Direct observation of prefreezing at the interfacemelt–solid in polymer crystallizationAnn-Kristin Löhmann, Thomas Henze, and Thomas Thurn-Albrecht1

Institute of Physics, Martin Luther University Halle-Wittenberg, 06099 Halle, Germany

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 21, 2014 (received for review May 8, 2014)

Crystallization is almost always initiated at an interface to a solid.This observation is classically explained by the assumption of areduced barrier for crystal nucleation at the interface. However, aninterface can also induce crystallization by prefreezing (i.e., theformation of a crystalline layer that is already stable above thebulk melting temperature). We present an atomic force microscopy(AFM)-based in situ observation of a prefreezing process at theinterface of a polymeric model system and a crystalline solid.Explicitly, we show an interfacial ordered layer that forms wellabove the bulk melting temperature with thickness that increaseson approaching melt–solid coexistence. Below the melting temper-ature, the ordered layer initiates crystal growth into the bulk,leading to an oriented, homogeneous semicrystalline structure.

semicrystalline polymers | AFM | thin films | epitaxy

The fundamental process of crystallization from the liquid orgaseous state is of importance in many areas of condensed

matter physics and materials science. In practice, crystallizationis, in most cases, initiated at an interface to a solid. Crystalgrowth on solid substrates from the gaseous state has beenstudied in depth, and detailed understanding of different growthmodes as well as interfacial thermodynamics has been achieved(1–3). Much less experimental data are available for crystalliza-tion occurring at the interface from the solid to the melt. Gen-erally, crystallization can be initiated at the solid–melt interfaceby two processes: heterogeneous nucleation or formation of acrystalline wetting layer (so-called prefreezing) (4–6). In terms ofthermodynamics, these processes are very different. Whereasnucleation takes place under nonequilibrium conditions at finitesupercooling below the melting temperature Tm of the bulkmaterial, the formation of a wetting layer is an equilibrium phe-nomenon taking place above Tm (4). It is often assumed thatheterogeneous nucleation is the more relevant process (7), but insimulations, nucleation as well as prefreezing have been shown tooccur (4, 8). Prefreezing is expected for strongly attractive surfacesor epitaxial systems for which the lattices of the substrate and thecrystallizing materials match well (9–12). In the case of polymers,prefreezing can also manifest itself in the conformational degreesof freedom, leading to an interfacial layer with nematic order,which was recently shown in simulations (13). Because of thedifficult accessibility of the buried interface between a melt anda solid, direct observation of crystallization of molecular systems atthe interface is lacking, and there is only limited, indirect evidencethat, in some cases, prefreezing at the solid interface exists (e.g.,for the growth of aluminum crystals on TiB2 particles) (14, 15).Recently, it has been suggested that prefreezing also plays a roleduring epitaxial crystallization in some polymeric systems (16). It iswell-known, however, that one or sometimes several ordered lay-ers of organic molecules can form on suitable substrates at tem-peratures above the bulk melting point, which was observed for,for example, alkanes or similar molecules on graphite by scanningtunneling microscopy (17), atomic force microscopy (AFM) (18–20), or scattering methods (21, 22; review in ref. 23). A related butmore special phenomenon is surface freezing of liquids (22). Insome liquids, an ordered monolayer forms at the free surface ina finite temperature range above the bulk melting temperature

[e.g., alkanes (24), alkylated side chain polymers (25), and AuSialloys (26)]. It is an open question, however, which exact role all ofthese structures play for the initiation of crystal growth (27) and inmost cases, the temperature range around melt–solid coexistence,where crystallization starts has not been studied in detail. Only forcolloidal model systems has crystallization by prefreezing beendirectly observed (28) and studied in simulations (8, 10, 11).We here present direct AFM observations of an ordered

wetting layer at the interface to a solid close to coexistence of thesolid and the liquid phases of a polymeric model system. We showevidence for a temperature-dependent thickness of the wettinglayer and its disappearance at a prewetting transition at finitesuperheating above Tm. Our observations are in line with a di-vergence of the layer thickness at the bulk melting temperature asexpected for complete wetting. Below Tm, crystal growth into thefilm is initiated by the interfacial layer.

