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Thermal accommodation coefficients of neon and krypton on gas covered platinum
CIILhI1CAL I’IIYSICS LLITERS
Volurnc 48, number 3
THERMAL
ACCOMMODATION
ON GAS COVERED
COEFFICIENTS
I.5 June 1977
OF NEON AND KRYPTON
PLATINUM
Rccc~vcd 13 l)eccmbcr 1976 Kcviwd mxnwr~pt rcwvcd 28 hlsch
1977
A hot z~rc column type instrument i\ cmploycd to determme the thermal :lccommod&wn coeffuzicnt, P, of nwn .md krypton on :1gas covered platmum wrc in the tcmpcraturc range of 4OO-- 1400 K. The Q valucc are detcrruincd from hc,lt tr.m%fcr rate mcawrcmcnts taken in the temperature-Jump regime ‘I’he tc\t surf.sc was covcrcrl L& itb o\ygtin by scvcr~1 huatlng cycks rcxhlng up to Jbout 1400 K at an ovygcn pdrtlnt pressure of about 5 X to-” nun of mercury. h? cuparimcnhl imat tr.mcfcr data are .~ndly?cd .uxording to three dlffcrcnt procedure\ mid the resulting a valuec arc rqortcd md compared with the nvnktbk! data III the literature 1%IIILII are only m ihc ~CIII~C~.I~ZC F lnyc d &OU( 300 --SO0 K.
1 . introduction We have employed to determine in vacuum
an m~proved
the lIzat transfer
rates
column from
mstrument a heated
wire
and in the presence of a gas under continuum and temperature-jump conditions [2,3]. Thcsc papers [l-3] describe the expenmental apparatus and procedure, and data analysts schcmcs. Such details arc therefore not included here and only the relevant features characteristic of the present mvestlgntion will bc briefly mentioned. The experimental values of thermal accommodation cc,cfficient, OL,for NC-R and Kr-IY in the temperature range 400-1400 K as determined from the heat transfer rate medsurenicnts in the temperature-jump regime are reported here. Platinum is chosen due to its physical strength and mcreasing mdustrial importance specially as a surface catalyst. It IS supplied by Engelhard Industries and stated to be 99.9% pure. The neon and krypton gases, 99.95% pure,
[I J
arc supplied
by Mathescjn
Gas Products.
The
principal impurities in the neon sample itre 50 ppm helium, 1 ppm nitrogen, 1 ppm oxygen and 5 ppm hydrogen, and in the krypton sample arc 25 ppm xenon, 25 ppm nitrogen, 4 ppm oxygen, 4 ppm argon, 5 ppm hydrogen and less than 10 ppm hydrocarbons. The
platinum wire used in the column Is 30.0C 0.1rndin diameter and about 59 cm long. The experimental heat transfer data in the tl111[lCiilture-jump regime are analyrcd according to three different procedures to obtain 01values. ‘Fhe~ are the cmstant power method (CPM), constant temperature difference method (CTDXI), and the mean-free-path mcthod (MFPM). The CPM is based on the theory which has been elaborated by Harm 131 and has been used by UF earlier [3,5,6] _ III this method, the wiraz temperature, Trr , is plotted against the reciprocal of gas pressure, P, for constant values of the thermal power conducted throudi the test gas, QIt _11~ siopc of this linear plot gives a while the intercept gives the linearly extrapolate gas temperature at the wire surface, ‘Tc. The CTDM [S] IS based on the integration of the Fourier heat balance equation between the cold wall temperature, T,<,,,and T,.Accordmg to this method, the reciprocal piots of 1/Qtt versus 1/i’ for constant valuas of (T,, - T,.) arc lmear and their slopes yield Q as d function of Trr. IIou ever, in tha calculation, the impliclt assumption is mad that 7-e = TII and tills can ausc ~pprcciahfc error in p at high temperatures. The MFPM is devcIopcd by Wachmar [7] and gives 1y as a function of gas pressures and at a temperature about one mean-f&-path away from 545
Vol?lnK!48, nurrrber 3
- Since Q!is independent the hot WIM, T 5ure in the tcrnhplcirnture-jump rcginic of
CCICMICAL PHYSiCS LETTERS of 23s PM-
heat tr3nsfer
as implied in the CPM and CTDM, the MFPM providc~ a good check of the conditton of the gas--solid tnterface over the entire experm~ental tcmpcrature range. TIE QY vnlues dctcrrnmed according to above mentioned three procedures arc compared with each other and 3 single set of values are given as ;I filriction of temperature for the two systems. These Values are also ~-~mparcd with the data available 111the literature wh~h arc confined to tflc maximum temperature of about 500 K.
