Gen Spin 651 Static by Knor in Catal Revs Sci Eng v 1 Iss 1 Pp 257 313 y 1968

8/12/2019 Gen Spin 651 Static by Knor in Catal Revs Sci Eng v 1 Iss 1 Pp 257 313 y 1968

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Stat ic Volumetr ic Methodsfor Determination o AbsorbedAmount o Gases o n Clean Solid SurfacesZ . KnorInstitute of Physical ChemistryCzechoslovak Academy of SciencePrague. Czechoslovakia

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 25811. VOLUMETRIC DETERMINATION OF ADSORBED

AMOUNT IN STATIC APPARATUS . . . . . . . . . . . . . . . 260I11. APPARATUS REQUIREMENTS WITH REGARD TO

ACCURACY OF ADSORPTION MEASUREMENTS . . . . . .IV. ESTIMATE OF THE VOLUME OF AN ADSORPTION

APPARATUS .............................. 272V CONSTRUCTION OF STATIC ADSORPTION APPARATUS

FOR VOLUMETRIC MEASUREMENTS . . . . . . . . . . . . . 275VI. VACUUMSYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . 279

VII. ADSORPTION VESSEL ....................... 287VIII. BURETSPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289IX. RESERVOIRS AND DOSING OF GASES . . . . . . . . . . . . . 295X. SPECIAL TYPES OF ADSORPTION APPARATUS . . . . . 297

XI. SOME GENERAL NOTES . . . . . . . . . . . . . . . . . . . . . . 298XI1. APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 3

A. Example of the Calibration . . . . . . . . . . . . . . . . . . 303B. Example of Calculation of Amount Adsorbed . . . . . . . 305References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

267

2 5 7


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258 Z . KNORI. INTRODUCTION

The amount of ga s adsorbe d on the sur fa ce of sol ids is one of thefundamental dat a of adsorption st udies. The amount adsorbed can bedetermined either from pr es su re changes within a certa in constantvolume-volumetric determination-or more directly from the changeof weight of a solid substance (adsorbent) weight determination-ina static or flow apparatus.

In a static apparatus a known amount of gas is admitted to the ad-sorbent in doses, wher eas in a flow apparatus the ga s flows over theadsorbent for a cer tai n time . In this art ic le we shal l deal only withthe determination of the amount of adsorbed gas by me ans of sta ti capparatus.tal assumption that the studied gas is adsorbed only on a given ad-sorbent sample-there is no other sou rce of gas in the apparatus,nor any gas-a bsorbi ng par ts. Thi s assumption is, of cou rs e, onlyvalid for the ideal case. In real ity, one only approache s such a st atebecause rem ova l of gas so ur ce s within the apparatu s by perfect de-gassing can, in turn, give rise to s urf ace s which readily adsor bga se s during the adsorption experim ent itse lf, e.g., degas sed metalpar ts such a s valves or elect rodes of pr e ss ur e gauges or degassedfreez ing tr ap gl as s imme rse d in the cooling liquid during the co urs eof the experiment, etc.

Some types of p re ss ur e gauges have, on the one hand, the prop-e r t i e s of pumping element s (ionic pumping by ionization p re ssu regauges) and, on the other hand, they can re le as e g ase s during ope ra-tion (e.g., ionization p res su re gauges with hot cathode) o r change thega s phase composition. They can thus influence the co ur se of ad -sorption. A s an example [ l - 3 1 the atomization of hydrogen can takeplace on a hot cathode; hydrogen atoms are then adsorbed by mate-r ia l s by which mo lecul ar hydrogen is not ad sorbe d at all. In re alsituations it is the refore the rela tiv e magnitude of these effect s whichis important: If the su rf ac e a rea of the studied adsorbent is suffi-ciently large so that the amount of g as captured by i t is large com-pared with the amount of g as es rel eased or captured by other pa rt sof the app ara tus , then these effects can be neglected. Th is is therea son , in many instances, it is of advantage to work with evapora tedfilm s of ma teri als. Their surf ace ar ea , in the majority of ca ses ,exceed s many ti me s the geome tric a re a of the su bst rat e on whichthe film is deposited. A s mentioned before , pe rfec t degass ing of theapparatus brings about not only the condition nece ssa ry for prepa ringclean and defined adsorbent sur fac es, but a t the sa me time it also

In all our f urt her considerations we shal l st ar t with the fundamen-


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STATIC VOLUMETRIC METHODS 259brings about the condition affecting the accuracy and reliabili ty ofmeasurement of amounts of gas adsorbed.an interaction between g as and adsorbent surface is involved, i sgiven by

The ma ss balance for adsorption in an ideal case, i.e., when only

where vg is the ra te of increase of the number of pa rt ic le s in the ga sphase over the adsorbent; v, is the ra te of addition of ga s pa rt ic le sto, and v, the ra te of removal of parti cl es from, a given space; Vaandvd ar e the ra te s of adsorption and desorption, respectively. A l lra te s can be expressed a s the numbers of par ticl es adsorbed o rtransported in 1 second, for example.In a classical static apparatus, beginning from a certain timeafter the admission of a gas dose , v, = 0. A steady state (vg = 0) isthen se t up i f

because v, = 0 als o in case of the cla ssi ca l measurement. In thiscase , the refore, the extent of surf ace coverage at a given steadystate pr es su re can be affected only by temperatu re changes.steady state isWith flow apparatus where v, * 0 and v, 0, the condition of the

so that the degree of coverage can al so be affected by the magnitudesof the ra tes v, and v2. This advantage of flow apparatus i s more thancounterbalanced by a drawback. With the sam e initial concentrationof impuri ties in the gas phase, the amount of the surface of the ad-sorbent covered by the impurity can be many times greater in aflow system than in stat ic apparatus because the impurity can accu-mulate successively.The type of adsorption appara tus to be used is dictated by thefollowing factors.1. Kind of Adsorbent

The kind of adsorben t predetermines the type of adsorption ves-sel. The surface ar ea of the adsorbent again l imits the volume ofthe whole apparatus.


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260 Z . KNOR2. Kind of Adsorbate

The adsorpt ion of g as es and vapors having low condensation te m-pe ra tu re s brings about a number of complicating fac tor s. It is nec-ess ary to use proper cooling for freezing tra ps in order that theadsorbent be sufficiently protecte d against mer cury or oil vaporscoming from vacuum pumps and at the same ti me to prevent conden-sation of the vapor under study in the tr ap s. In som e ca se s i t is nec-es sa ry to keep the whole appa ratus a t a temp era tur e higher than thatof condensation.3. Range of P re ssu re s in which Adsorption Is Being Studied

With pr es su re s p < 760 t o r r we spe ak of low-p ressu re adsorptionand in the c ase of p > 760 t o r r of high-pr essure adsorption. So fa r,adsorption on clean sur fac es has been studied only at low p re ss ur e sand the ref ore attention will be paid only to this ar ea .4. Type of Information Desired

Equipment of the app ara tus depends on the quantities we a r e tomea sur e. They can be equilibrium and/or steady stat e amounts ad-sorbed or desorbed, adsorption and/or desorption kinetics, etc. Thetype of the adsorption ve ss el depends, fu rth erm ore , on our possibleintention to av ai l ou rselve s of some additional method fo r studyingadsorption, such as the me asurem ent of e le ct ri c conductivity o r ofwork function of the adsorbent, of inf ra re d sp ec tr a of adsorbed pa r-ticles, etc.When designing an adsorption apparatus, due r eg ar d mus t be al -ways paid to two asp ect s. Some demands on the apparatus resultfr om the necess ity of working with defined su rf ac es (the us e of highvacuum technique); some others are dictated by the sensitivity andacc uracy req uir ed of the measurements . These two groups of de-mands often conflict. For example, large glass tube diameters offerthe possibility of perfect degassing of the apparatus, but then an ap-pa ra tu s of la rg e volume imp ai rs the accura cy of determination of th eadsorbed amount. It will be n ecess ary, therefore, t o tr y to find theoptimum solution in each individual case.

11. VOLUMETRIC DETERMINATION OF ADSORBEDAMOUNT IN STATIC APPARATUS

The pr inciple of volumetric de termination of the adso rbed amountin a s ta tic apparatus consis ts in the admission of a known amount of


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STATIC VOLUMETRIC METHODS 2 6 1gas-from a known volume of the so-called buret space * filled withgas of a mea sured pressure-i nto the adsorption ve ssel of knownvolume and in again measuring the pre ssur e. The adsorbed amountNa (in moles) is then calculated fr om

where N and N are the number of moles of gas in the bure t sp aceand in the free volume of the adsorption vessel (in the volume notfilled with adsorbent), respectively. With the first dose of ga s, NA= 0. Symbols with pr ime s denote numbers of moles in the appro priat evolumes af ter opening the valve separating the buret space from the

P

FIG. 1. Scheme of simple a dsorption apparatus. A , Adsorption ves sel; B ,buret space; M , pressure gauge; D , dosing syste m; R, gas reservoir; P , con-nection to vacuum pump; v, valves.adsorption vessel (Fig. 1). Symbols without pr im es r ef er to the stat epr io r to the admis sion of a dose. Mentioned numbers may be equi-librium or stationary stat e values or they may be time dependent.

To be able to dete rmine the adsorb ed amount, i t is necessary toex pr es s the numb ers of moles in individual pa r t s of the apparatu s bymeans of the mea sure d quantities: pr es su re , p; volume, V; and te m-perature, T.

At te mpe rat ure s sufficiently high above the cr iti cal temp era tur eo r a t low pre ssu res , the studied gas can be considered a s an idealone and th e cor rect io n accounting for the nonideal behavior [s eeEq. (2111 can be neglected.

