Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis

The dynamic mechanical response of mesoporous silica with coated inner surfaces confining the glass-forming liquid salol is measured as a function of temperature and frequency (1–100 Hz) for various pore sizes (2.4–7.3 nm). Compared to former results on natural pores, a distinct acceleration of dynamics due to the removal of surface-related retardation of molecular dynamics is found now, which can be fitted by a homogeneous relaxation using an unmodified Vogel-Fulcher-Tammann relation. This lubrication effect leads to a stronger decrease in the glass transition temperature $T_g$ with decreasing pore size. The present data allow to quantify and separate competing side effects as surface bondings and negative pressure from the pure confinement induced acceleration of molecular dynamics with decreasing pore size. We analyze the dynamic elastic susceptibility data in terms of a recently proposed procedure [C. Dalle-Ferrier et al., Phys. Rev. E 76, 041510 (2007)], which relates the number $N_{corr,T}$ of molecules, whose dynamics is correlated with a local enthalpy fluctuation, to the three-point dynamic susceptibility ${\chi }_T$. The observed increase of $N_{corr,T}$ with decreasing temperature strongly indicates that the size $\xi$ of dynamic heterogeneities increases when approaching the glass transition.

Figure 1

(a) Real (b) and imaginary parts of the complex Young´s modulus of silanated Gelsil (4.8 nm) filled with salol (filling fraction $f=0.87$) measured in three-point bending geometry (diamond DMA). 1 Hz signal are original data, other signals are offset for sake of clarity since there is no frequency dependence of low and high-temperature values aside the glass transition.

Figure 2

(Color online) Comparison of DMA data: black lines represent untreated samples; green (gray) lines are data for silanated pore surface. Since contact losses inhibit direct comparison, $Y^{\prime }$ and $Y^{″}$ signals of silanated samples were scaled i.o. to match $Y^{″}$ peak heights.

Figure 3

(Color online) Real part $Y^{\prime }$ and imaginary part $Y^{″}$ of different porous samples filled with salol, calibrated using RUS results at room temperature. Lines are fits using Eqs. (1, 3a, 3b) with parameters of Table .

Figure 4

Modeled relaxation time in untreated and silanated pores of Gelsil 5 from Eq. (1) used in Ref. 23 and in Eqs. (3a, 3b) for fits of data in Figs. 3b, 3e herein, at $T=220\text{K}$.

Figure 5

Relaxation time in pore centers calculated from Eq. (1) with corresponding parameters from Table . Horizontal line shows $\tau =100\text{s}$. Gray lines are relaxation times in untreated pores from Ref. 23.

Figure 6

Shift of glass transition temperature against inverse pore diameter. Open circles display the maximum negative pressure contribution (see Sec. IIIC of Ref. 23); boxes are $\Delta T_g$’s Ref. 23, filled triangles show literature values from Ref. 21. Open triangles are the present results, and crosses mark corresponding literature data from Ref. 25.

Figure 7

(Color online) Linear thermal expansion of untreated (black) and silanated (red/gray) Gelsil 5.0 nm, both empty and filled. Sample height is normalized at 280 K.

Figure 8

Shift in glass transition temperature $T_g$ and Vogel-Fulcher temperature $T_0$ against pore diameter $d$. The points are determined from fitting the experimental data with Eqs. (1, 3a, 3b), where $T_g\left(d\right)$ is obtained from $\tau \left(T,d\right)=100\text{s}$, as shown in Fig. 5. The lines are fits using Eq. (6) yielding $c=0.13$ and $T_g^{bulk}=216\text{K}$. For calculating $T_0\left(d\right)$ the relation $T_g-T_0=\frac{E}{\text{ln}\left(100/{\tau }_0\right)}=50.6\text{K}$ was used, as indicated in the text.

Figure 9

Temperature dependence of $N_{corr,T}$ for various pore sizes. Lines are calculated from Eq. (8) using the procedure described in the text. Symbols are calculated from DMA data using Eq. (7). Inset shows $N_{corr,T}$ against relaxation time $\tau /{\tau }_0$ in the corresponding temperature range on logarithmic scales.