Direct observation of prefreezing at the interface melt–solid in polymer crystallization

Significance

The microscopic ordering process that a liquid undergoes during crystallization is often initiated at an interface to a solid. Different processes have been suggested by theory to occur at this interface. Of special interest is prefreezing—the formation of a thin crystalline layer at the interface already at temperatures above the melting temperature. Because of the difficult accessibility of the buried interface, experimental proof of crystallization by prefreezing has been elusive in molecular systems. We here present direct in situ observations of such a process in a polymeric model system. The results not only contribute to our fundamental understanding of crystallization but might also be useful for the preparation of well-ordered oriented thin films of crystalline organic materials.

Abstract

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

The fundamental process of crystallization from the liquid or gaseous state is of importance in many areas of condensed matter physics and materials science. In practice, crystallization is, in most cases, initiated at an interface to a solid. Crystal growth on solid substrates from the gaseous state has been studied in depth, and detailed understanding of different growth modes as well as interfacial thermodynamics has been achieved (1–3). Much less experimental data are available for crystallization occurring at the interface from the solid to the melt. Generally, crystallization can be initiated at the solid–melt interface by two processes: heterogeneous nucleation or formation of a crystalline wetting layer (so-called prefreezing) (4–6). In terms of thermodynamics, these processes are very different. Whereas nucleation takes place under nonequilibrium conditions at finite supercooling below the melting temperature $T_m$ of the bulk material, the formation of a wetting layer is an equilibrium phenomenon taking place above $T_m$ (4). It is often assumed that heterogeneous nucleation is the more relevant process (7), but in simulations, nucleation as well as prefreezing have been shown to occur (4, 8). Prefreezing is expected for strongly attractive surfaces or epitaxial systems for which the lattices of the substrate and the crystallizing materials match well (9–12). In the case of polymers, prefreezing can also manifest itself in the conformational degrees of freedom, leading to an interfacial layer with nematic order, which was recently shown in simulations (13). Because of the difficult accessibility of the buried interface between a melt and a solid, direct observation of crystallization of molecular systems at the interface is lacking, and there is only limited, indirect evidence that, 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 role during epitaxial crystallization in some polymeric systems (16). It is well-known, however, that one or sometimes several ordered layers of organic molecules can form on suitable substrates at temperatures above the bulk melting point, which was observed for, for example, alkanes or similar molecules on graphite by scanning tunneling microscopy (17), atomic force microscopy (AFM) (18–20), or scattering methods (21, 22; review in ref. 23). A related but more special phenomenon is surface freezing of liquids (22). In some liquids, an ordered monolayer forms at the free surface in a finite temperature range above the bulk melting temperature [e.g., alkanes (24), alkylated side chain polymers (25), and AuSi alloys (26)]. It is an open question, however, which exact role all of these structures play for the initiation of crystal growth (27) and in most cases, the temperature range around melt–solid coexistence, where crystallization starts has not been studied in detail. Only for colloidal model systems has crystallization by prefreezing been directly 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 the solid and the liquid phases of a polymeric model system. We show evidence for a temperature-dependent thickness of the wetting layer and its disappearance at a prewetting transition at finite superheating above $T_m$. Our observations are in line with a divergence of the layer thickness at the bulk melting temperature as expected for complete wetting. Below $T_m$, crystal growth into the film is initiated by the interfacial layer.

Theory

The formation of a crystalline phase out of the liquid is in a first approximation described in the framework of classical nucleation theory, in which the difference in free energy between the bulk crystal phase and a small crystal is described by surface contributions to the free energy. Generally, a small crystal is less stable, which leads to a barrier for the formation of a crystal nucleus (4). In case of homogeneous nucleation, the nucleus is assumed to have the shape of a sphere, and for heterogeneous nucleation on a flat substrate, the nucleus is assumed to have the shape of a spherical cap. For the latter case, there are three interfacial energies between substrate, liquid, and crystal that determine the shape of the nucleus (i.e., the contact angle θ by Young’s equation):

$${\gamma }_{sub,liq}={\gamma }_{sub,cry}+{\gamma }_{cry,liq}\cdot \cos \theta .$$ [1]

Compared with homogeneous nucleation, the barrier for the formation of a new crystal is lowered by the interface by a factor $f\left(\theta \right)$, with $0\le f\left(\theta \right)<1$ for $\theta >0$ and $f\left(0\right)=0$ (4). For heterogeneous nucleation, θ has a finite value (7). If, however, ${\gamma }_{sub,liq}>{\gamma }_{sub,cry}+{\gamma }_{cry,liq}$, the contact angle $\theta =0$, the barrier vanishes, and the crystal phase wets the interface. Even above the bulk melting temperature, now a layer of ordered material can form on the substrate in equilibrium (4, 6). Wetting theory predicts that, in general, the thickness of such a wetting layer should diverge on approaching the bulk melting temperature from above.

