May, 1953
DYNAMIC GASADSORPTION METHODS OF SURFACE AREADETERMINATIONS
surrounding chlorine atoms. The electron responsible for the paramagnetism is assumed to spend part of the time in p-orbitals on the chlorine atoms, and a reduction in the orbital contributiop to the g-value is associated with this. A number of compounds of the uranium group have been examined by Baker and Bleaney a t temperatures down to 20 OK. without any resonance being discovered. As these compounds have not been listed elsewhere, it may be useful to give them here. They are: UOz, u(So&, UF4 (both concentrated and diluted with ThFd), UBr4, UC13, UBr3, PuF3, Na (PuOz) (CH3COO)3. 9. Conclusion I n this brief review it has not been possible to mention more than a few of the main results of the application of resonance methods to the investigation of paramagnetism in the solid state. No attempt has been made to give an exhaustive list of references, but a fuller list will be found in a forthcoming review by B. Bleaney and IC W. H. Stevens (Volume 16 of the Annual Reports on the Progress of Physics; London, Physical Society). Earlier papers of a general nature which may be found useful are listed in 35.
DISCUSSION J. J. I~RITZ(Department of Chemistry, Pennsylvania
State College).-Do the two resonance peaks in K2Cu(SO4)26&0 show any differences other than those produced by the fact that there are two non-equivalent positions for the copper ions? B. BLEANEY.-The two resonance peaks shown in Fig. 4 occur at different values of the field because of the aniso(35) D. M. S. Bagguley, B. Bleaney, J. H. E. Criffiths, R. P. Penrose and B. I. Plumpton, Pmc. Phys. SOC.,61, 542 (1948); A. Abragam and M. H. L. Pryce, Proc. R o y . SOC.(London), A205, 135 (1951); B. Bleaney. Physicta, 17, 175 (1981); B. Bleaney, Phil. Mag., 42, 441 (1951).
517
tropy in the g-factor, and the intensities differ because they depend on the value of the anisotropic g-factor in the direction of the r. f. magnetic field. The difference in the widths is due to the presence of unresolved anisotropic hyperfine structure whose width is different for the two ions. B. BOLGER(Department of Chemistry, Pennsylvania State College).-What is the influence of positive or negative exchange, or superior change energies on line width and signal strength? B. BLEANEY.-Exchange forces do not in general alter the total intensity of the lines (that is, the total area under the absorption curve) but they affect the line width, and hence' the intensity a t the center of a line. The main effects of exchange are outlined in $5.
G. K. FRAENKEL (Department of Chemistry, Columbia University).-At what temperature were the paramagnetic resonance measurements made on the potassium ferricyanide? B. BLEANEY.-The measurements were made at 20'K. to avoid broadening of the lines because of the very short spin-lattice relaxation time (see ref. 4).
R. N. VARIAN (Varian Associates, San Carlos, California).-There has been considerable interest recently in just how narrow electronic paramagnetic resonance lines can be. What is your view of the matter? B. BLEANEY.-where narrow lines are obtained in concentrated compounds exchange forces must be responsible for the narrowing. It is not easy to see what limit can be set to this process, though it is only with a set of identical spins with no anisotropy and no splittings due to fine or hyperfine structure that exchange narrowing can operate fully. In magnetically dilute compounds the residual line width is due generally to the magnetic fields of nuclear dipole moments in neighboring diamagnetic atoms. Because of the large moment of the proton anhydrous salts should give the narrowest lines. (K. D. Bowers (see ref. 10) has obtained lines of under 2 gauss full width a t half intensity in KsCr(CN)e diluted with the diamagnetic salt K3Co(CN)a). The best salts for narrow lines would appear to be anhydrous sulfates, carbonates and silicates, where the negative radical contains no nuclear moments except those of the rare isotopes 0 3 or Site.
DYNAMIC GAS ADSORPTION METHODS OF SURFACE' AREA DETERMINATION' BY H. G. BLOCKER, SUSANL. CRAIGAND CLYDEORR,JR. Georgia Institute of Technology, Atlanta, Georgia Received Auoust 8, 1968
Investigations of the phenomenon of gns adsorption, as well as investigations of gas adsorption methods for surface area determinations, have been primarily concerned with equilibrium measurements, and dynamic measurements have received little attention. Therefore, two techniques, one approximating equilibrium conditions and one requiring a measure of the rate of adsorption, have been investigated. Both are shown to give surface area results in satisfactory agreement with those of equilibrium measurements.
