Surface Mobility of Amorphous o-Terphenyl: A Strong Inhibitory Effect

of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53705, United States. J. Phys. Chem. B , 2016, 120 (27), pp 6842–6847. DOI: 10...
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Surface Mobility of Amorphous o‑Terphenyl: A Strong Inhibitory Effect of Low-Concentration Polystyrene Wei Zhang,† Rattavut Teerakapibal,† and Lian Yu*,†,‡ †

School of Pharmacy and ‡Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53705, United States S Supporting Information *

ABSTRACT: Previous work has shown that a surface wave on amorphous o-terphenyl (OTP) decays by viscous flow at high temperatures and by surface diffusion at low temperatures. We report that the surface mass transport can be efficiently suppressed by low-concentration polymers. Surface-grating decay has been measured for OTP containing 1 wt % polystyrene (PS, Mw = 1−8 kg/mol), which is miscible with OTP. The additive has no significant effect on the decay kinetics in the viscous-flow regime, but a significant effect in the surface-diffusion regime. In the latter case, surface evolution slows down and becomes nonexponential (decelerating over time). The effect increases with falling temperature and the molecular weight of PS. These results are attributed to the very different mobility of PS (slow) and OTP (fast) and their segregation during surface evolution, and relevant for understanding the surface mobility of multicomponent amorphous materials.

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INTRODUCTION Surface mobility influences many important processes in science and technology, including catalysis, sintering, crystal growth, and vapor deposition. Of the various measures of surface mobility, surface diffusivity characterizes the rate of lateral translation of surface molecules. While extensive studies on surface diffusion have been performed on metals and semiconductors,1 little data exist for organic materials.2−5 Such information is particularly important as organic glasses are studied for biomedical and electronic applications,6,7 and for understanding phenomena that have been observed for organic glasses, for example, fast surface crystal growth,8,9 formation of stable glasses by vapor deposition,10 and the surface mobility of polymer glasses.5,11 In recent work, surface-grating decay has been used to study the surface diffusion of organic glasses.2 Driven by surface tension, a rough surface flattens over time, and at short enough length scale, surface diffusion dominates the process.12 For the systems studied to dateindomethacin (IMC),2 nifedipine (NIF),3 o-terphenyl (OTP),4 and short-chain polystyrene (PS),5 surface diffusion prevails at the micron and submicron length scales, and vastly outpaces bulk diffusion (by 5−8 orders of magnitude at the glass transition temperature Tg). These results confirm the significant role of surface mobility in the crystallization of organic glasses8,9 and the formation of stable glasses by vapor deposition.10 Recent work has also shown a strong material dependence of surface diffusion in organic glasses relative to bulk diffusion.5 For example, bulk diffusivity at Tg is approximately 10−20 m2/ s,13−16 but surface diffusivity spans the range 10−12−10−16 m2/ s.2−5 Surface diffusion is slower with increasing molecular size and intermolecular forces (e.g., hydrogen bonding). This strong material dependence motivates studies of surface mobility in © 2016 American Chemical Society

multicomponent systems in which both fast and slow diffusing species are present. To date all measurements of surface diffusion have been limited to pure systems, and it is important to understand the process in multicomponent systems since such systems constitute most amorphous materials in service, for example, metallic glasses and amorphous drug−polymer dispersions. Polymer additives are especially important for improving the properties of small-molecule glasses, including their resistance to crystallization17−19 and fracture.20 In this study, we measured the surface mobility of the smallmolecule glass OTP that contains low-concentration PS. In pure systems, PS has substantially lower surface diffusivity than OTP if compared at the same bulk diffusivity, by roughly 3 orders of magnitude for the fractions used in this work (Mw = 1.1−8.4 kg/mol).5 We used a relatively low PS concentration (1 wt %) so that it has little effect on the dynamics of host molecules. Grating decay experiments were performed at the wavelength of 1000 nm both at high temperatures at which viscous flow controls the grating decay, and at lower temperatures at which surface diffusion does. The PS additives have no effect on decay kinetics in the viscous-flow regime, but a strong effect in the surface-diffusion regime, causing the decay to slow down and deviate from exponential kinetics. This effect increases with the PS molecular weight and falling temperature. These results are consistent with the segregation of PS from OTP during the surface grating decay process. Received: May 6, 2016 Revised: June 5, 2016 Published: June 7, 2016 6842

