Measuring the Surface Dynamics of Glassy Polymers

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Science  01 Feb 2008:
Vol. 319, Issue 5863, pp. 600-604
DOI: 10.1126/science.1151205


The motion of polymer chain segments cooled below the glass transition temperature slows markedly; with sufficient cooling, segmental motion becomes completely arrested. There is debate as to whether the chain segments near the free surface, or in thin films, are affected in the same way as the bulk material. By partially embedding and then removing gold nanospheres, we produced a high surface coverage of well-defined nanodeformations on a polystyrene surface; to probe the surface dynamics, we measured the time-dependent relaxation of these surface deformations as a function of temperature from 277 to 369 kelvin. Surface relaxation was observed at all temperatures, providing strong direct evidence for enhanced surface mobility relative to the bulk. The deviation from bulk α relaxation became more pronounced as the temperature was decreased below the bulk glass transition temperature. The temperature dependence of the relaxation time was much weaker than that of the bulk α relaxation of polystyrene, and the process exhibited no discernible temperature dependence between 277 and 307 kelvin.

Over the past 15 years there has been debate as to whether the molecular surface of polystyrene (PS) is glassy or not (1, 2) at temperatures below the bulk glass transition temperature. This question applies to other polymers and surface properties and has important implications for friction, lubrication, adhesion, and any applications involving polymer modification by way of coatings. Surfaces of polymers that do not crystallize, such as atactic PS, represent excellent model systems for amorphous material surfaces. There is growing evidence that the properties of the free polymer surface play a crucial role in observed anomalies in the glass transition temperature of thin polymer films (3).

Two types of experiments have been used to probe the relaxation properties of the polymer surface. One class of experiments measures changes in a physical property of the surface combined with established techniques to measure the glass transition temperature, Tg. In the case of PS, experiments using positron annihilation to directly probe the near-surface region have yielded contradictory results (4, 5), whereas experiments involving Tg measurements of a fluorescently labeled surface layer have given strong evidence for a reduced surface Tg value (6). Any measurement of a Tg probes the average response of the system at a certain relaxation time, depending on the experimental conditions (such as cooling/heating rate) and cannot provide any more information about the temperature dependence of the relaxation function. For this reason, measurements of Tg are at best indirect probes of the structural relaxation. A second class of experiments involves monitoring the response of the material to a surface perturbation. This perturbation can be oscillatory, as in the case of atomic force microscopy (AFM)–based surface rheology experiments (7, 8), or it can be applied and then allowed to relax over time (914). However, AFM-based methods usually use a time-dependent and often oscillatory perturbation. Recent results show that anomalous dynamics in thin films are observed only for slow (longer than 1 s) relaxation processes (15). If observed anomalies in thin-film Tg values are indeed related to the surface properties, the implication is that sub-Hz frequencies may have to be used. AFM-based techniques have been used to support (7) and refute (8) the idea of enhanced surface mobility.

For all such experiments, introduction of a surface perturbation necessarily involves introducing a stress. This stress should be as small as possible and should certainly be smaller than the yield stress of PS (∼3 × 107 Pa) (16). Many experiments involving AFM tips in contact with the sample, as well as samples that are characterized by a deformation applied at room temperature (9, 10), may be subject to a very large stress. Experiments where the surface perturbation is applied by rubbing the polymer (9, 10) have also led to conflicting results. Some experiments that probe free-surface dynamics do so while the surface is in constant contact with a solid probe; both nanoparticle embedding and AFM-based experiments suffer from this difficulty (17, 18). In such cases it is possible to argue that the near-surface region underneath the probe is affected by both the free surface and the covering particle, and that for some length scales the free-surface effect dominates. Such an argument is not ideal, as the interaction between the polymer and the solid is not necessarily well understood (19, 20).

The length scale of the perturbation is also important. Even if there is enhanced relaxation at the surface, this region involves only fractions of polymer chains. If a mobile surface region exists, it may be thought of as being tethered to a glassy substrate. There are two consequences that arise from this: (i) Measurements really should be carried out on a single length scale if possible, and this length scale should be of the order of a few nanometers. (ii) For dynamics at length scales larger than that of any region of enhanced mobility, there may never be complete structural relaxation below the bulk Tg value. Recently Papaléo et al. (21) monitored the relaxation of nanostructures produced by ion bombardment of the surfaces of poly(methyl methacrylate) (PMMA) and found strong deviations of surface relaxation from bulk behavior. Unfortunately, these nanodeformations were produced by a very-high-energy process, and the bombardment could produce high local stress, radiation-induced cross-links, or chemical changes; these authors noted (21) that the latter two effects likely occurred within a few nanometers of the probed region.

