Triple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is a well-known phenomenon. This property persists even for the mixed system of H₂ and D₂. There exists an effective triple-point temperature T₃⁽mix⁾ , between the T₃ of pure H₂ and the one of pure D₂, which depends on the species concentrations. We present new investigations for a wide range of H₂–D₂ concentrations measured under different thermodynamic conditions. This allows us to map out T₃⁽mix⁾ as function of concentration, which can be different in the melting or solidifying direction. Furthermore, it turns out that the time the system needs to reach an equilibrium state can be very long and depends on concentration. This is not observed for the pure H₂ and D₂ system. Sometimes the relaxation times are so extremely long that significant hysteresis occurs during ramping the temperature, even if this is done very slowly on a scale of hours. This behavior can be understood on the basis of mixing and demixing processes. Possible differences in the species concentrations in the gas, liquid, and especially solid phase of the system are discussed. A preliminary phase diagram of the H₂–D₂ system is established

Klier, Jürgen

Leiderer, Paul

Sohaili, Masoud

Tibus, Stefan

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 970–974Influence of the concentration of H2–D2 mixtures on theirtriple-point dewetting behaviorStefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul LeidererDepartment of Physics, University of Konstanz, Konstanz D-78457, GermanyE-mail: Stefan.Tibus@uni-konstaz.deTriple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is awell-known phenomenon. This property persists even for the mixed system of H2 and D2. Thereexists an effective triple-point temperature T3( )mix , between the T3 of pure H2 and the one of pureD2, which depends on the species concentrations. We present new investigations for a wide rangeof H2–D2 concentrations measured under different thermodynamic conditions. This allows us tomap out T3mix( ) as function of concentration, which can be different in the melting or solidifyingdirection. Furthermore, it turns out that the time the system needs to reach an equilibrium statecan be very long and depends on concentration. This is not observed for the pure H2 and D2 sys-tem. Sometimes the relaxation times are so extremely long that significant hysteresis occurs duringramping the temperature, even if this is done very slowly on a scale of hours. This behavior can beunderstood on the basis of mixing and demixing processes. Possible differences in the species con-centrations in the gas, liquid, and especially solid phase of the system are discussed. A preliminaryphase diagram of the H2–D2 system is established.PACS: 67.70.+n, 67.70.–s, 64.70.Dv, 64.75.+g1. IntroductionWetting of solid substrates, exposed to a gas in ther-modynamic equilibrium, is an ubiquitous phenomenonwith both fundamental aspects [1,2] and important ap-plications [3–5]. Microscopically the wetting of a sub-strate by a liquid film is caused by a strong sub-strate-particle attraction mediated by van der Waalsforces. At present an almost complete microscopic un-derstanding of wetting on a well-defined solid sub-strate is available [1,2,6]. The main prediction of allthese studies, for given thermodynamic parameterssuch as temperature and pressure, is that the thicknessof the liquid film is a function of the substrate-particleand interparticle interactions. In other words, if thevan der Waals force between substrate-adsorbate be-comes stronger than the interparticle interaction thencomplete wetting of the substrate, i.e., diverging of thethickness of the liquid layer at the coexistence line isexpected. Dewetting will occur if the attraction isweak. In the latter case the growing of the liquid filmwill become energetically unfavorable and dewettingwill take place by forming droplets on a very thin (afew atomic layers) liquid film on the substrate. In thesolid phase, however, even in the case of strong sub-strate-adsorbate interaction dewetting occurs due to thelateral stress induced by substrate roughness [7,8]. Thisleads to the T3 dewetting as observed in our systems.In this work, we have investigated the wet-ting-dewetting of both pure and binary system of H2and D2 on a gold substrate. Applying D2 as impuritycomponent in the H2–D2 dilute mixture was moti-vated by both its similar structure to H2 and its differ-ent physical properties from H2. Moreover, D2 is aslightly weaker wetting agent in the solid phase thanH2 [9] and has a relatively small