*Note: The buret spac e is that pa rt of the apparatus i n which w e measurethe amount of gas prio r to admission of a dose of ga s to the adsorbent.


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262 Z KNORFurthermore, i f the whole apparatus has a constant tem per atu reT, then it is possible to writ e for number s of moles in individual

pa r t s of apparatus ( N i = N A YN,, NA, NA):Pivi

1 - R TN . (5)Here R is the ga s constant, pi is the pre ssu re in Vi, and Vi is thevolume of the s pa ce in question. The adsorbed amount Na is then[see Eq. l)] a s im ple function of products PiVi. A s far as some par t sof the appa ratus ar e kept at the temp erat ure differing f rom otherpa rt s (freezing traps , adsorption vessel), we must write f or theamount of gas in the buret space or in the adsorption vesse l spac e

where NTK is number of ga s moles in volume V of that pa rt of theappara tus which has the temp erature TK. In deriving the exp res sio nN i = N i ( & , V,, TK, we must now distinguish two cases:1. The mean free path of ga s molecules* is much less than thedia meter of tubes cr ossing the region of the gradient of te mpera-tures. In this case the press ure is the s am e in the whole app aratu sand equals the pr es su re m easur ed by a pressure gauge working attemperature T . Thus we can write for the p ar t kept at TK:

PivKN,, =- RTKand furtherm ore

where a, = T1/TK.2. The mean free path of g as molecules is gre ate r than or equal

to the diam ete r of tubes cro ssi ng the region of tempe ratur e gradient.In this cas e the so-cal led ther mal transpiration effect (thermomo-lecular effect [ 5,6]) occurs.

Let u s consider two volumes, V, and V,, each immersed in a bath*Note: To esti mat e the mean free path h ( in centimeters), i t is possibleto use the approximate relation 141 hp = 5 x 10 (cm. tor r) with the majority

of simple gases.


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STATIC VOLUMETRIC METHODS 263of different temperature. Depending on the rat io of the diameter ofthe tube (connecting the volumes and crossing the temperature gr a-dient) and of the length of mean f ree path, the pressure p1 in volumeV, may differ fro m the pres su re pz in volume V,. According toKnudsen [ 5 6 ] we can conceive the microscopic p icture of processesin the region of the temperat ure gradient as follows: A moleculearri ving from the side of the higher temperature t ra ns fe rs to thewall a momentum which is gr ea ter than that trans ferred to the wallby a molecule arriving from the side of the lower temperature. Ac-cording to the action and reaction principle, the momentum re tr an s-fe rr ed by the wall to molecules and directed toward the higher t em-perature is greater than the momentum transferred to the moleculesin the direction toward the lower temperatu re. A s a consequence, aflow of molecules fro m the low-temperature region to the higher-temperature region occurs at the wall. Molecules flow through theinner region of the tube back into the lower- temperature volume tocompensate the flow along the walls. After a certain time a station-ary st ate of flows in both directions is established.*The extent in which this w a l l effect operates is in the firstplace determined by the ra tio of the number of mutual col lisions ofmolecules to the number of impact s of molecules on the walls, i.e.,by the ra tio of the mean fr ee path and the tube diameter . Obviously,the thermal transpiration effect will thus at a given pressure mainlyoperate with tubes of smal l diameters . With them the layer of gasflowing along the wall represents a volume which cannot be neglected.In the region of very low pressures (n >> 2r, where n is the meanfree path of molecules and r i s the tube rad ius) , a relation can beobtained between pre ssure p1 in volume V, at temperature T, andpr es su re pz in volume V, at temperat ure T,. The relation is derivedby consider ing the number of impact s in a time unit on an area unitof the cr oss section of the tube passing through the tempera turegradient. The number of impact s must be equal in the stationarystate fro m both sides-both from the side of the higher temperatureand fr om that of the lower one-so that

T Pz = pp2 (9)p = lTzEquation (9) gives one limiting value of the correction factor P withreg ard to the thermomolecular effect. The other limiting value (aswas seen under l ) ,equals unity.

*Note: The se considerations, of cou rse , a r e fully valid only provided themolecules rebound from the wall (the sur fac e of which is rough) elasti callyand provided no adsorption or desorption oc curs on walls.


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264 Z KNORIn the transient region of pr ess ure s, the therm al transpiration

influences the amount of ga s in individual pa r t s of the apparatus. Itmus t be taken into account eit her empirically-by calibration of ap-par atu s volumes in the whole range of pr e ss ur e s involved and foreach gas separately [7,8],-or the correction factor P can be cal-culated by mean s of the s emie mpir ic al Liang equation [9] o r itsnewer modifications. The Liang equation can be written in the form:

Ay2 By + C G D d mAy2 + B y + C f i + 1P =

where y = 2rp, (r is the radius of the tube cr ossin g the tem peratu regradient and pz is pr es su re measured at room temperature). Equa-tion (10) forma lly sum ma ri ze s th re e modifications of the originalLiang equation. Modifications differ by the significance and valuesof the constants A B, C, and D. According to Bennett and Tompkins[ l o ] , the constants of Eq. (10) a r e given by the relations:

A = a f 2 G Z B = p f @ C = O D = 1 (11)where y and /3 a r e constants fo r helium; Q is the dimensionlessfacto r character izing the kind of gas used (for helium = 1);and fis the corr ectio n fac tor having the values: f = 1.0 for 2r < 1.0 cm,and f 1.0 cm. Values of Q for some gases are givenin Table 1. For other gases Q can be estimated by using the em-pi ri ca l equation:

TABLE 1Values of the Constant @ of the

Liang Equation [ l o , 2151G a s QH eN eK rXeA2

H20 2NZc 2NH3

coC2H4

1.001 .302.703 . 9 06.411.442.873.533.314.526.722.22


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STATIC VOLUMETRIC METHODS 265

where d is the diameter of the part icula r gas molecule in Angstroms,computed from the collision c ross section. Constants a and p a r egiven by the relations:a = 6.29 - 9.6 X 10-'(T2 - T,) (1 )/3 = 7.88 (1-p)T,

Bennett and Tompkins verified Eq. (10) with the given constants forca se s where T, < T,.kins, the only difference being that they take D 1. The formerauthors showed that Eq. (10) with values of constants given by rela-tions (11) holds exactly only in cases when the reg ions of diffe renttemperatures, separated by a thin diaphragm, a r e connected by anaper ture . If volumes at different tempe rat ure s a re connected by atube, then even relation (9) does not hold exactly, but

Edmonds and Hobson use the sa me equation a s Bennett and Tomp-

p1 = D&P2applies. D is an empiri ca l constant which must be determined fromthe limiting case li >> 2r. For example, Edmonds and Hobson deter-mined for argon D 1.1 at temperatures T, = 77.4"K and T, = 295'Kin the region of pr essures lo- < p < 60 torr. Only by a number ofspecial proc esse s, enabling them to reduce the experimental er r o rof pressure determination [ l l ] ,were they in a position to determinerel iably the deviation of value D from 1. The physical meaning ofthe constant D is relat ed to the different probabilities of the passingthrough a tube of molecules coming from volumes at different tem -peratures.are given by the relations:According to Takaishi and Sensui [12], the constants of Eq. (10)

A = A,T-2 B = B,T-l C = C,T-lh D 1 (16)where = (T, + T2) /2 and constants A,, B,, and C, for some gasesa r e given in Table 2. Values A,, B,, and C, for the other gases canbe approximately estimated by means of empi rical formulas:

A,, = 1.4 x l o 4 x exp (0.57d) (17)


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Z . KNOR-66TABLE 2

Thermal Transpira tion EffectValues of the Constants of Takaishi Equations [121

Range ofA, x B, x lo- , C temp.,Gas grad 2*tor r-2mm-2 grad.torr- mm- grad0.5.torr-0.5mm-0.5 K

H2 1.2 8 .0 1 0 .6 1 4 - 6 7 3N2 1 2 1 0 1 0 - 1 8 7 7 - 19 50 2 * 9 -7 16-19 (13)b 90CH4 14 1 5 1 3 4 7 3 - 6 7 3He 1 .4 -1 .6 1 .1 -1 .2 18-20 4 .2 -90Ne 2 .6 1 .9 30 20 .4 -673Ar 11 8 .1 1 6 7 7 - 6 7 3K r 14 1 5 14 7 7 - 6 7 3Xe 3 5 41 10 77-90

aValues A, and Bo ere obtained only for a n a r r o w range of pressures sothat i t was not possible to determine these values mor e accura tely and itwas not at all possible to determi ne C .bValue C, was obtained by calculation fr om Eq. ( 8 ) for D 4 A [ l l ] .B, = 5.6 x exp (0.607d) 18)c, =--lo 114d

where d is the dia meter of molecules in Angstroms, computed fr omthe collision cr o s s section. Takai shi and Sensui verified the validityof Eq. (10) in the ran ge of te mp eratures 77 to 673K. They used theequation in such a fo rm that they always took p, < pz and T, < T,, sothe pre ssu re measured at room t emperature was considered eitheras p, or as p, according to the tem peratu re.kins) has been mor e frequently use d in the li ter atu re. The value ofcorrection factor P, computed fr om both equations (Bennett-Tomp-kins and Takaishi-Sensui), does not change much. The p re ssu re co r-recti on accounting for the ther mal tr anspi ratio n effect can be veryhigh i f temperatures T, and T, differ substantially. For instance,for T, = 78"K, T, = 300K is the lim it of P in the region of low p re s -su re s n >> 2r), roughly P = 0.5.In calculating the amount adsorbed, we can then wri te for i tem N ian equation analogous to Eq. (8):

So far the old er Liang equation (as modified by Bennett and Tomp-


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The magnitude of the correction in calculating gas amounts dependson the ratio of volumes VKwhich are at different temperature s [seeEq. (20)]. The volumes VK are usually determined by gas calibrationat higher p re ss ur es , when the thermal transpiration effect does notplay any role (PK 1).Insofar a s we work in the region of temperature s o r pre ss ur eswhere the given gas cannot be cons idered as an ideal one, the non-idea l behavior is expressed by correction:

where V, is the volume of free volume of a part of the apparatus,TABLE 3

Values of the Constant y for Correctionfor Nonideal Behavior of Gases [2141

Temp.,Gas K y x torr-*NZ 7 8

9 00 2 7 8

90co 9 0co2 1 9 52 9 8

NH3 2372 9 8

CH4 9 0A r 7 89 0

6 . 63 . 86 . 34.23 . 52.70 .83 .51 . 67 .1

11.43.9

V the volume corresponding with the nonideal gas behavior, and ya constant dependent on the kind of gas and on temperature (Table 3) .