In recent years the measurement of the surface area of finely divided materials has become increasingly important, especially in fields employing catalytic and adsorption processes. Several methods are available for evaluating surface area, but most attention has been focused upon gas adsorption methods such as those used by Brunauer,
Emmett and Teller2 and by Harkins and Jura.3 These and most of the other methods employed to date have dealt with some appropriate treatment of equilibrium measurements, and very little work has been done with any other method. The authors wish to report here some observations on two dynamic methods and to point out what may
(1) The work reported herein waB conducted by the Georgia Tech. Engineering Experiment Station through the Bponsorship of the U. 8. Army Signal Corps under Contract No. DA-36-039-se-5411.
60, 300 (1938).
(2) S. Brunauer, P. H. E m m e t t and E. Teller, J . Am. Chem. Soc., (3)
W. D.
Harkins and G. Jura, ibid., 66, 1366 (1944).
H. G. BLOCKER, SUSANL. CRAIGAND CLYDEORR,JR.
518
Vol. 57
be expected of dynamic surface area measurements. them a t 110’ for several hours and then cooling in a The first method is a modification of the steady- desiccator. Weighed samples were taken from this material the adsorption studies. The removal of other adsorbed flow adsorption techniques of I n n e ~ . I~n this for gases from the adsorbents was accomplished for each of the technique, equilibrium is approximated, but, be- methods by heating the sample to between 200 and 250’ e the space about the sample for a t least 16 cause complete equilibrium is not attained, less ~ h i l evacuating time is required than is necessary in a conventional hours (usually overnight) to a pressure of approximately 5 X 10-5 nim. Since many of the determinations were Brunauer-Emmett-Teller determination. made for routine surface area evaluation, and since it has The second method is that suggested by Jura been shown8 that further evacuation after a pressure of only mm. is reached increases the specific surface area value and PowelL6 These investigators have shown that a measurement of the rate of adsorption will lead that will be obtained no more than 3%, great care was not to ensure more uniform pretreatment. to an independent determination of the surface taken After the samples had been degassed, the voIume of the area of a solid, provided that there is a significant adsorption space was determined with helium. Emmett6 change in the rate upon completion of the first and others have shown that the adsorption of helium a t adsorbed monolayer. They found that this was temperatures of 77’K. or higher is quite small and can safely be neglected. Upon completion of the determination .of the case for the adsorption of NHs on a silica- adsorption space volume, the sample tube was filled with alumina cracking catalyst and for H20 on anatase helium to a pressure of about 200 mm., a liquid nitrogen treated with aluminum oxide. The authors have bath was placed around the sample tube, and the sample applied this method in the study of several other was left until thoroughly cooled. Cooling usually required about 30 minutes. Without helium in the sample tube to solids. act as a heat transfer medium, a much longer time is reI n the investigation of each of these methods, quired to cool the sample uniformly to the temperature of nitrogen gas, at the temperature of liquid nitrogen, liquid nitrogen. I n the steady-flow technique, nitrogen gas was introduced was used as the adsorbate. Procedure.-The apparatus used to obtain data for each of the methods was essentially the same as that described by Emmett.6 A Cartesian manostat, such as described by Gilmont,’ was used to obtain the constant flow rates required in the steady-flow technique. By means of this system, constant flow rates of from one to ten ml./min. were easily attained. Moisture was removed from the adsorbents by heating
32 28
24
-9 g 20 %*
e$ 16 2
8
2 12 8
I
4
I
I
o
aorso
0
00746 ml./mn
mt./min
-I
0
0
50
100 150 200 250 300 Pressure, mm. Fig. 1.-Adsorption isotherms for nitrogen on Kaolin M obtained by the steady-flow and equilibrium methods. The flow rates are on the basis of one square meter of sample surface: A, 0 , equilibrium; B, 0, 0.0240 ml./min.; C, 8 , 0.0745 ml./min. (4) W. B. Innes, Anal. Chem., 23, 759 (1951). (5) G. Jura and R. E. Powell, J . Chem. Phys., 19, 251 (1951). (6) P. H. Emmett, Sumposium on New Methods f o r Particle Size Determination in the Subskeve Range, ASTM, March 4 , 1841, pp. 95105. (7) R. Gilmont, Anal. Chem., 23, 157 (1951).