The hcnt tr:lnk.fer coiumn, G mm mtcrnal diameter, of the general design used earlier by Jody and Sa.uena [‘_I ISev~~~~~t~d to a pressure of about 2.5 X I#- s mm of mercury while the glass wall is mdintarned dt 3 17 K by Glculating water from 3 constarit tcmperature bath. The wire is dnncalcd for about three and a half hours at 1400 I(. This annealing process does not clenn the platrnum surface as tke adsorption of oxygen is irreversible with pressure and cannot be dcsorbed to any appreciable cxtcnt [8-l i] by such a thermal treatment. The relattvcly low melting point of ptstlnum is responsible for the latter. Further, platirzum does not adsorb mtrogc:cn [12--141, and dcsorbs hydrogen and carbon monoxide at tcmpcratutcs below about 460 K [f&IS] and G20 K [13] rcspectwely. In view of t?msc comments tt may be lnfcrred that annealing leaves probably oxygen as the dominant adsorbate on the platinum surface. Adsorbed oxygen has the ~~pab~~~tyto replace f 161 weaker adsorbates llke carbon monoxide, and this wtll also favor oxygen as the major adsorbate on the platinum surfitce. IIowever, annealing at an oxygen partial pressure of about 5.3 X 10V6 mm of mercury may not be enough to fully cover the platinum surface with a monolayer of oxygen, since as pointed out by Lewis and Gomer f9] several heating cycies arc essential to accnmphsh full covcragc. in this work, therefore, the pla[inuril wire is subjected to eight heating cycles with the Idea to achieve co~plcte covcmgc. ~nuthcr cornplication that results during this thcrmat treatment is Corn the diffusion of ttw bulk mct.zlIic impurAes to the surfaces which is fouad to be rapid above about 536
15Juno 1977
IO00 K, Brewer [17]. Once these impurities are at the surface, they can get oxidized and the resulting oxides r%iyRot be soluble in pfatinum but rather get epitaxaily attached to the surface and spread over it resulting in a substantial change in the surface condition, I_cwh and Gomcr [9). With impurities in the platinum sample amounting to about 0.1%~~appreciable surface CORta~~ijyation by oxides ic therefore anticipated. TIE heat transfer rates arc measured in vacuum, r&, and in the prcscncc of neon, Q-,-, at pressures of 1.03, 3.1 i. 6.07,8.17, 10.00 and IS.00 mm of mercury over the entrre tempcraturc range. From these, tfle thermal energy conducted by the gas, QIr, at a particular prcssure and as a function of ternpcrature is detcrruined. The plots of Ttr and ZL/Qir against 118’are found to be linear for tkc entire temperature range for pressures between 6.07 to 15.00 mm of mercury. Here 22, IS the length of the platmurn wire at the tenlpcr;lturc to wlrrcit Q~ rcfcrs. From these data, cr is computed as a function of tempcraturc (T,, TFi, TAH) according to
Fig. 1. Thermat. ~~caI~~rn~d3tion rocfftcient~ for the nwnpl,ftinum \ystorn ;1sn firnction of tcmpcraturc. Curve 1.2 ,md 3 rcpreccnt the rcwltr based on the constant power, constant temperdttrrc diffcrcnce .~nd mwn-fret-p.ath methods, rcspectivcly.
06
Volume 48, number 3
o.d400
t
I
CHEMJCAL PHYSICS LETTERS
I
I
600
I
1000
800
I
1200
1400
T,,T,,T,&W
Fig. 3. Thermal accommodation coefficients of the krypton platinum system, as a function of temperature. Curves 1, 2 and 3 represent the results based on the constant power constant temperature difference and mean-free-path methods,
respectively.
o.gl 0 0.
i 0.71 300
1 500
I 700
I 900
1100
TA,W
Fig. 4. Thermal accommodation coefficients for the kryptonplatinum system based on the mean-free-path method (o 10.02 mm Hg), (0 - 2.99 mm Hg), (0 - 0.80 mm Hg), (fi 0.5 1 mm Hg).
the three meLhods following the procedure detailed earlier [3,5]. These results are given in figs. 1 and 2. Similar measurements are taken for krypton at pressures of 0.10,0.31,0.51,0.80,2.99,10.02, 19.45 and 30.15 mm of mercury. The gas pressures in the range 051 to 10.02 are employed to calculate a values and these are given in figs. 3 and 4.