DOI: 10.1021/acs.jpcb.6b04606 J. Phys. Chem. B 2016, 120, 6842−6847

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MATERIALS AND METHODS

OTP (99% purity) was purchased from Sigma-Aldrich and used as received. Five PS fractions were obtained from Scientific Polymer Products: “PS1110” (Mw = 1110 g/mol, Mw/Mn = 1.12), “PS1780” (Mw = 1780 g/mol, Mw/Mn = 1.09), “PS3680” (Mw = 3680 g/mol, Mw/Mn = 1.08), “PS8400” (Mw = 8400 g/ mol, Mw/Mn = 1.05), and “PS13200” (Mw = 13200 g/mol, Mw/ Mn = 1.06). To prepare an OTP-PS solution, the components were weighed in the correct amounts that totaled 1−2 g, mixed, and heated in a sealed vial at 353 K for at least 12 h. All solutions were transparent with no sign of undissolved materials. To prepare a surface-grating sample, 10 mg of the OTP-PS solution was pipetted onto a silicate coverslip and was cooled to 273 K on a Linkam heating/cooling stage. If crystallization occurred in the stock solution, it was heated to 353 K for 2 h to melt the crystals before use. A gold-coated master grating was placed onto the sample in flowing nitrogen. The master grating was sinusoidal with a wavelength of 1000 nm and an amplitude of 100 nm. Upon further cooling to 243 K, the master was peeled off, yielding a sinusoidal surface on the OTP glass. The decay of a surface grating was followed by laser diffraction in transmission at constant temperature. The laser wavelength was 632.8 nm. During measurement the sample resided in the chamber of the Linkam stage purged with nitrogen. The diffraction intensity was measured with a Si amplified photodetector interfaced with a data acquisition device (DAQ, National Instruments) and a LabView virtual instrument program. Previous work confirmed that the diffraction intensity is proportional to the square of the grating amplitude.4 Differential scanning calorimetry (DSC) was performed with a TA Instruments DSC Q2000 unit. The glass transition temperature Tg was detected by first cooling a liquid at 10 K/ min to the glassy state and performing modulated DSC during heating at 2 K/min with a temperature modulation of ±0.5 K/ min. The melting-point depression of OTP by PS was determined by crystallizing a supersaturated OTP solution (typically 90 wt % OTP) and allowing the system to equilibrate at a chosen temperature controlled within ±1 K. Upon reaching equilibrium, the equilibration temperature is the depressed melting point Tm and the concentration of the residual amorphous phase is the solubility of crystalline OTP. The latter was obtained from the Tg of the residual amorphous phase detected by DSC and the predetermined Tg vs concentration curve.

Figure 1. (a) DSC traces of the glass transition event in OTPPS13200 solutions. (b) Glass transition temperatures (Tg) and depressed melting points (Tm) of OTP by PS. The curve through the Tm data is calculated using the Flory−Huggins model with χ = 0.03 and M = 2 kg/mol.

chosen temperature, and the concentration of OTP in the residual amorphous phase was determined from its Tg (see Supporting Information Figure S1 for example) and the Tg vs concentration curve in Figure 1b. This yielded the open data points in Figure 1b. Note that at a given weight fraction, the depressed melting points are approximately the same for different PS fractions, consistent with previous results on other systems.22 The overall trend is reproduced by the Flory− Huggins (FH) model with χ = 0.03 for the OTP-PS interaction parameter.23 In the FH calculation, weight fraction is equated with volume fraction because of the similar densities of PS and OTP. Figure 2 shows the kinetics of surface grating decay for PSdoped OTP at four different temperatures, 259, 257, 248, and 245 K. For reference, the data are also shown for pure OTP, from ref 4 and this work. The PS additive has no significant effect on the decay kinetics at the two higher temperatures, but significantly slows down the decay at the two lower temperatures. The effect becomes greater with increasing molecular weight of PS and with falling temperature. At 245 K, the time for the diffraction intensity to decay by 90% is 100 times longer in the presence of 1 wt % PS8400 than in pure OTP. It is noteworthy that, at the two lower temperatures, the inhibitory effect of a PS additive is stronger at the later stage of the decay (as the grating surface approaches flatness) than at the early stage. As a result, the overall decay kinetics becomes highly nonexponential. The observed kinetics are reasonably well described by a stretched exponential function ϕ = exp[−(KIt)β], where ϕ = I/I0 is the fraction of the diffraction intensity not yet decayed, β is the stretch exponent (β = 1 corresponds to exponential decay), and KI is the decay

