For a glass-forming liquid, the mechanism by which its surface contour evolves can change from bulk viscous flow at high temperatures to surface diffusion at low temperatures. We show that this mechanistic change can be conveniently detected by the exposure of nano-particles native in the material. Despite its high chemical purity, the often-studied molecular glass indomethacin contains low-concentration particles approximately 100 nm in size and 0.3% in volume fraction. Similar particles are present in polystyrene, another often-used model. In the surface-diffusion regime, particles are gradually exposed in regions vacated by host molecules, for example, the peak of a surface grating and the depletion zone near a surface crystal. In the viscous-flow regime, particle exposure is not observed. The surface contour around an exposed particle widens over time in a self-similar manner as 3 (Bt)1/4, where B is a surface mobility constant and the same constant obtained by surface grating decay. This work suggests that in a binary system composed of slow- and fast-diffusing molecules, slow-diffusing molecules can be stranded in surface regions vacated by fast-diffusing molecules, effectively leading to phase separation.

The surface that encloses a condensed material evolves under the driving force of surface tension by several mechanisms, including bulk viscous flow, evaporation-condensation, bulk diffusion, and surface diffusion.1 Understanding the mechanism of surface mass transport is relevant for many areas, including surface crystallization,2 formation of stable glasses by vapor deposition,3 and surface mobility of polymer glasses.4–7 For a glass-forming molecular liquid, recent work has shown that the mechanism by which a rough surface flattens can change with temperature, from bulk viscous flow at high temperatures to surface diffusion at low temperatures.7–12 Here viscous flow refers to the collective motion of a liquid responding to a pressure difference, while surface diffusion is described by Mullins’ equation

W/t+B4W/x4=0.
(1)

In Eq. (1), W is the surface height, x is the lateral dimension, and B = DsγΩ2νkT is the surface mobility constant, where γ is the surface tension, Ds is the surface diffusion coefficient, Ω is the molecular volume, and ν is the areal density of surface molecules. Molecular simulations have found agreement between the Ds values obtained from Mullins’ model and a particle’s mean-squared displacement.13 It is noteworthy that the surface-transport process conforming to Eq. (1) has also been called “glassy thin-film flow” for which an equation mathematically equivalent as Eq. (1) has been obtained for a thin fluid layer with no slip from the bulk and for which the mobility constant B is written γd3/3η, where d is the thickness of the mobile surface layer and η is its viscosity.7 For simplicity we shall use “surface diffusion” to designate a process that conforms to Eq. (1).

To date, two types of experiments have been conducted to investigate the nature of surface mass transport. In the first type, a surface contour evolves over time in response to some initial or boundary condition and the transport mechanism is assigned according to whether the evolution follows Eq. (1) (surface diffusion) or the Stokes-Navier equation (viscous flow). In this type of experiment, the initial condition for the surface may be a sinusoidal profile,8 a step,7 a scratch,14 or some other rough feature that flattens over time. The boundary condition driving surface evolution may be a constant flux of molecules leaving the amorphous surface for a nearby crystal to sustain its growth.15,16 In the second type of experiment, small foreign particles are placed on a surface and the response of the host material is measured.17–20 For example, gold nanoparticles placed on the molecular glass 1,3-bis-(1-naphthyl)-5-(2-naphthyl) benzene (TNB) elicit two kinds of responses: an initial “wetting” by host molecules assigned to a surface process and the subsequent embedding against viscosity assigned to a bulk process. In this work, we introduce a new method that in essence combines the two types of experiments, enabling a consistency test of the two approaches. Instead of adding foreign particles, we show that often-studied molecular glasses indomethacin and polystyrene already contain low-concentration nano-particles, despite their high stated chemical purity, and that these particles are convenient indicators for the mechanism of surface mass transport as a surface contour evolves. Specifically, the particles flow with the host liquid at high temperatures (viscous-flow regime) but are exposed at low temperatures (surface-diffusion regime); the particle exposure occurs in regions vacated by host molecules, including the peak of a surface grating and the depletion zone near a surface crystal. We find that the same surface-diffusion model describes the decay of the surface grating and the contour evolution around a nano-particle, indicating the consistency between the two approaches. In a standard atomic force microscopy (AFM) experiment, this particle exposure test is extremely sensitive, able to detect nano-particles at a volume fraction of 0.1%. Since impurities at this level are common in molecular materials, this technique is potentially a general tool for characterizing surface mobility.