3. Discussion The 01values for both the systems, figs. 1 and 3, as obtained from the CPM (curves I) are smaller than the corresponding values from the CTDM (curve 2). The CPM values are estimated to have a percentage random error uf 3.4,3.3 and 3.0 at 400,800 and 1 100 K respectively for neon-platinum system, and 5.3, 3.6 and 2.4 at 500,800 and 1100 K respectively for kryptonplatinum system. The percentage random errors for the CTDM are 4.8, 5.5 and 4.7 at 400,800 and 1100 K respectively for the neon-platinum, and are 4.9,5.3
l5Junc
1977
and 4.8 at 500,850 and 1100 K respectively for the krypton-p!atinum system. In these calculations the error introduced in replacing Te by TH is nor account. ed. The trend and magnitude of the differences in the CYvalues for the two systems according to the two methods cannot be completely accounted by the above mentioned estimates of the random errors. A substan. tial portion of this disagreement lies in the apprctximations [3,5,6] made in the heat transfer equations while analyzing the experimental data to obtain o values. For instance in the CTDM, replacement of Tc by TH tends to increase the o vaiue and this increase will be larger at higher temperatures. Thus, this can partially explain why the ty values determined by CTDM are larger than those obtained from the CPM. From this point of view CPM values (curves 1)are preferable over the CTDU vaiues (curves 2). The MFPM of Wachman [7] is less ambiguous in this respect and gives a values as a function of temperature from heat transfer data taken at a particular pressure. In figs. 2 and 4 these different sets are reported for neon-platinum and krypton-platinum systems respectively. The percentage random errors are S-1,4.2 and 3.5 at 400, 800 and 1100 K respectively for neon-platinum, and 5.0,4.7 and 4.6 at 500,800 and 1100 K respective/y fur krypton-platintim. For both the systems there is a good consistency in the various sets of o values, and mean values obtained on the basis of these data are reproduced in figs. 1 and 3 as curves 3. WC regard these as the most reliable o! values. The agreement observed amongst the different sets of MFPM c( values for the two systems confirms the constancy and stability of the platinum surface during the entire course of experimentation. It is tlrerefore valid to assume that the slow increase in 01values with temperature is an inherent feature asslrciated with the mechanism of heat transfer efficiency tor these solid gas interfaces. In figs. 5 and 6 arc displayed the earlier milsmments ofa for neon-platinum and krypton---pln:inrinl systems respectively. The continuous curves ill fJleSe figures are,the results of the present work 3~ obthcd by the Wachman [7] “IFPM. It may be noreN that there are no other measurements above 500 K for cOr11. parison against the presently obtained VZI~LICL Aruciur et al. [18], and hdur [.i9] have reported o at 293 K and found it to vary with pressure. The valuc~ bcirl]: 0.466 at 0.01 1 nlnl of mercury and 0.700 al 0.17 111111
CIIEhIICAL I’iIYSICS LITTFKS
Volun~c 48, nurnbcr 3
‘O\
ing the wirG to the bright orange color under vacuum
and their results 120,211 arc to be regarded as most reliable and referring to a surface somewhat similar to that used in this work. Their value at 485 K agrees well
08-
a
l
O6
with our measurements and it is likely that there is a chp in cv versus T plot at about 400 K as observed in
Cl
l
0.d 700
/-400
600
T(Y) Fig. 5.
Conlp.lrlu~nof tlrc prc$cnt tllcrnld accolnniodation
LWffiClCJlt
ddI.1
fix
thC IICOn-phtiIltJlTI
of otllcr worker\. -.uxl co-norkcrs 1 X,2 .uid 0 Purslow [12 1.
work
~Y~.lUll
1%ith
the
rLYlJhS
lwscd on
MPPhl. ‘3 Thornac Arntiur ,~nd co-workers [ 18.I9 1,
prcwnt I 1. l
1977
Brown [2OJ prepared their platinum surface by hcat-
I
1
’
0 0
15Junc
several other systems [3,5,63. The origin of such a dip may bc attributed to the desorption of weakly held adsorbates [13] on vacant sites on the metal surface and/or on the top of a chemisorbed gas layer. The h~dur et al. [!8] value of a for gas covered platinum at 300 K is 0.844 For krypton-platinum system, and Amdur [ 191 found Q to be pressure dcpcndent. The value ranging from 0.445 to 0.857 in the pressure range 0.01 to 0.477 mm of mercury at 293 K. These data arc shown in fig. 6 but as explained above for neon--platinum system, the observed pressure dependcncc of (JIby hrwlur [ 191 is questionable. It is
200
600
400 T(K)
rig.