into the adsorption system at a constant, low rate so that equilibrium was approximated at all times. The volume of gas required to form a monolayer on the surface of the adsorbent was assumed by Innes4 to be that volume adsorbed when the system pressure was two-tenths of the vapor pressure of the liquefied adsorbate. This volume, in milliliters at standard conditions, was then multiplied by an empirical factor, 3.5, to obtain the surface area in square meters. A critical inspection of a large number of adsorption isotherms reveals that the volume of gas adsorbed at a relative pressure of 0.2 does not, in general, constitute a monolayer, although this may be a satisfactory assumption for the high specific surface materials investigated by Innes. Therefore, while the gas was introduced at a constant, low rate, the volume of gas required to form a monolayer was obtained from the isotherm by the “point B” method of Emmett6 and with the BET equation.2 The volume of gas in the system at any time was determined from the flow rate and the elapsed time. The temperature was measured with an oxygen vapor pressure thermometer. From these data, adsorption isotherms could be calculated. Isotherms obtained by this method for one sample are shown in Fig. 1, as is the corresponding isotherm obtained by the conventional equilibrium method. The same apparatus, but without the flow-controlling system, was used for the rate determinations by the method of Jura and Powell. I n this method a volume of gas more than aufficient to form a monolayer on the adsorbent was admitted at one time to the sample, and the change in pressure with time was observed. Assuming that the rate of gas adsorption is proportional to the gas pressure and that the adsorbed gas molecules are in equilibrium over the entire surface of the solid, assumptions that apply only when diffusion is not rate controlling, Jura and Powell arrived at the relationship (-dPt/dt)/(Pt P ) = F(Vt) (1) where Pt is the pressure a t any time, t , Vt is the volume of gas adsorbed at time t , and P is the equilibrium pressure when the amount of gas adsorbed is Vt. For ideal L a w muir adsorption the function F(Vt) will be linear when plotted against Vt, becoming zero when a monolayer is completed. When multimolecular adsorption is possible, the function does not become zero when a monolayer is completed and is not always linear a t low adsorption, but becomes nearly so as a monolayer nears completion. After the completion of a monolayer, the value of F ( V t ) has a small constant value. Figure 2 shows the type of curves obtained for three clays by this method.
-
Results I n the cases of the steady-flow and the equilibrium determinations the quantity of gas forming (8) P. E. Bugge and R. H. Kerlogue, J . SOC.Chem. In&, 66, 377 (1947).
.
May, 1953
519
DYNAMIC GASADSORPTION METHODS OF SURFACE AREADETERMINATIONS
TABLE I EXPERIMENTAL CONDITIONS EMPLOYED AND SURFACE AREAVALUESOBTAINED WITH VARIOUS METHODS
Materiala
Georgia umber Kaolin M Kaolin 5DS Kaolin 785 Kaolin 858 Kaolin 859 Kaolin 860 Kaolin 884 Kaolin 8% Kaolin 887 Kaolin 888
Flow rate in steady flow measurement per square meter of sample surfaceb (ml./min.)
Specific surface area (m.Z/g.) by Steady-Bow method Equilibrium method BET BET Point B equation Point B equation
...
...
...
0.0240 .0745 ,0849
94.6 95.1 23.6
84.5 85.0 27.2
...
... .0627 ,250 ,0238 ,891 ,0586 ,219
...
20.4 18.5 42.5 42.7 31.8 24.6
...
... ...
30.0 16.1 49.7 36.9 27.8 22.5
...
...
...
... ...
...
Rate method
126 92.3
119 87.9
161 89.1
22.3 21.4 19.1
22.6 22.1 22.8
21.9 21.0
47.8
41.5
...
28.G
26.3
...
