Equilibrium helium film in the thick film limit

For the thickness of a liquid or solid quantum film, like liquid helium or solid hydrogen, there exist still open questions about how the film thickness develops in certain limits. One of these is the thick film limit, i.e., the crossover from the thick film to bulk. We have performed measurements i...

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Datum:	2003
Hauptverfasser:	Klier, J., Schletterer, F., Leiderer, P., Shikin, V.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2003
Schriftenreihe:	Физика низких температур
Schlagworte:	Physics in Quantum Crystals
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/128915
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Zitieren:	Equilibrium helium film in the thick film limit / J. Klier, F. Schletterer, P. Leiderer, V. Shikin // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 957-960. — Бібліогр.: 6 назв. — англ.

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spelling	irk-123456789-1289152018-01-15T03:03:38Z Equilibrium helium film in the thick film limit Klier, J. Schletterer, F. Leiderer, P. Shikin, V. Physics in Quantum Crystals For the thickness of a liquid or solid quantum film, like liquid helium or solid hydrogen, there exist still open questions about how the film thickness develops in certain limits. One of these is the thick film limit, i.e., the crossover from the thick film to bulk. We have performed measurements in this range using the surface plasmon resonance technique and an evaporated Ag film deposited on glass as substrate. The thickness of the adsorbed helium film is varied by changing the distance h of the bulk reservoir to the surface of the substrate. In the limiting case, when h → 0, the film thickness approaches about 100 nm following the van der Waals law in the retarded regime. The film thickness and its dependence on h is precisely determined and theoretically modeled. The equilibrium film thickness behaviour is discussed in detail. The agreement between theory and experiment is very good. 2003 Article Equilibrium helium film in the thick film limit / J. Klier, F. Schletterer, P. Leiderer, V. Shikin // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 957-960. — Бібліогр.: 6 назв. — англ. 0132-6414 PACS: 67.70.+n, 68.15.+e, 68.43.-h, 68.55.-a http://dspace.nbuv.gov.ua/handle/123456789/128915 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Physics in Quantum Crystals Physics in Quantum Crystals
spellingShingle	Physics in Quantum Crystals Physics in Quantum Crystals Klier, J. Schletterer, F. Leiderer, P. Shikin, V. Equilibrium helium film in the thick film limit Физика низких температур
description	For the thickness of a liquid or solid quantum film, like liquid helium or solid hydrogen, there exist still open questions about how the film thickness develops in certain limits. One of these is the thick film limit, i.e., the crossover from the thick film to bulk. We have performed measurements in this range using the surface plasmon resonance technique and an evaporated Ag film deposited on glass as substrate. The thickness of the adsorbed helium film is varied by changing the distance h of the bulk reservoir to the surface of the substrate. In the limiting case, when h → 0, the film thickness approaches about 100 nm following the van der Waals law in the retarded regime. The film thickness and its dependence on h is precisely determined and theoretically modeled. The equilibrium film thickness behaviour is discussed in detail. The agreement between theory and experiment is very good.
format	Article
author	Klier, J. Schletterer, F. Leiderer, P. Shikin, V.
author_facet	Klier, J. Schletterer, F. Leiderer, P. Shikin, V.
author_sort	Klier, J.
