ppm G B using a n enzymatic reagent with the time period for complete analysis of only forty minutes (5). A factor of obvious importance in the sensitivity attainable is the ratio of the bimolecular rate constants in the reactions between a given phosphorus ester and hydroxamic acid and hydroxide ion (see Choice of Reaction Conditions), a relatively higher rate of the hydroxamic acid reaction being desirable for attainment of more sensitive detection procedures. Table VII, taken from the publication of Green et al. (13) gives
the bimolecular rate constants of several phosphorus esters with the anions of benzhydroxamic acid and hydroxide ion and the ratio of the two constants. Of the compounds listed, G B has the least favorable ratio of reactivities. The ultimate sensitivity attainable in the detection of tetraethylphosphonate (TEPP) (e.g.,) should be somewhat higher than that attainable with GB, although the optimum conditions for the reaction would be different because of the lower reactivity of the hydroxamic acid anion with TEPP.
(13) A. L. Green, G. L. Sainsbury, B. Saville, and M. Stansfield, J . Chem. SOC.,1958, p. 1583.
1967.
for review January
Accepted May
297
Studies of Ion Exchange Materials Homogeneous Fractional Sulfonation of Copolymers of Styrene and Divinylbenzene David H. Freeman and A. S. Aiyar' National Bureau of Standards, Washington, D . C. 20234 The feasibility of slow sulfonation of bead copolymers of styrene and divinylbenzene to give homogeneous and fractionally substituted ion exchange materials is shown. The reaction of copolymer with dilute solutions of sulfuric acid in nitrobenzene at 23.51~ approaches second-order kinetics at less than 60% sulfonation; at higher values the rate constant falls toward a value of zero at 100% sulfonation. Volume swelling measurements of the fractionally substituted ion exchangers agree by extrapolation to corresponding measurements by Wiley on the fully substituted materials.
THE SIGNIFICANCE of ion exchange measurements depends upon the nature and definition of the ion exchange material. Ordinarily available ion exchange resin beads are seriously heterogeneous (1, 2) and, therefore, incapable of being precisely defined. In particular, the diffusion-controlled partial sulfonation (3) of copolymers of styrene and divinylbenzene must yield resin beads that are more highly sulfonated o n their exterior. By contrast, sulfonation which reaches the upper limit of one sulfonate group per aromatic nucleus yields homogeneous and uniform ion exchange material ( 4 , 5). This also depends upon access to uniform copolymer whose availability from commercial (2, 5) and laboratory ( 5 ) synthesis is already known. The preparation of well defined copolymers that have been sulfonated to less than their maximum extents is a more difficult experimental problem. Such fractional sulfonation affords an important possibility Present address, Chemicals and Plastics (India) Ltd., Raman Nagar P.O., Salem District, India. ~
for tailoring the properties of the ion exchange material to best meet the demands, for example, of a particular separations scheme. To this end, we have made the present exploratory study of slow sulfonation reactions of copolymers of styrene and divinylbenzene, and of the homogeneity and swelling behavior of the fractionally substituted products. Two processes are required for the sulfonation of a bead of crosslinked copolymer of styrene and divinylbenzene: diffusion of the sulfonating agent into the copolymer bead matrix, and reaction of that agent with the matrix. The sulfonation reaction causes localized depletion of the concentration of sulfonating agent. This causes more sulfonating agent t o enter the matrix. As a result, the bead exterior tends to become exposed to a higher concentration of sulfonating agent and, accordingly, to become more highly sulfonated. Such effects have been characterized (2). Homogeneous fractional sulfonation may occur if there is no concentration gradient of the sulfonating agent. The removal of this gradient can be expected, as in the present experimental approach, if conditions permit the diffusion rate t o be infinitely fast compared to the rate of sulfonation reaction. Then, the concentration of the sulfonating agent in the copolymer phase can be required to follow an isothermal Donnan equilibrium path where the sulfonating agent is as uniformly distributed in the copolymer gel as the copolymer network itself is distributed. The sulfonation of mono- and dialkyl substituted benzenes may proceed irreversibly to completion (6). Then, if the sulfonating agent is diluted with the same inert solvent that swells the copolymer, second-order kinetic behavior is expected:
~~
(1) E. Hogfeldt, Scieme, 128, 1435 (1958). (2) D. H. Freeman, V. C. Patel, and M. E. Smith, J . Polymer Sci., A3, 2893 (1965). (3) R. H. Wiley and T. K. Venkatachalam, Ibid., p. 1063. (4) K. W. Pepper, J . Appl. Clzem., 1, 124 (1951). (5) R. H. Wiley, J. K. Allen, S. P. Chang, K. E. Musselman, and T. K. Venkatachalam, J. Phys. Chem., 67, 1766 (1964).