Results

For 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) measurements of PE with graphite added in pulverized form confirm that the latter also initiates crystallization in bulk, because the crystallization temperature observed during cooling is raised (Fig. S1). Direct evidence for the effect of the substrate on crystallization on a microscopic scale is presented in Fig. 1, which shows AFM phase images of thin PE films on a silicon wafer (covered by a native layer of silicon oxide) and graphite, both measured at room temperature after cooling from the melt state. Crystallizable polymers like PE show a semicrystalline morphology on the nanoscale consisting of lamellar crystals separated by amorphous layers (30). In general, the thickness of the lamellar crystals and therefore, the melting temperature depend on the thermal history of the sample. PE made by hydrogenation of polybutadiene as it is used here contains a small fraction of ethyl branches, which for our experiments, has the advantage that thickening of the lamellar crystals, a well-known phenomenon for linear PE, is suppressed. As a consequence, the maximum thickness of the lamellar crystals and the melting temperature are controlled by the chemical structure of the molecules and lower than for linear PE. On a larger scale, crystal growth typically leads to the formation of spherulites caused by branching of lamellar crystals during growth. Although on silicon, such a spherulitic structure, initiated by isolated nucleation events in the centers of the spherulites, is clearly visible (Fig. 1A), the morphology on graphite is remarkably homogeneous (Fig. 1B). On a smaller scale, a terraced structure consisting of laterally growing lamellar crystals is visible on silicon, (Fig. 1C), whereas on graphite, well-ordered crystalline lamellae have grown in the direction perpendicular to the substrate (Fig. 1D). These observations suggest that graphite does not simply cause an enhanced nucleation rate, which would only lead to a higher density of spherulites, but rather, that, during cooling, a crystalline layer wets the interface solid–melt, which then induces the observed homogeneous growth. X-ray diffraction experiments confirm oriented growth with the (110)-planes being parallel to the substrate (Fig. S2).

Fig. 1.

Morphology of thin films of semicrystalline polymer after cooling from the melt. Large-scale AFM height images of PE on (A) silicon (film thickness = 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 (film thickness = 25 nm) on (C) silicon and (D) graphite.

To directly image the interfacial layer, we investigated ultrathin PE films on graphite with a thickness of only a few nanometers at elevated temperatures by in situ AFM measurements performed in the net attractive regime of the intermittent contact mode (Materials and Methods). Because of the reduced interaction between the AFM tip and the sample in this mode, penetration of the tip into the sample is minimized, which allows measuring of height profiles of liquid polymer surfaces (31). Because of the smaller indentation, the tip is also less susceptible to contamination. Fig. 2 shows amplitude and height images of a part of an ultrathin PE film on graphite measured at T = 120 °C and T = 125 °C (both well above the bulk melting temperature T_m = 108 °C, which was determined by DSC and AFM measurements on thicker films). At T = 120 °C, several domains of lamellar crystalline layers are observed that are obviously aligned with the underlying graphite lattice and partially covered by structureless liquid material. The long period is the same as observed on a thick film and temperature-independent, which is in line with the above-mentioned absence of lamellar thickening. Obviously, the interaction between the PE chains and the graphite surface stabilizes an ordered surface layer, which disorders only at a higher temperature $T_{max}$ around 124 °C (Fig. S3). Material that is not directly in contact with the graphite surface dewets from the underlying ordered layer and forms very shallow droplets with a height of some nanometers (Fig. 2B, Inset), a contact angle in the range from 2° to 5°, and a size of the order 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.

Fig. 2.

High-temperature AFM images of melting and recrystallization of ultrathin PE film on graphite. Images were measured during (A–D) heating and (E and F) subsequent cooling. (G and H) Schematic illustration of the structures observed in A–D. (A, B, and E–G) The semicrystalline layer is partially 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 a droplet, with a height of about 5 nm measured along the path indicated by the solid black line. All images correspond to the same part of the sample, as visible from the common feature pointed out by the white triangles.