We describe an experiment aimed at circumventing many of these experimental difficulties and provide definitive evidence for enhanced mobility at the polymer surface. We produced nanodeformations (holes) by coating a solution of gold nanospheres (diameter 23 ± 3 nm) onto the surface of a spin-cast and annealed (413 K for 12 hours under dry nitrogen) PS film (thickness 100 nm, Mw = 641,000, Mw/Mn = 1.11; Polymer Source Inc.). The nanospheres were prepared in our lab by means of a standard citrate reduction technique (22) and were thus charge-stabilized against aggregation (rather than surfactant-stabilized). We then heated the samples at 378 K for 10 to 15 min to allow the spheres to partially embed into the polymer surface (18). We chose embedding times and temperatures that produced average embedding values of ∼2 to 4 nm. An embedding temperature above the bulk Tg of PS was chosen to ensure that the relaxation time of the system was less than the embedding time and that the structure was locally relaxed around the gold nanoparticles.

After embedding the gold nanoparticles into the PS surface, it is necessary to remove them without applying a large stress to the surface. This is done by placing a drop of mercury on the surface. The mercury forms an amalgam with the gold, which essentially dissolves the gold into the mercury droplet (23). When the sample is turned at an angle, the mercury droplet slides off. After this process, what is left in place of the nanoparticles are small holes that can be measured by AFM. The imaging was done with an atomic force microscope (Explorer, Veeco) operating in tapping mode. Images of the sample after removal of the gold nanospheres in this way did not show any evidence for surface damage. (When water was used to remove the gold particles, large craters were observed in place of the gold particles, indicating surface damage due to large induced stress on the surface.) The Tg values of the films made using this procedure were measured using ellipsometry (EXACTA 2000, Waterloo Digital Electronics) to be the same as the bulk value, and energy-dispersive x-ray analysis (LEO 1350 SEM system) did not show residual mercury or gold on the polymer surface.

Figure 1 illustrates the sample preparation technique. In comparing Fig. 1A and Fig. 1B, it is clear that in place of nanospheres there are holes surrounded by a rim of PS. Figure 1C shows a histogram of hole depth data (from a 5 μm by 5 μm image) from which we determine the average hole depth. A line profile used to find the depth of a single hole is shown in Fig. 1D. Each sample is measured after nanohole formation to ensure that there are enough holes on the surface to get adequate statistics. There is an inherent sensitivity to the sharpness of the AFM tip; if the radius of curvature of the AFM tip is much larger than that of the nanohole, there is a reduced ability to measure the depth of the hole. This problem is minimized by using sharp tips and frequently changing the tip. The average initial depth of the nanodeformations can be compared to the average embedding depth of the spheres before dissolution to ensure that the tips and the imaging resolutions are chosen properly and the depths of the nanodeformations can be measured accurately and reproducibly. This technique is applicable to other polymers, and we have also seen similar effects in isotactic PMMA.

Fig. 1.

Illustration of the process used to create nanoholes in the PS surface. (A) PS surface covered by Au nanospheres that have been partially embedded. (B) The surface of the same PS sample, but at a different location, after Au nanospheres have been removed by exposure to liquid Hg. (C) Histogram showing hole depth. (D) Line scan of the indicated line in (B) used to measure the depth of a single hole. Note the existence of the rim around the hole.

The principal driving force that relaxes the surface roughness is stress due to the polymer surface tension. The magnitude of the initial stress σ0 depends on the radius of curvature of the nanodeformation: σ0 = 2γ/R, where γ is the PS surface tension and R is the radius of the nano-sphere used to make the hole. For a spherical cap with a radius of curvature of 11.5 nm, σ0 = 1.3× 106 Pa. This is at least an order of magnitude smaller than the yield stress of PS and provides confidence that we are observing a linear response. The stress gradually decreases as the nanohole anneals and becomes flat. This is the only driving force present in the system that can cause a complete annealing of the surface deformations. The stress on the sample due to a mismatch in thermal expansion between the polymer and the gold particles results in at most a 1% change in the nanodeformation and would not be observable. The depth of the surface region probed is determined by the extent to which the particles are allowed to embed, and the initial driving force for annealing at the bottom of the nanodeformation is determined only by R and is independent of the embedding depth, h. The embedding depth defines the lateral radius of the hole to be [R2 – (RH)2]1/2. These two quantities, R and h, can be independently varied (subject to the constraint h < R) by the choice of sphere size and annealing time. For shallow holes like those used in our experiment, it is only the measurement of the hole radius, and not the depth, that is limited by the shape of the AFM tip.