RiR2CeH4
+ HzS04
k_
+
RIR~C~H~SO~ H20 H
(1)
where R I is alkyl (chain) and R 2 is either alkyl (chain) or hydrogen. We use the following definitions: (6) M. Kilpatrick and M. W. Meyer, J . Phys. Cliem., 65,530 (1961). VOL. 3 9 , NO. IO, AUGUST 1967
1141
f = mole fraction of sulfonated aromatic nuclei in the
copolymer matrix A = mole ratio of sulfuric acid t o aromatic nuclei a t start c = starting concentration sulfuric acid inside the copolymer gel t = time (hours) The differential rate equation is applicable: d f = ( l - n ( A - f ) ; kC dt
By integration and use of the boundary condition f = 0 a t t = 0, we have (3) where X = c k / A . In the special case that a
=
1, Equation 2 becomes (4)
Upon integrating and settingf
=
0 at t
f = At 1 -f
=
Vawallen/Vnnswollen.
0, we obtain
(5)
F o r the purposes of the present study, we will assume that the sulfuric acid concentration c(1 - f ) / A is identical inside and outside of the solvent-swollen copolymer gel; this is the same as assuming a perfectly ideal Donnan distribution of the acid in the two phases. Similarly, the same assumption applies to the integrations leading to Equations 3 and 5. EXPERIMENTAL
Samples of styrene divinylbenzene copolymers were similar t o those which we have studied in earlier work (2). They were pretreated by Soxhlet extraction for several hours with either methylene chloride o r with benzene; the solvent was then removed by vacuum evaporation. Prior to sulfonation, weighed samples of copolymer beads were preswollen with measured quantities of nitrobenzene. Sulfonation was preceded by batchwise addition of various quantities of a solution of sulfuric acid in nitrobenzene t o the preswollen samples. The sulfuric acid was prepared by mixing sulfuric acid and oleum reagents until the resulting specific gravity agreed with the value of 1.8275 gram/ml a t 23.5" obtained from the International Critical Tables. The measurements, reproducible to f0.0005 gram/ml, corresponded t o 100 i. 0.2% H2SOa. In the reaction mixtures, the starting mole ratio of sulfuric acid to nitrobenzene was fixed a t a value of 6.2. This corresponds t o 1.13 ml of 100% sulfuric acid per 20 ml of nitrobenzene. The starting mole ratio of sulfuric acid t o copolymer aromatic group, designated by A , was varied t o give corresponding changes in the reaction rate, (Such design calculations are simplified by use of the copolymer equivalent weight per aromatic group; this can be determined accurately and it is approximately equal to the molecular weight of styrene.) The mixture of copolymer, solvent, and acid was rotated in glass bottles whose surfaces were pretreated with Desicote t o lessen the sticking of sulfonated particles of resin. Temperature was controlled at 23.5" i.0.5" by circulating thermostated air. F o r analysis, a procedure was developed to extract the sulfonating mixture without mechanically injuring the derived ion exchange beads. This was accomplished as follows. Particles were transferred to a coarse porous glass frit using a wash bottle containing concentrated sulfuric acid. The particles were washed first with nitrobenzene t o remove the sulfuric acid and then three times more with tetrahydrofuran to remove most of the nitrobenzene; this 1142
ANALYTICAL CHEMISTRY
was followed by three prolonged washes with the same solvent to remove the remaining traces. The filtered particles were held over water in a closed chamber and allowed to hydrate isopiestically during a 1- o r 2-day period. Before analysis, a given sample was washed successively with aqueous solutions of 1M NaOH and 1M HCI. Finally, it was thoroughly washed with water. For analysis and determination of the exchange capacity, excess base was added, agitated for several hours, and filtered. The sample was washed with water and the combined alkaline filtrate was then titrated potentiometrically with standard acid. The resin was dried under vacuum in its sodium form and the dry weight was then obtained. The value of X was thus measured point-wise for each sample using Equation 3 or 5, the determined initial value of A , and the measured values o f f and t. The calculation of f depended upon the limiting sulfonation capacities calculated by Pepper (4) which agreed to within 2 % of our own similar measurements of maximum capacity. The swelling ratios of individual beads by water were made using the same microsc6pical techniques which we have described elsewhere (2). The swelling ratio is given by the ratio of the cube of the bead diameters so that q = D39aol~en/D3unsao~~en =
