$pril, 1963
949
SOTES
perimental section. The diff ereiices of work function under steady state conditions of reaction or subsequently in argon did not correlate with catalyst activity as shown by data in Fig. 2 on measurements in argon (contact potential measurements on rubidium and lit,hinm promoted catalyst,s were not madr). The values plotted are averages of t\vo or inorc sa’mplc preparations for each point; deviations from the average were normally no more than a few hundredths of a volt. Contact potentials under reaction conditions were randomly displaced from those shown in Fig. 2. No significance could be given to potential changes caused by different gases, because this changes the work function of both the catalyst and reference in an unknown way. The work function a t GOOo of the argon-quenched samples should be similar to those in vucuo, since no argon is adsorbed a t this temperature. The results with contact potential measurements indicat’ed that the group I or I1 promoters lowered the effective work function of the catalysts as expected. However, the lack of a monotonic trend in this direction indicates that different concentrations of promoter existed a t the surface in various cases. On the other hand, Fig. 1 indicates a correlation between atomic properties (ionization energies) of the promoters and catalyst activity. It is concluded that in this case, only a fraction of the catalyst surface was responsible for its catalytic activity, and thus the electronic work function, in this case integrated, over the whole surface, could not be related to catalytic properties. This illustrates the conclusion of Thompson and Wishlade6 that gross physical measurements on solids may not be related to catalyst propert,ies in some mses because only parts of the surface are catalytically active. On the other hand, Roginskii’ has demonstrated in some cases a direct relation between electronic work funct’ion and catalytic activity of solids. Acknowledgments.-We wish to thank H. C. Tucker for assistance on electronic gear, and Professors Herman Pines, W. H. Urry, and Norman Hackerman for helpful discussions.
When a linear porous body of length I, and containing dead-end pores is discharging matter by diffusion from the outflow end at steady state the initial conditions are
Definition of terms is given in the section labeled “Nomenclature.” If the outflow end is suddenly closed while the inflow end is maintained at constant concentratioii the boundaiy conditions are
bC - ( L ,t ) ax
= 0 and
C(0, t )
=
Cr,
(2)
The concentration at any point and time can be obtained1-3 by solving equations 3 and 4 subject to the conditions given by equations 1 and 2 . N ~ Z -C _ v ,_x 2 -- D -_
at
e2
bx’
vl at
(3)
The solution, by methods described p r e v i o ~ s l y , ~is- ~
where x
pn = (2n - 1) 2L
and 8, are all roots of
(6) S. J. Thompson and J. L. Wishlade, Trans. Faradag Soc., 58, 1170 (1962).
(7) 9. 2. Roginskii, Kinelika i Kataliz. I, 15 (1960) (English translation).
-
SURFACE COXCENTRATION BUILD-UP DURING DIFFUSION IT\’POROUS MEDIA WITH DEAD4EYD PORE VOLUME
That is
BY RICHARD C. GOODKNIGHT California Research Corporation, La Habra. California AND
IRVING FATT
Miller Institute for Basic Research in Science and Department of iMineral Xechnoloog, Univevszty of California, Rerkeleu, California
and
Received October 10, 1961
Recent t r e a t m e n t ~ l - of ~ non-steady state diffusion through porous media which contain dead-end pores did not include the case of surface concentration buildup when a linear system at steady state was sudd.enly closed off a t the exit end.4 This case is presented here. (1) R. C. Goodknight. W. 9. Klikoff, Jr., and I. F a t t , J . Phys. Chem., 64, 1162 (1960). (2) R. C. Goodknight and I. F a t t , ibid., 65, 1709 (1961). (3) 1. F a t t , ibid., 66, 760 (1962). (4) The equivalence of the equations describing non-steady state diffusion to those for flow of a slightly compressible fluid in [t porous medium has been
diaoussed in reference8 1 and 2.
Equation 5 was evaluated by use of a Fortran program on an IBM 704 computer for several laboratory systems of interest. Nomenclature Ao cross-sectional area of neck of dead-end pore C concn. in flow channels (variable) CL concn. a t downstream end Co concn. at upstream end Cz concn. in de&d+md pore
NOTES
950 D H
diffusion coefficient a system parameter, D&/lOV0 length of neck of dead-end pore 10 L length of porous medium S parameter of the Laplace transform t time VI pore volume of flow channels VZ total volume of dead-end pores V , volume of a single dead-end pore x distance coordinate a a system parameter, D / P a constant defined by equation 6 p B tortuosity, diffusion path 1engthjL 4 porosity I .o I I I
Vol. 67
Figure 1shows a typical comparison of experimental and theoretical curves. The experimental curve was obtained as a continuous recording from an electronic pressure transducer.l-3 The maximum difference between theory and experiment is one per cent.
Discussion
-
I
Problems in non-steady state diffusion are usually treated graphically by plotting the solution of the governing differential equation in dimensionless form. For a porous system without dead-end pores equations 3 and 4 reduce to the dimensionless form
--
b(C/Co) - - b2(CICo) Dt a( d L ) b __(02L2)
-
--'
01 0
I
I
20
I
60
40
THEORY EXPERIMENTAL
I
I
I
I
I
140
I60
180
200
I
80
100 120 TIME, SECONDS.
