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Direct PNAS a is article This interest. of conflict no declare authors paper. The the wrote Z.F. and Y.Z. and data; analyzed Z.F. (h films acti- thinnest the are the Furthermore, films of magnitude. these energy of in dynamics vation orders average 6–14 the by and films enhanced dependence 12-nm in no the K has whereas 20 diffusion thickness, film surface T the film the thin on that or show bulk results the error below The experimental temperatures the within measuring sur- constant four ultra- be their at these to measure on found to are coefficients nm, films diffusion thin 53 surface to molecular The nm ultrathin diffusion. 12 of face from surfaces ranging the films, on glass applied TMV- is the study, method the this probe of In perturbation. evolution TMV’s temporal to the response monitoring surface by mobil- evaluated surface be the can of method, surface ity this the In study films. to glass extended a no molecular easily ultrathin is requires be this can and such, that As surface method surface. robust free gen- sample’s the the it of on that modification additional perturbation is mild method a TMV-probe The erates the substrates. of silicon diffusion on advantage surface supported important the films glass measure TPD to ultrathin of 11) (4, method applications. 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Email: addressed. be should correspondence whom To h eaaindnmc n ufc diffusion. of surface decoupling and dynamics complete energy relaxation a activation the indicating the diffusion, than surface lower the becomes for invari- film activation the remains the of when diffusion even energy surface dynamics relaxation fast films’ ultrathin the the of of ant that times find relaxation we and relationshipfilms, the diffusion their investigating reducing surface By by nm. between magnitude 50 of below be orders thickness 14 can film to glasses dynamics up these glassy by of enhanced the dynamics to Relaxation relation unclear. its remain and diffusion with the surface of diffusion nature fast bulk physical the However, the to energies. with activation observed lower compared is glasses enhanced molecular greatly of be surfaces the on Diffusion Significance eew pl u eetydvlpdtbcomsi virus mosaic tobacco developed recently our apply we Here PNAS | a ,2017 9, May . 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PHYSICS SEE COMMENTARY film thickness) is lower than that of the surface diffusion on the A same films. These results suggest that the fast surface diffusion is fully decoupled from the overall film relaxation dynamics, down to film thicknesses where the film dynamics become compara- ble with the surface diffusion enhancement. Once the film is no longer glassy, the virus embeds into the film and surface diffusion can no longer be measured. Results and Discussion

Tg Reduction and Enhanced Overall Dynamics in Ultrathin Films. The model system studied here is the organic molecular glass TPD (Tg = 330 K, molecular structure shown in Fig. 1B). Fig. 1A shows the measured Tg values as a function of film thick- ness. (Sample preparation, temperature ramping, and ellipsom- etry details can be found in Figs. S1–S4.) Fig. 1A, Inset shows representative normalized thickness profiles for four different films during the cooling ramps. The glass transition temperature B is defined as the intercept of the supercooled liquid line with the glassy line. As the temperature is decreased, ultrathin films maintain equilibrium at lower temperatures compared with the 120-nm film and show broader Tg transitions. As a result, the Tg is reduced as the film thickness is decreased, with an onset of devi- ation from bulk Tg around 50 nm. This observation is consistent with previous measurements of Tg reductions in ultrathin films of molecular (24–26) and polymeric glasses (12, 13, 15, 22, 23) and shows a similar range of thickness over which the Tgs of the ultrathin films are affected by the enhanced surface dynamics. We recently measured the effective viscosity and average relaxation times of ultrathin TPD films at various temperatures below bulk Tg (24). Using cooling-rate–dependent Tg (CR- Tg) measurements, the film’s average relaxation time at Tg can be estimated based on the inverse of cooling rates. Isothermal dewetting measurements were also performed in these studies to Fig. 1. (A) Glass transition temperatures, Tg, vs. film thickness for TPD films characterize the effective viscosity within films of various thick- supported on Si substrates measured using ellipsometry at a