Indomethacin (1-(p-chlorobenzoyl)-5-methoxy-2- methylindole-3-acetic acid, 99+%, γ polymorph) was purchased from Sigma-Aldrich. To produce a surface grating on IMC glass, a 1000 nm wavelength master was placed on liquid IMC 45 K above Tg (315 K). The sample then was cooled to room temperature and the master was peeled off, yielding a corrugated surface on IMC. The masters were purchased from Rainbow Symphony Inc. and coated with gold to avoid the transfer of contaminants. The master gratings were determined by atomic force microscopy (AFM, Veeco Multimode IV) to be sinusoidal. A similar embossing procedure was used to make surface-grating samples for two polystyrene oligomers: “PS 1110”: Mw = 1110 g/mol, Mw/Mn = 1.12, Tg = 307 K (onset); “PS 1700”: Mw = 1700 g/mol, Mw/Mn = 1.06, Tg=319 K (onset). PS 1110 was purchased from Scientific Polymer Products and PS 1700 from Polymer Source, Inc. The PS glass films were made by melting and cooling the as-purchased materials. For all experiments performed, the sample thickness was at least 50 μm, much larger than the wavelength of the surface grating so that its decay process was unaffected by the substrate. The exposure of particles in IMC was measured by an AFM at a constant temperature in dry N2.

To prepare a sample for scanning electron microscopy (SEM) measurements, IMC crystals were melted on a clean square coverslip at 15 K above the melting point and then covered with a smaller round coverslip (typically 15 mm in diameter). The assembly was cooled to below Tg by contact with a metal block, pre-equilibrated at room temperature. The sample was confirmed to be free of crystals by polarized light microscopy. The square coverslip was detached by bending its edges away from the organic glass, which created a glass film with a free surface. The films were 10–100 μm thick. Surface crystallization was initiated at 313 K (Tg−2 K) spontaneously or with seeding.

Samples used for SEM experiments had the bottom coverslip previously scratched along the diameter before being used as the substrate for liquid IMC. Each sample was split in half along the scratch and immediately coated with a 10 nm thick gold film using a Denton Vacuum Desk II (Denton Vacuum, Moorestown, NJ) at 50 mTorr pressure, 45 mA current, and 30 s deposition. The gold film was used to inhibit the growth of IMC surface crystals and to prevent electron charging of the samples during SEM analysis. For further charging prevention, the coated samples were attached to round metal stubs using a carbon tape. The SEM analysis was performed in a cross-sectional view on a field-emission LEO 1530 low-voltage and high-resolution SEM operated at 6 kV and 12-14 mm working distance using an in-lens secondary electron detector.

Physical vapor deposition (PVD) was performed in a vacuum chamber at a base pressure of 10−7 Torr. Crystalline IMC was placed in a crucible that was resistively heated. The deposition rate was monitored by a quartz crystal microbalance (QCM) and controlled by tuning the heater power to a constant value of 0.2 nm/s. Deposition was made onto a 1000 nm wavelength master grating attached to a copper finger with a thermally conductive glue. The substrate temperature was 295 K.

IMC and PS are often-used models for studying molecular glasses and surface mobility phenomena.3–8 Both materials are described as highly pure by the manufacturers, but as we report here, they contain low-concentration nano-particles roughly 0.1% in volume fraction, which can serve as convenient probes for the mechanism of surface mass transport. Since impurities at this concentration are common in molecular materials, the particle exposure phenomenon is potentially a general tool for investigating surface mobility. Figure 1 shows the AFM images of a 1000 nm wavelength IMC surface grating as a function of time at 308 K (Tg−7 K). The grating surface is initially smooth (aside from the sinusoidal contour). As its amplitude decreases over time (from 90 to 20 nm for these images), raised bumps appear on the grating peaks, but not in the valleys. Since the grating decay involves the movement of host molecules from the peak to the valley, the particles are exposed in regions vacated by host molecules, not in regions to which host molecules migrate.