6. Compxlwn
cocf&xnt results
of the prcscnt
of other worhcrs.
uorkcrs rurslow
thcrn~~l .rccommodation
data for the plarlnulll-krypton
[IO,? 11, l
-
Amdur
\y\tcm with
the
Ilrcsrnt work. (1 Thon~as .lnti coand
co-workers
\18,19], and 0
[ 27 1.
of mercury. Their rcsdts refer to a gas saturated platinum surhcc and as pomtcd out by Thomas and Brown 120) this
apparent
dcpcndence
of o on gas pressure
IS
the changing phtinum surface III the work of Amdur et al. [ 18,I9] and the mapplicability of the Boyle’s law due to adsorption-dcsorption phenomcnon. Tllomns and Olmer [2 I], and Thomas and Brown [201 measured a for a partially covered platmum surface at temperatures 303 K, 361 K and 485 K and
due
important to note that the values of Amdur differ among themselves by a factor of two. Purslow 122) found (Yfor krypton on platinum filament flashed at 1 173 K to be 0.70 at 283 K. Tl1o11~s and Brown [20] found CYfor a partially covered surface to be 0.902 and 0.692 at 3 12 and 405 K respectively. The ar value of Thomas and Brown [20] at 405 K and Purslow [22] .at 283 appear to be in rcasonable ngrccmcnt with the present data above 400 K. However, llmms and Rrown [2OJ data at 312 K would suggest a different temperature dependence and a possibility of a dip 111 Q value at about 350 K. The existence of such a dip of course can be explained on the basis of desorption of a weakly held adsorbed gas on either the platinum surface and/or on the top of a chernisorbcd gas layer. In this context future work cn a well controlled surface at temperatures below 400 K will be very useful. Figs. 5 and 6 hrghlight the large differences that exist amongst the CYvalues measured
by different
workers.
to
found Purslow
Its value
lo
bu
1221 reports
0.37,0.55
3n average
;~r~d 0.45
rcspcctivcly.
v3luc of nbout
0.%4
for a nonflashcd surface at 283 K and an avcragc value of about 0.9 12 after flashing the surface. Thomas and
Acknowledgement
This work is supported by the United States National Scicncc Foundation Grant No. ENG 75-02992 u&r a USA-USSR cooperative research program. Computing Scrviccs used the computer center
in
this rcscarcfl
of the University
Chicago Circle. Their assistance
edged.
wcrc provided by of Illinois at
is gratefully
acknowl-
Volume 48, number 3
CHCMICAL PIIYSICS LETTtRS
References B J. Jody and S.C. Saxend, 3. Phys. E 9 (1976) 359. D J. Jody and S.C. Saucna, Phys. Ptu~ds 18 (1975) 20. B.J. Judy and S.C. Saucna. 5th International Ilcat Trdnsfcr Confcrcncc. Tokyo, Jqxm. Cu 4.6 (1974) 264. RX Ilarris, J. Chem. Phys. 46 (1967) 3217. S.1l.P. Chcn .~nd S c. S.IWILI, Intern. 1. Ilt~t h¶:w’rrmsfer 17 (1974) 185. S.H.P. Chen and S.C. Silxcnil, Ilrgh Tcnrp. Sci. 8 (1976) 1. 13-Y. Wachm.m. J. Chcm Phys. 42 (1965) 1850. C.B hld\tcd and N.J. H~swJ, Tran\. I-aradny Sot. 29 (1933) 698. R. LCWISnnd R. Gomcr, Surface Sci. 12 (1968) 157. D.L. Chnpm.m and P.W. Reynolds. Proc. Roy. Sot. At56 (1936) 284. K. Vanslow and W.A. Schmidt, Z. Naturforsch. 22a (1967) 717.
I.5 June 1977
1121 D.O. Hayward and B.M.W. Trapncll, Chemisorption (Academic Press, New York. 1964). [I31 H.U.D. Wcsendangcr, J. Catalysis 2 (1963) 538. I141 II S. Taylor and KM Burns. J. Am. Chcm. Sac. 43 (1921) 1273. 1151 R. Lewis and R. Gomcr. Surfacc Sci. 17 (1969) 333. 1161 G. Byholdcr and R. Sheets, J. Phy< Chem. 74 (1970) 433.5. 1171 L. Rrcvwr. Clwm. Rev. 52 (1953) I. 1181 I, Amdur, MM. Jones and El. Pc~rlma~, J. Chcm. Ptrys. 12 (1944) 159. 1191 I. Amdur. J Chcm. Phy\ 14 (1916) 339. I201 L.R. Thum,!r and ItI-. &own, J. Chcm. t’hyq_ iS (1950) 1367. 1211 L.1). rtmu~ .rnd r. Olmer, J. Am. Chcm. Sac. 65 (I 94 3) 1036. 1221 t3.W. Purslow, Ph.D. rhcbiS Umvcrsity of London, L’nptand (1952).
