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Mechanical responses of helium films adsorbed on two-dimensional mesoporous hectorite
Physica B 263—264 (1999) 370—372
Mechanical responses of helium films adsorbed on two-dimensional mesoporous hectorite M. Hieda , M. Suzuki *, K. Torii, H. Yano, N. Wada Division of Natural Sciences, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan Tohoku National Industrial Research Institute, Miyagi-ku, Sendai 983-8551, Japan Graduate School of Arts and Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
Abstract The mechanical responses of physisorbed films to the vibration of a substrate were investigated by measuring the sound velocity and attenuation of a two-dimensional mesoporous hectorite. The sound velocity of a hectorite pellet adsorbed by both He and He submonolayer films increased drastically at low temperatures accompanied by the attenuation. The most plausible explanation for this behavior is that helium films decouple from the vibrating substrate at low temperatures. 1999 Elsevier Science B.V. All rights reserved. Keywords: Helium film; Hectorite; Ultrasonic measurement; Slippage
The interfacial friction on an atomic scale is a topic of current interest known as “nanotribology” [1]. Regarding physisorbed films, Krim et al. [2,3] measured the mechanical responses of several monolayers on a solid surface at 77 K using the quartz-crystal microbalance (QCM) technique, and showed that solid-like films (Kr on smooth Au) more easily slip from the vibrations of substrate than liquid-like films. On the other hand, Mohandas et al. [4] performed torsional oscillator measurements of submonolayer helium films adsorbed on graphite, and studied the temperature dependence of the slippage of helium films. They found that the he-
* Corresponding author. Tel.: #81-424-43-5556; fax: #81424-43-5563; e-mail: [email protected].
lium films undergo decoupling from the substrate at low temperatures. However, the ratio of the decoupled film to the total adatoms remained less than 1% because of the heterogeneity of the substrate. Ultrasonic measurements of porous materials also allow us to study the mechanical responses of physisorbed films on a solid surface. We present here ultrasonic measurements of submonolayer helium films in a two-dimensional porous material hectorite. Hectorite [5] is a kind of layer silicate, which has two-dimensional open spacing of 17—20 As between 9.6 As thick smectite layers separated by pillars standing about 37 As apart, and a huge surface area (484$3 m/g). A cylindrical pellet ( 12.4 mm; 7.9 mm) was fabricated by pressing hectorite powder, and 10 MHz longitudinal LiNbO transducers
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 3 8 8 - X
M. Hieda et al. / Physica B 263—264 (1999) 370—372
371
were then bonded to both ends of the pellet with silicone adhesive. The sound velocity and attenuation of the pellet with various submonolayer coverages of He and He were measured in the temperature range 130 mK—20 K. At these coverages, helium films are thought to be solid-like at low temperatures. The sound velocity of the pellet is related to both the density o and the elastic modulus c. In case where the adsorbed film is viscously locked to the substrate and the elastic modulus is unchanged, the change in sound velocity *v is written as *v 1 *o "! , 2o v
(1)
where o is the density of the pellet and *o is the density change due to the absorbed film. When the film decouples from the vibration of the sound wave of the substrate, the sound velocity increases due to the decrease in the effective density of adsorbed film *o. To study the decrease in velocity due to the adsorbate on hectorite, we first measured the velocity change of the pellet adsorbed with various amounts of nitrogen at 77 K. Nitrogen adsorbed on hectorite is believed to be solid-like, and is viscously locked to the surface of hectorite. As determined by Eq. (1), the velocity decrease with increasing coverage was well fitted by a straight line. However, the slope of this line was about 60% less than that estimated by Eq. (1) because of the weak bonds of hectorite grains in the pellet. The sound velocity and attenuation of the typical helium coverages are shown in Figs. 1 and 2. The temperature dependence of zero-helium coverage was subtracted from these data. It is found that the decrease of the sound velocity from zero-helium coverage around 10 K is proportional to the density change *o due to helium adatoms and was about 60% less than the estimation by Eq. (1) without respect to either He or He. Comparison with the results of nitrogen allows us to conclude that helium adatoms are viscously locked to the surface of hectorite. (At higher temperatures, the sound velocity approached that of zero-helium coverage because of the desorption of helium adatoms.)
Fig. 1. Typical data of the variation of the sound velocity of a hectorite pellet adsorbed with both He (lower) and He (upper) submonolayer film. The areal density of helium films is in the figure. The curves represent the calculation of the Debye relaxation.