111. APPARATUS REQUIREMENTS WITH REGARD TOACCURACY OF ADSORPTION MEASUREMENTS

In volumetric determinations the measured quantities ar e tem-perature, volume, and pressu re . In studying adsorption at low pres-


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268 Z. KNORsu res on clean surf ace s, the demands upon thermost ating of thewhole apparatus ar e not, a s a rule, stri ct. Fro m the point of view ofacc uracy of determining the adsorb ed amount, it will usually be suf-ficient to maintain the te mperature constant within the li mi ts of1-2 K, ecause the relative deviation of temperature 6, is, in thiscase (in the t emper ature region T > 100K), of the order of 6, 1 .In some particular c as es it is, of course, n ece ssa ry to maintain aconstant temperature of the adsorption ve sse l with much gr ea te raccuracy for other reaso ns (for mea sur eme nts of ele ctr ica l conduc -tivity of films, etc.). When measu ring a t tem peratu res differentfrom the room temperature, it is mostly assu med that the therm alcapacity of gas admitted to the adsorption ve ssel from a volume kepta t room temperature is negligibly sm al l and that the prop er adsorp-tion pro ces s proceeds at the tempera tu re of the wall of the adsorp -tion vessel. It is only in tl?e cas e of cal orim etri c measu remen ts atp ressu res p >fere, but, as to the adsorption process prope r, it is again assumedthat it is not affected. Often the ga s is admitted to the adsorptionvessel so that it pa ss es through a cooling o r warming bath before iten te rs the adsorption vesse l (e.g., [13,14,206]).its fundamental pa ra me te rs . The adsorbed and/or desorbed amountof gas is determined as a dif ference of the amount of g as in the gasphase within the whole free volume of the app ara tus before and afteradsorption or desorption [see Eq. (4)]. It is therefore obvious that i fwe are t o mea sur e the adsorbed amount with sufficient accura cy, theamount of ga s in the whole free volume of apparatus must not be toolarge as compar ed with the adsorbed or desorbed amount. The e r r o rof determining the amount of gas is given by the e r r o r in determiningthe volume and pr es su re . The rel ati ve standard deviation of individualmeasurement of pressure 6 is mostly of the or de r of 6 = 1 . It ispossible to re ach a reduction of the deviation by a number of steps[11,15-181, which, however, fo r prac ti cal re aso ns do not come intoconsideration for adsorption measurements. * The calibration ofvolumes of individual pa r t s of ap para tus is made e it he r by means ofliquids [16] (mercury, water) or with the help of a nonadsorbing ga s,e. g., helium.

to rr that heat tra nsfer by the gas phase can inter -

The magnitude of the volume of the appara tus constitutes one of

*Note: The error of absolute pr es su re measurement with any pr es su regauge is always greater o r , at best, practically equal to that made when mea-suring pr es su re with an absolute m anom eter, against which the given pr es su regauge was calibrated. Therefo re, when measuring at low pr es su re s, the er r o ris essentially determined by the e rr o r of the McLeod pr es su re gauge. It i spossible to reduce the e r r o r of individual measureme nt by repeated readings


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STATIC VOLUMETRIC METHODS 269Calibration of volumes by means of liquids and especially of mer-cury is usually a very precise one and a deviation of only 6 0.1%

can be easily attained. Calibration with gases consisting of the ad-mission of a known amount of gas into the volume being measuredand in the measurement of pressure is not, however, a quite inde-pendent method, because we must know the initial volume, e.g., thevolume of the McLeod manometer, with the grea test accuracy possi-ble. Provided w e know this volume, the amount of gas used for thecalibration can be determined by pr es su re measurement with anerror given essentially by the accuracy of the pres sur e measurement.Therefore the fundamental calibration of the selected pa rt of appa-ratus-gas buret, McLeod manometer-is always made by means ofa liquid, prefe rably mercury. In the calibrat ion of fur ther par ts ofthe apparatus by means of gases, it i s suitable that the init ial volumeVc be approximately equal to the calibrated volume V, because thee r ro r of calibration is minimal when V = VC,* and that the calibra-tion be made in the region of pr es su re s where the manometer usedmeasures with the least relative error. There is, of course, the ob-vious assumption that pr io r to the admission of gas the calibratedvolume must have been evacuated so that the amount of gas in it isnegligible compared with the amount of gas admitted.and by use of the mean value, but an er r o r in absolute pr es sur e is , in the cas eof the McLeod pr es su re gauge, given by the e r r o r of determina tion of its con-tent. It cannot b e affected by number of r eadings, The absolute er r o r of pres-su re determination by a McLeod manometer i s determined by the e r r o r incalibrations of volume o r of diamete r of the sea led capillary. The la tt er erroris usually of the order of units of per cent. Calib ration of the total volume ofa McLeod pr es su re gauge can be made with a much gr ea te r accuracy. Suitableconst ructi on and equipment fo r acc ura te reading of the height of me rc ury col-umn or that of some other liquid in pre ssu re gauges is described in literatur e[11,15-181.

Wote: Let u s consider an ideal gas, admitted fr om a known volume VC(where it was closed under pr es su re pi) into the evacuated volume V. If bothvolumes have the same temperature, the relation:

v = Vc- P1 -PiPz

holds, where p2 i s the pr es su re measured after equalization of pr essure s.The standard absolute deviation of V - u v is with the given deviations u v cand up, = opz= up determined by [191


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2 7 0 Z . KNORIn measur ing the adsorbed amount, not only dimensions of theapparatus matt er but also the geometr ic arrangement of the appa-

ratus is important i n some cases . The influence of the geometricarrangement shows itself on the one hand in the so-called layeringeffect ,* and on the other hand in unfavorably affecting the study ofadsorption kinetics.The gas inlet to the adsorption vessel should be arranged so as t orender the larges t possible surface ar ea (at least the geometric su r-face a rea) of the adsorbent exposed to the direct impact of g as mole-cules. This should prevent the successive covering of surface startingfr om the place of gas inlet (Fig. 2) . The planar layering effect (Fig. 2)can simulate some other than the re a l degree of homogeneous cover-age of surface. Thus it can affect the conclusions drawn from themeasured dependences of various physical quantities on su rfacecoverage. For instance , dependences of the heat of adsorption, ofelectric conductivity, o r of the work function on surface coverage,etc., can be distorted.

By substitution from Eq. (a) into (b), we arrive at:

The rel at ive deviation (ov,/VC) = 6v, - 0.1% and (up/pz) = 6p2- 1 . t i spossible to neglect the fi rst ter m on the right side of Eq. (c)with reg ard tothe second te rm and the resulting error of determination V is thus reallygiven by acc ura cy of the measu rem ent of pre ss ur e. The deviation u willthen be minimal when

a-(2VS + v2 + 2VCV)= 0avthat is, when

v = vc (e)*Note: Two types of layer ing effect ar e discussed in the liter atu re:

(1)suc ces sive perme ation of the adso rba te into the bulk of the adsorbe nt (itprocee ds along por es or by d irect penetration into the crystallographic lat-tice) and (2) succe ssive covering of the adsorbent in the surfa ce plane (pa rtswhich a r e nea rest to the gas inlet are covered first and immediately up to acerta in depth of the adsorbent). The fi rs t type of layering effect cannot beeliminated. O u r discussion concern s only the planary layering effect (2).


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STATIC VOLUMETRIC METHODS 2 7 1

FIG. 2. Scheme of the plana r layerin g effect. 1 , Gas inlet to adsorptionvessel; 2 , thin layer of adsorbent; 3 layers of adsorbate.

the geometric center of a spherical adsorption vess el [21,22] (Fig. 3 )or to use the inle t in the form of the Lava1 je t [23-251 (Fig. 3), whichcauses scatter ing of molecules to a wider space angle even thoughstill not fully homogeneously.

The transport of gas w i l l not essentially affect the equilibriumamount because it will suffi ce simply to wait long enough until equi-librium is estab lished. When measuring adsorption kinetics, how-ever, it is neces sar y to fulfill the fundamental condition: the manom-et er used must always be placed so that the pr es su re being measuredat a particular time and the pre ss ur e in the adsorption vess el beequal. This can be attained first by placing the manometer in the im-mediate neighborhood of the adsorption vessel, and al so by using

surface coverage, it is of advantage, then, to place the ga s inlet inInsofar as we a r e interested in questions concerning the degree of

3 3FIG. 3 . Variou s kinds of gas inlets to the adsorption ves sel with sphe ricalsymm etry of the adsorbent layer. 1,Gas inlet; 2, connection to vacuum pump;3, adsorption vessel.


16/57

272 Z . KNORsufficiently wide connecting tubes (Fig. 4 ) * and by suppressingchanges in pr es su re s caused by the operation of the manometer itself.