Detailed inspection of the height image of the completely molten film in Fig. 2D reveals that the former domain structure of the crystalline layer is still visible. Fine dark lines separate parts of the sample, which were part of different crystalline domains at lower temperature. Profiles taken from the height image show that these dark lines are very shallow trenches with a depth of up to about 1 nm. These observations also indicate that, in the molten film above $T_{max}$, some order is retained directly at the interface that cannot be imaged with the AFM either because of low contrast or because it is covered by a small amount of amorphous material as schematically illustrated in Fig. 2H. Additional evidence for some remaining order in the molten state is given by the fact that the domain structure observed during heating is recovered during subsequent cooling (Fig. 2 A and E). This result is in agreement with molecular dynamics simulations that show adsorption of PE on graphite even far above the melting point (32). Additional measurements showed that the domain structure changes 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 were performed (31). Depending on the set point (amplitude) chosen for imaging, the AFM tip will either penetrate deeply enough through the molten droplet and image the underlying ordered layer or not. Fig. 3 shows such a measurement taken at 115 °C, in which the set point was reduced by about 20% during the measurement in Fig. 3, Upper as indicated by the broken line. A molten droplet, which can be identified best by the low value of the phase signal (dark area), extends over Fig. 3 from the bottom to the top. Fig. 3, Lower (high set point) shows the elevated shape of the droplet in the height signal, and the lamellar structure is only visible beside the droplet. In Fig. 3, Upper, the set point is reduced, the tip penetrates through the droplet, and the lamellar pattern becomes visible in the amplitude signal even below the molten droplet, which can still be identified in the phase (Fig. 3C).

Fig. 3.

Detection of the ordered interfacial layer underneath a molten droplet. AFM measurement of partially molten ultrathin PE film on graphite at 115 °C performed in the net repulsive mode with a change of set points applied during imaging. Soft tapping in shown in Lower, and hard tapping is shown in Upper (more details in the main text). The color scale in A covers a range from 0 to 4 nm. (A) Height image. (B) Amplitude image. (C) Phase image.

More details about the temperature dependence of the interfacial ordering process can be obtained by a closer analysis of experiments as shown in Fig. 2. The volume of the molten droplets above the temperature where the thin film starts to melt was determined by summation over the height images (calculations performed using the analysis software Gwyddion):

$$V={\displaystyle \sum _{i,j}\left(h\left(i,j\right)-h_0\left(i,j\right)\right)\mathrm{\Delta }A}.$$ [2]

Here, $h\left(i,j\right)$ is the height value, and ΔA is the area of 1 pixel; $h_0\left(i,j\right)$ is the height of the interpolated background at the position $\left(i,j\right)$, which was calculated by a Laplace interpolation using the surface surrounding a droplet. We assume hereby that the surface of the crystalline layer is locally flat and that its thickness is independent of the overlaying liquid droplet, which is in line with the measurements shown in Fig. 3. The pixels belonging to a droplet were, in a first step, automatically identified by setting a threshold height corresponding to an approximate average height of the underlying crystalline surface. To correct for image artifacts and effects of roughness of the graphite substrate, this assignment was cross-checked using the amplitude images and corrected manually, where necessary. We estimate the error in the values of V resulting from this procedure to be about 20%. Fig. 4 shows the results. At about T = 111 °C, melting sets in, and the amount of molten material increases with temperature. The data obtained during cooling show that, apart from a certain hysteresis, the process is reversible. At present, we cannot distinguish if the hysteresis is a real effect or an experimental artifact. Certainly, the data for the heating cycle are more reliable, because the quality of the measurements deteriorates during the series of measurements because of contamination of the tip.

Fig. 4.

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

Discussion

The observations described above fit perfectly to the scenario expected from general wetting theory for the case of complete wetting at the transition melt–crystal (6). Far above the melting temperature, ordering phenomena at the substrate are restricted to microscopic thicknesses; on cooling, a prewetting transition occurs at $T_{max}$, where a crystalline layer forms with a thickness l that increases with decreasing temperature and presumably, diverges at $T_m$. We analyzed our data quantitatively with a phenomenological theory of prefreezing, which uses the following expression for the grand canonical free energy per unit area (10):

$$\mathrm{\Sigma }\left(l\right)={\gamma }_{sub,cry}+{\gamma }_{cry,liq}-{\gamma }_{sub,liq}+\mathrm{\Delta }s\cdot \mathrm{\Delta }T\cdot l+{\gamma }_0\cdot \exp \left(-l/l_0\right).$$ [3]