FIG. 1.

Real time AFM images of IMC grating decay experiment at 308 K. During the time period shown, the grating’s amplitude decreased from 90 nm to 20 nm. The numbers in each image mark individually tracked particles.

FIG. 1.

Real time AFM images of IMC grating decay experiment at 308 K. During the time period shown, the grating’s amplitude decreased from 90 nm to 20 nm. The numbers in each image mark individually tracked particles.

Close modal

In the exposure process, the particles are stationary as the surface grating flattens. Their lack of lateral motion is evident from Figure 1; the lack of vertical motion is shown in Figure 2(a), where the height of a typical particle is plotted against time, along with the vertical positions of the grating’s peak and valley (measured in regions free of particles). The peak and valley positions approach zero symmetrically, while the particle height remains relatively constant. As reported previously,8 the grating amplitude decreases over time as h = h0 exp (−Kt), where h0 is the initial amplitude (90 nm) and K is the decay constant. For the sample in Figure 2(a), K = 2.8 × 10−5/s, consistent with the previous report.

FIG. 2.

(a) The height of a particle and the peak and valley positions of the grating as functions of time at 308 K. (b) Schematic for the particle exposure process. The enlarged view illustrates the dome-like amorphous surface over a protruding particle detailed in Figure 6 

FIG. 2.

(a) The height of a particle and the peak and valley positions of the grating as functions of time at 308 K. (b) Schematic for the particle exposure process. The enlarged view illustrates the dome-like amorphous surface over a protruding particle detailed in Figure 6 

Close modal

It is significant that the particle-exposure phenomenon is temperature dependent. Figure 3 shows the AFM images of surface gratings that have been decayed at different temperatures, but to a common amplitude (20 nm). The exposure of particles is evident at low temperatures, but less noticeable at high temperatures. The transition temperature, approximately 325 K, agrees well with the previously obtained 328 K, the temperature at which the grating decay mechanism changes from viscous flow to surface diffusion.8 In previous work, Zhu et al. found that the grating decay constant K is given by Bq4 in the surface-diffusion regime, but by (γ/2η)q in the viscous-flow regime, where γ is the surface tension, η is the viscosity, and q = 2π/λ is the spatial frequency of the grating. The transition between the two mechanisms occurs at 328 K for 1000 nm surface gratings. The present results suggest that the exposure of particles can be used as an indicator for the mechanisms of surface mass transport.

FIG. 3.

AFM images of IMC surface gratings for which the decay occurred at different temperatures, but to a common amplitude (20 nm).

FIG. 3.

AFM images of IMC surface gratings for which the decay occurred at different temperatures, but to a common amplitude (20 nm).

Close modal

In addition to surface grating decay, the particle exposure phenomenon was observed during surface crystal growth. IMC glasses can grow crystals rapidly on the free surface, with the crystals rising upward and being surrounded by depressed grooves or depletion zones.15 Figures 4(a)–4(d) show the SEM images of this process at 313 K. Note the slightly rougher surface of the depletion zones and the exposed particles (marked by arrows). The glass surface far from the crystals is smooth and free of exposed particles. From the SEM images, we estimate the average size of the particles to be d0≈100 nm and their volume fraction to be ν≈0.2%. The latter is calculated from the volume of the groove next to a crystal and the volume of the exposed particles in the groove. The volume fraction is also calculated from the AFM images of surface grating decay (Figure 1). From the heights of the exposed particles and their average size (100 nm), we calculate their total volume; dividing this volume by the volume removed off the grating peaks yields ν ≈ 0.3%, in reasonable agreement with the 0.2% figure above. The low volume fraction of impurity particles is consistent with the high chemical purity of IMC (>99%).

FIG. 4.

