PerspectiveMaterials Science

The Surface Mobility of Glasses

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Science  28 Feb 2014:
Vol. 343, Issue 6174, pp. 975-976
DOI: 10.1126/science.1248113

The diffusion of atoms and molecules on a crystal surface plays an important role in myriad applications including thin-film deposition, sintering, and heterogeneous catalysis (1, 2). Surface diffusion is frequently observed at temperatures appreciably below the crystal's melting point, implying a role for enhanced surface mobility in the process. However, understanding the dynamics of surface diffusion in glasses is a research area still in its infancy. On page 994 of this issue, Chai et al. (3) present an experimental technique that enables detailed quantification of the near-surface mobility of glasses.

Although enhanced surface mobility was found by Chai et al. as well as by others in small-molecule and polymer glasses (47), there is a noteworthy distinction between these and the analogous observations in crystals. In crystals, the substrate surface is frequently much less mobile than the surface atoms or molecules (see the figure, panel A). In glasses, however, the first or several surface monolayers are molten even below the glass transition temperature Tg (where the glass freezes), and the change in dynamics from the surface is gradual (see the figure, panels B and C). The reason for such a difference may be that the temperatures commonly used in studies of glass surfaces are close to Tg. This proximity in temperature is attributable to a broad interest in connecting enhanced surface mobility, if present, with the anomalous Tg reduction observed in polymer films (8) and, more recently, fast organic crystal growth and the formation of ultrastable glasses (7).

Moving along.

Mobile adatoms on a crystal surface (A) and their counterparts in the surface mobile layer of an organic glass (B) and a polymer glass (C). The mobile species are shown in red; the less mobile bulk-like species are in blue.

Computer simulations have consistently revealed the presence of a surface mobile layer in glasses (9). Experimental verification has been made only recently. In one method, the relaxation time for the flattening of nano-dimples created on a polymer surface was measured (4). In another, polymer films were doped with fluorescent molecules whose dynamics are tied to those of the polymer (6); the relaxation time and relative population of the component exhibiting faster dynamics were measured. However, it is generally not straightforward to relate these relaxation times to familiar transport measures such as mobility or diffusivity. Typically, the mobility is determined by monitoring the evolution of the surface morphology of a specimen and then analyzing the result by means of the Navier-Stokes equation (5, 10) or an equivalent model of fluid flow (7). The basic idea is that any nonflat surface structure (artificially or spontaneously created) produces pressure gradients that then drive the specimen to flow. In the lubrication approximation (usually applicable to thin-film specimens with thickness less than ~100 nm), the flow is planar and on average parallel to the pressure gradient. The current (or flow of fluid) per unit width is proportional to the pressure gradient and the film mobility, which can be used to determine the viscosity (5).

In one example study, the dynamics for the Brownian height fluctuations of an equilibrated film was monitored and modeled against that of overdamped surface capillary waves (10). In two others, surface structures, either shorter (5) or taller (7) than equilibrium, were created and the dissipative dynamics toward equilibrium (equivalent to that of the former example by the fluctuation-dissipation theorem) was monitored. To discern any anomalous surface mobility, the Navier-Stokes equation was solved for a bilayer film comprising a mobile layer on top of a bulk-like layer. The solution predicts that a crossover from bulk flow to surface flow can occur by either decreasing the thickness or lowering the temperature. The former has been verified by systematically decreasing the thickness from 86 to 2 nm (5).

Chai et al. measured the flattening dynamics of a step edge created on the surface of polymer films with an average thickness around 100 nm. Upon cooling the films, they observed an analogous flow transition at Tg. A previous experiment (7) studying the flattening of surface gratings imprinted on micrometer-thick films of an organic glass also observed a transition from bulk diffusion [a mechanism only feasible in thick films (2)] to surface diffusion at Tg ÷ 12 K upon cooling the films. All these findings reinforce the conclusion that surface diffusion is directly tied to the phenomenon of enhanced surface mobility of glasses. Indeed, it becomes the dominant transport process upon lowering the temperature or thinning the specimen.

It remains unknown whether surface diffusion is possible for long-chain polymers, particularly for those with radii of gyration exceeding several nanometers [the thickness of the surface mobile region as derived from surface relaxation time studies (4, 6), which can reveal local motions besides surface flow]. Efforts to understand the dynamics of these materials will have to incorporate material viscoelasticity in the data analysis, which has hitherto been treated sparingly (1113).

References and Notes

  1. Acknowledgments: O.K.C.T. is supported by NSF through projects DMR-1004648 and DMR-1310536.
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