I
220
Fig. 1.-Comparison of solution of equations 3 and 4 with experimental data from fluid flow model with initial and boundary conditions of equations 1 and 2: X / L = 1.0; VI = 926 CC.; V2 = 450 cc.; H = 0.04540 see.-'; a = 341 cm.2 sec.-l. I
I
I
I
I
I
I
I
I
I
I
I
I
I
0 60 0.40
3 0.20 I
4
2 \
G
0.10
'-1 0.08
0
0.06
0.04
0.02
1 I 0.01
0
I
4
11.0)926145010.04541 225 I
02
I
I
0.4
I
I
I
06
I
0 8
1
I IO
12
D t /02 L ~ .
Fig. 2.-Dimensionless concentration parameter a t X = L as a function of dimensionless time. System parameters used in equations 3 and 4 are shown in the insert table. Experimental The solution to equations 3 and 4 as given in equation 6 wa8 checked experimentally by using the mathematically equivalent fluid flow system. This method of studying solutions of the diffusion equation has been described in detail previously."-3 Briefly, it is a method in which pressure transients during nonsteady state flow of a slightly compressible fluid in a porous medium are measured for initial and boundary conditions equivalent to the diffusion problem of interest. Air, a t a mean pressure near atmospheric and a one per cent pressure gradient, is a satisfactory slightly compressible fluid. The porous medium is a plastic coated sandstone bar, five feet long and of cross-section 2 in. by 2 in. Parameters used in both the experiment and equation 5 are shown in the caption of Fig. 1.
(10)
If the terms accounting for dead-end pore space are included then equations 3 and 4 cannot be reduced to a convenient dimensionless form. I n the dimensionless form equation 3 will still have the ratio V2/V1. This prevents solutions of equation 3 from being independent of system parameters. For each VdV1 there will be a separate solution. Figure 2 shows a semilogarithmic plot of the dimensionless concentration parameter (CL - C)/(CL CJ, measured at the outflow end when this end is closed after being a t steady-state flow, as a fuiiction of the dimensionless time parameter Dt/02L2. Concentration as a function of time can be read from this curve because all other terms are constants for a given system. The curve labeled 1 is for a porous body without dead-end pores, This curve is independent of the system parameters and therefore applicable to all linear diffusing systems with the conditions given by equations 1 and 2 and with known D and 8. D must be measured independently by the methods conventionally used for measuring molecular diffusion coefficients. t? may be calculated from a steady state diffusion or an electrical resistivity measurement.6 A measurement of tortuosity by steady-state diffusion or electrical resistivity always gives 4/02. If the porous material has no dead-end pores then 4 is unambiguous and 0 is easily calculated. However, if there are deadend pores then a gravimetric or volumetric measurement of 4 mill normally include these pores. If, for a system with dead-end pores, 4 from total pore volume is used to calculate 0 from the measured 4/02 and then this 0 is used in the term Dt/02L2,the solution of equations 3 and 4 will give the curve labeled 4 in Fig. 2 . This curve is for a system of the same total pore volume as for curve 1 but some of the volume is in dead-end pores. Curves 2 and 3 in Fig. 2 are for systems in which the dead-end pore volume is known and only the connected pore volume was used to calculate 4. Unfortunately, there is no method at present whereby the dead-end pore volume can be measured. If experimental diffusion data together vith an experimental 02 term are plotted on Fig. 2 then any deviation from curve 1 is an indication of the presence of dead-end pores. Thomas6 has reported deviations of this kind in sandstone for which other evidence also points to the presence of dead-end pore space. ( 5 ) I. Fatt, J. Phys. Chem., 63,781 (1959). (6) G. H. Thomas, hi. S. Thesis, University of California, Berkeley, June, 1962.
KOTES
April, 1963 Acknowledgment.--The authors wish to thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, for their support of the research which led to this paper.