549
Volurnc 48, number 3
THERMAL
ACCOMMODATION
ON GAS COVERED
COEFFICIENTS
I.5 June 1977
OF NEON AND KRYPTON
PLATINUM
Rccc~vcd 13 l)eccmbcr 1976 Kcviwd mxnwr~pt rcwvcd 28 hlsch
1977
A hot z~rc column type instrument i\ cmploycd to determme the thermal :lccommod&wn coeffuzicnt, P, of nwn .md krypton on :1gas covered platmum wrc in the tcmpcraturc range of 4OO-- 1400 K. The Q valucc are detcrruincd from hc,lt tr.m%fcr rate mcawrcmcnts taken in the temperature-Jump regime ‘I’he tc\t surf.sc was covcrcrl L& itb o\ygtin by scvcr~1 huatlng cycks rcxhlng up to Jbout 1400 K at an ovygcn pdrtlnt pressure of about 5 X to-” nun of mercury. h? cuparimcnhl imat tr.mcfcr data are .~ndly?cd .uxording to three dlffcrcnt procedure\ mid the resulting a valuec arc rqortcd md compared with the nvnktbk! data III the literature 1%IIILII are only m ihc ~CIII~C~.I~ZC F lnyc d &OU( 300 --SO0 K.
1 . introduction We have employed to determine in vacuum
an m~proved
the lIzat transfer
rates
column from
mstrument a heated
wire
and in the presence of a gas under continuum and temperature-jump conditions [2,3]. Thcsc papers [l-3] describe the expenmental apparatus and procedure, and data analysts schcmcs. Such details arc therefore not included here and only the relevant features characteristic of the present mvestlgntion will bc briefly mentioned. The experimental values of thermal accommodation cc,cfficient, OL,for NC-R and Kr-IY in the temperature range 400-1400 K as determined from the heat transfer rate medsurenicnts in the temperature-jump regime are reported here. Platinum is chosen due to its physical strength and mcreasing mdustrial importance specially as a surface catalyst. It IS supplied by Engelhard Industries and stated to be 99.9% pure. The neon and krypton gases, 99.95% pure,
[I J
arc supplied
by Mathescjn
Gas Products.
The
principal impurities in the neon sample itre 50 ppm helium, 1 ppm nitrogen, 1 ppm oxygen and 5 ppm hydrogen, and in the krypton sample arc 25 ppm xenon, 25 ppm nitrogen, 4 ppm oxygen, 4 ppm argon, 5 ppm hydrogen and less than 10 ppm hydrocarbons. The
platinum wire used in the column Is 30.0C 0.1rndin diameter and about 59 cm long. The experimental heat transfer data in the tl111[lCiilture-jump regime are analyrcd according to three different procedures to obtain 01values. ‘Fhe~ are the cmstant power method (CPM), constant temperature difference method (CTDXI), and the mean-free-path mcthod (MFPM). The CPM is based on the theory which has been elaborated by Harm 131 and has been used by UF earlier [3,5,6] _ III this method, the wiraz temperature, Trr , is plotted against the reciprocal of gas pressure, P, for constant values of the thermal power conducted throudi the test gas, QIt _11~ siopc of this linear plot gives a while the intercept gives the linearly extrapolate gas temperature at the wire surface, ‘Tc. The CTDM [S] IS based on the integration of the Fourier heat balance equation between the cold wall temperature, T,<,,,and T,.Accordmg to this method, the reciprocal piots of 1/Qtt versus 1/i’ for constant valuas of (T,, - T,.) arc lmear and their slopes yield Q as d function of Trr. IIou ever, in tha calculation, the impliclt assumption is mad that 7-e = TII and tills can ausc ~pprcciahfc error in p at high temperatures. The MFPM is devcIopcd by Wachmar [7] and gives 1y as a function of gas pressures and at a temperature about one mean-f&-path away from 545
Vol?lnK!48, nurrrber 3
- Since Q!is independent the hot WIM, T 5ure in the tcrnhplcirnture-jump rcginic of
CCICMICAL PHYSiCS LETTERS of 23s PM-
heat tr3nsfer
as implied in the CPM and CTDM, the MFPM providc~ a good check of the conditton of the gas--solid tnterface over the entire experm~ental tcmpcrature range. TIE QY vnlues dctcrrnmed according to above mentioned three procedures arc compared with each other and 3 single set of values are given as ;I filriction of temperature for the two systems. These Values are also ~-~mparcd with the data available 111the literature wh~h arc confined to tflc maximum temperature of about 500 K.