SEM images of surface crystals growing on an IMC glass. Panels (a)–(d) show that at 313 K, surface crystals are surrounded by depletion zones in which exposed particles are visible (arrows). The phenomenon is not seen at 323 K (e).

FIG. 4.

SEM images of surface crystals growing on an IMC glass. Panels (a)–(d) show that at 313 K, surface crystals are surrounded by depletion zones in which exposed particles are visible (arrows). The phenomenon is not seen at 323 K (e).

Close modal

As in the case of surface-grating decay, particle exposure is temperature dependent: exposure occurs at low temperatures (Figures 4(a)–4(d)), but not at high temperatures (Figure 4(e)). At high temperatures, crystals do not rise high above the amorphous surface and appear to sink into the liquid. Interestingly there are occasional holes near the crystals; how these holes formed is still unclear.

The particle exposure process during surface crystal growth is similar to that during surface grating decay. Here, a depressed groove is formed as molecules migrate toward the crystal, in analogy to the diminished peak in the case of grating decay. In both cases, particles are exposed in regions vacated by host molecules. The difference between the two processes in that the chemical-potential gradient is greater for molecular migration in surface crystal growth than in surface grating decay (see below).

To further characterize the exposed particles, surface gratings of IMC were prepared by vapor deposition instead of liquid cooling. An IMC vapor was deposited directly onto a master grating in vacuum yielding an IMC film 700 nm thick with a sinusoidal surface conforming to the master. In contrast to the liquid-cooled IMC, vapor-deposited samples showed no exposure of particles under the same condition of testing (Figure 5). This result is attributed to the fact that the material of the impurity particles has low vapor pressure and cannot be transferred through the vapor phase.

FIG. 5.

Comparison between the AFM images of partially decayed surface gratings of an ordinary liquid-cooled glass and a vapor-deposited glass. In both cases, the decay temperature was 303 K, the initial grating amplitude was 90 nm, and the amplitude at the time of this comparison was 20 nm.

FIG. 5.

Comparison between the AFM images of partially decayed surface gratings of an ordinary liquid-cooled glass and a vapor-deposited glass. In both cases, the decay temperature was 303 K, the initial grating amplitude was 90 nm, and the amplitude at the time of this comparison was 20 nm.

Close modal

Each exposed particle is surrounded by a dome-like amorphous surface (Figure 1). In Figure 6, we show this local surface contour for a typical particle. At time zero, the particle is under the amorphous surface; over time it is gradually exposed. The height z of the particle remains constant while the surrounding amorphous surface descends. In the lateral dimension x, the amorphous surface falls gently away with increasing distance from the particle and becomes wider over time. The width of the surface contour increases approximately as t1/4, a feature shown in Figure 6(b). After scaling x by t1/4 and normalizing the height z so the curves coincide at the far-field baselines, the surface contours collapse to a master curve. As we discuss later, this self-similarity is consistent with surface diffusion following Eq. (1). Also for later discussion, the x-scaling in Figure 6(b) includes the constant B in Eq. (1) (1.8 × 10−32 m4/s) to reveal the fact that the contour width is approximately 3 (Bt)1/4.

FIG. 6.

(a) Surface contour around a particle measured along the grating peak during grating decay at 308 K. The ellipse indicates the particle (the elliptical shape is the result of unequal x and z scales). (b) Master curve obtained by scaling x by (Bt)1/4, where B = 1.8 × 10−32 m4/s is from the grating decay rate, and normalizing z

FIG. 6.