zero-point motion (incomparison with H2 negligible [10]). Therefore the in-teraction between molecules and substrate atoms is tobe different for H2 and D2. Regarding substrateroughness our experiments are in a range where thedifference between the two isotopes (in their pureform) is negligible. We discuss how the concentrationof D2 modifies the effective triple-point of thetwo-component system.2. Experimental procedureAll the experiments presented here were performedby utilizing the surface plasmon spectroscopy, whichallows to determine the layer thickness of an adsorbed© Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leiderer, 2003medium with high resolution (up to a few tenths of amonolayer). The substrate in our measurements was agold film (45 nm thick) evaporated onto the base of aglass prism. The experimental setup is shown inFig. 1, more details can be found in Ref. 11. However,the signal processing in comparison to the previous ex-periments has improved, therefore it resulted in moreprecise measurements giving results with improved ac-curacy. The system was fully computer controlled, so,e.g., parameters like temperature could be swept upand down in time very slowly in small steps. This wasdone several times to check for reproducibility of themeasured data. The height and width of the rampingsteps, as will be discussed in the results, were chosen,firstly, according to the normal relaxation of the sys-tem under investigation and, secondly, to fulfill theequilibrium thermodynamic conditions during theexperiment.3. ResultsPresented here are the results of wetting-dewettingmeasurements of both pure H2 and D2 as well as mix-tures of both isotopes. As typical examples for themixed systems we discuss 10 and 50 % D2 samples.The numbers are molar-percentages of D2 in the mix-ture of H2 and D2, and the samples were prepared asfollows: after taking an adsorption isotherm of H2 at16 K and then raising the temperature to 19 Kfollowed an adsorption isotherm of D2 in order toreach a certain concentration ratio. Afterwards,ramping the temperature in the range of 10 to 20 Kwas done. In Fig. 2 the T3 dewetting of pure H2 andD2 and the effective triple-point wetting-dewetting ofthe mixture of them are plotted. It is observed that foreach mixed system the cooling and warming curves re-veal a large hysteresis, which is not found for the pureH2 and D2 temperature runs. The hysteresis reveals tobe solid and stable.The triple-point temperatures for pure H2 and D2are 13.85 and 18.55 K, respectively. These tempera-tures, which indicate the onset of dewetting, showwithin an accuracy of 50 mK no significant hysteresis.For the 10 %-doped system, the dewetting (cooling)and wetting (warming) temperatures are 14.30 and14.65 K, respectively. For the 50 %-doped system thedewetting and wetting temperatures are 16.75 and17.30 K, respectively. In order to examine the genuine-ness of the hysteresis, another 50 % mixture of H2–D2was prepared, but this time at room temperature.Thereafter the adsorption isotherm of the mixture wastaken at 20 K. Furthermore three complete cycles, i.e.,cooling from 20 K down to 10 K and return with stepsof 25 mK/min and a resolved time of 2 min betweentwo successive steps, were done. Figure 3 summarizesthe results. A hysteresis of essentially the same widthexists even when doing the measurements at lowerInfluence of the concentration of H2–D2 mixtures on their triple-point dewetting behaviorFizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 97110 12 14 16 18 2050100150 pure H 2mix.1, coolingmix.1, warmingmix. 2,coolingmix. 2,warmingpure D213.85K14.30K14.65K16.75K17.30K18.55KT, Kd,Å0Fig. 2. The dewetting curves (film thickness d againsttemperature) of pure H2 (), pure D2 (), cooling ()and warming () of 10 %-doped mixture (mix. 1), andcooling () and warming () of 50 %-doped mixture(mix. 2). For pure systems the cooling and warmingcurves trace the same path. Arrows show the positions to-gether with the values of the wetting transition, i.e., theeffective T3.CryostateGoldsurfacesteppingmotorto minimumof resonanceSMCU2Lock-inamplifierDetectorResonanceangleResonancewidthSMPBimorph+Fig. 1. Experimental setup: Surface plasmon resonance isenhanced at the interface of a gold substrate and an ad-sorbed medium. The angle of the incident light is modu-lated by means of a bimorph. Via a lock-in amplifier theintensity signal is coupled back to a stepping motor con-trol unit (SMCU) so that the angle of minimum intensity(i.e. resonance) is kept. From the shift in angle relative tothe bare gold surface the thickness