cooling rate of 10 K/min. A, Inset shows representative normalized thickness vs. temper- nesses and were related to relaxation times. Within the error ature plots for various film thicknesses. The black dashed lines show the of the experiments, both measures of dynamics (isothermal and slopes for thermal expansion coefficients of a bulk film in the supercooled temperature ramps) produced similar average relaxation times in liquid and glassy regimes. The black and green arrows show the values of Tg ultrathin films. Using these data from ref. 24, the average relax- for the 120-nm and 26-nm films, respectively. (B) Estimated average relax- ation time at each temperature of interest (ranging from 296 K ation times at four temperatures vs. film thickness (data taken from ref. 24). to 313 K) for each film thickness can be calculated. Fig. 1B shows B, Inset shows the molecular structure of TPD. that depending on the temperature, the dynamics in ultrathin films can be 6–14 orders of magnitude faster than the corre- sponding bulk dynamics at the same temperature, with the dif- cus formation process on a 25-nm TPD film held isothermally ferences increasing in magnitude with decreasing temperature, at 296 K. The bright halos around TMV are indicative of the mostly due to stronger temperature dependence of bulk films material accumulation resulting from the meniscus formation compared with ultrathin films. and growth with isothermal holding time. Fig. 2B plots the tem- poral evolution of the line profiles across the center of the TMV Surface Diffusion Measurements on Ultrathin Films. The TMV- probe, extracted from line profiles perpendicular to the center probe technique (4, 11) was applied to measure the surface dif- of the TMV. All measurements in this study were performed fusion of ultrathin TPD films. Dilute TMV particles were intro- below the bulk Tg, as well as each film’s corresponding Tg or duced onto the surfaces of ultrathin films by spin coating and the lower onset of the transition temperature T− (details in Fig. the response of the surface to the perturbation induced by TMV S5), to ensure that the profile evolution is due to surface diffu- was monitored using noncontact atomic force microscope (AFM, sion as opposed to embedding due to viscous flow (4). During the Agilent 5420) equipped with an in situ heating stage (Custom time and temperature windows of these measurements, no obvi- Thermoelectric TEC) to control the temperatures to within 2 K. ous embedding was observed. As such it is safe to assume that Details of the setup can be found in our previous publications (4, the surface flow is solely due to surface diffusion. The Mullins 24). Briefly, once a virus is placed on a glassy film surface, due (27) model describes the surface diffusion-mediated flow in two to the surface energy differences, molecules on the free surface dimensions as would flow toward TMV and form a meniscus around it that grows 2 4 ∂h(x, t) DsγΩ ν ∂ h(x, t) with time. Given the large aspect ratio of the virus (∼18), the = − [1] ∂t kT ∂x 4 probe can be simply viewed as a semiinfinite 1D nanorod. The reduced dimension of the probe simplifies the flow toward the with Ds representing the surface diffusion coefficient, γ the sur- center of the TMV as a semi-two–dimensional flow that is self- face tension, Ω the molecular volume, ν the number of atoms per similar with time. We note that the technique works only on glassy unit area, and k the Boltzmann constant. Various earlier exper- surfaces, where the embedding due to viscous flow is much slower iments and simulations demonstrated the self-similar nature of than the time to form self-similar profiles due to surface diffusion. the profiles that follow Eq. 1 (4, 11, 27, 28). Fig. 2C confirms Fig. 2 shows a typical example of the TMV-probe experi- the self-similarity of the surface diffusion-mediated surface flow ment. Fig. 2A shows representative AFM images of the menis- process, where after scaling x with t 1/4 all profiles collapse onto