TheoryThe formation of a crystalline phase out of the liquid is in a firstapproximation described in the framework of classical nucleationtheory, in which the difference in free energy between the bulkcrystal phase and a small crystal is described by surface con-tributions to the free energy. Generally, a small crystal is lessstable, which leads to a barrier for the formation of a crystalnucleus (4). In case of homogeneous nucleation, the nucleus isassumed to have the shape of a sphere, and for heterogeneousnucleation on a flat substrate, the nucleus is assumed to have theshape of a spherical cap. For the latter case, there are threeinterfacial energies between substrate, liquid, and crystal that

Significance

The microscopic ordering process that a liquid undergoes dur-ing crystallization is often initiated at an interface to a solid.Different processes have been suggested by theory to occur atthis interface. Of special interest is prefreezing—the formationof a thin crystalline layer at the interface already at temper-atures above the melting temperature. Because of the difficultaccessibility of the buried interface, experimental proof ofcrystallization by prefreezing has been elusive in molecularsystems. We here present direct in situ observations of sucha process in a polymeric model system. The results not onlycontribute to our fundamental understanding of crystallizationbut might also be useful for the preparation of well-orderedoriented thin films of crystalline organic materials.

Author contributions: T.T.-A. designed research; A.-K.L. and T.H. performed research;A.-K.L. and T.H. analyzed data; and A.-K.L. and T.T.-A. wrote the paper.

Conflict of interest statement: T.H., who contributed to this work while working at theMartin Luther University, was later employed by JPK Instruments. The atomic force mi-croscope used in this work was produced by JPK Instruments.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1To whom correspondence should be addressed. Email: thurn-albrecht@physik.uni-halle.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1408492111/-/DCSupplemental.

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determine the shape of the nucleus (i.e., the contact angle θ byYoung’s equation):

γsub;liq = γsub;cry + γcry;liq · cos θ: [1]

Compared with homogeneous nucleation, the barrier for theformation of a new crystal is lowered by the interface by a factorf ðθÞ, with 0≤ f ðθÞ< 1 for θ> 0 and f ð0Þ= 0 (4). For heteroge-neous nucleation, θ has a finite value (7). If, however, γsub;liq >γsub;cry + γcry;liq, the contact angle θ= 0, the barrier vanishes, andthe crystal phase wets the interface. Even above the bulk meltingtemperature, now a layer of ordered material can form on thesubstrate in equilibrium (4, 6). Wetting theory predicts that, ingeneral, the thickness of such a wetting layer should diverge onapproaching the bulk melting temperature from above.

ResultsFor our experiments, we used a polyethylene (PE) with well-defined molecular weight produced by hydrogenation of 1,4,-polybutadiene on substrates of highly ordered pyrolytic graphite.It is well-known that PE crystallizes epitaxially on graphite (29).Standard differential scanning calorimetry (DSC) measurementsof PE with graphite added in pulverized form confirm that thelatter also initiates crystallization in bulk, because the crystalli-zation temperature observed during cooling is raised (Fig. S1).Direct evidence for the effect of the substrate on crystallizationon a microscopic scale is presented in Fig. 1, which shows AFMphase images of thin PE films on a silicon wafer (covered bya native layer of silicon oxide) and graphite, both measured atroom temperature after cooling from the melt state. Crystalliz-able polymers like PE show a semicrystalline morphology on thenanoscale consisting of lamellar crystals separated by amorphous

layers (30). In general, the thickness of the lamellar crystals andtherefore, the melting temperature depend on the thermal his-tory of the sample. PE made by hydrogenation of polybutadieneas it is used here contains a small fraction of ethyl branches,which for our experiments, has the advantage that thickening ofthe lamellar crystals, a well-known phenomenon for linear PE, issuppressed. As a consequence, the maximum thickness of thelamellar crystals and the melting temperature are controlled bythe chemical structure of the molecules and lower than for linearPE. On a larger scale, crystal growth typically leads to the for-mation of spherulites caused by branching of lamellar crystalsduring growth. Although on silicon, such a spherulitic structure,initiated by isolated nucleation events in the centers of thespherulites, is clearly visible (Fig. 1A), the morphology on graphiteis remarkably homogeneous (Fig. 1B). On a smaller scale, a ter-raced structure consisting of laterally growing lamellar crystals isvisible on silicon, (Fig. 1C), whereas on graphite, well-orderedcrystalline lamellae have grown in the direction perpendicular tothe substrate (Fig. 1D). These observations suggest that graphitedoes not simply cause an enhanced nucleation rate, which wouldonly lead to a higher density of spherulites, but rather, that, duringcooling, a crystalline layer wets the interface solid–melt, whichthen induces the observed homogeneous growth. X-ray diffractionexperiments confirm oriented growth with the (110)-planes beingparallel to the substrate (Fig. S2).To directly image the interfacial layer, we investigated ultra-

thin PE films on graphite with a thickness of only a few nano-meters at elevated temperatures by in situ AFM measurementsperformed in the net attractive regime of the intermittent con-tact mode (Materials and Methods). Because of the reduced in-teraction between the AFM tip and the sample in this mode,penetration of the tip into the sample is minimized, which allows