(a) Surface contour around a particle measured along the grating peak during grating decay at 308 K. The ellipse indicates the particle (the elliptical shape is the result of unequal x and z scales). (b) Master curve obtained by scaling x by (Bt)1/4, where B = 1.8 × 10−32 m4/s is from the grating decay rate, and normalizing z

Close modal

The particle-exposure phenomenon reported above for IMC is also observed for another well-studied molecular glass, polystyrene. Figure 7 shows an example for a polystyrene oligomer (Mw = 1110 g/mol, Tg = 307 K).12 For this system, Zhang and Yu have measured the decay kinetics of surface gratings, concluding that at λ = 1000 nm, the decay mechanism changes from viscous flow at high temperatures to surface diffusion at low temperatures.12 The temperature for this transition is 307 K. Figure 7 shows the AFM images of 1000 nm wavelength surface gratings decayed at different temperatures to a common amplitude (20 nm). At 298 K and 303 K, particles are exposed, while at 308 and 313 K, there is no obvious exposure of particles. The transition temperature between exposure and non-exposure is approximately 305 K, in excellent agreement with the temperature 307 K of Ref. 12. Similar observation has been made with the PS fraction with Mw= 1700 g/mol (Tg = 319 K) (results not shown). These results suggest that the particle-exposure phenomenon could serve as a convenient and general tool for determining the mechanism of surface mass transport in molecular glasses.

FIG. 7.

AFM images of surface gratings of PS 1100 decayed at different temperatures to a common amplitude (20 nm).

FIG. 7.

AFM images of surface gratings of PS 1100 decayed at different temperatures to a common amplitude (20 nm).

Close modal

This study has shown that as a surface contour evolves, slow-moving particles in a glass-forming liquid can flow with the host liquid at high temperatures and be exposed at low temperatures. Particle exposure occurs in regions vacated by host molecules, including the peaks of surface gratings and the depletion zones near surface crystals. The surface contour around an exposed particle widens as 3 (Bt)1/4. Here we interpret these results on the basis of different mechanisms of surface mass transport—surface diffusion at low temperatures and viscous flow at high temperatures.

Previous work has shown that for IMC8 and PS oligomers,12 the mechanism of surface grating decay is surface diffusion at low temperatures and viscous flow at high temperatures. These two modes of mass transport differ in that surface diffusion occurs through a thin surface layer according to Eq. (1), while viscous flow is the collective motion of the liquid responding to a pressure difference. We hypothesize that if host molecules have fast surface diffusion, slow-moving impurity particles become exposed in regions from which host molecules vacate, but not in regions to which host molecules migrate. An analogy is the exposure of rocks on a seashore by a receding tide. In the two processes considered in this study, host molecules leave the peak of a grating for its valley or leave the amorphous surface for an adjoining crystal; in both cases, slow-moving impurity particles are exposed in regions of displaced material, but not in regions of added material. Our hypothesis has support from the fact that the transition temperature between the exposure and non-exposure of particles agrees well with that determined previously from the kinetics of surface grating decay.8,12

An important test for our hypothesis is whether the amorphous surface near an exposed particle evolves according to the surface-diffusion mechanism [Eq. (1)]. A flat surface can be perturbed by a local disturbance, for example, contact with a small lump of identical material (a point concentration),1 a scratch,14 a step,7 and a protruding foreign object.21 If the effect of the perturbation spreads according to Eq. (1), the previous studies have found that the distance of spreading increases as t1/4 at long time. This means that after an initial transient, the surface contours are self-similar (form a master curve) in the variable x/t1/4, where x is the distance from the site of perturbation. Furthermore, the distance of spreading is given by C(Bt)1/4, where C is on the order of unity: C = 5 for a point concentration1 and 3 for a scratch14 and for a shallow linear protrusion.21 Here the “distance of spreading” refers to the distance from the site of perturbation to the first minimum in an oscillatory surface profile that is characteristic of surface diffusion. Based on these results, we expect that in the surface-diffusion regime, a self-similar surface evolution is observed around an emerging particle. As Figure 6(b) shows, this is indeed the case. The observed width of the surface profile is approximately 3(Bt)1/4, where B is obtained from the rate of surface grating decay.8 This width is consistent with the prediction for a shallow linear protrusion.21 We note, however, that the observed profile does not contain the predicted minima and maxima, a disagreement also noted in the surface evolution around crystals.15,16