34.8 104 261 16.6
34.8 105 260 22.9
29.5 109 266
...
... ,0468 16.5 24.5 ,165 14.6 16.3 Kaolin 889 ,0383 39.4 39.1 38.6 37.1 ... Abrasive alumina ,127 2.32 4.23 2.19 3.3G ,.. Adsorbent alumina ,127 200 234 195 226 ... Potassium perchlorate . 170 1.21 4.30 1.15 1.52 ... Magnesium carbonate ,0779 G1.0 70.7 60.9 57.3 ... Iron powder ,0568 0.64 0.74 0.78 0.74 ... Copper powder .151 0.22 0.76 0.24 0.30 ... .661 0.33 0.31 Surface calculated by BET equation from a Kaolin samples obtained from Georgia Kaolin Co., Dry Branch, Ca. equilibrium data. a monolayer was taken as point B, the lower extremity of the straight-line segment of the isotherm, and was also calculated by the BET equation. I n the case of the rate determinations, the monolayer volume was taken as that given by the intersection of the straight line through the plotted data with the abscissa on a plot such as Fig. 2. A cross-sectional area of 15.4 square Angstroms per molecule of adsorbed nitrogen, as recommended by L i v i n g ~ t o n was , ~ used for calculating the surface area of the materials from the quantity of nitrogen required to form an adsorbed monolayer. Some of the experimental conditions employed and the surface area values obtained by these dynamic methods, along with values obtained by the usual equilibrium method, are given in Table I.
Discussion An examination of isotherms obtained by the conventional equilibrium and by the steady-flow techniques (Fig. 1) shows that, while the isotherms are similar in shape, they are not identical. However, when point B is located at the lower end of the straight-line portion of the isotherms as Emmett suggests, the quantities of gas adsorbed a t point B are quite close together and are in agreement with the quantities indicated by the BET equation. The steady-flow method is not a strictly dynamic gas adsorption technique since the flow rates employed were low enough to approximate equilibrium. Therefore, it cannot be considered an inde(9) H. K. Livingston, J . Colloid Sei., 4, 447 (1949).
0.28
0.24
o
0.20
Go. Kaolin No 785
0 Ga. Kaolin Na 50s 0
h
Ga Kaolin No. 884
6 I 0.16 F;,
v
=: ? 6 0.12 V v
I
0.08
0.04
0
5 6 7 8 Volume adsorbed, cc./g. a t S.T.P. Fig. 2.-Adsorption isotherms for nitrogen plotted by the method of Jura and Powell: A, 0, Ga. Kaolin No. 785; B, 0 , Ga. Kaolin No. 5 Ds; C, @, Ga. Kaolin No. 884.
4
JOHND. HOFFMAN AND BEULAH F. DECKER
520
pendent method of area determination, but rather a different technique. The only advantage of this steady-flow method is that, by using it, data for an adsorption isotherm may be determined more rapidly than by the usual method, usually in less than 20 minutes after the sample has been cooled. The rate method depends directly upon the rate of adsorption and, therefore, affords an independent means of surface area determination. Surface area values obtained by the method, while not in as close agreement with the results of the equilibrium method as are those of the steady-flow method, are generally satisfactory. The rate method is not suited for routine determinations. The value of P in equation (I) must be determined from an equilibrium isotherm, and, while even a n approxi-
VOl. 57
mate isotherm is satisfactory, the time required for its determination renders the method impractical. These two methods serve to show what may be expected of dynamic gas adsorption techniques of surface area determination, but many more experimental observations must be made to determine the range of applications and the dependability of the methods. There is also a need’for theoretical investigations of the subject so that the mechanisms of these and other adsorption processes may be more clearly understood. Acknowledgment.-The authors wish to acknowledge their indebtedness to Prof. J. M. DallaValle for his encouragement and many helpful suggestions and to Prof. R. L. Sessions for reading and criticizing the manuscript.