of an adsorbed film canbe determined.ramping speeds, e.g., 10 mK/min. We should mentionthat during the first scan the hysteresis appeared in amore pronounced way as shown in Fig. 3.In the inset of Fig. 3 the associated vapour pressurecurves are plotted. It shows that the slope of eachcurve levels off somewhere in the middle of the curveand rises again. The effective triple-points of wettingand dewetting occur exactly at the point of the lowerkink for both cooling and warming curves. In order tounderstand this behavior, in Fig. 4 we have redrawnthe supplementary vapour pressure curves of Fig. 2.The solid curves, placed between the vapour pressurecurves of pure H2 and D2, are calculated pressurecurves of the binary systems of H2–D2 with differentconcentrations of D2 derived from the partial pressurelawP T C P T C P Ttotal D D D H( ) ( ) ( ) ( )  2 2 2 21 , (1)where CD2 is the D2 concentration in the mixture andP TD2 ( ) and P TH2 ( ) are the pressure of H2 and D2 atgiven temperature T, respectively. Having obtainedthese values, one can calculate the total pressure ofthe mixture under the assumption that the concentra-tion of the species remains constant in the solid, li-quid and gas phase. It is known, that even for anideal binary mixture this condition does not hold, andthe data plotted in Fig. 4 illustrate this deviation.The data demonstrate that the concentration of D2 inthe liquid phase increases as the temperature raisesand vice versa. Furthermore, the size of the hysteresisand the deviations from the predicted standard curvesdepend on the concentration of the D2 phase in themixture. The size of the hysteresis is largest for con-centrations around 50 % and diminishes with increas-ing fraction of either species.Using Eq. (1), one can extract the D2 concentra-tion in the liquid phase from the measured vapourpressure curves of the pure H2, D2, and the mixture ofthem. So we haveCP T P TP T P TDmix HD H222 2( ) ( )( ) ( ), (2)where P Tmix( ) is the vapour pressure of the mixtureat a given temperature. Figure 5 displays the evolvingof the D2 concentration in the liquid phase of the twopreviously introduced sets of mixtures (see Figs. 2and 4). The solid line, which is extended between theT3’s of the pure H2 and D2, is a fit to the transitionline obtained from Fig. 6. The small dips in thecurves, near 13.85 K, occur precisely at the positionof the T3 of pure H2. The concentration of D2 in theliquid phase increases gradually as the temperaturerises and vice versa. The noticeable effect is the steepincrease (decrease) of D2 concentration along thetransition line during warming (cooling) of the sys-tem. In summary, in Fig. 6 the effective triple-pointsof all the investigations are plotted against the D2concentration in the liquid phase. The curve fitted tothe data shows that the behavior of the wet-ting-dewetting temperature against the liquid concen-tration of D2 is not linear. (It should be pointed outthat the effective T3 values of both heating and cool-ing, T3( )up and T3( )down , lie on this curve.)The observed behavior can be interpreted by takinginto account the temperature dependent differences inconcentration in the gaseous, liquid and solid phasesinside the sample cell. Let us consider, e.g., a mixturewith a nominal D2 concentration of 50 %: i) When we972 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leidererd,Å10050010 12 14 16 18 20T,  KT,  K16 17 18 19100200300P, mbarWetting transitionHysteresisdiminishesafter 1 stcooling butdoes notvanishwarmingcooling1st cooling1st warmingwarming2ndcooling2nd3rd3rdFig. 3. The dynamics of an equimolar mixture of H2–D2is shown by monitoring the film thickness d over tempera-ture. The temperature scans are done three times. The bighysteresis during the first cooling and warming is attri-buted to incomplete mixing. The inset shows the associ-ated vapour pressure curves.pure H22pure D14 16 18T,  K100200P,  mbarsatmix.1,warmingmix.2,warmingisoconcentrationsmix. 1, coolingmix. 2, coolingFig. 4. The corresponding vapour pressure curves ofFig. 