IV. ESTIMATE OF THE VOL UME OF ANADSORPTION APPARATUSNow we shall make a rough est imate? of the maximum si ze of thefr ee volume V, of the apparatus which still allows working with cer-

tain desir ed accuracy, i.e., with a given relat ive standard deviationof the individual measurement of the total adsorbed amount Na,:

The estimate is made on the basi s of the following assumptions:(1) the studied gas behaves as an ideal gas; (2) the studied gas is ad-mitted to the adsorbent in an amount just sufficient for completemonolayer coverage of the adsorbent a t equilibrium pr es su re pe$;(3) the whole apparatus has a constant temperature T. Then it canbe written for the adsorbed amount Na,:

*Note: The rate of gas transport Q can be est ima ted with the help of agrap h (Fig. 4) where Q is given in lit er s sec units. To compa re the r at e withthe adsorption ra te being measured, we must usually exp res s it in molessec-i units. The rate of g as trans por t in these units Q can be calculated fromthe relation:

Pi -Pz = rwhe re p1 - pz is the difference of pr es su re s in t o r r at en ds of th e given tube,T is temperature, and R is the gas constant: R = 0.62 x 10 t o r r li te r grad-

tNote: This estimate does not r epres ent a full analy sis of e r r o r s affectingthe accu racy of measur ement of the adsorbed amount but it s er ve s as a guidein th e const ructi on of a volumetric adsorption apparatus.

%Note: The te r m equilibrium is used in this artic le, for reaso ns ofconciseness, both in the s ens e of re al thermodynamic equilibrium and, insome instances, of stationary states, i.e., in cases where the given systempract icall y d oes not change with t ime without being in thermodyn amic equi-librium (e.g., at irreversible chemisorption).


17/57

S T A T I C V O L U M E T R I C M E T H O D S 2 7 3

D i am e t e r o f tube i n cmFIG. 4. Conductance of cylindrical tubes for a i r at 293K. [Fig ure taken

from S. , Dushman, Scientific Foundations of Va cuum Technique Chapman andHall, London, 1949): p. 97.1where N, is the amount of ga s admitted to adsorbent and N, is theamount of gas in the ga s phase aft er establishment of the equilibriumpressu re pz. The standard deviation a, of the individual de termina-tion Na,iS given by [19]:

Substituting from Eq. (22) we have


18/57

274 Z . KNORand af ter rea rranging by means of Eq. (22):

where 6, = Uv/V, and 6, = u,/T. If there is up1 = up, = up, we canwrite

where P = Up/pe. By further rearrangement we obtain

From Eq. 27) it follows:

If there is 62 >> 62, + 6 ., we get the rough estimate:

For the desired deviation of measurement of the adsorbed amount6, and the given e r r o r of measurement of pr es su re b p , Eq. (29) givesthe relation between the permissible volume V, and the amount Na,adsorbed at equilibrium pr es su re Pe a t temperature T (Table 4).

TABLE 4Suitable Volumes of Apparatus fo r Various Types of Sorbents

Surface area, Permissible volume,Type of sorbent A, om2 V, cm3

Film 1 3-1o4 1 4Crushed cry sta l l o 3 l o 3Filament 1 10

aV, is the permissible volume estimated with the aid of Eq. 29) for6a = 0.05, 6p = 0.02 Le., 6a = 5%, 6p = 2 ), pe = lo - torr, and N a = lo i56.O23.1Oz3 moles. /


19/57

STATIC VOLUMETRIC METHODS 2 7 5V. CONSTRUCTION OF STATIC ADSORPTION APPARATUSF O R VOLUMETRIC MEASUREMENTSEach apparatus for the study of gas adsorption on soli ds is com-

posed of four fundamental pa rt s: vacuum (pumping) system, a dso rp-tion vess el, bu ret space, and re se rv oi rs with a dosing system , The

F IG . 5. Mercu ry float valve, (a), Overal l schem e: 1, connection to appar-a t u s ; 2 , connection to apparatus (from this side the value will withstand anoverpressure); 3 , connection to mercury reservoir; 4 nd 5, ground joint s u r -faces; 6 . t rap for grease t rac es from valve 8; 7 , capillar y for outlet of m er-cury from trap. (b) Scheme of using m erc ur y float valve fo r controlled s l o wadmiss ion of ga se s: capilla ry K is equipped with a sca le f or setting the mer -cury level a t a partia l ov erla p of the group joint. (c) Scheme of using a pai rof mer cur y float values a s a dosing device; valves thus connected will with-stand overp ressure from any side.


20/57

TA

5

CoUnHgVmTq[3

T

A

a

Daw

Cuo

Ne

eme

U-S (mcy

co

Mecy

-3

go jon vv

Dygo vv

Pacyumeda

bysmecuo

aoaohdn

repmnraen

sopoopsoco

Pacyumeda

bysmempao

thwhahgo

peuepbyo

unacayfosow

fenoghdn

repmnraen

d

osopo

Nsocov

pa

tcyumeday

smempaop

sbyounacay

(owamsoogn

d

osopocb

wd

Psewhmecyc

nbd

ssaoy

pe

omecyv

inaauncosma

dmohwnwh

sahgopeue

Mecyepscb

d

ssaoyd

ccuo(ofuo

wre

efaego

jonspeeayba

so1opay[1

pe

omecyv

inhaau

[234,31

1 [711

DnwhahgopeIsoaa

[2331

sueeavydc

touocy

1

cuocbu

pshsu

oyfosansp

faneo

apeuepto

gosua


21/57

Meavv

Cofe

whowmnmas

GSo

ao6%

G2%In

1Sn

lqdaromem

paue

Eympaowh

sahgopeue

cboeuavv

fororeaoo

gamsocb

wdSmecuoa

mpaowha

sodmawha

hgopeueae

osmdmo

loweoov

eahgemaue

cbwd

Rhdccuo

lmedaysopo

owsnaaoy

tyuuysuaay

dmnshraeopmn

D

oodo(oo

snqeown

tohgcsomeas

(Gaeuuyc

suensmadm

sohcnre

raeopmnn

y

ohn(won

aconoahg

temaue(en

lqdao

[262933

11

Onoey

[211

odom

2

bfewh

memava

thcayn

vmamgm

oodza

remanrean

aeao

cay

aJTey

aYuA.Bo

pvenomo


22/57

278 2 . KNOR

individual par ts a r e separated from each other by cutoffs of widelydifferent types (Table 5). The most frequently used cutoffs in ad-sorption apparatus a r e mercury U-shaped cutoffs or float valves,cutoffs filled with low melting metals or alloys, and all-metal valvesof the Alpert type. For apparatus operating with mercury (with mer-cury diffusion vacuum pump, McLeod monometer, etc.), mercuryfloat valves ar e of greatest advantage (with ball-and-socket or planeground joint) [72,153] (Fig. 5). They offer some advantages as com-pared with conventional U-shaped cutoffs. A ground joint coveredwith mercury withstands an overp ress ure of 1 or more f rom oneside. When two valves a r e connected i n se rie s (Fig. 5) , they canwithstand atmospheric overpressure from both sides; ground jointnot covered by mercury makes it possible to admit gases into vac-uum slowly by diffusion. Finally , the volume of the appara tus on theside of the ground joint is not affected by the height of mercurylevel setting.

FIG. 6. Alpert type all-metal valve 1, driver; 2 , diaphragm; 3 , nose;4 , cup; 5, vacuum leads.

Alperts all-metal valves (e.g., Refs. [26,29,33]) and cutoffsfilled with low-melting metals o r alloys ar e of advantage for appa-ratu s without mercu ry vapors (see Fig. 6). Operation of an all-metal valve i s simple and quick. These valves can also be used forslow admission of sm al l amounts of gas. They al so withstand even ahigh overpressure. Their durability, however, is limited. In somecases the presence of a lot of metal, from which the valve is made,ac t s as a drawback. Complete degassing of these valves i s difficultand an interaction of gases with the surface of the degassed meta lcan occasionally occur.Cutoffs filled with low-melting meta ls or alloys (for example,see Fig. 7) mostly offer the advantages of very simple construction


23/57


C )21 b )FIG. 7. Examples of cutoffs filled with low-melting me ta ls and/or alloys

(a) 12121, b) [165], c) [1671. 1, Fasteting plug with sealed iron core; 2, low-melting metal or alloy; 3 , level-controlling plug with sea led iron c ore ; 4,heating; 5, asbesto s fabr ic f or sp ringing different th erm al expansion of glassand i r o n and f o r preventing mechanical shocks. All operations of these cut-offs are effected by means of external magnets.and manipulation. If we do not work with an alloy which i s liquid a troom temperature, however, it is necessary, to heat the cutoff toan elevated temperature for each operation. This both complicatesthe work and br ings the danger of r e le as e of gases from walls .

In the forepumping part of the appara tus and sometimes even inthe pa rt for preparat ion of gases-provided they a r e being preparedat high enough pressures p > 10 tom)-even greased glass cocks,e.g., Ref. [35], can be used. The main difficulty caused by thesecocks lies i n the impossibility of degassing them at a n elevated tem-per atu re. In the majority of c as es the source of gases rel eased intothe apparatus volume is not, a s a rule, the vacuum grease itself(the vapor tension of which can be very low) but ra ther water andgases dissolved o r trapped in the grease . When using the gre ase dcocks it is also necessary to reckon with the fact that, even whiledegassing other parts of the apparatus by heating, the temperatureof cocks must as a rule not exceed T 300K. At higher tempera-tures grease is soon pres se d out of the ground joint. For this reasonwater-cooled cocks a r e sometimes used [216].