4916 | www.pnas.org/cgi/doi/10.1073/pnas.1701400114 Zhang and Fakhraai Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 hn n Fakhraai and Zhang 2D Fig. in be can coefficients diffusion values surface absolute determined. the the thus and (4), prefactor publication the the earlier of 400-nm comparing our bulk the in By of reported (4). intercept film, exper- the diffusion with these films surface of ultrathin to of window intercepts due time the solely in is that profiles iments and the self-similar of are evolution profiles the the obser- tempera- that These other confirm height. further all TMV of vations constant at indication by no data with measured as law, as power well 1/4 embedding, as the follows 2D, study, Fig. this in in tures shown as K 296 in other shown at are Measurements K) S6 2D. (303–313 Fig. temperatures in shown holding are isothermal tem- K a at 296 thicknesses time. of various holding perature of isothermal films vs. for plotted plots representative are The height constant a at files prefactor the on only depends shape whose profile universal a dashed black The law. K. power 296 1/4 at the held (y indicates thicknesses TMV line various the of of films bottom for time the holding from height scaling constant after a profiles at all shown of images collapse AFM the in as (C virus virus. the the of meniscus of axis the long of the at evolution to isothermally in profile normal Temporal held lines (B) while the nm.) TMV 400 along of bars, introduction (Scale upon K. film 296 TPD 25-nm a of 2. Fig. D C B A D s ahpol lte steaeaeo v iepolsna h center the near profiles line five of average the is plotted profile Each A. h odoelpo l ftedt nvrosfimthicknesses film various on data the of all of overlap good The pro- the of half-widths the prefactor, the quantify better To h vlto ftepol itsfralfim esrdat measured films all for widths profile the of evolution The . k γ T Ω 2 ν 4mn21mn1554min 231min 44 min yia F mgso h eicsfraino h surface the on formation meniscus the of images AFM Typical (A) . niae hta 9 h ufc ifso osnot does diffusion surface the K 296 at that indicates eosrto ftesl-iiaiyo h rfie shown profiles the of self-similarity the of Demonstration ) x with 44 min-1554 t 1/4 afpol width Half-profile (D) . = m s isothermal vs. nm) 2 Fig. hsfim h ufc ifso ofcetrmisivratand value. invariant bulk the remains as coefficient same in diffusion the viscosity surface the low the significantly of film, film and growth this rearrangement, activa- the the lower for in despite measure energy However, grow to tion virus. and TMV required the nucleate fast is around holes meniscus that so 4B, timescale are Fig. the dynamics in at relaxation shown film as average that, the energies of in activation timescales shown of thickness (plot film diffusion surface vs. the for energy tion 58.5 to 679.7 nm from decreases 50 relaxation for energy activation effective the with thickness. significantly and film decrease times decreasing both relaxation relaxation for film barriers average activation the despite thicknesses, that all fact of films the mag- for of bulk dif- orders the Surface same with the nm. compared by nitude 400 temperatures to all nm at enhanced 169.1 12 is thick- from be fusion thickness film to in measured and ranging films is temperatures for and of here diffusion range studied surface the nesses for in A 4 barrier constant Fig. activation remains from apparent evident the is thickness, It S7). Fig. about bulk at D that about relation are empirical 29. and the 24 on refs. T based from is times relaxation comparison bulk This and 24 ref. from films plotted 4A are Fig. thicknesses in various with films Times. of Relaxation coefficients diffusion and Diffusion Surface of Decoupling 1B. in Fig. decreased in is shown thickness as film range the temperature as this magnitude enhanced of are orders dynamics relaxation 6–14 average by despite films’ is the This var- that temperatures. fact of the measuring films of four for at value error thicknesses the experimental ious the Indeed, within temperatures. constant thick- isothermal remains film four vs. coefficients at similar diffusion ness surface A measured Fig. nm. S6). the (Fig. 12 plots temperatures 3 to measuring other down at observed thickness is effect film with significantly vary otm 1 ,38K 0 ,ad26K epciey h ahdln in line dashed The respectively. K, 296 D of and value K, to average the 303 top represents K, from panel each 308 temperatures K, Measurement 313 thickness. bottom: film vs. plotted atures 3. Fig. g hntefimtikesi eue o1 m h effective the nm, 12 to reduced is thickness film the When h ukdfuin(D diffusion bulk the , τ ufc ifso ofcet esrda oriohra temper- isothermal four at measured coefficients diffusion Surface α ≈ ln ihteaeaerlxto times relaxation average the with along 0 a lentv oprsnmto ssonin shown is method comparison alternative (an s 100 bulk au mle hnta fteactiva- the of that than smaller value a kJ/mol, ≈ 10 −20 PNAS bulk m | 2 ofcet fms rai glasses organic most of coefficients ) .A hsfimtikes the thickness, film this At S8). Fig. /s a ,2017 9, May n h ukrlxto ie are times relaxation bulk the and htrgrls ftefilm the of regardless that s tec temperature. each at | o.114 vol. ± | τ α 15.3 o 19 no. h surface The fultrathin of kJ /mol kJ | /mol 4917 D at s