title	Equilibrium helium film in the thick film limit
title_short	Equilibrium helium film in the thick film limit
title_full	Equilibrium helium film in the thick film limit
title_fullStr	Equilibrium helium film in the thick film limit
title_full_unstemmed	Equilibrium helium film in the thick film limit
title_sort	equilibrium helium film in the thick film limit
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2003
topic_facet	Physics in Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/128915
citation_txt	Equilibrium helium film in the thick film limit / J. Klier, F. Schletterer, P. Leiderer, V. Shikin // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 957-960. — Бібліогр.: 6 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT klierj equilibriumheliumfilminthethickfilmlimit AT schlettererf equilibriumheliumfilminthethickfilmlimit AT leidererp equilibriumheliumfilminthethickfilmlimit AT shikinv equilibriumheliumfilminthethickfilmlimit
first_indexed	2025-07-09T10:13:29Z
last_indexed	2025-07-09T10:13:29Z
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fulltext	Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 957–960 Equilibrium helium film in the thick film limit J. Klier, F. Schletterer, and P. Leiderer Department of Physics, University of Konstanz, Konstanz D-78457, Germany V. Shikin Institute of Solid State Physics of the Russian Academy of Sciences Moscow District, Chernogolovka 142432, Russia E-mail: shikin@issp.ac.ru For the thickness of a liquid or solid quantum film, like liquid helium or solid hydrogen, there exist still open questions about how the film thickness develops in certain limits. One of these is the thick film limit, i.e., the crossover from the thick film to bulk. We have performed measure- ments in this range using the surface plasmon resonance technique and an evaporated Ag film de- posited on glass as substrate. The thickness of the adsorbed helium film is varied by changing the distance h of the bulk reservoir to the surface of the substrate. In the limiting case, when h � 0, the film thickness approaches about 100 nm following the van der Waals law in the retarded re- gime. The film thickness and its dependence on h is precisely determined and theoretically mo- deled. The equilibrium film thickness behaviour is discussed in detail. The agreement between the- ory and experiment is very good. PACS: 67.70.+n, 68.15.+e, 68.43.-h, 68.55.-a Introduction The thickness of a liquid film grown under com- plete wetting conditions on a horizontal substrate is an important parameter for many areas of condensed matter physics, especially for surface science studies. This film thickness, under thermodynamical equilib- rium conditions (i.e., in coexistence with its saturated vapour pressure), is very dependent on the distance of the bulk liquid level to the surface of the substrate, see Fig. 1. The existing description of thick adsorbed films [1,2] generally deals with van der Waals forces. In the case when retardation plays a role the depend- ence of the film thickness, d, is d h� �1 4. (1) However, the singularity in definition (1), when h � 0, is not physical, i.e., d would go to infinity al- though the bulk level is just at the height of the sub- strate (see Fig. 2). This shows that this limiting case has to be described more accurately, see below. There are some alternative interpretations to the van der Waals dependence of d(h). One of them can be formulated as the meniscus problem. It is well known that the vertical substrate walls can lift some amount of the liquid above the bulk level due to the competition between Laplace force and gravitational force [3], a scenario known as suspended films. The same mechanism could, in principle, be responsible for the creation of a macroscopically thick liquid film when h � 0 without the participation of van der Waals forces (see Figs. 3,4). In addition to the theoretical discussion we have performed precise measurements of the thickness of a © J. Klier, F. Schletterer, P. Leiderer, and V. Shikin, 2003 d substrate bulk liquid level thin liquid film (+) h ( )� h Fig. 1. The thickness of a thin liquid film, d, completely wetting a horizontal substrate and being in coexistence with its saturated vapour pressure, i.e., in the presence of bulk liquid. The distance between the substrate and the bulk liquid level is h. liquid helium film on a silver substrate using the sur- face plasmon technique [4]. The experimental depend- ence of d(h), for h � 0, follows the corrected van der Waals scenario. Theoretical description 1. First we will consider the general van der Waals scenario for the behaviour of d(h). If the substrate, on which a helium film is adsorbed, is perfect (i.e. ideally flat), then the definition of the thickness of this film, d, in the van der Waals approximation is given by k d d hw� � � � � � 4 . (2) Here kw is the van der Waals constant including re- tardation. For the definition of h see Fig. 1. Typical values of kw are of the order 10 6 5 4� cm [5]. Under the conditions h > 0, the solution of Eq. (2) with respect to d is possible provided h d� . So we get d � h k h w� � � � � � 4 , for h k h w � � � � � 4 . (3) At the special point h = 0, i.e., when the bulk level is at the height of the substrate, we have k d dw 0 4 0 � � �� , or d kw0 4 5 . (4) For the bulk helium level below the substrate, i.e., when h < 0, we get k d hw� � � � � � 4 , for h < 0 . (5) The predicted behaviour of d(h) in the van der Waals approximation is presented in Fig. 2. 