VI. VACUUM SYSTEMIn this ar ticle we shal l not dea l in detai l with the fundamentals of

vacuum technique. These can be found in the lit er atur e [15,16,26-30,34-36]. Only the basic proper tie s of some currently used pumpingelements (Table 6) and pressure gauges (Table 7) w i l l be mentioned.


24/57

TABLE

VmPmPoe[16

3

Lmovm

T

tor

Fe

Reo

vm

pmn

to

1s

A

a

Daw

Cutoe

Ne

ampe

Meco-

1~

sa opm

Duolo-

opm

7

05-3 (a

7to 011(a tom)

21

42 (a to

Depmn

fomam

spcpe

suepm

oakn

og Nmoes

pmoa

g

sma

dm

o

dnre

qeap

tcaaa

ryepm

Scoo

v

ae

poou(hn

ooaso

oowh

dob

Scoo

v

re

qefoe

pmnsa

Pnped

[133

sbnR

3poeo

anov

pfen

ta33

c

fo2

mease

[4ooa

[44 sbnR4

poeo

anov

pfena

[22333

c

fo34

mease

[444aum

nmod4

1223

3334

Pnped

[2233

[1233


25/57

Mecylo

3x11

duoPm Io

pm

12

incm1~

1~

bnwh

N3

ge

Spo

7

oa

lo-?-

12

tv comea

se

31

Smaa

Ao-

aduo

to

opm

D

oPmoa

pmc

g(bn

suo

whee

amefev

ralaoncamn

knog

tooam

015(aspedry

lo

o

vm)

D

oSmecu

tyosotoamp

b

suaonp

peaoluooam

aknospe

g(eovm

raeoc

inhso

beg01

(ao-

to

ScomePnped

[1233

cyv

sbn

2455

reefoeR12

5

pmnsa

33po

teoan

mecyv

pfen

ta33

45(e

whmnan

inca

leoqd

no45

Rea

Pnped

[1233

iayep

sbn

23

m

meR

12

pmnc

2333

pypm

mmy

ogreee

mnb

n

thaau

[1333

cysowfodgee

6344

d

no

thhv

66

sob

umosob

pmo

ispmo

gremnfomam

inhaaspcpe

tuamysueoo-

topeue

1

LmepmnVumo2

Faaoyypm


26/57

TABLE7

PeueMamePoe[

Romue

To

peue

mme

to

Aa

Daw

Cuo

Ne

eme

l 3 l

McL

10-6-10

Aouemme

mme

(cbaonre

qegep

suerasme

mpaom

sueoapeue

iepvog

pcmo

OaewhmcyPnpedb

[

(mcyv

inR[

7

mbfoo

d

odsoo

odaowno

2233u

focbaoo

ohmme

thmmeae

fe[

p

sbydofen

tapmnee

Mocofom[

swneoo

c

ev

[

aeds

cnyreavy

lomesee

fodemnoo

peue25mn

peuecb

aomcyre

cdmbeo

muepeueo

c

ev

whcmco


27/57

j

Pa

1512

Pbyoao

mme

mcredn

mmeren

rend

o

cm

oog

p(mme

cbuaa

ync

o

whahyo

mmeegwh

MoLg

na

socome

v

wnb

dobvoe

amsoohg

peue

Memamme

131

Aouemme

pbyoauto

mcredn

mmedad

nd

ocm

poogp

nasocom

peav

oaeaaem

pauesuay

cue

Mameren

Pnpedb

[1189

d

ocm

inF11

toogp

2233

[910

(nsuaefom

sunpeuen

po

am

Tmctvyay

pebc

o

gpcm

todcewh

sayomun

capbyo

eeoccc

oaeahg

temaueoh

fam12C

DccuoPnped

[113

(pcayfoh

sbnR

11

raoowpe

[1122

sue

33

cn


28/57

TA

7cn

Ro

mue

To

peue

Cuo

mmme

to

A

a

Daw

Ne

eme

K

1712Pbyoao

DccuoPnped

b

[113

mme

mcredn

sh

v

inR[15,16,

11

aouemm

oaeaeee

2233

eensoco

im

ea

cwm

v

fephsshe

thdmoo

tunhcba

tosnna

mmeren

d

payo

gpcm

to[1

tempauen


29/57

Byd

Ap mnme

1113P

byoauo

mcreodn

wdmun

randwore

goovyow

peuerea

tvysme

mnpao

ManmeredndPnpedcbd

pnocom

oinRs[112

ogeoae

233mmy

mywhhchee[123

o(12

K)

1

cnbued

caknoho

apmnee

cbhon

mnaeo

aomzoec)

pmndpn

dnobnnh

oknogfo

chhpmn

Nsab01

eereavycomlesseB

pcedcoruo

pmneecn

foeeroccrcusbsueedb

redooemis

socuen[2

1

undp

tenaowscn

cuechnoma

nmesenvy

[511

Cruo

[1122

2331

Crcus[2

111

1 Mofco

fohgpe

sue(o

to[31

11 co

nd


30/57

TA

cond

Rno

mued

peue to

Anag

Dawk

To

mnme

Iozo

guwh

codems

so Masp

tromes

10-12-10-3

Pbyoauomc

reodnoae

aomemaue

whanro

hnnegsun

peuenee

whdmgo

muncre

lavysmeco

sruoanmp

lao

Manmeredn

dpnog

qyreqre

somohg

vag2kV

dfcudgn

omvee

trohpm

inee

10-2-10-4

PbyoauomcCmcedcoru

reodnfuno

toanmnpa

moocom

otonsomce

ogpensocdfcuogn

om

ecnboasyem

wdgeddpn

ocoseoyom

sprome

Ne

Pnpedcbd

in[15,16,26,27,

34-361;mmy

ee[15,26,33,

1131

Cnbuedapm

ineemnch

omdfomT)

Wihspaco

sruop-

byomu-

inexremyow

peue

po-

to

Pnpedcbd

inF[15,16,26,

27,34-361;mm

oryee[15,26,

33,1131

Cruo

exme

[15,26,33,36,

141,1421

[26,36,1431

[26,144,145,

1461

[26,33,36,

147-1501


31/57

STATIC VOLUMETRIC METHODS 2 87Apparatus fo r studying adsorption on clean su rf aces of sol ids are

mostly pumped with diffusion pumps. Th is brings the n ece ssi ty ofworking with other construction elemen ts (baffles and cold tr aps) torem ove fr om the gas phase the vapor s of liquids use d in vacuumpumps (se e Table 6) [3 4 , 3 5 ] . In the adsorption apparatus prope r,where mercur y cutoffs and/or mercu ry manomet ers ar e used, it isnecessary to use freezing trap s. Traps protect other pre ss ur egauges (ionization, Pirani , and thermocouple pr es su re gauges) andthe adsorption vesse l against mer cur y vapors. Freezing traps of

1

FIG. 8. Examples of single freezing traps. 1 , Cooling liquid level.simpl e constructions are used as a ru le (e.g., Fig. 8), whe re a tubeof equal diame ter and shape cr os se s the region of t emp era tur e gr a-dient. Thi s s impli fies the calculation of the thermal transpirationeffect corrections.If we a r e to deal with well-defined sur fa ces of sorben ts, it isnec ess ary to work in the pr es su re region of the so-called ultrahighvacuum (p


32/57

288 Z. KNORbe followed, and heat of adsorption may be measured calorimet rically[31,168-1701. Furthermore, e lect ric conductivity of the adsorbent[171-1731, work function [31,174-178,183,1841, magnetic proper ties[31,179], Hall voltage [31,180-1821, diffraction of slow elec trons[31,185,186], etc., may be studied in a suitable adsorption vessel.Adsorption ve ssel s f or various form of clean surfaces a r e describedin another section of th is arti cle .

The adsorption vesse l is constructed so that ionization and Piranigauges, as a rule, a r e protected against vapors of liquids fro m vac-uum pumps, liquid manometers, and/or cutoffs by a t leas t two fre ez-ing traps . These, a fte r having been degassed by heating, a r e suc-cessively immersed into a cooling bath. At fi rs t that freezing trapwhich is located fart hest f rom the adsorption vess el is cooled whilethe vess el and the r e s t of the apparatus a r e still heated.In the course of the experiment proper it is necessary to keepconstant the level of the liquid cooling within the traps. This preventsback release of condensed and/or adsorbed gases . A number of auto-matic devices have been described in the lite ratur e, e.g., Refs.[49-561. As an example, a device [51] can be mentioned for keepinga constant leve l of liquid nitrogen o r oxygen (Fig. 9) . It uses the

FIG. 9. Device for maintaining a constant level of liquefied gases. G , Ves-sel; Z , rubbe r stopp er for setting rubbe r diaphragm R to suitable distancefro m the opening h; T , tube connection to the source of compressed a ir (thetube is closed when liquid is drive n by pr es su re of ga s evaporated in stora geDewar); K , valve used for filling up the gas thermometer, the sensitive ele-ment of which is the bulb b; t, soft tightening; D , storage Dewar; r , rubberhose; m, metal tubes.


33/57

STATIC VOLUMETRIC METHODS 289principle of a gas the rmome ter filled with atmospheric ai r or oxygen.The device is prepared for operat ion by imme rs io n of a thin wallbulb b (Fig. 9) into liquid nit rogen and by filling it with air (or oxy-gen) through valve K, opened for an in te rval of 2 - 3 sec. Locationand connection of the instrument a r e shown in Fig. 9. A s long a s thebulb b touches the nitrogen level, rubber diaphragm R does notsti ck to opening h, and nitrogen evaporating fro m the res er vo irDewar vessel leaks into the atmosphere. A drop of the level (by about4-6 mm) cau ses the ga s to expand fro m the fla sk, rubber diaphragmR closes the opening, and the ov erpressu re of evaporated nitrogenpumps liquid nitrogen out of the storage ves se l through tubing Puntil the level again touches the bulb. Fo r pumping of the liquid ni-trogen, one can use co mpress ed ai r introduced into the tube T. Bythis adjustment it is possible to diminish fur the r fluctuation of thelevel. Frequently, an ionization and/or Pi ra ni manometer is con-nected direc tly to the adsorption vessel. The fo rm er is used for de-termining the degree of degassing of the apparatus or for measuringadsorption at very low pres su re s; the l att er for studying adsorptionkinetics.