PHYSICS SEE COMMENTARY A the activation energy for rearrangement (or fragility) of ultra- thin films (h < 20 nm) decreases below that of the surface diffu- sion of the film of the same thickness. The observation that the activation barrier for surface diffusion does not correlate with the activation barrier for rearrangement in the thinnest film is another evidence of the decoupling of surface diffusion from bulk relaxation dynamics, suggesting that the surface diffusion process is possibly a distinct process and is uncorrelated to the viscosity or relaxation dynamics within the film or at the film sur- face. Direct measurements of free surface relaxation dynamics become important to directly verify this hypothesis. This obser- vation, however, does not necessarily dispute the picture that enhanced dynamics at the free surface and its propagation into the film are the reason behind the overall enhanced film dynam- ics. It is instead an indication that surface diffusion alone, mea- sured at temperatures below Tg where the system is out of equi- librium, is not a complete reporter of free surface dynamics and B other experiments may be required. Our observation of the decoupling of Ds from τα is also con- 222 min sistent with grating decay measurements on various molecular glasses where the surface diffusion varies strongly from molecule to molecule whereas the bulk diffusion or relaxation dynam- ics show little difference between those molecules (1, 5, 6). In another extreme, polymer surfaces have been shown to have enhanced segmental relaxation dynamics (18, 19, 21, 30), but their long chain can suppress their free surface diffusion (5), potentially due to the fact that part of the chain (or molecule in large molecular glass systems) at the free surface is anchored in layers underneath with significantly slower dynamics. The decoupling of Ds and τα could be rationalized in two pos- sible ways. One possibility is that Ds is not a direct measure of 1 μm relaxation dynamics of the free surface and is instead a property that is only due to the potential energy that a molecule with a par- ticular size located at the free surface feels, which is provided by Fig. 4. (A) Surface diffusion coefficients measured on TPD films with thick- the out-of-equilibrium molecules underneath. This is consistent nesses ranging from 12 nm to 400 nm (colored solid circles) are plotted with the fact that Ds is measured only when the rest of the sys- along with average bulk relaxation times, τα, measured by bulk viscosity tem either is out of equilibrium or has dynamics that are slower (navy blue squares) (24) and dielectric relaxation measurements (solid navy than the timescale of measurements of Ds (5–7). Alternatively, it blue line) (29) as a function of 1/T. The average relaxation times in ultra- is possible that Ds is correlated with the surface relaxation time thin films of 12–30 nm from ref. 24 are also plotted for comparison (col- τ τ ored open circles). (B) An AFM image of TMV on a 12-nm film after 222 min surface, whereas surface itself for the layer immediately close of isothermal hold at 296 K. The overall dynamics in these films are fast, to the free surface is insensitive to changes in the bulk. In this 2 such that the nucleation and growth of holes due to viscous flow occur case, τsurface can be estimated to be τsurface = d /(6Ds), where at the same timescale as the meniscus formation due to surface diffusion- d is the molecular size (31, 32). The predicted surface relax- controlled flow. No embedding of the virus is observed in the timescale of ation times estimated from Ds based on this model are shown these experiments and the meniscus formation follows the self-similar flow. in Fig. S7. Whereas these values are larger than the average dynamics for the 12-nm film, as one would expect, the activa- tion energy at the free surface is estimated to be larger than that The complete independence of Ds from τα, while τα is of the 12-nm film, which is not expected, as the motion at the enhanced by 6–14 orders of magnitude via decreasing film thick- free surface is always expected to have lower activation energy ness, is consistent with previous observations where Ds was also than the average film dynamics. As such, the only way to ratio- found to be independent of τα, when τα was suppressed by 13–20 nalize the data in Fig. 4 and Figs. S7 and S8 is to assume that Ds orders of magnitude via physical aging or stable glass