SOLID STATE PHASE CHANGES IN LONG CHAIN COMPOUNDS BY JOHND. HOFFMAN AND BEULAH F. DECKER General Electric Research Laboratory, Schenectady, N . Y . Received November 7 , 1966
Three types of phase changes in n-bromides and paraffins of high chain length are discussed. Cooling curve and revised specific heat data are presented to show that the rotational transitions which appear just below the freezing points of some bromides and paraffins are of the first order. The phase below the transition temperature is given the general name p, and that above it is called a. It is demonstrated that the rotational transitions in purified n-paraffins are thermodynamically reversible, and that the transition temperature varies in a linear way with chain length. The entropy of transition of a number of bromides and paraffins is shown to be independent of chain length. Some X-ray data on purified paraffins are also given. The results quoted above are in accord with a recent theory of cooperative hindered rotation in long chain compounds. One conclusion reached is that torsional twisting of hydrocarbon chains in the solid state is not severe. a~-&and &-P2 transformations are discussed next. The cy- and p-phases of certain materials are unstable and spontaneously transform to a stable form on storage (the subscript 1 means unstable while 2 means stable). Such changes take place over a wide temperature range. The thermodynamic consequences of a1-p2 and &-p2 transformations, which occur in impure C-18 and C-22-Br, are considered in some detail. The behavior of pure and impure (2-18is compared, and the concept of “monophase” remelting criticized. Finally, brief consideration is given the A-lransilions which occur at low temperatures in some long c%ainbromides and paraffins.
I. Introduction 1. General.-Several
types of solid state phase changes are known to occur in n-paraffins and bromides. Among these are (a) the thermodynamically reversible rotationa2 transitions between the a- and @-typephases which take place just below the freezing point; (b) the slow and irreversible al-pz and p1-p2 transformations which take place on prolonged storage a t constant temperature and ( c ) the A-transitions which occur well below the freezing or rotational transition points. This paper will be concerned principally with the first two types of phase change mentioned above, but some experimental evidence having a bearing on the A-transitions will be mentioned. A discussion of torsional twisting of hydrocarbon chains in the solid state will also he presented. 2. Rotational Transitions.-Rotational transitions are generally associated with the onset of hindered rotation of the rod-like paraffin chain molecules about their long axes. A number of solid n-paraffins,1g2 alcohols, 2n3,4 esters6.6 and bro(1) A. Muller, Proc. Roy. Soc. (London),A138, 514 (1932). (2) E. R . Andrew, J . Chem. Phya., 18, 670 (1950). 0. Baker and C. P. Srryth, J . A m . Chem. Soc., 80, 1229 (3) (1938). (4) J. D. Hoffman and C. P. Smyth, i d d . , 71, 431 (1949). (5) R. W. Crowe and C. P. Smyth, ibid., 73, 5401 (1951).
W.
(6) R. W. Crow?, J,
20, 550 (1952).
D.Hoffmao
and C. P. Smyth, J . Chem. Phys.,
mides7s8exhibit discontinuous changes in a number of physical properties at a transition temperature, Tt, which have been attributed to the onset of hindered molecular rotation. I n a recent paper, the rotation of long chain molecules has been treated as a typical cooperative effect.8 In accord with previous notattion,‘ the phase above Tt is denoted a,and that below T t is denoted by the general symbol p. Any unst,able subtransitional form is denoted PI, and st,able forms are called 02, i.e., the subscript 1means unstable and the subscript 2 means stable. Two variants of the stable (Pz) forms of pure paraffins, &-A and 0s-B, which are easily differentiated by X-ray methods will be mentioned in Sees. 111 and V. The p-forms always show less evidence of molecular rotation than or-forrn~.~ One of the principal objects of this paper is to check some of the predictions obtained from a recent theory of rotational disordering in long chain compounds,g especially in regard to the thermal changes a t T t in n-bromides and paraffins. (7) J. D. Hoffman and C. P. Smyth, J . A m . Chem. Soc., 72, 171 (1950). ( 8 ) J. D. Hoffman, J . Chem. Phys., 80, 541 (1952). (9) The a-form has sometimes been called the waxy, rotalionally melted or rofator phase (ref. 4 , 8). The unstable subtranaitional phase
(81)has been called sub-alpha and the stable (82) form haa been called beta (ref. 11). The general term rotalionally frozen or prerolator has sometimes been used to describe any &phase (ref. 8).