VIII. BURET SPACEVarious pr es su re gauges covering the range of p re ss ur es one is

inter ested in and possibly al so a gas buret a r e usually included inthi s pa r t of the app ara tus . In the study of adsorpt ion on clean su rfac esof solids, we need to meas ure pre ss ur es p < tor r) up to pre s-su re of 0 .1-5 tor r. Higher pr es su re s ar e used in the calibration ofvolumes of the appara tus in a region where the thermomolecul areffect does not exe rt any mo re influence and in the study of physicaladsorption, e.g., of Krypton, the satura tio n p re ssu re ps of which,at T 78"K, is ps - 2 to rr . There fore the adsorption apparatus isusually equipped with an ionization manometer of the Bayard-Alperttype, with a Pirani monometer, and a McLeod manometer. It is ofadvantage to u s e so me type of McLeod pr es su re gauge which enable sus to measure a wide range of pr es su re s 10-6-10 torr). It is thuspossible to cal ibrat e not only the other manome ters , but al so thevolumes of the appa ratus with a single McLeod manometer.A s an example, we ca n name the following type [72] (Fig. 10) ofthe McLeod which, a s comp ared with other types , off ers two princ i-pa l advantages: (1) the capillary is not deformed when constructingthe pressure gauge a s is the case with sev era l capill aries connectedin one of stepwise changing di am et er ; and (2) this manometer h a s a


34/57

290

f

Z. KNOR2

a

3FIG. 10. McLeod manome ter fo r wide range of pre ssu res . 1 , Permanently

pumped-off a r m (eventually sea led ); 2 , connection to the apparatus; 3 , connec-tion to the mercury reservoir; 4,mer cu ry U-cutoff closing the pumped-offa r m from undesirable admission of gas when measuring; 5 , capillary for thedelayed outflow of me rc ur y (delay in the m ercury outflow gives sufficient timefor adjusting the m erc ur y level in the manom eter between repeated readings).minimum volume fo r the given range of pre ssu res . The relation:

P = m h ,can be used for pr es su re determination with this pr es su re gauge,where K is a constant for the narrow and/or wide capillary (Fig. lo),h, the difference of heights of merc ury leve ls in the comparing andmeasur ing (sealed) capi ll ar ie s, and h, the distance of merc ury level


35/57


36/57

292 Z. KNOR

for the wide capi llary ; V, is the total manometer volume frommark a , V, the manometer volume fro m ma rk b, V, the volume ofthe tube and sealed capillary c, and r l and r2 the ra di i of the narrowand wide capillary, respectively.

An ionization gauge of the Bayard-Alpert type [15,16,26-361 ismost frequently used for measuring the lowest pre ssu res , both inthe determination of the deg re e of degassing the apparatu s and in thestudy of adsorption a t lowest sur fa ce coverages. To minimize in-fluencing the pr essu re and che mic al composition of the ga s phase bythe manometer itself, it is cus tom ary to use a cathode covered witha la ye r of lanthanum hexaboride. The cathode then emi ts el ec tronsa t lower tempera ture s and is sufficiently stabile [2271, Commercial

2 113 2

FIG. 11. Bayard-Alpert ionization pr es su re gauge. (a) Commercial type;(b) construction used in o ur laboratory. 1, Cathode heated by electric current;2 , grid; 3 collector; 4, lead to the conductive coating of inner gauge walls.ionization manom ete rs mostly have the leads for a l l elect rodes inone socket (Fig. 11). If the pr es su re gauge is homemade, it is pref-erabl e to divide the lea ds among se ver al joints. Repairs such asBy substituting from Eq. (e) into (d), e.g., fo r hi and finding

(i.e., the condition for minimum X at a given hi) we obtain

that is,


37/57


b i

FIG. 1 2 . Scheme of the electric circuit for ionization guage operation.I o M , Ionization gauge; E, , stabilized sourc e fo r heating the cathode (storagebattery); G , so ur ce of g rid voltage; C , source of collect or voltage; A , , mea-suring instrument fo r monitoring em ission curren t; A , , instrument for measur-ing cathode heating cur ren t; A , direct current amplifier for measuring ioniccur ren t. Electron emi ssio n cur ren t is usually of the or de r of 10-6-10-3 A L o wemi ssio n cu rre nt d ec re as es the pump effect of the gauge.changing the cathode, coll ector , etc., a r e then easier (Fig. 11). Astabilized source or bat ter ies and accum ulato rs can be used to runthe gauge. Typica l va lues [16,26,33] of voltages used a r e given inFig. 1 2 .given by

The relat ion between ionic curr en t i, and emission cur re nt i- is

where the constant k has a value dependent on the geo metri c arra nge -ment of the ele ct rodes and on the kind of g as . The value of constantk is usually of the order of k = 10 torr-I and is determined by cali-bration, e.g., by means of the McLeod monometer. To eliminate theinfluence of the undefined potentials of manometer walls [50,139,1401,it is of advantage t o cover them on the inside with a conducting layer,e.g., 218Sn0, or 50Pt.The layer is then grounded.Thermoconductive (resi stanc e or thermocouple cell) pre ss ur egauges a r e used for following adsorption kinetics and, particularly,for measuring pr es su re s in the range of 10A5-10 o rr in apparatusoperating with the so-call ed dry vacuum 261, i.e., without usingliquids eit he r in vacuum pumps or in m anometers [15,16,26,34-361.The main problem with these gauges is the stability of their reading.Stabilization of the proper ti es of these man ometer s is usually ef-fected by heating them in low pre ss ur es (0.1 torr) of air at a higher


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294 Z . KNOR

/

FIG. 13. Pirani gauge. 1,Heating cu rrent supply; 2 , connection to appar-atus; 3 , spir al s tretching the filament 4; , supporting rod.temperature (800- 000K) han that of the measurement .The filament or s t r ip of these manometers is usually made fromtungsten or nickel from 0.001 to 0.005 cm thick. In the cour se ofmeasurement the filament temperature usually amounts to 42O-47O0K,whereas the jacket temperature is 273K or lower. The filamentfor ms one branch of the Wheatstone bridge and pressure is measured:(1)at a constant intensity of cur rent passing through the bridge (inthis case the deviation of the ze ro inst rument of the bridge i s cali-brated as a function of p re ss ur e) ; (2) at a constant voltage on thebridge [ in which c as e calibration is made as in ( l )] ; 3) at a constanttemperature of the filament (in thi s case one calib rates the voltagerequired to establish the equilibrium of the bridge a s a function ofpres sure . The las t way is particularly advantageous, because in thiscase the calibration curve is least steep [219] and enables us tomeasure more precisely over a great er range of pr es su re s than with thethe two other ways. To attain a grea ter stability, it is of advantage touse symmetrical connection of two equal thermoconductive manom-et er s in the bridge. One manometer s erve s for measurement and theother (a sealed one) for comparison, both being immersed in the samethermosta ted bath [ 151.

When using a McLeod gauge fo r calibrat ion of the other manom-eters, it is necessary t o pay due attention to the pumping effect ofthe mercury drag from the McLeod gauge [77-811 nto the freezingtraps. n e r ro r caused by this effect can run up to 50-200% of thepressure reading, depending on the gas and diameter of the tubing[77-811. It is advantageous to eliminate the influence of the men-tioned effect by suitable experimental arrangement rather than by

Resistance manometers a r e most frequently used (e.g., Fig. 13).


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STATIC VOLUMETRIC METHODS 295theoretical calculation [77-801. We can use a nar row tube supplyingmercury from the re se rv oi r to the gauge bulb and separate the gaugefrom freezing t raps by means of a nonlubricated ground joint 771.It is al so advisable to cool the part of the tube which connects themanometer to freezing tr ap s and to the mercury re se rv oi r down tothe temperature of solid CO, [78] or to cool the whole gauge downto 273K [81].