formation and τsurface are completely decoupled and measure two distinct (11). Overall, we have varied the average bulk relaxation time properties. For example, it is possible that Ds primarily samples τα over as large as 34 orders of magnitude either by enhancing in-plane motions, whereas τsurface measures an average between the dynamics upon confinement or by suppressing the dynamics in-plane and out-of-plane relaxations, with out-of-plane relax- upon vapor deposition/aging. Over this huge window of varia- ations having a lower energy barrier due to modified elasticity tions in average relaxation dynamics, no change of the fast sur- and anisotropy in interaction energies (31, 32). Direct measure- face diffusion Ds is observed. ments of surface relaxation times are required to elucidate these The surprising aspect of the data presented in this study, com- differences and test these hypotheses. pared with our previous study on aged and ultrastable glasses, is Regardless of which hypothesis correctly describes the decou- that the decoupling of surface diffusion and relaxation dynam- pling between the dynamics, surface diffusion measurements ics in ultrathin films is observed despite the fact that as the film alone cannot provide a full picture of the extent of the observed thickness is decreased, the average relaxation times of ultra- nanoconfinement effects in molecular glasses or the length scale thin films become comparable to the fast surface diffusion (to of enhanced dynamics from the free surfaces. Here we have within one to two orders of magnitude). As such, a wide range assumed that only the top monolayer of molecules partici- of dynamical differences between the glass dynamics and its sur- pates in the surface diffusion process. However, the analysis face dynamics cannot be the reason behind the decoupling of the used here does not provide the thickness of the mobile layer dynamics. It is also notable that as shown in Fig. 4 and Fig. S8, from the free surface. The invariance of fast surface diffusion

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Ediger organic Z, an of Fakhraai self-diffusion CR, Surface Daley (2011) al. 2. et L, Zhu 1. stability. fluidity. by glasses molecular in growth upward. crystals growing by surfaces glasses. molecular glasses. benzene tris-naphthyl of growth 731–735. glasses. molecular of diffusion surface enhanced Phys Chem J former. glass molecular a of aocpclycnndgasformers. glass confined nanoscopically films. polymer in temperature tion glasses. molecular aged h aoer iescale. size nanometre the future. the to view A films: polymer thin films. polymers. confined in Solids transition Cryst glass Non the J of measurements dynamic and modynamic ence 319:600–604. hmPhys Chem J Science 140:054509. 315:353–356. 407:288–295. hsCe B Chem Phys J 141:194505. hsRvLett Rev Phys hsCnesMatter Condens Phys J otMatter Soft 120:8007–80015. uohsLett Europhys rcNt cdSiUSA Sci Acad Natl Proc 118:066101. a Mater Nat hsCe Lett Chem Phys J 8:2206. 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Z Fakhraai RJ, Composto films. polymer EC, thin Glor supported in 23. dynamics slow Probing (2005) JA Forrest Z, Fakhraai 22. 8 ae ,e l 21)Nmrclsltoso hnfimeutosfrplmrflows. polymer for equations thin-film of solutions Numerical (2012) al. capillarity. et T, to Salez due surface 28. solid plane nearly a tempera- of transition Flattening glass (1959) the WW Mullins on confinement of 27. to Effects confined (1992) J liquids Jonas organic G, Liu of J, transition Zhang glass 26. The (1991) GB McKenna CL, Jackson 25. 5 ersK,SilT ya ,Eie 21)Hg-ouu rai lse rprdby prepared glasses organic High-modulus (2010) M Ediger G, Fytas T, strain. Still KL, plane Kearns in impact vapor 35. elastic-plastic physical Normal of (1998) stability W the Stronge on C, structure Lim chemical of 34. effect The (2015) al. et T, gra- Liu mobility 33. relaxation, glassy activated of Theory (2015) KS Schweizer S, Mirigian gra- 32. mobility spatial relaxation, Slow Communication: (2014) probe KS to Schweizer embedding S, Mirigian nanoparticle of 31. imaging Direct (2003) JA stable Forrest vapor-deposited JH, of Teichroeb stability Thermal 30. (2015) MD Ediger R, Richert DM, Walters 29. eeomn CRE)Pormaad rn DMR-1350044. Grant award, Program (CAREER) Development ACKNOWLEDGMENTS. Films TPD Ultrathin ( of Temperatures Transition Glass Discussions, Measurements Additional Ellipsoemtry and Annealing in measurements described ellipsometry are and procedures, annealing preparation, sample Woollam). A. 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