A limited number of sulfonations were carried out at elevated temperature t o demonstrate that the copolymers were capable of being sulfonated at least approximately to the maximum calculated degree of sulfonation. The copolymer beads were initially preswollen in o-dichlorobenzene. Sulfonation was done without catalyst using a n excess of 96% sulfuric acid. The reaction mixture was stirred for 5 hours while the reaction vessel was immersed in a refluxing system of methylcyclohexane a t 97" C. The previously described purification and analytical procedures were then followed. The following test for diffusion control of the sulfonation reactions were made. Twenty-four individual samples of variable and partially sulfonated beads, 0.25 and 0.7 mm in diameter, were individually separated according t o particle size into two or three subsamples using the reverse sedimentation methods of Hamilton (7). These subsamples were then measured for exchange capacity of the anhydrous, sodium-form material. From each group of two or three subsamples the lowest measurement was subtracted from the highest t o obtain a maximum difference. The measurements did not show a significant correlation with particle size. The differences were then taken to compute a relative standard deviation, giving a value of 2.3%. This gives a n upper limit t o the analytical errors and it is a strong indication that diffusion effects are not evident under the conditions of the sulfonation experiments at low temperature. RESULTS
The present study yields a consistent indication that a dilute solution of sulfuric acid in nitrobenzene provides homogeneous sulfonation a t 23.5 O throughout the range of fractional substitution from f = 0.2 to f = 0.9. Examples of the kinetic measurements are given in Table I. Swelling ratios were obtained by microscopic measurement of individual bead diameters and these are reported in Table I as q l for toluene swelling of copolymer, and as qw for water swelling of the sulfonated copolymer. The standard deviation for these quantities tends to indicate maximum nonuniformity among the beads. The basis for this interpretation is more fully described elsewhere (8). Table I includes the result of microscopic measurements of ion exchange capacity C (meq/gram) for the dry sodium form materials obtained after sulfonating a t 97" C. (7) P. B. Hamilton, ANAL.CHEM., 30,914 (1958). (8) D. H. Freeman, "Ion Exchange," J. A. Marinsky, Ed., Marcel Dekker, New York, 1966, chap. 5 .
x x lo4 ( hours-') 2
t
q; - 1 0.5
0 0.2
0.4
0.6
0.8
1.0
f Figure 1. Rate constant for sulfonation of copolymers of styrene with 27, ( 0 ) and 47, (0) divinylbenzene is measured batchwise for varying fractional sulfonation of available groups in copolymer network
For comparison, a theoretical capacity C* is computed for Table I on the assumption that sulfonation occurs once a t each aromatic group from available composition estimates ( 4 ) of the original monomer mixture. The degree of fractional substitution f is taken as the ratio of the measured capacity divided by the required value of C*. Rate constants were computed according to the assumptions stated earlier using Equations 3 and 5 . The results for copolymers with 2 and 4 % divinylbenzene show good agreement with each other, and collected measurements o n these materials are presented in Figure 1. Within the limits of experimental reproducibility, the second-order rate equations are obeyed with fair precision in the range of less than 6 0 x of full sulfonation. The swelling measurements are given in Table I and plotted in Figure 2 in reduced form using the measurement of qw a t a given crosslinking and degree of substitution relative to the corresponding value qwomeasured by Wiley (5) on similar copolymers which were sulfonated to their limit. There is a consistent pattern of curvature. The swelling dependence upon degree of sulfonation is small a t low substitution. I t becomes greater and approaches linearity with increasing sulfonation. The present measurements appear by extrapolation to show good agreement with those obtained independently by Wiley a t f = 1. Pepper's earlier measurements ( 4 ) of water uptake by partially sulfonated copolymer ( 5 divinylbenzene) are linear throughout the range of partial substitution. This result, shown in Figure 2, disagrees with the curvature found in the present results. To explain Pepper's observations, it should be recognized that linear swelling behavior must be obtained if fully sulfonated copolymer were mixed with pure copolymer and then measured for apparent capacity and water content. This suggests the likely possibility that exterior shell sulfonation was achieved by Pepper with a resultant additivity in the swelling behavior of the adjacent sulfonated and unsulfonated regions in individual beads. The kinetic results a t high degrees of fractional sulfonation are more complicated. Figure 1 shows a marked rate decrease toward 0 a t complete sulfonation. The trend of the results with 1 % divinylbenzene in Table I also shows this. This is not the result of a transition t o diffusion control of the sulfonation process, or there would have been a departure from the observed homogeneity of the more highly sulfonated samples. I t is possible that the rate slowing results from the effect of water that is formed as a normal reaction product.