In Eq. 3,$\mathrm{\Delta }s$ is the change in entropy density at the transition, and $\mathrm{\Delta }T=T-T_m$ is the superheating; ${\gamma }_0$ and $l_0$ are parameters of the effective interface potential. We here neglected any possible contributions to Σ because of lattice distortions. Minimizing Eq. 3 with respect to l gives an equilibrium thickness of

$$l\left(T\right)=l_0\ln \left(\frac{{\gamma }_0}{l_0\mathrm{\Delta }s\mathrm{\Delta }T}\right)=l_0\ln \left(\frac{\mathrm{\Delta }{T}_{max}}{\mathrm{\Delta }T}\right).$$ [4]

The interfacial crystalline layer exists over a finite temperature range up to a maximal superheating $\mathrm{\Delta }{T}_{max}$ and shows a logarithmic divergence on approaching the transition at $T_m$ from above. Note that the result for $l\left(T\right)$ is independent of the surface energies. The fact that the liquid top layer in our case wets the crystalline layer only partially will, therefore, not affect the value of l. Applying this result to the case of a film of finite thickness L with area A gives the following prediction for the temperature dependence of the molten volume, which can be compared with our data:

$$V_{melt}\left(T\right)=A\left[L-l\left(T\right)\right]=A\cdot l_0\ln \left(\frac{\mathrm{\Delta }T}{\mathrm{\Delta }{T}_{min}}\right).$$ [5]

Here, we take into account that for finite L, a minimal superheating, $\mathrm{\Delta }{T}_{min}$, is needed before melting starts. As shown in Fig. 4, Eq. 5 describes the data well and explains the shape of the temperature dependence of the molten volume. The analysis yielded l₀ = 0.36 nm, T_m = 109.5 °C, and ΔT_min = 1.2 K. The value for $T_m$ is in reasonable agreement with direct measurements on thick films as mentioned above; $l_0$ contains a systematic error, which we estimate to be on the order of 20%, because of the fact that the area A contains a systematic error, since the area from which the droplets source the liquid material might be somewhat larger or smaller than the area of the image and since the film carries a certain roughness. Clearly, the value of $l_0$ shows that the observed wetting phenomenon takes place on a molecular scale, which is in agreement with the expectation that the relevant interactions are of molecular range and origin.

Conclusions

In conclusion, our results show direct in situ observations of interfacial prefreezing at the interface solid–melt as predicted by simulations. Below a certain $T_{max}$ higher than the bulk melting temperature, an ordered interfacial layer is formed, which thickens logarithmically during additional cooling. At temperatures below the bulk melting point $T_m$, crystallization starts from the existing interfacial layer, resulting in a well-oriented, homogeneous, semicrystalline structure as visible in Fig. 1 B and D. For the observation of this process, we made use of the fact that, in a polymeric system, crystallization goes along with the formation of a semicrystalline nanostructure, which can easily be imaged by AFM. Thin films of crystalline polymers are also a system for which the observed phenomena might be of practical relevance. Functional (e.g., semiconducting) polymers are often semicrystalline, and devices are typically based on thin films prepared by spin coating or solution casting. Subsequent crystallization is often achieved by either cooling from the melt or annealing of a quenched, amorphous film at elevated temperatures close to the melting temperature.

Materials and Methods

Materials.

PE with a molecular mass M_n = 33 kDa (M_w/M_n = 1.04) was purchased from Polymer Source. Because of the existence of some ethyl branches, the material has a lower crystallinity and melting temperature (here, T_m = 108 °C) than linear PE without branches.

Film Preparation.

Thin and ultrathin PE films were produced by spin coating hot 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 ultrathin films 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 evaporation; then, they were heated to 150 °C and slowly cooled. The film thickness was determined by AFM measurements of films prepared in the same way on a silicon wafer. Ultrathin films could not be measured in this way, because at these low-concentrations continuous films only formed on highly ordered pyrolytic graphite and not on silicon wafer.

AFM.

For AFM measurements, the atomic force microscope NanoWizard I from JPK Instruments equipped with a heatable sample holder was used. Cantilevers were purchased from NT-MDT. Measurements in the net repulsive regime were performed with NSG30 cantilevers (k = 40 N/m and ω₀ = 320 kHz) with an excitation frequency $\omega <{\omega }_0$ 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 nm and an excitation frequency $\omega >{\omega }_0$ were chosen. To ensure measuring in the net attractive regime, amplitude and phase distance curves were checked before imaging; an example is shown in Fig. S5. AFM height images were corrected by plane and line leveling, and amplitude and phase images were corrected only by line leveling (software Gwyddion).

DSC.

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

X-Ray Scattering.

Scans of $\theta -2\theta$ were measured on a PANanlytical Empyrean X-Ray Diffraction System. The 2D diffraction pattern was measured on Beamline ID10B at the European Synchrotron Radiation Facility (ESRF).