When the temperature was lowered, we observed a rapid increase in sound velocity accompanied with the attenuation. As discussed in Ref. [4], to study the temperature dependence of the sound velocity and attenuation due to decoupling, we consider the Debye relaxation written as Auq *a" , 1#uq
(2)
*v A " , (3) v 1#uq where A and A are constants and u is the angular frequency of ultrasound. We assume that the relaxation time q obeys the Arrhenius relation q"q exp(E/¹). Here, the relaxation time q is
372
M. Hieda et al. / Physica B 263—264 (1999) 370—372
reported the adsorption and motional state of helium on hectorite by measurements of the isosteric heat and heat capacity. In the low density region, helium adatoms are localized in the dips of the registered site as a commensurate layer, while in the high-density region they form an incommensurate layer. Thus, we consider that the observed stepwise change is attributable to the structure change of the helium film. We explained the observed behavior due to the decoupling of adsorbed helium film. There may be some other mechanisms that account for the present results: for example, the internal friction in the film could cause the Debye relaxation. However, it seems that these dissipative mechanisms cannot explain the amount of increase in sound velocity at low temperatures. In summary, we measured the sound velocity and attenuation of a two-dimensional mesoporous hectorite pellet adsorbed with He and He. The sound velocity of the pellet adsorbed with helium films increased drastically at low temperatures accompanied by the attenuation. The most plausible explanation for this behavior is that helium films decouple from the vibrating substrate at low temperatures. Fig. 2. Typical data of the variation of the attenuation of a hectorite pellet adsorbed with both He (triangles) and He (circles) submonolayer film.
References
associated with the film-substrate momentum transfer. The temperature dependence of the sound velocity and attenuation of both He and He was found to be well described by the Debye relaxation over the whole submonolayer coverage. Furthermore, we found that E and q show a stepwise change with respect to the coverage. Wada et al. [6]
[1] B. Bhushan, J.N. Israelachvili, U. Landman, Nature 374 (1995) 607. [2] C. Daly, J. Krim, Phys. Rev. Lett. 76 (1996) 803. [3] J. Krim, in: H. Taub et al. (Ed.), Phase Transitions in Surface Films 2, Plenum, New York, 1991, p. 169. [4] P. Mohandas, C.P. Lusher, V.A. Mikheev, B. Cowan, J. Saunders, J. Low Temp. Phys. 101 (1995) 481. [5] K. Torii, T. Iwasaki, Y. Onodera, K. Hatanaka, Chemistry of Microporous Crystals, Kodansha, Tokyo, 1991, p. 81. [6] N. Wada, A. Inoue, H. Yano, K. Torii, Phys. Rev. B 52 (1995) 1167.
Mechanical responses of helium films adsorbed on two-dimensional mesoporous hectorite M. Hieda , M. Suzuki *, K. Torii, H. Yano, N. Wada Division of Natural Sciences, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan Tohoku National Industrial Research Institute, Miyagi-ku, Sendai 983-8551, Japan Graduate School of Arts and Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
Abstract The mechanical responses of physisorbed films to the vibration of a substrate were investigated by measuring the sound velocity and attenuation of a two-dimensional mesoporous hectorite. The sound velocity of a hectorite pellet adsorbed by both He and He submonolayer films increased drastically at low temperatures accompanied by the attenuation. The most plausible explanation for this behavior is that helium films decouple from the vibrating substrate at low temperatures. 1999 Elsevier Science B.V. All rights reserved. Keywords: Helium film; Hectorite; Ultrasonic measurement; Slippage
The interfacial friction on an atomic scale is a topic of current interest known as “nanotribology” [1]. Regarding physisorbed films, Krim et al. [2,3] measured the mechanical responses of several monolayers on a solid surface at 77 K using the quartz-crystal microbalance (QCM) technique, and showed that solid-like films (Kr on smooth Au) more easily slip from the vibrations of substrate than liquid-like films. On the other hand, Mohandas et al. [4] performed torsional oscillator measurements of submonolayer helium films adsorbed on graphite, and studied the temperature dependence of the slippage of helium films. They found that the he-
* Corresponding author. Tel.: #81-424-43-5556; fax: #81424-43-5563; e-mail: [email protected].