ON THE CONFORMATIOK OF THE D-GLUCOPYRASOSE RISG IN MALTOSE ASD IN HIGHElt POLWNERS OF D - G L U C ~ S E BY V. S. R. RAOAND JOSEPH F. FOSTER Departmbnt of Chemzstry, Purdue Unzversaty, LaJauette, Indzana Reeeaved October 18, 1968
I n considerations of the configuration in solution of amylose and other polysaccharides the question of ring conformation of the monomer units is of utmost importance.' Thus 130110 and Szejdli' have pointed out that if the D-glucose residues in amylose exist in the C1 conformation the chain should be relatively rigid and possess an essentially helical configuration. Of the two possible chair forms and innumerable boat forms it has been suggested from stability considerations that either the C1, B1, or 3B conformations are most probable.2 While it seems to have been generally accepted that D-glucose (in common with most monosaccharides), simple D-glucosides, and the glucose units of cellobiose and cellulose exist exclusively in the C1 conformation, there have been several suggestions that the same is not true for maltose and higher polysaccharides of the amylose series. Reeves3 called attention to the difficulty of forming a-1,4-glucosidic bonds between two glucose residues both of which are in the C1 conformation. He further suggested, on the basis of the incomplete reaction of amylose with cupraminonium reagent and as an explanation for the decrease in optical rotation in alkaline solution, that approximately half of the glucose residues of amylose exist in a boat conformation. This conclusion has been questioned by Greenwood and RossottL2 who favored the C1 conformation. Since methyl p-maltoside also shows a decrease in rotation of alkali Reeves further suggested that the non-reducing residue of maltose exists in a boat conformation.3 B e n t l e ~ ,on ~ the basis of comparative studies of the rates of oxidative bromination and hydrolysis, also concluded that the non-reducing unit of maltose possesses a boat conformation, while the reducing unit of maltose and both units of cellobiose have the usual C1 conformation. It would appear that clear answers to such questions should be attainable through nuclear magnetic resonance (n.m.r.) spectroscopy. It has been shown that in sugars5and in acetylated sugars6the signal due to the anomeric proton appears a t lower field than that of any of the other casbon-bonded hydrogen atoms. Furthermore, it seems clear from those same studies that the signal for an equatorial anomeric proton (HI,) occurs a t a somewhat lower field by about 0.5-0.7 p.p.m. than for an axial ansmeric proton (Hla). I n addition, the dihedral angle between the anomeric proton and (1) J. Hollo and J. Szejdli, Die Starke, 13, 222 (1961). (2) C. T. Greenwood and 13. Rossotti, J Pclynaer SCL.27, 481 (1958) (3) R. E. Reeves, J . A m . Chem. Sue., 7 6 , 4595 (1954); A n n . Rev. Bzochena., 27, 15 (1958). (4) R. Bentley, J A m . Chem. Soc., 81, 1962 (1969). ( 5 ) R . W. Lenz and J. P. Heeschen, J . Polymer. Scz , 61,247 (1961). (6) R. U. Lemieux, R. K. Kullnig, H. J. Bernstein. and W.G . Schneider, J . A m . Chem. Sue., 79, I005 (1957); 80, 6098 (1958).
95 1
the hydrogen on the adjacent carbon atom may be obtained from the magnitude of the splitting of the corresponding absorption peak through application of the Karplus eq~ation.~.' The n.m.r. spectra of maltose and a number of related compounds have been determined a t 60 Me./ sec. with a Varian A-60 n.m.r. spectrometer employing 10-20ojo by weight solutions of the carbohydrates in D20. The assignment of r values was made by taking the water peak (5.2 r ) as an internal standard. Results are shown in Table I. I n the case of cellobiose two peaks have been observed in the lower field region a t 4.70 and 5.38 r . From intensity considerations it seems clear that the peak a t 5.38 is due to the anomeric proton of the non-reducing unit plus the anomeric proton a t the reducing end when it is in the axial position @-anomer). The peak at 1.70 is due to the anomeric proton at the reducing end when it is in the equatorial position (a-anomer). These two peak positions approximately coincide with those of the P- and a-anomers, respectively, of D-glucose and the methyl D-glucosides. The dihedral angles deduced using the modified Karplus equation, namely, 5-1 and 160' for the peaks a t 4.70 and 5.38 T , respectively, while not in agreement with the expected angles for the C1 conformation (60 and 180') do agree well with the corresponding values deduced in the same way for a- and P-glucose and the methylglucosides. Hence these results are in agreement with Bentley's conclusion and with the recent demonstration by Jacobson, Wunderlich and Lipscornb8 that both glucose units in cellobiose exist in the C1 conformation. I n the case of maltose three peaks are seen in the lower field range a t 4.58, 4.74, and 5.30. From the intensity of these peaks it can be concluded that the peak a t 4.58 is due to the anomeric proton (HI) of the ncmreducing unit. Because of mutarotation the signal due to the protons Hl of the reducing glucose units appears a t two places, 4.74 and 5.30. The dihedral angles obtained from the splitting of these peaks are 54 and 154O, respectively. From the dihedral angles and the peak locations, it may be concluded that the reducing glucose unit in maltose is in the C1 conformation. The dihedral angle obtained from the splitting of the peak at 4.58 is about 55", in accord with either the C1 or B1 but not the 3B conformation. The T value of this peak is slightly lower than that of a-glucose (4.78). If this unit were in the B1 conformation this proton should be in an essentially axial position and it might be expected that its signal would appear at a much higher T value (above 5.0). However, this cannot be stated with certainty in the absence of suitable test compounds known to exist in a boat conformation. It is, nevertheless, very unlikely that the glucose ring would occur in a perfect B1 conformation due to repulsion between the protons a t C1 and C4, which would be very close in this conformation. Any twisting to relieve this repulsion would lead to a considerable change in dihedral angle. Bentley4 has suggested that the conformaiion is between that of the idealized B1 and 3B, which seems very unlikely from the observed dihedral splitting. Furthermore, due to the ready interconvertability of the boat forms it would be (7) M. Karplus. J . Chem. Phys., S O , 11 (1959). (8) R. A. Jacobson, J. A. Wunderhch, and W. N. Lipsoomb, Acta Cryst., 14, 598 (1961).