To avoid extra stress caused by repeated heating and cooling of the samples, we measure each sample only once after annealing has begun. This means that we need at least one sample per annealing time, and determination of the relaxation curve for any sample temperature requires 10 to 15 samples with identical thermal history and similar initial hole depth distributions. For a given sample temperature, all of the prepared samples are placed in the sample oven in dry nitrogen. After some time interval, one of the samples is removed, cooled down to room temperature in a few seconds, and then measured by AFM. Each AFM image contains many holes (∼50), and we use the average depth over all holes. This procedure is repeated at a number of elapsed annealing times until holes are no longer observed. Even when the holes have relaxed to the point where their depth is too small to be measured, their rims persist and so they can still be located; the depths of these holes are assumed to be zero. If these holes simply disappeared, then we would only observe the largest holes at long times and the resulting analysis would provide average values that are too large. The measured hole depths are used to determine the time dependence of the indentation depth at constant annealing temperature. The entire experiment is then performed at different annealing temperatures.

Figure 2 shows the time evolution of nanodeformations at a sample temperature of 293 K. As the annealing time is increased, both the depth of the holes and the size of the rims are decreased. The rims relax more slowly because they have a different shape with a larger radius of curvature (and hence a smaller driving force) than the holes. The holes (and rims) relax at a temperature that is almost 80 K below the bulk Tg value. Images such as those in Fig. 2, but over a larger distance (typically 5 μm by 5 μm), are used to provide the hole depth values for each time and annealing temperature. At all measured temperatures, the time dependence of the average hole depths is well described by a single-exponential function within the scatter of the data. Hence, it is possible to find a relationship between the time constant of this annealing and the characteristic relaxation time of the system near the free surface. The depth of a hole as a function of time is described by h = h0 exp(–t/τ), where τ is the time constant of the annealing. Because at each given time the surface stress is derived from the radius of curvature of the deformation at that time, it can be assumed that at the bottom of the hole, the stress due to the surface tension also exhibits single-exponential decay with the same time constant τ. Because the time dependences of both the stress and strain functions are single-exponential, the time and position dependences can be separated Embedded Image(1)Embedded Image(2) where ϵ and σ are the general strain and stress functions. Given the single-exponential relaxation observed, it is a reasonable assumption that the creep modulus has a similar dependence Embedded Image(3) where G0 is the longitudinal glassy creep modulus, and τα is the characteristic time that is governing the dynamics of the observed surface relaxation. Separating the position dependence reveals the time-dependent part of the differential equation of the system (24) Embedded Image(4) Using this equation, it is easy to show that for single-exponential relaxation Embedded Image(5) The longitudinal modulus is used because we are only measuring changes in the depth of the hole, and only a longitudinal stress drives the changes in depth at the bottom of the nanohole. This relationship can be used to obtain the characteristic relaxation time of the surface from the measured hole annealing time constants.

Fig. 2.

Evolution of nanoholes at a sample temperature of 293 K. Annealing times are (A) 0 hours, (B) 74 hours, (C) 495 hours, and (D) 1607 hours. The inset of each panel shows the line scan of the indicated holes used to find their depth.

The time evolution of the hole depth can be used to obtain the surface relaxation function for each temperature studied. If the shape of the relaxation function is not temperature-dependent, then it is possible to find a shift factor, αT, in time such that the relaxation curves at different temperatures can be superimposed. This is a commonly used technique to describe the temperature dependence of relaxation times in glass-forming materials. Figure 3 shows the superposition plot as well as the shift factors used to arrive at the cumulative plot. Note that each data point on this plot is obtained from a different sample, and the resulting scatter is mainly a result of the fact that each sample has a slightly different distribution of hole sizes (all with average values between 2 and 4 nm). The data in Fig. 3 are scaled to a reference temperature of 369 K, which is the highest temperature for which we were able to get reliable relaxation measurements. It is clear that the relaxation function can be well described by a single exponential. This is in contrast to the relaxation function of bulk PS, which exhibits stretching (ϕ = ϕ0 exp[–(t/τ)β]) with a β value of 0.4 (dashed curve in Fig. 3).

Fig. 3.

Time dependence of the relaxation of nano-holes for all temperatures. The time data are shifted by a factor aT so that they agree with the data at the reference temperature of 369 K. The solid line is a single-exponential fit; the dashed line is a stretched exponential with bulk value of β = 0.4, with the same average lifetime as the single-exponential fit. The inset shows logarithms of the shift factors used to produce superposition; the solid curve in the inset corresponds to the bulk shift factors of PS above and below bulk Tg, obtained by the SHG technique (26).