lium films undergo decoupling from the substrate at low temperatures. However, the ratio of the decoupled film to the total adatoms remained less than 1% because of the heterogeneity of the substrate. Ultrasonic measurements of porous materials also allow us to study the mechanical responses of physisorbed films on a solid surface. We present here ultrasonic measurements of submonolayer helium films in a two-dimensional porous material hectorite. Hectorite [5] is a kind of layer silicate, which has two-dimensional open spacing of 17—20 As between 9.6 As thick smectite layers separated by pillars standing about 37 As apart, and a huge surface area (484$3 m/g). A cylindrical pellet ( 12.4 mm; 7.9 mm) was fabricated by pressing hectorite powder, and 10 MHz longitudinal LiNbO transducers
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 3 8 8 - X
M. Hieda et al. / Physica B 263—264 (1999) 370—372
371
were then bonded to both ends of the pellet with silicone adhesive. The sound velocity and attenuation of the pellet with various submonolayer coverages of He and He were measured in the temperature range 130 mK—20 K. At these coverages, helium films are thought to be solid-like at low temperatures. The sound velocity of the pellet is related to both the density o and the elastic modulus c. In case where the adsorbed film is viscously locked to the substrate and the elastic modulus is unchanged, the change in sound velocity *v is written as *v 1 *o "! , 2o v
(1)
where o is the density of the pellet and *o is the density change due to the absorbed film. When the film decouples from the vibration of the sound wave of the substrate, the sound velocity increases due to the decrease in the effective density of adsorbed film *o. To study the decrease in velocity due to the adsorbate on hectorite, we first measured the velocity change of the pellet adsorbed with various amounts of nitrogen at 77 K. Nitrogen adsorbed on hectorite is believed to be solid-like, and is viscously locked to the surface of hectorite. As determined by Eq. (1), the velocity decrease with increasing coverage was well fitted by a straight line. However, the slope of this line was about 60% less than that estimated by Eq. (1) because of the weak bonds of hectorite grains in the pellet. The sound velocity and attenuation of the typical helium coverages are shown in Figs. 1 and 2. The temperature dependence of zero-helium coverage was subtracted from these data. It is found that the decrease of the sound velocity from zero-helium coverage around 10 K is proportional to the density change *o due to helium adatoms and was about 60% less than the estimation by Eq. (1) without respect to either He or He. Comparison with the results of nitrogen allows us to conclude that helium adatoms are viscously locked to the surface of hectorite. (At higher temperatures, the sound velocity approached that of zero-helium coverage because of the desorption of helium adatoms.)
Fig. 1. Typical data of the variation of the sound velocity of a hectorite pellet adsorbed with both He (lower) and He (upper) submonolayer film. The areal density of helium films is in the figure. The curves represent the calculation of the Debye relaxation.
When the temperature was lowered, we observed a rapid increase in sound velocity accompanied with the attenuation. As discussed in Ref. [4], to study the temperature dependence of the sound velocity and attenuation due to decoupling, we consider the Debye relaxation written as Auq *a" , 1#uq
(2)
*v A " , (3) v 1#uq where A and A are constants and u is the angular frequency of ultrasound. We assume that the relaxation time q obeys the Arrhenius relation q"q exp(E/¹). Here, the relaxation time q is
372
M. Hieda et al. / Physica B 263—264 (1999) 370—372
reported the adsorption and motional state of helium on hectorite by measurements of the isosteric heat and heat capacity. In the low density region, helium adatoms are localized in the dips of the registered site as a commensurate layer, while in the high-density region they form an incommensurate layer. Thus, we consider that the observed stepwise change is attributable to the structure change of the helium film. We explained the observed behavior due to the decoupling of adsorbed helium film. There may be some other mechanisms that account for the present results: for example, the internal friction in the film could cause the Debye relaxation. However, it seems that these dissipative mechanisms cannot explain the amount of increase in sound velocity at low temperatures. In summary, we measured the sound velocity and attenuation of a two-dimensional mesoporous hectorite pellet adsorbed with He and He. The sound velocity of the pellet adsorbed with helium films increased drastically at low temperatures accompanied by the attenuation. The most plausible explanation for this behavior is that helium films decouple from the vibrating substrate at low temperatures. Fig. 2. Typical data of the variation of the attenuation of a hectorite pellet adsorbed with both He (triangles) and He (circles) submonolayer film.
References
associated with the film-substrate momentum transfer. The temperature dependence of the sound velocity and attenuation of both He and He was found to be well described by the Debye relaxation over the whole submonolayer coverage. Furthermore, we found that E and q show a stepwise change with respect to the coverage. Wada et al. [6]
[1] B. Bhushan, J.N. Israelachvili, U. Landman, Nature 374 (1995) 607. [2] C. Daly, J. Krim, Phys. Rev. Lett. 76 (1996) 803. [3] J. Krim, in: H. Taub et al. (Ed.), Phase Transitions in Surface Films 2, Plenum, New York, 1991, p. 169. [4] P. Mohandas, C.P. Lusher, V.A. Mikheev, B. Cowan, J. Saunders, J. Low Temp. Phys. 101 (1995) 481. [5] K. Torii, T. Iwasaki, Y. Onodera, K. Hatanaka, Chemistry of Microporous Crystals, Kodansha, Tokyo, 1991, p. 81. [6] N. Wada, A. Inoue, H. Yano, K. Torii, Phys. Rev. B 52 (1995) 1167.