The hcnt tr:lnk.fer coiumn, G mm mtcrnal diameter, of the general design used earlier by Jody and Sa.uena [‘_I ISev~~~~~t~d to a pressure of about 2.5 X I#- s mm of mercury while the glass wall is mdintarned dt 3 17 K by Glculating water from 3 constarit tcmperature bath. The wire is dnncalcd for about three and a half hours at 1400 I(. This annealing process does not clenn the platrnum surface as tke adsorption of oxygen is irreversible with pressure and cannot be dcsorbed to any appreciable cxtcnt [8-l i] by such a thermal treatment. The relattvcly low melting point of ptstlnum is responsible for the latter. Further, platirzum does not adsorb mtrogc:cn [12--141, and dcsorbs hydrogen and carbon monoxide at tcmpcratutcs below about 460 K [f&IS] and G20 K [13] rcspectwely. In view of t?msc comments tt may be lnfcrred that annealing leaves probably oxygen as the dominant adsorbate on the platinum surface. Adsorbed oxygen has the ~~pab~~~tyto replace f 161 weaker adsorbates llke carbon monoxide, and this wtll also favor oxygen as the major adsorbate on the platinum surfitce. IIowever, annealing at an oxygen partial pressure of about 5.3 X 10V6 mm of mercury may not be enough to fully cover the platinum surface with a monolayer of oxygen, since as pointed out by Lewis and Gomer f9] several heating cycies arc essential to accnmphsh full covcragc. in this work, therefore, the pla[inuril wire is subjected to eight heating cycles with the Idea to achieve co~plcte covcmgc. ~nuthcr cornplication that results during this thcrmat treatment is Corn the diffusion of ttw bulk mct.zlIic impurAes to the surfaces which is fouad to be rapid above about 536
15Juno 1977
IO00 K, Brewer [17]. Once these impurities are at the surface, they can get oxidized and the resulting oxides r%iyRot be soluble in pfatinum but rather get epitaxaily attached to the surface and spread over it resulting in a substantial change in the surface condition, I_cwh and Gomcr [9). With impurities in the platinum sample amounting to about 0.1%~~appreciable surface CORta~~ijyation by oxides ic therefore anticipated. TIE heat transfer rates arc measured in vacuum, r&, and in the prcscncc of neon, Q-,-, at pressures of 1.03, 3.1 i. 6.07,8.17, 10.00 and IS.00 mm of mercury over the entrre tempcraturc range. From these, tfle thermal energy conducted by the gas, QIr, at a particular prcssure and as a function of ternpcrature is detcrruined. The plots of Ttr and ZL/Qir against 118’are found to be linear for tkc entire temperature range for pressures between 6.07 to 15.00 mm of mercury. Here 22, IS the length of the platmurn wire at the tenlpcr;lturc to wlrrcit Q~ rcfcrs. From these data, cr is computed as a function of tempcraturc (T,, TFi, TAH) according to
Fig. 1. Thermat. ~~caI~~rn~d3tion rocfftcient~ for the nwnpl,ftinum \ystorn ;1sn firnction of tcmpcraturc. Curve 1.2 ,md 3 rcpreccnt the rcwltr based on the constant power, constant temperdttrrc diffcrcnce .~nd mwn-fret-p.ath methods, rcspectivcly.
06
Volume 48, number 3
o.d400
t
I
CHEMJCAL PHYSICS LETTERS
I
I
600
I
1000
800
I
1200
1400
T,,T,,T,&W
Fig. 3. Thermal accommodation coefficients of the krypton platinum system, as a function of temperature. Curves 1, 2 and 3 represent the results based on the constant power constant temperature difference and mean-free-path methods,
respectively.
o.gl 0 0.
i 0.71 300
1 500
I 700
I 900
1100
TA,W
Fig. 4. Thermal accommodation coefficients for the kryptonplatinum system based on the mean-free-path method (o 10.02 mm Hg), (0 - 2.99 mm Hg), (0 - 0.80 mm Hg), (fi 0.5 1 mm Hg).
the three meLhods following the procedure detailed earlier [3,5]. These results are given in figs. 1 and 2. Similar measurements are taken for krypton at pressures of 0.10,0.31,0.51,0.80,2.99,10.02, 19.45 and 30.15 mm of mercury. The gas pressures in the range 051 to 10.02 are employed to calculate a values and these are given in figs. 3 and 4.