Our study provides an important consistency test for the two types of experiments described in the introduction that have been used to study surface mobility. The first type of experiment does not involve foreign particles, while the second type does. The experiments of this study are noteworthy in that both types of experiments were conducted simultaneously in the same sample, allowing a consistency test of the two approaches. The very low volume fraction of the nano-particles (0.3%) means that they have minimal effect on the dynamics of host molecules. Our results indicate that the same surface-diffusion model (Eq. (1)) simultaneously accounts for the results of the two types of experiments on the same sample: surface-grating decay and contour evolution around a particle. This is seen in the self-similarity in t1/4 of surface profiles around a particle (Figure 6(b)) and in the q4 dependence of the grating decay constant K,8 both direct consequences of Eq. (1) being a 4th-order partial differential equation. Furthermore, the preceding paragraph shows that the same surface mobility constant B describes the flattening of surface grating and the widening of surface contour around a particle.

There is a noticeable difference between the particles exposed near the surface crystals and on the grating peaks. In the latter case, the local amorphous surface forms a domed region, falling away gently from the particle over a distance of several hundred nanometers (Figure 6(a)). For particles exposed near a surface crystal, however, the domed region is smaller, even apparently missing (Figures 4(a)–4(d)), that is, the particles are more fully exposed. This difference might be a result of the higher flux toward surface crystals. In surface crystallization, the chemical potential difference is ∼4 kT between the crystalline and amorphous IMC. In contrast, the chemical potential difference between the peak and the valley of a surface grating is approximately 0.1 kT at time zero for our gratings and vanishes over time. For a particle near a crystal, the molecular flux is large toward the crystal and the local surface is strongly shaped by this flux. In contrast, for a particle on a surface grating, this effect is much weaker, allowing the particle to control the local surface evolution.

Despite its high chemical purity, the often-studied molecular glass indomethacin contains slow-moving nano-particles approximately 100 nm in size and 0.3% in volume fraction. Similar particles are present in another often-used model system, polystyrene. These particles can serve as a convenient probe for the mechanism of surface mass transport. If a surface contour evolves by surface diffusion, the particles are gradually exposed in regions vacated by host molecules, for example, the peak of a surface grating and the depletion zone near a surface crystal. If bulk viscous flow is the mechanism of surface evolution, the particles flow with the host liquid and are not exposed. In the surface-diffusion regime, the surface contour around an exposed particle widens over time in a self-similar manner as 3 (Bt)1/4, consistent with a surface diffusion mechanism. Indomethacin and polystyrene are models for studying surface mobility in molecular glasses.3–8 This work has shown that a standard AFM experiment can easily detect the exposure of nano-particles at a very low volume fraction (∼0.1%). Given that impurities at this level are common, this technique may be generally applicable for characterizing the surface mobility in molecular glasses. In this work, we simultaneously measured the surface grating decay and contour broadening around a particle—two types of experiments for investigating surface mobility that had hitherto been performed separately. The fact that the same model accounts for the results of both types of experiments demonstrates the consistency of the two approaches.

This study is relevant for understanding the surface mass transport in a system composed of fast- and slow-diffusing molecules. In this context, the nano-particles investigated here represent extremely large, virtually stationary molecules. Our finding suggests that slow-diffusing molecules could be stranded in regions vacated by fast-diffusing molecules, effectively causing phase separation. This picture is consistent with the report of Zhang et al.22 on o-terphenyl (OTP) containing 1 wt. % polystyrene (PS), two components of very different mobility (PS slow, OTP fast). The low-concentration PS strongly inhibits the surface-grating decay of OTP at low temperatures at which surface diffusion is the decay mechanism, but not at high temperatures at which viscous flow is the mechanism. A similar explanation is given to this result as given to the behavior of nano-particles in IMC: in the viscous-flow regime, PS molecules flow with the host liquid; in the surface-diffusion regime, PS molecules segregate from the fast-diffusing host molecules in regions vacated by OTP molecules (grating peaks) and form a low-mobility coating to retard further decay.

We thank the NSF (No. DMR-1206724) for supporting this work and Zahra Fakhraai for valuable discussions and the NSF-supported UW-Madison MRSEC for the use of its characterization facility.

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