40µm

1µm

40µm

1µm

A B

C D

Fig. 1. Morphology of thin films of semicrystallinepolymer after cooling from the melt. Large-scaleAFM height images of PE on (A) silicon (film thick-ness = 160 nm; height scale = 0–100 nm) and (B)graphite (film thickness = 160 nm; height scale =0–250 nm) and small-scale AFM phase images (filmthickness = 25 nm) on (C) silicon and (D) graphite.

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measuring of height profiles of liquid polymer surfaces (31).Because of the smaller indentation, the tip is also less susceptibleto contamination. Fig. 2 shows amplitude and height images ofa part of an ultrathin PE film on graphite measured at T = 120 °Cand T = 125 °C (both well above the bulk melting temperatureTm = 108 °C, which was determined by DSC and AFM mea-surements on thicker films). At T = 120 °C, several domains oflamellar crystalline layers are observed that are obviously aligned

with the underlying graphite lattice and partially covered bystructureless liquid material. The long period is the same asobserved on a thick film and temperature-independent, which isin line with the above-mentioned absence of lamellar thickening.Obviously, the interaction between the PE chains and thegraphite surface stabilizes an ordered surface layer, which dis-orders only at a higher temperature Tmax around 124 °C (Fig.S3). Material that is not directly in contact with the graphitesurface dewets from the underlying ordered layer and forms veryshallow droplets with a height of some nanometers (Fig. 2B,Inset), a contact angle in the range from 2° to 5°, and a size of theorder of 1 μm. Fig. 2 G and H show corresponding illustrations.On cooling, the ordered structure reappears (Fig. 2 E and F),confirming that the process is reversible.Detailed inspection of the height image of the completely

molten film in Fig. 2D reveals that the former domain structure ofthe crystalline layer is still visible. Fine dark lines separate parts ofthe sample, which were part of different crystalline domains atlower temperature. Profiles taken from the height image show thatthese dark lines are very shallow trenches with a depth of up toabout 1 nm. These observations also indicate that, in the moltenfilm above Tmax, some order is retained directly at the interfacethat cannot be imaged with the AFM either because of low con-trast or because it is covered by a small amount of amorphousmaterial as schematically illustrated in Fig. 2H. Additional evi-dence for some remaining order in the molten state is given by thefact that the domain structure observed during heating is re-covered during subsequent cooling (Fig. 2 A and E). This result isin agreement with molecular dynamics simulations that show ad-sorption of PE on graphite even far above the melting point (32).Additional measurements showed that the domain structurechanges after heating the samples above T = 150 °C (Fig. S4).To prove that the crystalline layer is also present underneath

the molten droplets formed because of autophobic dewetting(33), AFM measurements in the net repulsive regime wereperformed (31). Depending on the set point (amplitude) chosenfor imaging, the AFM tip will either penetrate deeply enoughthrough the molten droplet and image the underlying orderedlayer or not. Fig. 3 shows such a measurement taken at 115 °C, inwhich the set point was reduced by about 20% during the mea-surement in Fig. 3, Upper as indicated by the broken line. Amolten droplet, which can be identified best by the low value ofthe phase signal (dark area), extends over Fig. 3 from the bottomto the top. Fig. 3, Lower (high set point) shows the elevated shapeof the droplet in the height signal, and the lamellar structure isonly visible beside the droplet. In Fig. 3, Upper, the set point is

Tm < T < Tmax T > Tmax

Graphite Graphite

1µm

0 500 1000 nm

4

6

8

10 nm

A B

C D

E F

G H

Fig. 2. High-temperature AFM images of melting and recrystallization ofultrathin PE film on graphite. Images were measured during (A–D) heatingand (E and F) subsequent cooling. (G and H) Schematic illustration of thestructures observed in A–D. (A, B, and E–G) The semicrystalline layer is par-tially covered by molten droplets at T = 120 °C. (C, D, and H) At T = 125 °C,the interfacial layer is molten. (A, C, and E) Amplitude images. (B, D, and F)Height images (scale: 0–8.5 nm). Inset in B shows a height profile over adroplet, with a height of about 5 nmmeasured along the path indicated by thesolid black line. All images correspond to the same part of the sample, as visiblefrom the common feature pointed out by the white triangles.

