experiments. As a consequence, the simulated crystalswere not faceted and the lamellar thickness, on average, was smaller. However,the inhomogeneous distribution of crystal thickness was similar to that of ourpresent experiments.

Received 19 February 2008; accepted 12 February 2009;published online 15 March 2009

References1. Wunderlich, B. Macromolecular Physics, vol. 2: Crystal Nucleation, Growth,

Annealing Ch. V (Academic, 1976).2. Weissbuch, I., Lahav, M. & Leiserowitz, L. Toward stereochemical control,

monitoring, and understanding of crystal nucleation. Cryst. Growth Des. 3,125–150 (2003).

3. Wittmann, J. C. & Lotz, B. Epitaxial crystallization of polymers on organic andpolymeric substrates. Prog. Polym. Sci. 15, 909–948 (1990).

4. Blundell, D. J., Keller, A. & Kovacs, A. J. A new self-nucleation phenomenonand its application to the growing of polymer crystals from solution. J. Polym.Sci. B 4, 481–486 (1966).

5. Blundell, D. J. & Keller, A. Nature of self-seeding polyethylene crystal nuclei.J. Macromol. Sci.-Phys. B 2, 301–336 (1968).

6. Fillon, B., Wittmann, J. C., Lotz, B. & Thierry, A. Self-nucleation andrecrystallization of isotactic polypropylene (α phase) investigated bydifferential scanning calorimetry. J. Polym. Sci. B 31, 1383–1393 (1993).

7. Massa, M. V., Lee, M. S. M. & Dalnoki-Veress, K. Crystal nucleationof polymers confined to droplets: Memory effects. J. Polym. Sci. B 43,3438–3443 (2005).

8. Maus, A., Hempel, E., Thurn-Albrecht, T. & Saalwächter, K. Memory effect inisothermal crystallization of syndiotactic polypropylene—role of melt structureand dynamics? Eur. Phys. J. E 23, 91–101 (2007).

9. Lorenzo, A. T., Arnal, M. L., Sanchez, J. J. & Müller, A. J. Effect ofannealing time on the self-nucleation behaviour of semicrystalline polymers.J. Polym. Sci. B 44, 1738–1750 (2006).

10. Müller, A. J. & Arnal, M. L. Thermal fractionation of polymers. Prog. Polym. Sci.30, 559–603 (2005).

11. Reiter, G. et al. Morphologies of polymer crystals in thin films.Lecture Notes Phys. 714, 179–200 (2007).

12. Grozev, N., Botiz, I. & Reiter, G.Morphological instabilities of polymer crystals.Eur. Phys. J. E 27, 63–71 (2008).

13. Xiao, R.-F., Alexander, J. I. D. & Rosenberger, F. Growth morphology withanisotropic surface kinetics. J. Cryst. Growth 100, 313–329 (1990).

14. Brener, E., Müller-Krumbhaar, H. & Temkin, D. Structure formation and themorphology diagram of possible structures in two-dimensional diffusionalgrowth. Phys. Rev. E 54, 2714–2722 (1996).

15. Libbrecht, K. G. The physics of snow crystals. Rep. Prog. Phys. 68,855–895 (2005).

16. Mullins, W.W. & Sekerka, R.F. Morphological stability of a particle growing bydiffusion or heat flow. J. Appl. Phys. 34, 323–329 (1963).

17. Sekerka, R. F. Role of instabilities in determination of the shapes of growingcrystals. J. Cryst. Growth 128, 1–12 (1993).

18. Kovacs, A. J., Lotz, B. & Keller, A. Multiple twinning in polyethylene oxidesingle crystals-a scheme for the formation of growth twins from self-seedingnuclei. J. Macromol. Sci. - Phys. B 3, 385–425 (1969).

19. Reiter, G. Model experiments for a molecular understanding of polymercrystallization. J. Polym. Sci. Part B 41, 1869–1877 (2003).

20. Sommer, J. -U. & Reiter, G. Morphogenesis of lamellar polymer crystals.Europhys. Lett. 56, 755–761 (2001).

21. Sommer, J. -U. & Reiter, G. Morphogenesis and nonequilibrium patternformation in two-dimensional polymer crystallization. Phase Transit. 77,703–745 (2004).

22. Manners, I. Polymer science with transition metals and main group elements:Towards functional, supramolecular inorganic polymeric materials. J. Polym.Sci. A 40, 179–191 (2002).