2. The lift of the thin liquid film by the bulk menis- cus is estimated using the geometry shown in Fig. 3. The calculations, like in Ref. 3, show that h a a g lv menis with � ( sin )1 21 2 2� � � . (6) Here � is the liquid density, g the acceleration due to gravity, � lv the liquid helium surface tension, and a the capillary length. It becomes evident that for the limiting case � � � 2 then h amenis �� . Therefore, a lift of the liquid by the meniscus in case of an ideal wetted horizontal substrate is not effective. 3. However, if the solid substrate is not flat (which is usually the case), then there is another channel for a 958 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 J. Klier, F. Schletterer, P. Leiderer, and V. Shikin d h 0 –1/4d log h d0 h = 0 substrate Fig. 2. The dependence of d(h) in the van der Waals ap- proximation (qualitatively), considering Eqs. (4) and (5) in a semi-log scale. The dashed line indicates the behav- iour of d(h) if it is only described by Eq. (1). The inset illustrates the limiting case when h = 0, and so the thick- ness of the adsorbed film is d0. substrate h 0 z menis � bulk liquid level thin liquid film Fig. 3. A tilted substrate, with tilt angle � which is par- tially immersed in bulk liquid. The upper part of the sub- strate, i.e., for h > 0, is covered by a thin liquid film. How- ever, just above the value h = 0 the liquid film is lifted by the meniscus forming between the substrate wall and the bulk liquid level. The height hmenis up to which the film is governed by the meniscus, is described by Eq. (6). thick He-film b a (+)h corrugation topsthin He-film R 2�0 �0 bulk liquid helium 0 ( )� h S Fig. 4. A schematic sketch of a corrugated surface where, due to the meniscus effect, a suspended thick liquid helium film can be formed. The symbols are explained in the text. d(h) dependence. This arises also from the meniscus effect [3]. Now we will formulate this dependence for a corrugated perturbation of the surface of the solid substrate, see Fig. 4. In this case we have � � � � d h S h a b a a b d h( ) ( ) ~ ( ), (7) where S b lR b R � � �2 1 20 0� �[ ( )] (8) and l b �2 0 16 3 � , �0 2 2 4 � �R R b , R h gh lv( ) 2� � . (9) Here ~ ( )d h represents the van der Waals contribution, from Eq. (5), in <d>. Under the condition R(h) >> b the value S(h), Eq. (8), is not sensitive to h, and so the dependence d(h) can be presented as � d h( ) � d d h a a bcor � � ~ ( ) , with dcor � 2 0� b a b� , (10) with the asymptotic behaviour of ~ ( )d h as k d w ~ ( )0 4 � � � � � � � �0 0� ~ ( )d for h � 0, (11) k d h w ~ ( ) � � � � � � 4 � h for h d � ~ ( )0 0� . (12) One can see that the meniscus effect S(h) in <d(h)> can be dominant if �0 0 d , where d0 is from Eq. (4). It can also be sensitive to h if the Laplace ra- dius R(h) is comparable with the characteristic of the corrugation b. In the opposite limit, Eq. (10), the presence of roughness of the solid substrate (more pre- cisely — solid corrugation) leads to a shift of the film thickness in the dependence <d(h)>. Experimental verification In order to check above predictions for the limiting case when h � 0 we have performed preliminary mea- surements of the thickness of a growing 4He film. As experimental technique we used a surface plasmon (SP) resonance setup which allows for a resolution of the helium film thickness of about 1 Å, see Ref. 4. The surface plasmons are excited, using a monochromatic light source, at the interface of a thin quench-con- densed Ag film, deposited on a glass prism, and the adsorbed helium film, see Fig. 5. This light beam is re- flected at the prism and the reflected light is measured with a very sensitive photodiode (for a more detailed description of such a setup see Ref. 6). Under reso- nance conditions, i.e., when the angle of incidence corresponds to the surface plasmon resonance angle, little or no light is detected. Keeping this resonance conditions via a feedback loop the thickness of the ad- sorbed helium film can be measured. The thickness of the helium film is determined as function of the bulk helium level. This bulk level is changed in small steps by slowly condensing in helium gas from a known volume. It turns out that the relax- ation times to achieve a stable bulk level is of the or- der of hours. The experiment is performed at 1.4 K, i.e., when the helium is superfluid. The height of the bulk level is measured with a cylindrical capacitor, see Fig. 5, which gives a resolution of about 50 �m. This height measurement is cross-checked by the total vol- ume of gas