3. Discussion The 01values for both the systems, figs. 1 and 3, as obtained from the CPM (curves I) are smaller than the corresponding values from the CTDM (curve 2). The CPM values are estimated to have a percentage random error uf 3.4,3.3 and 3.0 at 400,800 and 1 100 K respectively for neon-platinum system, and 5.3, 3.6 and 2.4 at 500,800 and 1100 K respectively for kryptonplatinum system. The percentage random errors for the CTDM are 4.8, 5.5 and 4.7 at 400,800 and 1100 K respectively for the neon-platinum, and are 4.9,5.3
l5Junc
1977
and 4.8 at 500,850 and 1100 K respectively for the krypton-p!atinum system. In these calculations the error introduced in replacing Te by TH is nor account. ed. The trend and magnitude of the differences in the CYvalues for the two systems according to the two methods cannot be completely accounted by the above mentioned estimates of the random errors. A substan. tial portion of this disagreement lies in the apprctximations [3,5,6] made in the heat transfer equations while analyzing the experimental data to obtain o values. For instance in the CTDM, replacement of Tc by TH tends to increase the o vaiue and this increase will be larger at higher temperatures. Thus, this can partially explain why the ty values determined by CTDM are larger than those obtained from the CPM. From this point of view CPM values (curves 1)are preferable over the CTDU vaiues (curves 2). The MFPM of Wachman [7] is less ambiguous in this respect and gives a values as a function of temperature from heat transfer data taken at a particular pressure. In figs. 2 and 4 these different sets are reported for neon-platinum and krypton-platinum systems respectively. The percentage random errors are S-1,4.2 and 3.5 at 400, 800 and 1100 K respectively for neon-platinum, and 5.0,4.7 and 4.6 at 500,800 and 1100 K respective/y fur krypton-platintim. For both the systems there is a good consistency in the various sets of o values, and mean values obtained on the basis of these data are reproduced in figs. 1 and 3 as curves 3. WC regard these as the most reliable o! values. The agreement observed amongst the different sets of MFPM c( values for the two systems confirms the constancy and stability of the platinum surface during the entire course of experimentation. It is tlrerefore valid to assume that the slow increase in 01values with temperature is an inherent feature asslrciated with the mechanism of heat transfer efficiency tor these solid gas interfaces. In figs. 5 and 6 arc displayed the earlier milsmments ofa for neon-platinum and krypton---pln:inrinl systems respectively. The continuous curves ill fJleSe figures are,the results of the present work 3~ obthcd by the Wachman [7] “IFPM. It may be noreN that there are no other measurements above 500 K for cOr11. parison against the presently obtained VZI~LICL Aruciur et al. [18], and hdur [.i9] have reported o at 293 K and found it to vary with pressure. The valuc~ bcirl]: 0.466 at 0.01 1 nlnl of mercury and 0.700 al 0.17 111111
CIIEhIICAL I’iIYSICS LITTFKS
Volun~c 48, nurnbcr 3
‘O\
ing the wirG to the bright orange color under vacuum
and their results 120,211 arc to be regarded as most reliable and referring to a surface somewhat similar to that used in this work. Their value at 485 K agrees well
08-
a
l
O6
with our measurements and it is likely that there is a chp in cv versus T plot at about 400 K as observed in
Cl
l
0.d 700
/-400
600
T(Y) Fig. 5.
Conlp.lrlu~nof tlrc prc$cnt tllcrnld accolnniodation
LWffiClCJlt
ddI.1
fix
thC IICOn-phtiIltJlTI
of otllcr worker\. -.uxl co-norkcrs 1 X,2 .uid 0 Purslow [12 1.
work
~Y~.lUll
1%ith
the
rLYlJhS
lwscd on
MPPhl. ‘3 Thornac Arntiur ,~nd co-workers [ 18.I9 1,
prcwnt I 1. l
1977
Brown [2OJ prepared their platinum surface by hcat-
I
1
’
0 0
15Junc
several other systems [3,5,63. The origin of such a dip may bc attributed to the desorption of weakly held adsorbates [13] on vacant sites on the metal surface and/or on the top of a chemisorbed gas layer. The h~dur et al. [!8] value of a for gas covered platinum at 300 K is 0.844 For krypton-platinum system, and Amdur [ 191 found Q to be pressure dcpcndent. The value ranging from 0.445 to 0.857 in the pressure range 0.01 to 0.477 mm of mercury at 293 K. These data arc shown in fig. 6 but as explained above for neon--platinum system, the observed pressure dependcncc of (JIby hrwlur [ 191 is questionable. It is
200
600
400 T(K)
rig.