23. Lammertink, R. G. H., Hempenius, M. A., Manners, I. & Vancso, G. J.Crystallization and melting behavior of poly(ferrocenyldimethylsilanes)obtained by anionic polymerization.Macromolecules 31, 795–800 (1998).

24. Manners, I. Putting metals into polymers. Science 294, 1664–1666 (2001).25. Sunagawa, I. Crystals: Growth, Morphology, and Perfection (Cambridge Univ.

Press, 2005).26. Sommer, J.-U. Theoretical aspects of the equilibrium state of chain crystals.

Lecture Notes Phys. 714, 19–45 (2007).27. Wunderlich, B.Macromolecular Physics, vol. 1: Crystal Structure, Morphology,

Defects Ch. III, 194 (Academic, 1973).28. Strobl, G. Crystallization and melting of bulk polymers: New observations,

conclusions and a thermodynamic scheme. Prog. Polym. Sci. 31,398–442 (2006).

29. Weeks, J. J. Melting temperature and change of lamellar thickness with timefor bulk polyethylene. J. Res. Natl Bur. Stand. A 67, 441–451 (1963).

30. Anderson, K. L. & Goldbeck-Wood, G. Simulation of thickening growth inpolymer crystallisation. Polymer 41, 8849–8855 (2000).

31. Doye, J. P. K. & Frenkel, D. Mechanism of thickness determination in polymercrystals. Phys. Rev. Lett. 81, 2160–2163 (1998).

32. Thomson, W. On the equilibrium of vapour at a curved surface of liquid.Phil. Mag. 42, 448–453 (1871).

33. Hu, W.-B. & Frenkel, D. Polymer crystallization driven by anisotropicinteractions. Adv. Polym. Sci. 191, 1–35 (2005).

34. Hu, W.-B., Frenkel, D. & Mathot, V.B.F. Sectorization of a lamellar polymercrystal studied by dynamic Monte Carlo simulations. Macromolecules 36,549–552 (2003).

35. Pashley, W. The nucleation, growth, structure and epitaxy of thin surface films.Adv. Phys. 14, 327–416 (1965).

36. Hu, Z., Baralia, G., Bayot, V., Gohy, J.-F. & Jonas, A. M. Nanoscale controlof polymer crystallization by nanoimprint lithography. Nano Lett. 5,1738–1743 (2005).

37. Zhang, K.-Q. & Liu, X. Y. In situ observation of colloidal monolayer nucleationdriven by an alternating electric field. Nature 429, 739–743 (2004).

38. Liu, X. et al. The controlled evolution of a polymer single crystal. Science 307,1763–1766 (2005).

39. Mullin, J. W. Crystallization 3rd edn, Ch. 5 and 6 (Butterworth–Heinemann, 1992).

40. Capper, P. (ed.) Bulk Crystal Growth of Electronic, Optical and OptoelectronicMaterials (Wiley–VCH, 2005).

41. Huang, Y. et al. Crystallization, melting, and morphology ofpoly(ethylene oxide) diblock copolymer containing a tablet-like block ofpoly{2,5-bid[(4-bis-methoxyphenyl)oxycarbonyl]styrene}. Polymer 46,10148–10157 (2005).

42. Xu, J. et al. Equilibrium melting point of poly(ferrocenyl dimethylsilane).DESY Annu. Rep. 1131–1132 (2006).

AcknowledgementsWe acknowledge V. Bellas (Technische Universität Darmstadt, Germany) for synthesizingthe PFS polymer, and K. Albrecht, A. Mourran and M. Möller (DWI Aachen, Germany)for providing the P2VP-PEO block copolymer. J.X. is grateful to B. Stühn, I. Alig andB.-J. Jungnickel for helpful discussions. Financial support provided through the GermanResearch Foundation (DFG), the European Community’s ‘Marie-Curie Actions’ undercontract MRTN-CT-2004-005516 [BioPolySurf] and by the European COST ActionP12 is acknowledged. W.H. is grateful for research support from the Chinese Ministryof Education (NCET-04-0448) and the National Natural Science Foundation of China(NNSFC Grants 20474027, 20674036, 20825415).

Author contributionsThe idea for this work arose from a visit by J.X. to ICSI-Mulhouse. J.X. and Y.M. carriedout all experiments. Computer simulations were done by Y.M. and W.H. The controland coordination of polymer synthesis at TUD/DKI was assured by M.R. G.R. supervisedand coordinated the whole project. All authors have contributed equally in defining thecontent and writing the present manuscript.

Additional informationReprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should beaddressed to J.X. or W.H.

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