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RESULTS The glass transition temperature Tg was measured for OTP-PS solutions of different concentrations to assess the miscibility of the two components. Figure 1a shows a typical set of data collected for PS13200 as the solute. Each solution exhibits a single glass transition event whose temperature systematically increases with PS concentration. Figure 1b shows the Tg vs concentration curves for PS of several molecular weights. For each PS fraction tested, a smoothly changing T g vs concentration curve was observed, indicating that OTP and PS are continuously miscible, in agreement with an earlier result on PS of higher molecular weight.21 To further characterize the OTP-PS interaction, the activity of OTP was determined from the depressed melting point Tm of crystalline OTP (Figure 1b). For this purpose, a supersaturated OTP solution was crystallized and equilibrated at a 6843

DOI: 10.1021/acs.jpcb.6b04606 J. Phys. Chem. B 2016, 120, 6842−6847

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The Journal of Physical Chemistry B

Figure 3. (a) Surface-grating decay constant K of PS-doped OTP vs PS molecular weight. (b) Stretch exponent β vs PS molecular weight. The values of pure OTP are included on the left. Both K and β decrease with increasing PS molecular weight and falling temperature.

Figure 2. Effect of 1 wt % PS on the decay kinetics of OTP surface grating. The additive does not alter the decay kinetics at the two higher temperatures (259 and 257 K) but significantly slows down the process at two lower temperatures (248 and 245 K). The effect becomes greater as the PS molecular weight increases and as temperature decreases. The solid curve illustrates the quality of fitting using a stretched exponential function. The data on pure OTP are from ref 4 (T = 259, 257, and 248 K) and this work (T = 248 and 245 K); the data from the two sources are consistent and not distinguished.

constant. Figure 3 summarizes the results of this analysis. There we have converted KI to the more fundamental gratingamplitude decay constant K using KI = 21/β K. Figure 3a shows that in the presence of a PS additive, the decay constant K is largely unchanged at higher temperatures, but is significantly reduced at lower temperatures. The effect increases with the PS molecular weight and falling temperature. At 245 K, 1 wt % PS8400 decreases the decay constant by nearly 2 orders of magnitude. Figure 3b shows that the stretch exponent β is close to unity (exponential kinetics) for pure OTP and for PS-doped OTP decaying at higher temperatures, but much smaller than unity for PS-doped OTP decaying at lower temperatures. The departure from unity increases as the molecular weight of PS increases or as temperature decreases. Figure 4 shows the decay constants K for the surface gratings on OTP4 and PS-doped OTP as functions of temperature. Again, note that K is unaffected by the PS additive at higher temperatures, but significantly reduced at lower temperatures.

Figure 4. Decay constants K of 1000 nm wavelength surface gratings for OTP (this work and ref 4) and PS-doped OTP as functions of temperature. The dashed curve is the calculated viscous flow term Fq for pure OTP. The solid line indicates the regime where surface diffusion levels the grating. At 259 and 257 K, the K values of all systems coincide with each other but diverge at lower temperatures.

Later we shall attribute these results to a minor effect of PS dopants on the viscous relaxation of OTP but a strong effect on the surface diffusion process. 6844

DOI: 10.1021/acs.jpcb.6b04606 J. Phys. Chem. B 2016, 120, 6842−6847

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DISCUSSION We have measured the effect of dilute PS on the surface-grating decay of amorphous OTP. At the concentration used (1 wt %), the additives do not alter the glass transition temperature of OTP. We find that the PS additive has no effect on the decay kinetics at high temperatures, but at low temperatures, the PS additive can significantly slow down the decay and make the kinetics nonexponential. This effect intensifies with the PS molecular weight and with falling temperature. In this section, we discuss these results in terms of the influence of PS on the viscous relaxation and surface diffusion of amorphous OTP. Zhang et al. have shown4 that for a 1000-nm-wavelength surface grating of OTP, the high-temperature decay occurs by viscous flow and the low-temperature decay occurs by surface diffusion. In Figure 4, these two mechanisms are indicated for the relevant temperature ranges. The two mechanisms differ from each other in that viscous flow is the collective movement of a liquid driven by a pressure gradient and surface diffusion is the lateral migration of molecules on a free surface. The viscous-flow mechanism was established by the observed wavelength dependence K ∝ λ−1 which is expected for this mechanism, and by the nearly exact match between the observed decay rate K and the expected rate: K (viscous flow) = Fq = (γ/2η)(2π/λ), where γ is surface tension and η is viscosity.12 As temperature decreases, however, the observed K greatly exceeds the Fq term and scales with λ−4, consistent with surface diffusion being the decay mechanism.12 It is significant that the PS effect on surface-grating decay becomes important below the temperature at which the mechanism of surface evolution changes f rom viscous f low to surface dif f usion (Figure 4). This result suggests that 1 wt % PS has little effect on the decay of a surface wave by viscous relaxation, but has a strong effect if the process occurs by lateral surface diffusion. To see the first result, recall that viscous flow levels a surface grating at the rate Fq, which at a fixed wavelength (1000 nm in our case), depends on viscosity and surface tension. The fact that 1 wt % PS does not change the Tg of OTP (Figure 1a) argues that it has a small effect on OTP’s viscosity. Meanwhile, the presence of PS in OTP is not expected to alter its surface tension to a great extent, given the similar surface tensions of the two pure liquids (see Supporting Information Figure S2 for a summary of literature data). Thus, the viscous relaxation of a surface wave should not be strongly affected by 1 wt % PS, consistent with experiment. To understand how a PS additive can slow the surface evolution of OTP, we recall that the additive causes the decay kinetics to be nonexponential. This effect is evident from the systematic decrease of the β value below unity (Figure 3b). This nonexponential kinetics argues against the mutualdiffusion model,24 in which mass transport occurs by the simultaneous diffusion of both components without any local change of concentration. The mutual diffusion process is characterized by a single diffusion coefficient Dm that depends on the two self-diffusivities and the concentration. For a dilute solution, Dm is expected to approach the self-diffusion coefficient of the minor component (PS in our case). This model is consistent with the slowdown of surface evolution by the PS additive and the increase of the effect with the PS molecular weight, but would imply an exponential decay process, in conflict with experiment. We propose that the PS effect on the surface mobility of OTP arises from its substantially slower rate of surface