Height Amplitude

Soft

tapp

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Har

d ta

ppin

g

0.3µmPhase

A B C

Fig. 3. Detection of the ordered interfacial layer underneath a moltendroplet. AFM measurement of partially molten ultrathin PE film ongraphite at 115 °C performed in the net repulsive mode with a change ofset points applied during imaging. Soft tapping in shown in Lower, andhard tapping is shown in Upper (more details in the main text). The colorscale in A covers a range from 0 to 4 nm. (A) Height image. (B) Amplitudeimage. (C) Phase image.

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reduced, the tip penetrates through the droplet, and the lamellarpattern becomes visible in the amplitude signal even below themolten droplet, which can still be identified in the phase (Fig. 3C).More details about the temperature dependence of the in-

terfacial ordering process can be obtained by a closer analysis ofexperiments as shown in Fig. 2. The volume of the moltendroplets above the temperature where the thin film starts to meltwas determined by summation over the height images (calcu-lations performed using the analysis software Gwyddion):

V =Xi;j

�hði; jÞ− h0ði; jÞ

�ΔA: [2]

Here, hði; jÞ is the height value, and ΔA is the area of 1 pixel;h0ði; jÞ is the height of the interpolated background at the posi-tion ði; jÞ, which was calculated by a Laplace interpolation usingthe surface surrounding a droplet. We assume hereby that thesurface of the crystalline layer is locally flat and that its thicknessis independent of the overlaying liquid droplet, which is in linewith the measurements shown in Fig. 3. The pixels belonging toa droplet were, in a first step, automatically identified by settinga threshold height corresponding to an approximate averageheight of the underlying crystalline surface. To correct for imageartifacts and effects of roughness of the graphite substrate, thisassignment was cross-checked using the amplitude images andcorrected manually, where necessary. We estimate the error inthe values of V resulting from this procedure to be about 20%.Fig. 4 shows the results. At about T = 111 °C, melting sets in, andthe amount of molten material increases with temperature. Thedata obtained during cooling show that, apart from a certain hys-teresis, the process is reversible. At present, we cannot distinguishif the hysteresis is a real effect or an experimental artifact. Cer-tainly, the data for the heating cycle are more reliable, because thequality of the measurements deteriorates during the series of meas-urements because of contamination of the tip.

DiscussionThe observations described above fit perfectly to the scenarioexpected from general wetting theory for the case of completewetting at the transition melt–crystal (6). Far above the meltingtemperature, ordering phenomena at the substrate are re-stricted to microscopic thicknesses; on cooling, a prewettingtransition occurs at Tmax, where a crystalline layer forms witha thickness l that increases with decreasing temperature andpresumably, diverges at Tm. We analyzed our data quantita-tively with a phenomenological theory of prefreezing, which

uses the following expression for the grand canonical free en-ergy per unit area (10):

ΣðlÞ= γsub;cry + γcry;liq − γsub;liq +Δs ·ΔT · l+ γ0 · expð−l=l0Þ: [3]

In Eq. 3,Δs is the change in entropy density at the transition, andΔT =T −Tm is the superheating; γ0 and l0 are parameters of theeffective interface potential. We here neglected any possiblecontributions to Σ because of lattice distortions. MinimizingEq. 3 with respect to l gives an equilibrium thickness of

lðTÞ= l0 ln�

γ0l0ΔsΔT

�= l0 ln

�ΔTmax

ΔT

�: [4]

The interfacial crystalline layer exists over a finite temperaturerange up to a maximal superheatingΔTmax and shows a logarithmicdivergence on approaching the transition at Tm from above. Notethat the result for lðTÞ is independent of the surface energies. Thefact that the liquid top layer in our case wets the crystalline layeronly partially will, therefore, not affect the value of l. Applying thisresult to the case of a film of finite thickness L with area A givesthe following prediction for the temperature dependence of themolten volume, which can be compared with our data:

VmeltðTÞ=A�L− lðTÞ�=A · l0 ln

�ΔT

ΔTmin

�: [5]

Here, we take into account that for finite L, a minimal super-heating, ΔTmin, is needed before melting starts. As shown inFig. 4, Eq. 5 describes the data well and explains the shape ofthe temperature dependence of the molten volume. The analysisyielded l0 = 0.36 nm, Tm = 109.5 °C, and ΔTmin = 1.2 K. Thevalue for Tm is in reasonable agreement with direct measure-ments on thick films as mentioned above; l0 contains a systematicerror, which we estimate to be on the order of 20%, because ofthe fact that the area A contains a systematic error, since the areafrom which the droplets source the liquid material might besomewhat larger or smaller than the area of the image and sincethe film carries a certain roughness. Clearly, the value of l0 showsthat the observed wetting phenomenon takes place on a molecu-lar scale, which is in agreement with the expectation that therelevant interactions are of molecular range and origin.