added to the cell and a precise check of the cell volume and the inside geometry after the experi- ment. In Fig. 6 we show the growth of the helium film starting from a bulk level of (–) h = 0.5 cm below the surface of the substrate. At this point the thickness of the helium film d is about 73 nm. As the bulk level is raised the film thickness grows showing a h�1 4 de- pendence as described by Eq. (10)–(12). Within these Equilibrium helium film in the thick film limit Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 959 C G L PD S S Ag-film Fig. 5. The scketch of the experimental cell. An incoming light beam from a monochromatic source L is reflected from a mirror S towards the face of a glass prism G. From there the reflected light is detected by a sensitive photodiode P. The adsorbed helium is measured on top of a thin 40 nm thick Ag film evaporated onto the glass prism. The bulk he- lium level (not shown) is measured via a cylindrical capaci- tor C standing vertically inside the cell. Temperature equi- librium is checked both by a thermometer mounted onto the prism surface and via the vapour pressure measured with a high resolution pressure gauge outside the cryostat. results we can fit our experimental data. When fitting the data in the interval 0.1 cm < (–) h < 0.3 cm, using Eq. (10), the agreement is quite good, see Fig. 7, and the parameter dcor can be obtained. It turns out that dcor nm� 49 and so (if we assume that a b� ) we get �0� dcor nm 49 . We interpret this observation due to the fact that the surface must be very rough, but without Gaussian peaks, and so there is bulk condensation between some roughness peaks which adds to the measured film thickness. That our surface was indeed quite rough was seen in the measured SP resonance curves which showed a large resonance width, much wider than for an ideal smooth Ag-film. However, once the adsorbed helium film is thicker than the height of the roughness peaks its influence is screened and so a further growth in film thickness should show the ideal behaviour, seen in the data for h � 0. The influence of substrate roughness in the film thickness of adsorbed films will be investigated and presented elsewhere. When h drops below 0.1 cm the measured data de- viate from the above law, see Fig. 6. Eventually the film thickness levels off at around 100 nm, see Fig. 7. Using Eq. (11) and kw � � �6 4 10 7. cm5 4 one gets for ~ ( )d 0 102� nm. From Eq. (10) we get d( )0 � dcor � � 0 5 0 100. ~ ( )d nm, which corresponds well to the ex- perimental value for h � 0. Conclusions We have investigated the growing of an adsorbed liquid film d on a substrate as function of the distance between the bulk liquid level and the surface of the substrate h which is above the bulk level. The calcula- tions of the thickness of such a film are given for the thick film limit, i.e., when h � 0 and under retarda- tion conditions, on ideal smooth surfaces. These pre- dictions are confirmed by measurements of a liquid he- lium film adsorbed to a silver surface. Both the thickness of the helium film and the change in the bulk helium level are measured with high resolution in the range of 70 nm < d < 100 nm for 0.5 cm > (–) h > 0. Experiments to study the cross-over from the retarded to the non-retarded regime are currently running. The influence of substrate roughness on adsorbed quantum films is also under investigation, both theoretically and experimentally. This work was supported by the DFG-Schwerpunkt ‘Wetting and Structure Formation at Interfaces’ un- der Kl 1186/1. 1. H.B.G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948). 2. L.W. Bruch, M.W. Cole, and E. Zaremba, Physical Adsorption: Forces and Phenomena, Clarendon Press, Oxford (1997); and references therein. 3. L.D. Landau and E.M. Lifshitz, Hydrodynamics, Akademie Verlag, Berlin (1991). 4. D. Reinelt, J. Klier, and P. Leiderer, J. Low Temp. Phys. 113, 805 (1998). 5. E.Y. Andrei, Phys. Rev. Lett. 52, 1449 (1984). 6. V. Iov, J. Klier, and P. Leiderer, J. Low Temp. Phys. 126, 367 (2002). 960 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 J. Klier, F. Schletterer, P. Leiderer, and V. Shikin 0.01 0.1 80 90 100 , d H e -fi lm n m (�) h, cm Fig. 7. The same data points of d plotted against h as in Fig. 6, however now on a semi-log plot. The deviation from the expected h–1/4 behaviour (solid line) for small values of h is clearly seen. The thickness of the helium film approaches a final value of around 100 nm. This is the predicted behaviour shown in Fig. 2, and described by Eqs. (4) and (5). 0. . . . . .0 0 1 0 2 0 3 0 04 5 70 80 90 , 100 d H e -fi lm n m (�) h, cm Fig. 6. The thickness of the adsorbed helium film, d, as func- tion of the varying bulk helium level, h. Here h is already very small and so the dependence of d follows the h–1/4 law (solid line) for h � 0.06 cm, see text. For smaller values of h i.e. < 0.1 cm the film thickness deviates from this law.

Equilibrium helium film in the thick film limit

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