migration and its segregation from OTP molecules. Recent work showed that surface diffusion of an OTP glass is vastly faster than that of a PS glass; the difference is by a factor of 103 at Tg between OTP and PS1110, and increases with the molecular weight of PS.5 This difference is attributed to a steep mobility gradient beneath the free surface and the deeper penetration of polymer chains. We imagine that a similar situation exists at the surface of a PS-doped OTP glass, with OTP molecules diffusing rapidly and PS molecules at a much slower rate due to deeper penetration into regions of low mobility. Figure 5 illustrates this idea. Figure 5a shows the

Figure 5. (a) PS molecules are larger and penetrate deeper into the bulk than OTP molecules, making their surface diffusion slower.5 (b) Proposed mechanism for the decay of an OTP surface grating containing dilute PS molecules (black circles). PS molecules move slowly and segregate from OTP molecules as the latter diffuse from the peak to the valley. The enrichment of PS on the peak slows down further decay and leads to nonexponential kinetics.

different sizes of OTP and PS molecules and their different depths of penetration into the bulk consistent with molecular simulations.5 In a surface-grating-decay process (Figure 5b), molecules on average migrate from the concave part of the grating (the peak) to the convex part (the valley). The OTP molecules do so quickly and they may leave the slow-moving PS molecules behind at the peak. This would raise the local concentration of PS and create a “coating” that slows the further decay of the grating. This model predicts a gradual slowdown of the grating decay process over time and a nonexponential kinetics, consistent with experiment results. With increasing molecular weight, PS chains move more slowly and segregate more rapidly from OTP molecules. As temperature decreases, the mobility difference between OTP and PS increases, also accelerating the surface segregation of components. We now present a thermodynamic analysis to show that phase separation is possible during the decay of a surface grating. Polymer molecules are known to be enriched or depleted at the surface of a solution, depending on the relative surface tensions of the components.25 Similarly, Haji-Akbari 6845

DOI: 10.1021/acs.jpcb.6b04606 J. Phys. Chem. B 2016, 120, 6842−6847

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The Journal of Physical Chemistry B and Debenedetti have argued that the surface concentration of a binary Lennard-Jones liquid can be slightly different from the bulk concentration, owing to the special environment of surface particles.26 These analyses pertain to a f lat surface, and here we consider the possibility of phase separation during the smoothing of a rough surface. As a surface grating decays, the change of the Gibbs free energy is given by ΔG = ΔGs + ΔGdm

where ΔGs is the change of the surface free energy and ΔGdm is the change of the bulk free energy due to demixing. Both ΔGs and ΔGdm are in the unit of J/m2, referring to the change within a unit area of the flattened surface. ΔGs is negative, because the surface area decreases as a grating decays, but ΔGdm is positive, because there is a penalty for demixing a miscible system. The question is whether the ΔGs term can overcome the ΔGdm term, leading to an overall drop of free energy. The surface term is given by

Figure 6. Change of the Gibbs free energy as a surface grating decays. The calculation is for a surface grating of 1000 nm wavelength with an initial amplitude h0 of 100 nm on an OTP glass containing dilute PS (4 kg/mol, ϕ2 = 0.01). h0 − h is the decrease of the grating’s amplitude. ΔGs is the change of the surface free energy and ΔGdm is the change of the bulk free energy due to demixing. ΔG = ΔGs + ΔGdm is the overall change of free energy.