ConclusionsIn conclusion, our results show direct in situ observations ofinterfacial prefreezing at the interface solid–melt as predicted bysimulations. Below a certain Tmax higher than the bulk meltingtemperature, an ordered interfacial layer is formed, which thick-ens logarithmically during additional cooling. At temperaturesbelow the bulk melting point Tm, crystallization starts from theexisting interfacial layer, resulting in a well-oriented, homoge-neous, semicrystalline structure as visible in Fig. 1 B and D. Forthe observation of this process, we made use of the fact that, ina polymeric system, crystallization goes along with the formation ofa semicrystalline nanostructure, which can easily be imaged byAFM. Thin films of crystalline polymers are also a system for whichthe observed phenomena might be of practical relevance. Func-tional (e.g., semiconducting) polymers are often semicrystalline, anddevices are typically based on thin films prepared by spin coating orsolution casting. Subsequent crystallization is often achieved by ei-ther cooling from the melt or annealing of a quenched, amorphousfilm at elevated temperatures close to the melting temperature.

Materials and MethodsMaterials. PE with a molecular mass Mn = 33 kDa (Mw /Mn = 1.04) was pur-chased from Polymer Source. Because of the existence of some ethyl branches,

108 110 112 114 116 118 1200

2

4

6

8

10

12

14

Dro

plet

vol

ume

(10-2

1m

3 )

Temperature (°C)

Fig. 4. Volume of molten droplets on top of the ordered layer in ultrathinfilms as a function of temperature. Data resulted from an integration of theheight signal of AFM images as shown in Fig. 2. The solid line shows a fit ofthe model function in Eq. 5 to the data. The error of the individual values isabout 20%. Circles, heating; triangles, cooling.

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the material has a lower crystallinity and melting temperature (here, Tm =108 °C) than linear PE without branches.

Film Preparation. Thin and ultrathin PE films were produced by spin coatinghot solutions (105 °C) of PE in decahydronaphthalene for 60 s at 2,000 min−1

onto freshly cleaved graphite [concentrations: 0.03% (wt/wt) for ultrathinfilms and 0.5% and 2% (wt/wt) for 25- and 160-nm-thick films, respectively].The films were stored in a vacuum oven for 3 h at 85 °C for solvent evap-oration; then, they were heated to 150 °C and slowly cooled. The filmthickness was determined by AFM measurements of films prepared in thesame way on a silicon wafer. Ultrathin films could not be measured in thisway, because at these low-concentrations continuous films only formed onhighly ordered pyrolytic graphite and not on silicon wafer.

AFM. For AFM measurements, the atomic force microscope NanoWizard Ifrom JPK Instruments equipped with a heatable sample holder was used.Cantilevers were purchased fromNT-MDT.Measurements in the net repulsiveregime were performed with NSG30 cantilevers (k = 40 N/m and ω0 = 320kHz) with an excitation frequency ω<ω0 and a free amplitude in the range

of 60 nm. For net attractive measurements, softer NSG03 cantilevers (k =1.74 N/m and ω0 = 90 kHz) were used, and a free amplitude of about 45 nmand an excitation frequency ω>ω0 were chosen. To ensure measuring in thenet attractive regime, amplitude and phase distance curves were checkedbefore imaging; an example is shown in Fig. S5. AFM height images werecorrected by plane and line leveling, and amplitude and phase images werecorrected only by line leveling (software Gwyddion).

DSC. DSC measurements were performed with a DSC 7 from Perkin-Elmer.

X-Ray Scattering. Scans of θ− 2θ were measured on a PANanlytical EmpyreanX-Ray Diffraction System. The 2D diffraction pattern was measured on Beam-line ID10B at the European Synchrotron Radiation Facility (ESRF).

ACKNOWLEDGMENTS. We thank W. Widdra, W. Paul, M. Müller, andK. Saalwächter for helpful discussions. The ESRF Grenoble and R. Nero areacknowledged for the provision of synchrotron radiation facilities and assis-tance. Funding was provided by Deutsche Forschungsgemeinschaft GrantSFB TRR 102 and the state of Sachsen-Anhalt.

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