2. The solid lines are calculated vapour pressurecurves (Eq. (1)) for different concentrations of D2. PureH2 and D2 pressure curves are also plotted.start at high temperature at gas-liquid coexistence, athick liquid wetting film will be present on the sub-strate, as it is observed in our measurement. As thetemperature is lowered and the liquidus curve of themixture is reached (at  17 K in this case [12]), solidwill start to form at the bottom of the sample cell,with a concentration distinctly higher than 50 %(given by the solidus curve at that temperature).Upon decreasing T further, the D2 concentration inthe remaining liquid — both at the bottom of the cell,and on the surface where we measure the film thick-ness — drops, until eventually all bulk liquid hascrystallized. At that point (T3( )down ) the drop in filmthickness, characteristic of T3 dewetting, starts totake place. ii) For a run starting at low temperature,on the other hand, the bulk solid has — due tohomogenization at T > 12 K [12] — a homogeneousconcentration of about 50 % throughout the wholesample. Upon increasing T the first bulk liquid will ap-pear in the cell when the solidus curve is met (15.5 Kin this case). However, only at higher temperature thethickness of our film, when in coexistence with bulkliquid of the right concentration, will have reached its«complete wetting value» of about 100 Å, identifyingT3( )up . Since T3( )down and T3( )up do not coincide, due tothe paths in the phase diagram as described, a hyster-esis results, as it is in fact observed.4. ConclusionsIn summary we have shown that mixtures of thesimple van der Waals adsorbates of hydrogen isotopesare well-suited for investigations of the wetting be-havior of binary systems. In pure H2 and D2 the ad-sorbed films display the phenomenon of triple-pointwetting (i.e., dewetting sets in rapidly as the tempera-ture is decreased below T3), and we have studied howthis behavior is affected, when instead of a one-com-ponent system a mixture of H2 and D2 is used (wherestrictly speaking a triple-point does not exist). It isfound that the feature typical for triple-point wetting— the rapid drop in film thickness below T3 — per-sists, but the characteristic onset temperature is differ-ent for cooling and for heating, in contrast to pure sys-tems. We attribute this hysteretic behavior to thedifferent concentrations of the hydrogen isotopes inthe solid, liquid and gas phases, respectively. Our re-sults suggest that the method applied here does notonly yield insight into the wetting behavior of mixedsystems, but a further analysis of the data should alsoprovide detailed information on the phase diagram ofH2–D2 mixtures.AcknowledgmentsThis work is supported by the DeutscheForschungsgemeinschaft under grant Le 315/20within the Priority Program «Wetting and StructureFormation at Interfaces».1. S. Dietrich, in: Phase Transitions and CriticalPhenomena, C. Domb and J. Lebowitz (eds.),Academic Press, London (1988), Vol. 12.2. R. Evan, in: Liquids at Interfaces, Proceeding of theLes Houches Summer School, Session XLVII, J. Char-volin, J. F. Joanny, and J. Zinn-Justin (eds.),Elsevier, Amsterdam (1990).3. H. Gau et al., Science 283, 46 (1999).4. K. Kargupta and A. Sharma, Phys. Rev. Lett. 86,4536 (2001).Influence of the concentration of H2–D2 mixtures on their triple-point dewetting behaviorFizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 97312 14 16 18020406080T,  KCD2T of  H23mix.1, coolingmix.1, warmingmix. 2, coolingmix. 2, warmingtransition lineFig. 5. The rising (falling) of the D2 concentration in theliquid phase (Eq. (2)) during warming (cooling) for thetwo mixtures, as presented in Fig. 2. Along the transitionline the rising is rather steep, which in turn is the sign ofwetting (dewetting) when warming (cooling).0 20 40 60 80 100cD2, liquidT3, H2T3, D21416 1618 18T,  KT c3( )transition line14T = A + Bc + Cc3 D2 D22T,  KFig. 6. The experimental data of the effective triple-pointsof all the investigated mixtures as well as the ones for pureH2 and D2. The solid curve is a fit to the data, with A == 13.83 (which is the T3 of H2), B = 6.366 10–2, and C == –1.646 10–4.5. J. Bico, C. Marzolin, D. Quéré, et al., Europhys.Lett. 47, 220 (1999).6. S. Dietrich and M. Schick, Phys. Rev. B33, 4952(1986).7. F.T. Gittes and M. Schick, Phys. Rev. B30, 209(1984).8. A. Esztermann, M. Heni, and H. Löwen, Phys. Rev.Lett. 88, 055702 (2002).9. G. Mistura, H.C. Lee, and M.H.W. Chan, J. LowTemp. Phys. 96, 221 (1994).10. D.L. Demin, N.N. Grafov, V.G. Grebinnik, V.I.Pryanichnikov, A.I. Rudenko, S.A. Yukhimchuk, andV.G. Zinov, J. Low Temp. Phys. 120, 45 (2000).11. M. Sohaili, J. Klier, and P. Leiderer, J. Low Temp.Phys. 122, 249 (2001).12. M.A. Strzhemechny, A.I. Prokhvatilov, G.N.Shcherbakov, and N.N. Galtsov, J. Low Temp. Phys.115, 109 (1999).974 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leiderer

Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior

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Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior

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