ΔGs = γ ΔL/λ where γ = 0.05 N/m is the surface tension (assumed to be the same for OTP, PS, and their solution; see Figure S2), and ΔL is the reduction of the grating’s arc length per period λ (1000 nm). ΔL is easily calculated from the grating’s initial amplitude h0 (100 nm) and its present amplitude h. For simplicity, we calculate the worst case scenario for the demixing penalty, in which PS separates completely from OTP wherever volume is lost from the concave part of the grating. We calculate ΔGdm using the FH model

PS in OTP, the polymer is miscible with the host and has no effect on its glass transition temperature. Surface grating decay was used to assess how the PS additive influences surface mass transport. The additive has no effect on the decay rate at high temperatures at which the decay occurs by viscous flow, but significantly slows down the decay process at low temperatures at which grating decay occurs by surface diffusion. This effect becomes stronger with increasing molecular weight of the polymer and with falling temperature. The effect is attributed to the very different mobility of OTP and PS molecules and their segregation during surface evolution. This finding is relevant for understanding the surface mobility of multicomponent amorphous materials (e.g., amorphous drug−polymer dispersions and metallic glasses27). In these systems, a slowmoving component could significantly reduce the apparent surface mobility, even at low concentrations. Recent work has shown that molecular glasses can grow crystals much more rapidly at the free surface than in the interior and has linked the process to high surface mobility.4 This work finds that a polymer additive can slow down the rate at which surface diffusion flattens a rough surface of a molecular glass. One might expect a similar inhibitory effect of the polymer additive on surface crystal growth. The speculation is consistent with limited experimental results,19 and deserves further studies. We have speculated that slow-moving polystyrene molecules could separate from fast-moving OTP molecules as a rough surface flattens, even though such separation does not occur in the bulk. At present, this speculation is based solely on the nonexponential kinetics of grating decay. It will be of interest to directly test this hypothesis using high-resolution chemical mapping (e.g., by secondary ion mass spectrometry and atomic force microscope infrared spectroscopy). Additional systems could be tested in which the tendency to phase separate varies. The possibility that phase separation occurs at the surface, but not in the bulk, is relevant for understanding the stability of multicomponent amorphous materials. For simplicity, this study examined the effect of polymer additives at a relatively low concentration; it is of interest to increase the polymer’s concentration to study its effect on both viscous relaxation and surface diffusion of small-molecule glasses.

ΔGdm = −ΔgmΔV /Ω where Δgm is the free energy of mixing per site in creating the initial OTP-PS solution, ΔV is the total volume lost from the concave part of the grating per unit area of flattened surface, and Ω is the molecular volume of OTP (0.34 nm3).4 ΔV/Ω is the number of sites in the lost volume. According to the FH model, Δgm = −kT [ϕ1 ln ϕ1 + (ϕ2/N) ln ϕ2 + χ ϕ1 ϕ2], where ϕ2 is the volume fraction of PS (taken to be the same as its weight fraction, 0.01), ϕ1 = 1 − ϕ2 is the volume fraction of OTP, N is the ratio of the molar volumes of PS over OTP, and χ is the interaction parameter (taken to be 0.03 from fitting the OTP activity to the FH model, see Figure 1b). ΔV is obtained by integration: ΔV = (h0 − h)/π. Figure 6 shows the result of this analysis. Despite the penalty for demixing, the surface grating is still thermodynamically allowed to decay because the loss of surface free energy outweighs the increase of bulk free energy due to demixing. For this worst-case scenario, the grating amplitude can decrease from 100 to 40 nm before the free energy is driven up and further decay is thermodynamically forbidden. Note, however, that this scenario follows our assumptions of complete segregation and no lateral diffusion of PS: if these assumptions are relaxed, further decay may be possible. For a different polymer additive or a different host, this analysis will need to be repeated to reflect changes in surface tension and demixing tendency.

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CONCLUSIONS Recent work has observed that surface diffusion can be very fast on molecular glasses.4 This study finds that this mode of mass transport can be effectively inhibited by a low-concentration, low-mobility polymer additive. For the system studied, 1 wt % 6846

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b04606. DSC data of OTP-PS mixtures for evaluating the Flory− Huggins χ parameter; comparison of the literature data on the surface tensions of OTP and PS (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Office phone: +1 608 263 2263. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the NSF (DMR-1206724) for supporting this work. REFERENCES

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