6. Compxlwn
cocf&xnt results
of the prcscnt
of other worhcrs.
uorkcrs rurslow
thcrn~~l .rccommodation
data for the plarlnulll-krypton
[IO,? 11, l
-
Amdur
\y\tcm with
the
Ilrcsrnt work. (1 Thon~as .lnti coand
co-workers
\18,19], and 0
[ 27 1.
of mercury. Their rcsdts refer to a gas saturated platinum surhcc and as pomtcd out by Thomas and Brown 120) this
apparent
dcpcndence
of o on gas pressure
IS
the changing phtinum surface III the work of Amdur et al. [ 18,I9] and the mapplicability of the Boyle’s law due to adsorption-dcsorption phenomcnon. Tllomns and Olmer [2 I], and Thomas and Brown [201 measured a for a partially covered platmum surface at temperatures 303 K, 361 K and 485 K and
due
important to note that the values of Amdur differ among themselves by a factor of two. Purslow 122) found (Yfor krypton on platinum filament flashed at 1 173 K to be 0.70 at 283 K. Tl1o11~s and Brown [20] found CYfor a partially covered surface to be 0.902 and 0.692 at 3 12 and 405 K respectively. The ar value of Thomas and Brown [20] at 405 K and Purslow [22] .at 283 appear to be in rcasonable ngrccmcnt with the present data above 400 K. However, llmms and Rrown [2OJ data at 312 K would suggest a different temperature dependence and a possibility of a dip 111 Q value at about 350 K. The existence of such a dip of course can be explained on the basis of desorption of a weakly held adsorbed gas on either the platinum surface and/or on the top of a chernisorbcd gas layer. In this context future work cn a well controlled surface at temperatures below 400 K will be very useful. Figs. 5 and 6 hrghlight the large differences that exist amongst the CYvalues measured
by different
workers.
to
found Purslow
Its value
lo
bu
1221 reports
0.37,0.55
3n average
;~r~d 0.45
rcspcctivcly.
v3luc of nbout
0.%4
for a nonflashcd surface at 283 K and an avcragc value of about 0.9 12 after flashing the surface. Thomas and
Acknowledgement
This work is supported by the United States National Scicncc Foundation Grant No. ENG 75-02992 u&r a USA-USSR cooperative research program. Computing Scrviccs used the computer center
in
this rcscarcfl
of the University
Chicago Circle. Their assistance
edged.
wcrc provided by of Illinois at
is gratefully
acknowl-
Volume 48, number 3
CHCMICAL PIIYSICS LETTtRS
References B J. Jody and S.C. Saxend, 3. Phys. E 9 (1976) 359. D J. Jody and S.C. Saucna, Phys. Ptu~ds 18 (1975) 20. B.J. Judy and S.C. Saucna. 5th International Ilcat Trdnsfcr Confcrcncc. Tokyo, Jqxm. Cu 4.6 (1974) 264. RX Ilarris, J. Chem. Phys. 46 (1967) 3217. S.1l.P. Chcn .~nd S c. S.IWILI, Intern. 1. Ilt~t h¶:w’rrmsfer 17 (1974) 185. S.H.P. Chen and S.C. Silxcnil, Ilrgh Tcnrp. Sci. 8 (1976) 1. 13-Y. Wachm.m. J. Chcm Phys. 42 (1965) 1850. C.B hld\tcd and N.J. H~swJ, Tran\. I-aradny Sot. 29 (1933) 698. R. LCWISnnd R. Gomcr, Surface Sci. 12 (1968) 157. D.L. Chnpm.m and P.W. Reynolds. Proc. Roy. Sot. At56 (1936) 284. K. Vanslow and W.A. Schmidt, Z. Naturforsch. 22a (1967) 717.
I.5 June 1977
1121 D.O. Hayward and B.M.W. Trapncll, Chemisorption (Academic Press, New York. 1964). [I31 H.U.D. Wcsendangcr, J. Catalysis 2 (1963) 538. I141 II S. Taylor and KM Burns. J. Am. Chcm. Sac. 43 (1921) 1273. 1151 R. Lewis and R. Gomcr. Surfacc Sci. 17 (1969) 333. 1161 G. Byholdcr and R. Sheets, J. Phy< Chem. 74 (1970) 433.5. 1171 L. Rrcvwr. Clwm. Rev. 52 (1953) I. 1181 I, Amdur, MM. Jones and El. Pc~rlma~, J. Chcm. Ptrys. 12 (1944) 159. 1191 I. Amdur. J Chcm. Phy\ 14 (1916) 339. I201 L.R. Thum,!r and ItI-. &own, J. Chcm. t’hyq_ iS (1950) 1367. 1211 L.1). rtmu~ .rnd r. Olmer, J. Am. Chcm. Sac. 65 (I 94 3) 1036. 1221 t3.W. Purslow, Ph.D. rhcbiS Umvcrsity of London, L’nptand (1952).
549