IX. RESERVOIRS AND DOSING OF GASESVery clean gases suitable for adsorption studies on clean solid

surfaces are commercia lly available usually in the form of sea ledgla ss ampules containing gas under a pr es su re close to the atmo-

FIG. 14. G las s bre ak seals. 1, I ron co re s ea l ed in g l a s s , s e rv ing to breakthe thin-walled bulb 3 o r tip 4; 2 , asbes tos fabric .spheric one. Glass br ea k seal s [26] (Fig. 14) ar e used for admissionof gas into the apparatus. Gas then pass es through a dosing device.Most frequently , a system of two or three cutoffs enables one to ad-mit a certain amount of gas into the buret space. The gas volume iseither directly measured o r only estimated. Dosing can be also donein such a way that a se ri es of ampules is connected to the apparatus,each ampule containing an amount of ga s corresponding to 1 dose.This is of advantage especially in cases of condensable vapors (i.e.,of gases condensing a t room temperature) and in cases when wecannot us e other types of valves [23,205,220].72,187-189,2281 (e.g., Figs . 5 and 15). A gr ea t var iety of cutofftypes can be applied for dosing gases. Diffusion of g ases throughcerta in solids (Table 8) can be used for slow admission of ga se s intothe apparatus and the ir simultaneous cleaning. The admission of gasis usually effected by means of a tube made of a given sol id andheated either by direct passing of electr ic curre nt [142,194,195] or

Examples of simple dosing devices can be found in the literature


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296 Z. KNOR4 2

/ I3FIG. 15. Simple dosing system . 1 , Connection to the gas reservoir; 2 , Con-

nection to the apparatus; 3 , connection to the mercu ry r eser voi r. Capillary 4re ta rd s flow of me rcury fr om U-cutoff s o that it is possible to admit gas fromthe re se rv oi r to the s pa ce between both cutoffs and then to adm it only thetrapped gas into the apparatus. Hi, Starting position of m erc ury level; H,,position of mercury level when admitting gas to the dosing volume betweenboth cutoffs. Mercury, flowing out of U-cutoff, ra is es the leve l fro m positionH, so that i t clo ses the re ser vo ir b efore the U-cutoff opens.

by an external heate r. The lat ter is mostly made of Nichrome wirewound around the outside of a ve ss el surrounding the given tube [190]or, in case of higher temp era tur es, fastened on wir e (tungsten)catches or cer ami cs within the v essel in the immediate proximityof the tube [27,197,198]. Connection of quart z tubes to the appara tu sis effected by means of graded s e a l gla ss. In the case of metal tubesa tube f ro m Kovar is used to which the re spect ive metal (Pd, Ni, orAg) is soldered by silv er o r gold, and the Kovar metal tube is in turnconnected via Kovar glass to the apparatus prope r,

When studying adsorption kinetics, w e som eti mes meet with therequi remen t of measu ring a t a constant gas pres su re over the ad-sorbent. Constant pr es su re over the adsorbent can be secu red in


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STATIC VOLUMETRIC METHODS 297TABLE 8

Purification of G a s e s by Diffusion through Solids [311Wallthickness, Temp.,

G a s Solid cm O Purity Ref IH2, Dz Pd 0.08 400-700 1:10'0 [26, 57, 190, 19110 2 A g 0.03 800-1000 - 11981NZ FeHe SiO, 0.03 < 1020 10:106 (H2); 126, 1971

Ni 0.01 400-600 1:106 [26,57, 192-1961a

1:106w, 2 7 Nzco, cod1. I. Tret'yakov, private information.

two ways: (1) by admit ting ga s through a valve automatically con-trolled by the respective pres su re gauge [199-2011; (2) by attachinga calibrated volume compensator (essentially a gas buret) to theburet space [202-204,2121.

In some cases it is of in te re st to measure not only the amountadsorbed , but al so the amount of gas which can deso rb under thegiven conditions. In such an instance the apparatus can be constructeds o a s to enable us to repump gas from the adsorption ve ssel to thecalibrated volume by means of some pump (diffusion vacuum pump[24,25], Toepler pump [202]). If a diffusion vacuum pump is used, ititself forms a part of the cal ibrated volume, and the amount pumpedoff is measured aft er t his volume including the pump has been sepa -rated fro m the adsorption vessel; the pump is first switched off. Theamount desorbed can be also measured without modifying the ad-sorption apparatus by way of successive desorption ste ps from theve ssel into the buret space which fi rs t had been pumped off, i.e., bysuccessive lowering of the equilibrium pressur e.

X. SPECIAL TYPES OF ADSORPTION APPARATUSWhen studying condensable gases, it is necessary to work underconditions which w i l l prevent condensation within the apparatus

proper [23,31,205]. In some cases one must heat the whole apparatusto a higher temperature. Therefore, freezing tra ps and pa rt s in-volving the use of mercury cannot be used. However, one can take


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29 8 Z. KNORadvantage of the ea sy condensation fo r dosing and gas handling pu r-poses either by cooling a pa r t of t he res er vo ir down to a given tem-perat ure and thus setting the press ure in the re ser voi r or by mea-surin g the amount of vapors admitted to the ap paratus pro per fro mthe amount of liquid evaporated from the calib rat ed cap il lary. Thelast way is especially advantageous in measurements requi ring themaintenance of constant pr es su re, e.g., when measur ing adsorptionisoba rs, capil lary condensation, etc. Fo r such ca se s it is sufficientmerel y to maintain the liquid at a suitable tem perat ure correspond-ing to the required equilibrium pre ssu re.

XI. SOME GENERAL NOTESEvery ap paratus fo r studying adsorption of gases on clean su r -

f ace s of sol ids should, in principle, be an ultrahigh vacuum app aratu s.It is there fore neces sary, in working it, to observe the appropriateconstruction prin cip les and working pro ce ss es (baking the whole ap-par atu s for s ev er al days under continuous pumping, etc.). F ro mthese pr ocess es t here follows a number of r equirements touching onthe construction el ements of a pparatus to which due rega rd must bepaid.as described in the lite ratu re a r e constructed either vertically orhorizontally. To heat them we use, in the first case, heating tapesmade of gl as s fabri c; in the second case , it is possible to const ructovens with rel ativ e ease. Examples of apparatus fo r the study of ad-sorption of gase s at low pr es su re s, e.g., on film s, can be found in theliterature [13 ,14 ,25 ,26 ,170 ,171 ,177 ,179 ,201 ,202 ,204-2131 (Fig. 16, 17,and 18).

The construction princ iples of volumetric ap paratus a r e gene raland valid fo r designing appa ratus sui table fo r studying adsorption onadsorbent s of va rio us types: on films, crus hed crysta ls, and fila-ments. Static volumetric m eas ure men ts on fila ments wer e made, SOfa r, only in the very beginning of re se ar ch of adsorption of gases onclean surfa ces of metal s (Roberts clas sical experiments) [229] inthe 1930s. However, fundamental difficulties which would hinderfu rthe r pur sui t of the re se ar ch do not exist. One would, of course,update the equipment, such a s replacing gr ease- lubri cated cockswith all- met al valves o r cutoffs filled with low-melting metal s, etc.But it is easi ly unders tood that, in view of the smal l sur fa ce of fila-ment, the requirements on both the vacuum and the minimization ofthe free volume of the appara tus in crea se ,

With st ati c volumetric a ppara tus, it is possible to study both

Apparatus used for studying adsorption of g as es on cle an surf aces


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FIG. 16. Scheme of the adsorp tion appara tus [1771. 1, Mechanical pump;2, ve sse l with active charco al cooled by liquid nitrogen af ter dega ssing (about3 hrs a t 600K) [61); 3 single stage mercury diffusion pump; 4, McLeod mano-m ete r [721; 5 , Bayard-Alpert ionization gauge; 6, Pira ni gauge; adsorptionvessel; 8 and 9, cold trap s; 10 and 11, mer cury float valves [721; 12, re se r-voir; 13, sem iaut oma tic dosing sys tem 1721; 14 and 15, vessels with sodiumazide and potassium permanganate, respectively; 16 , 1 7 , and 18, protectionfrom fluidization of powd ers and active charcoal; 19, mercury cutoffs; 20,palladium thimble for purification of hydrogen; 21, free zing tr ap for dosingand purification of xenon; 2 2 , xenon reservoir; 0 reased stopcocks. P ar tsof the ap paratus frame d by dashed lines a r e baked out during outgasing byheating tapes. Vacuum up to lo- torr can be obtained. [Figure taken from Z .Knor, and V . Ponec, Collection Czech. Ch ew . Commun., 31, 1172, (1966).1chemisorption and physical adsorption by measuring adsorption iso-therms, capillary condensation, adsorption isobars, and isosteres. *When measuring capillary condensation, which is one of the meth-

*Note: Adsorption isoth erm i s the dependence of adsorbed amount onpressure at a constant tempe rature; adsorption isobar is the dependence ofadsorbed amount on tempera ture at a constant p re ss ur e; and adsorption iso-s t e re is the dependence of pre ss ure over the adsorbed layer on temperatureat a constant amount adsorbed.


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300 Z KNOR

Valve-

FIG. 17. An ultrahigh vacuum syst em [2301 used for studying the reactionof a gas with a clean metal film. This syst em is constructed from g las s andmet al and can be heated to a high temperature. Ultrahigh vacuum 10-9-10-i0to rr can be obtained. [Fig ure taken from R. W. Rober ts and L. E. St. Pierre,Science 147,1529 (1965).1ods of studying the porosity of a given substance, a further require-ment joins those already mentioned. With sorbents exhibiting a hys-te re si s loop* in their isotherms, the pr es su re of gas, in the adsorp-tion vessel when measuring a given point of the branch of isotherm,must not exceed at individual doses the value corresponding to thesimple expansion of gas from the buret space into the adsorptionvessel a t the fi rs t dose, used to reach this point.. This requiremen tis equivalent to the requirement of measuring each point of the iso-therm at a constant pres su re for the total time necessary to reachequilibrium.ples with small surfaces by means of adsorption of isopentane atFig. 19 illustrates an apparatus for the study of porosity of sam-

*Note: In cases where, at higher pres sures, the adsorption and desorptioncurves do not coincide into a single curve, we speak of a hysteresis loop.


