Elastic properties and freezing of argon confined in mesoporous glass

We study the elastic properties of argon confined in mesoporous Vycor glass with a mean pore diameter of 8 nm. For this purpose volumetric adsorption and desorption measurements are combined with simultaneous ultrasonic measurements. Therewith we obtain the effective shear modulus as a function of the pore filling reflecting both the spatial arrangement and the freezing process of confined argon. Below the freezing point of argon the adsorption process proceeds in three steps. (I) The first adsorbed layers of argon do not contribute to the measured shear modulus, i.e., they do not behave like a solid. (II) In an intermediate range of pore filling the shear modulus increases linearly with increasing amount of adsorbate, i.e., the process of freezing starts, probably with the formation of capillary sublimate. (III) At a certain filling fraction an abrupt rise of the shear modulus up to a plateau value is observed. This step indicates either a change in the spatial distribution of the capillary condensate or a change in its intrinsic properties. The lower the temperature, the smaller the characteristic filling fractions at which these transitions occur. During desorption a hysteresis of the shear modulus, of the attenuation, and hence of the state of the adsorbate is observed.

Figure 1

(a) Ultrasonic transit time (scaled with the transit time of the unfilled sample), and (b) ratio of the effective shear modulus to the shear modulus of the empty sample upon adsorption at 80 K, i.e., above the freezing point of confined argon.

Figure 2

(a) Comparison of sorption isotherms for argon in porous Vycor glass at 80 K determined volumetrically (closed circles) and via ultrasonic measurements (open circles). $f=n/n_0$ denotes the volume filling fraction of the pores, where $n_0$ is the maximum amount of pore condensate. $p/p_0$ is the reduced vapor pressure, i.e., the pressure normalized to that of bulk argon at 80 K. (b) Attenuation $\alpha$ of the ultrasonic signals as a function of the reduced vapor pressure during adsorption (closed squares) and desorption (open squares). $\alpha$ is measured via the amplitudes $A_i$ of the second and the third echo, $\alpha =20{\text{log}}_{10}\left(A_2/A_3\right)/\left(2d\right)$. At the desorption pressure of $p/p_0\simeq 0.74$, where strong variations in $A_2/A_3$ are observed, the displayed values do not correspond to an intrinsic attenuation: the pulse shapes of the echoes are distorted due to inhomogeneities in the range of the ultrasonic wavelength.

Figure 3

(a) Filling fraction of the pores, (b) shear modulus ratio $G/G_0$ with $G_0=6.88\text{GPa}$, and (c) attenuation $\alpha$ on adsorption (closed symbols) and desorption (open symbols) vs reduced vapor pressure at $T=72\text{K}$. Up to the adsorption pressure of $p/p_0\simeq 0.96$ the pore condensate behaves like a liquid. Then an abrupt increase in both the shear modulus and the attenuation is observed. The arrows labeled $\text{I}\to \text{II}$ and $\text{II}\to \text{III}$ in (a) indicate the transition points between characteristic regions (see text and Fig. 4).

Figure 4

(a) Ultrasonic transit time (scaled with the transit time of the unfilled sample), and (b) ratio of the effective shear modulus $G$ to the shear modulus of the empty sample on adsorption at $T=72\text{K}$. The process of freezing starts above a filling fraction of $f_1=0.53$. The abrupt increase in the shear modulus between regions II and III indicates a collective change in the intrinsic properties of the capillary condensate or in its spatial distribution.

Figure 5

Normalized effective shear modulus vs volume filling of the pores at different temperatures (70, 72, and 74 K). The curves shifts to lower filling fractions when the temperature is reduced (regions II and III, see Fig. 4), i.e., the process of freezing $\left(G/G_0>1\right)$ starts at lower fillings $f$. The shear modulus of the isotherm at 70 K could be evaluated only up to a filling fraction of about 0.75 (due to a defect of the capillary heater the gas distribution system was blocked by frozen argon).

Figure 6

Temperature dependence of the filling fraction at which the transition from region I to region II (process of freezing starts) and region II to region III was observed.

Figure 7

(a) The ultrasonic transit time, (b) the effective shear modulus, and (c) the attenuation show a hysteresis between adsorption and desorption (measurement at $T=72\text{K}$). From this behavior one can infer that during desorption the pore condensate is solid above a filling fraction of 0.33, whereas during adsorption solid regions appear only at a higher filling fraction $\left(>0.53\right)$.