Surface-Bulk Interplay in Vapor-Deposited Glasses: Crossover Length and the Origin of Front Transformation

Thin film stable glasses transform into a liquid by a moving front that propagates from surfaces or interfaces with higher mobility. We use calorimetric data of vapor-deposited glasses of different thicknesses and stabilities to identify the role of glassy and liquid dynamics on the transformation process. By invoking the existence of an ultrathin intermediate layer whose transformation strongly depends on the properties of both the liquid and the glass, we show that the recovery to equilibrium is driven by the mismatch in the dynamics between glass and liquid. The lifetime of this intermediate layer associated with the moving front is the geometric mean between the bulk transformation time and the alpha relaxation time. Within this view, we explain the observed dependencies of the growth front velocity and the crossover length with both stability and temperature. Extrapolation of these results points towards ordinary thin film glasses transforming via a frontlike transformation mechanism if heated sufficiently fast, establishing a close connection between vapor-deposited and liquid-cooled glasses.

Figure 1

(a)–(c) Transformation time of the intermediate layer (black dashed lines) for (a) IMC, (b) toluene, and (c) TPD, calculated from the average between $t_{\text{bulk}}$ ($T_{\mathrm{dep}}=0.85T_g$) (black solid lines and solid symbols) and ${\tau }_{\alpha }$ (orange solid symbols and VFT fits) [33, 46, 47]. Open black squares and blue circles correspond to $t_i=d/v_{\mathrm{gr}}$, with the experimental $v_{\mathrm{gr}}$ [27, 29, 48, 49] and $d=2$ and 0.5 nm, respectively. (d)–(f) $v_{\mathrm{gr}}$ calculated using Eq. (2) (black solid line) together with the reported experimental values (open symbols) for (d) IMC (in the inset, also $T_{\mathrm{dep}}=0.98T_g$, in blue [27]), (e) toluene, and (f) TPD. The black shaded regions correspond to $4>d>1\mathrm{nm}$. The dashed orange lines in (a) and (d) correspond to the hypothetic $t_i$ and $v_{\mathrm{gr}}$, respectively, considering $\gamma =1$ in $v_{\mathrm{gr}}(T,T_{\mathrm{dep}})=C(T_{\mathrm{dep}}){\tau }_{\alpha }^{-\gamma }$, in comparison with the actual value using the reported value of $\gamma =0.85$ [29] [solid orange line in d)]. Red stars in (a)–(c) correspond to the calculated $t_i$ using experimental rather than fitted data for $t_{\text{bulk}}$ and ${\tau }_{\alpha }$.

Figure 2

(a) Specific heat of glasses prepared at $T_{\mathrm{dep}}=0.95T_g$ and measured at $\sim {10}^4\mathrm{K}/\mathrm{s}$. Legend: Thickness of the films in nm. (b)—(f) $T_{\max }$ vs thickness for glasses grown at different $T_{\mathrm{dep}}$ and measured at different heating rates. The change from linear to constant regimes defines $\xi$, indicated in the graphs, with the corresponding error bars shown in Fig. 3.

Figure 3

(a) Experimental values of $\xi$ from Fig. 2, together with the value calculated from Eq. (3). Error bars are calculated as indicated in the SM [50]. (b) $t_{\text{bulk}}$, for films grown at $T_{\mathrm{dep}}/T_g=0.85$ (solid squares) and 0.98 (solid triangles), fitted with Eq. (1) [45], together with $t_i=(2\mathrm{nm}){/v}_{\mathrm{gr}}$ (open symbols) and using the reported $v_{\mathrm{gr}}$ values [29, 30, 48]. Orange data correspond to the $\alpha$-relaxation time of the liquid phase (points and VFT fit) [46]. Dashed lines for $t_i$ correspond to the average between $\log (t_{\text{bulk}})$ and $\log ({\tau }_{\alpha })$. Horizontal arrows show the $\mathrm{\Delta }{T}_{\mathrm{on}}$ for films dominated by the front (left) or bulk (right) process. The complete set of stabilities is given in Ref. [50].