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FIG. 18. Adsorption a ppara tus pumped off by oil diffusion vacuum pump.1, Mechanical vacuum pump; 2 , reservoir of forepumping stage; 3 , oil diffusionvacuum pump; 4, freezing tr ap cooled with liquid nitrogen; 5, ionization gauge;6 and 10, titanium getteri on pumps; 7 , Bayar d-Alpe rt ionization gauge; 8 and9, adsorption vesse ls; 11 and 13, Pira ni gauges; 1 2 , rese rvo ir; 14, palladiumthimble for purification of hydrogen; 15-23, cutoffs filled with tin and/or Ga-In-Sn alloy; 24, dosing volume. The appartus w o r k s as the one in Fig. 17.(Fig ure taken fr om Ref. [2311 p. 50.)201K [223]. For studying capillary condensation, isopentane or someother gas can be used which is liquid at the temperature of adsorp-tion and also has other suitable properties. For example, in the caseof samples with a smal l surface a re a in an apparatus of great vol-ume, a gas whose tension is sufficiently low at the temperature ofadsorption should be used. However, the gas must not also reactchemically with the adsorbent. For example, isopentane cannot beused in case of clean surfaces of metals because it decomposes ontheir surfaces.There are also similar limitations (low saturation pressure, in-ertness) in the use of gase s for determination of sma ll surface a re as


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302 Z. KNOR

14

FIG, 19. Scheme of the adsorp tion appartu s for studying capillar y condensa-t ion on small surfac es. 1, Adsorption vesse l with sam ple; 2 tube to the reser-voir with isopentane; 3 , freezing trap; 4-8, mer cury float valves; 9 and 1 0 ,McLeod manometers; 11, cryostat; 12, connection to dosing of isopentane;13 and 14 onnection to vacuum pump. ( Fig ure taken from Nabokov e t al.12231.)(e.g., of ethane at 9O L [220] , ethylene at 7 8 and 90K [221], butane at157K [221]). Therefore, inert gases such as krypton (at 78K) [206,20'7,224,2251 and xenon (at 78-90K) [206,207,224,225] a r e used inthese instances, particularly w i t h metals.tageous for both experimental r eas ons (adsorption equilibrium isreached readily) and reasons of further treatment of the measuredres ult s. Direct measurement of is os te re s offer a determination ofisosteric heat and entropy of adsorption [2261. Adsorption isosterescan be measu red in the simples t way i f , in the course of measuringthe iso st er the amount of gas over the adsorption layer in the gasphase is negligible as compared with the amount adsorbed. Then wecan assume with sufficient reliability that the adsorbed amount doesnot change during the measurement. Thi s condition c2n be fulfilledeither by diminishing the fr ee volume of the apparatus or by lowering

Direct measurement of adsorption isosteres is often very advan-


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303_.TATIC V O L U M E T R I C M E T H O D Sthe pressure at which adsorption is studied. The fo rm er way doesnot, a s a ru le , come into consideration with ultrahigh vacuum appa-rat us , but the latt er way has been used for studying adsorption onevaporated films [226].The main advantage of the stati c volumetric apparatus lie s in thepossibili ty of a relatively simple combination of the measurementswith other methods for studying adsorption. In static apparatus it ispossible to measure both small and large adsorbed amounts of gases-irrespective of the rate of pr oc es s of adsorption-and the ra te ofadsorption. It is for these reasons that the static apparatus is themost universal type for determination of the adsorbed amount ofgases.

XII. A P P E N D I XA. Example of the Calibration

A s can be seen from Eq. ZO), he volumes of individual pa rt s ofthe apparatus must be known for the determination of the adsorbedvolume. Let u s take, for our example, a simple apparatus (Fig. 20)and the respective volumes will then be:

G

FIG. 20. Scheme of simple adsorption appartus. V1, V, , and V g , valves; T ,freezing trap s; A , adsorption vessel ; M , manometer; G , inlet of gases; P , con-nection to vacuum pumps.V, = volume of the part of buret space having the temperature

VBi = volume of those pa rt s of fre,ezing tr ap s which a r e immersed inT - 300Ka cooling bath with temperature Tc


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304 Z.KNORVv = volume of the pa r t of the adsorption vesse l space with the tem-

Vvi = volume of those pa r t s of fr eezin g tr ap s in the adsorption ves selVva = volume of the adsorption ves se l immerse d in a bath of tem-VM= volume of McLeod gauge, the wall s of which have a temp erat ur e

All the volumes mentioned can be det ermine d by calibrat ion eit herby weighting the liquid-mercury or water-which fill the given vol-ume; or, more comfortably, by using ga se s (excepting fo r the volumeVM) which do not ads orb on the wall s of the appara tus (e.g., H2 efor all- glass apparatus). Calibration is effected at pressu res 10 1< p < 10 to rr for apparatus made of tubes of 1 . 0 - 2 . 0 cm in diameter ,i.e., in a pre ss ur e range where it is certain that the th ermal tran-sp irat ion effect will have no significance. The volume of the McLeodgauge is, a s a ru le , known to us with sufficient accuracy ; we cantherefore use it fo r calibra tion of o ther volumes. Gas is closed inthe McLeod gauge under p re ssu re p1 and the remaining ap paratu s ispumped off to pr es su re p


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STATIC VOLUMETRIC METHODS 3 0 5urne known. With the calibrat ion we obtain a sys tem of equations:

where pi7 pi, pg, and pi have an analogous meaning as pi in Eq. (Al)and (A2). Unknown volumes Vv, Vvi, and Vva can be computed fromEq. (A3) - A5).

B. Example of Calculation of Amount AdsorbedIn th is example the simple appara tus (Fig. 20) will again be con-

sidered. A s the freezing tr ap s both in the buret space and in theregion of the adsorption vesse l a r e made from tubes of the samedia met er, i t will do to compute a single correction fact or P, (p) forthem from Eq. (10); individually, of course, f o r each gas studied.For the adsorption vessel it is neces sary to calculate the correctionfacto r for the given diamet er of the tube cr oss ing the temp era tur egradient. This is to be done for all tem peratu res encountered in theco urse of studying the adsorption. For a chosen tem peratu re and ga swe denote the factor a s Pa(p). The ra tio of tempe ratu res T/Tc willbe denoted a s ac, and T/T, = a,. The pr es su re measured by themanometer in the bure t spac e pr io r to the admission of a dose ofgas into the adsorption vesse l space is p1 and simultaneously thepr es su re in the adsorption vessel space is pz (at the fi rs t dose of gaspz = 0). Furthermore, i f we denote the equilibrium pre ss ur e which isestab lish ed after the two spa ces had been connected a s p3, then theamount of ga s Na adsorbed at the dose i s given by

where P& s the value of c orr ect ion facto r Pc at pressure pl, PE andP: the values of thes e factors at pr es su re pz7and Pg and Pg thevalues at pr es su re p3. In current measurement it is of advantage to


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306 Z . KNORconstruct graphs for each gas and each temp erature of adsorptionves sel and of f reezing tr ap s such that:

v = f(p)RTboth for the buret space where

and for the adsorption ve ssel space where

The adsorbed amount is then determin ed graphically. Dependences(A7 are represen te d in bilogarithmic coordinates by lines onlymoderately curved , approximating straight lines, s o that the readingof values is sufficiently accurate in the whole range of p re s su re s .

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nik, Berlin, 1955.1938.

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STATIC VOLUMETRIC METHODS 307[13] R. Suhrmann, A. Hermann, and G. Wedler, 2 hysik. Chem.[14] Y. Mizushima, J . Phys. Soc. Jafian, 15, 1614 (1960).1151 J. H. Leck, Pressure Measurement in Vacuum Syste ms , The[161 S. Dushman, Scientifique Foundations of Vacuum Technique[17] C. G. J . Janse n and A . Venema, Vacuum, 9, 219 (1959).[18] H. H. Podgur ski and F. N. Davis, Vacuum, 10, 377 (1960).[19] H. D. Young, Statistzcal Treatment of Experimental Data ,[20] D. Brennan and J. M. Jackson, Proc. Chem. Soc., 1963, 375.[21] D. 0. Hayward, N. Taylor, and F. C. Tompkins, Discussions[22] G. Wedler and M. Fouad, 2 Physik. Chem. (Frankfurt),40, 12[23] R. Suhrmann, J. M. Herras, L. V. de Herras, and G. Wedler,[24] G. Wedler, 2 hysik. Chem. (Frankfurt),24, 73 (1960).[25] R. Suhrmann, H. J . Busse, and G. Wedler, 2 hysik. Chem.[26] R. W. Roberts and T. A . Vanderslice, Ultrahigh Vacuum, Pren-[27] G. Lewin, Fundamentals of Vucuum Sc im ce and Technology,[28] G. Ehrlich, Advan. Catalysis, 14, 256, (1964).[29] D. Alpert, Handbuch der Physik, Vol. 12 S . Flugge, ed.), Springer,Berlin, 1958, p. 609.[30] P. A . Redhead, J . P. Hobson, and E . V. Kornelsen, Aduanc.Electron. Electron Phys., 17, 323 (1962).[31] V . Ponec, Z. Knor, and S. Cerny, Adsorpce nu pevngch lcitkdch

(Adsorptionan So l zd s ) , SNTL, Prague , 1966, in pre ss .[32] H. A . Steinhertz and P. A . Redhead, S c i Am., 206, 2 (1962).[33] J . M. Lafferty and T. A. Vanderslice, Proc. IRE, 49, 1136 (1961).[341 J . Groszkowski, Technologia Wysokieg Prdzni (High VacuumTechnology), Panstwowe Wydawnictwa Techniczne, Warsaw, 1955;Russian translation, IIL, Moscow, 1957.[35] G. C. Monch, Neues und Bewahrles uus der Ho~hz)akuumterhnik,VEB W. Knapp, Halle/Saale, 1959.1361 A. B. Bar ri ng to n, High Vacuum Engineering, Prentice-Hall,Englewood Cliffs, N.J. , 1963.[37] N. Beecher and N . P. Hnilicka, 5th National Symposium onVacuum Technology of the AVS, San Francisco, 1958.

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Gen Spin 651 Static by Knor in Catal Revs Sci Eng v 1 Iss 1 Pp 257 313 y 1968

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Transcript of Gen Spin 651 Static by Knor in Catal Revs Sci Eng v 1 Iss 1 Pp 257 313 y 1968