Large deviations from the bulk are also seen in the shift factors used to collapse the relaxation functions. For bulk PS at temperatures greater than Tg, the shift factors for PS have the form log(aT)=[C1(TTref)]/(C2 + TTref), where C1 = 12.7 to 13.7, Tref = 373 K, and C2 = 49.9 (25) [solid (T > Tg) and dotted (T < Tg) curves, inset of Fig. 3]. An obvious consequence of this form is the divergence of shift factors at a temperature T*= TrefC2 = 322.9 K. Below bulk Tg, the sample is in a nonequilibrium glassy state. In this state the measured dynamics are faster than an extrapolation of the liquid dynamics and take on an Arrhenius form (solid line, inset of Fig. 3). This enhanced α relaxation in the glassy state (aging) is still substantially slower than what we observed for the surface; more important, it has a different temperature dependence. For the PS surface relaxation, at lower temperatures the temperature dependence of the shift factors becomes so weak that no substantial temperature dependence is observed below 307 K. In the inset of Fig. 3, the bulk dynamics are obtained from the α relaxation measurements as probed by the relaxation of dye molecules using the second harmonic generation (SHG) technique (26). The surface relaxation data clearly do not obey the behavior of bulk PS; instead, the slope decreases with decreasing temperature. Figure 3 represents a reasonably complete quantification of the dynamics of the top 2- to 4-nm surface layer of PS below the bulk glass transition temperature.

A more detailed comparison to the bulk α process (the main structural relaxation process in bulk glass-formers) is possible. Equation 5 can be used to convert the shift factors into temperature-dependent relaxation times of the surface. Figure 4 shows the relaxation times along with plots of α and β (local vibrational relaxation) of PS. Note that because different techniques are used for the bulk (26) and surface measurements, there may be a relative vertical shift (about one or two orders of magnitude) in one or both of the data sets, but the temperature dependences are independent of the technique and can be used to compare the two data sets. It can be seen that the relaxation times of the surface are similar to the bulk α relaxation times near the bulk value of Tg but deviate strongly from the bulk as the temperature is decreased further below the bulk value of Tg. To address the idea of using different driving forces (such as one would get with different sphere sizes), this plot also shows an analysis of the rim data (solid symbols) where they could also be determined. The similarity of the hole and rim data, combined with the fact that the radius of curvature of the rims is about twice as large (and hence subject to half the stress) as that of the holes, provides more evidence that the observed relaxation is a linear viscoelastic response.

Fig. 4.

Comparison of the calculated surface relaxation times (open triangles) with bulk α (26) and β (27) relaxations of PS. The solid curve shows α relaxation times in PS obtained from the SHG technique (26). The dashed curve indicates the β relaxation times of PS obtained from dynamic mechanical measurements (27). The solid triangles denote relaxation times obtained from the annealing of the rims, which have a larger radius of curvature than the holes.

Although the analysis provided by Eqs. 1 to 5 provides for a definite scale between the observed relaxation times and the characteristic relaxation time of the near-surface region, the essential results of this work (definitive enhanced surface mobility and weak temperature dependence of relaxation times) are robust and model-independent. Note that for temperatures near the bulk Tg, the relaxation time of the surface is very similar to the bulk α relaxation time, as was also observed in (21) for PMMA. As the temperature is decreased below the bulk Tg, the bulk dynamics freeze rapidly while the surface relaxation time changes only about two orders of magnitude over a temperature range of about 80 K. This results in a growing disparity between surface and bulk properties as the temperature is lowered below Tg. Of particular interest is that the temperature dependence of the surface relaxation becomes weaker as the temperature is decreased (opposite to the temperature dependence typical of glass-forming behavior, where an Arrhenius temperature dependence with a constant activation energy exists below Tg), and between 277 and 307 K no temperature dependence was discerned. These results alone are not sufficient to determine whether the surface relaxation is an α process that strongly deviates from the bulk, or whether it is a previously unobserved mode of relaxation that is only available near the free surface. The temperature dependence of the surface relaxation process can provide an explanation of some apparent contradictions in the literature. For example, experiments that probe the dynamics above or near the bulk Tg would show that the dynamics of the surface are very similar to the bulk dynamics—a result that would contradict measurements made at lower temperatures.

Our experiment enabled us to measure the temperature-dependent relaxation time for the very near (2 to 4 nm) surface region of PS films. The surface region showed relaxation at all temperatures measured (down to 277 K), and the resulting relaxation times displayed a surprisingly weak temperature dependence below the bulk Tg value, which became immeasurable for temperatures less than ∼307 K. These results are in stark contrast to the regular α and β relaxation processes that are observed in bulk glass-formers.

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