A?+' +
// / /
0.0
Results show a marked negative departure from derived second-order rate expression in the region where sulfonation approaches completion
I .o
0.5
f Figure 2. Measured swelling in water of homogeneous, fractionally sulfonated copolymers of styrene crosslinked with 1 % (+)¶ 2 x and 47, (0) divinylbenzene ¶) . (
Value of qw - 1, where q = Vsso,ien/Vunslroilen is a direct measure of the water volume imbibed per unit volume of matrix. These results are referred to the corresponding measurements (quo) reported by Wiley and coworkers (5) on the fully sulfonated materials. The dotted line describes similar measurements at 5 % divinylbenzene content, as reported by Pepper ( 4 ) ; the linear variation of swelling with sulfonation is attributed to a failure to achieve homogeneous sulfonation conditions
Table I. Measurements of Sulfonation Rate at 23.5" C and Swelling Ratio of Fractionally Sulfonated Beads of Copolymers of Styrene and Divinylbenzene
A. 1 % divinylbenzene 4.85 & 0.03,a C = 4.65, C* = 4.83 Reaction time = 1008 hr.
91
A
f
X X l o 4 (hr.-l)
1 2 4 8 16
0.378 0.617 0.793 0.853 0.932
5.9 5.9 4.5 2.6 1.7
QLC
1.83 f 0.13 4.29 k 0.30 10.2 f 0 . 5 11.9 k0.05 12.6 f 0 . 3
B. 2 % divinylbenzene 3.43 It 0.07, C = 4.75, C* = Reaction time = 1008 hr. h X lo4 (hr.-l) f 0,205 2.6 0.407 2.9 0,668 3.0 0.728 1.7
=
A
1 2 4 8
4.82 4w
1.19 'r 0 . 0 3 1.92 iz 0.09 3.83 =t0 . 0 7 4 . 6 4 =t0.09
C. 4 % divinylbenzene qt
2.60 & 0.03, C
4.66, C* = 4.79 1512 hr. 104 (hr. -1) qw 3.8 1.34 zk 0.02 3.2 1.86 f 0.11 2.5 2.51 f 0.03 1.7 2.89 iz 0.03 1.0 3.01 iz 0.03
Reaction time A 1 2 4 8 16 a
x
f 0.363 0.553 0,733 0.852 0.893
=
=
All tolerances are expressed as standard deviation.
VOL. 39, NO. 10, AUGUST 1967
1143
I t may be that the water is not evenly distributed between the two phases. This would be consistent with the known high affinity of water for sulfonated copolymer (9). The kinetic effects are in qualitative agreement with the known tendency for the rate of sulfonation of mono- and dialkyl substituted benzenes to vary with the water content (6). The present efforts have been devoted to the finding of conditions for preparing homogeneous fractionally sulfonated cation exchange materials. The experimental efforts include the development of a procedure which preserves the bead form of styrene divinylbenzene copolymer. Tests for homogeneity have been satisfied, and the results show that secondorder rate equations are obeyed in the region of less than 60% of full sulfonation, and that a rate slowing occurs at higher degrees of sulfonation. (9) G. E. Boyd and B. Z . Soldano, Z . Electrochern., 57,162 (1953).
The results of this study include necessary tests of th; conditions that must be explored if one is to establish whether a n ion exchanger is sufficiently well defined to justify the assumption that measurements of its properties can be reproduced. The present measurement of swelling ratios of the fractionally sulfonated materials and the good agreement by extrapolation to independent measurements by Wiley on corresponding full sulfonated materials show that this important physical property, at least, can be related among corresponding materials studied in different laboratories. RECEIVED for review January 30, 1967. Accepted June 14, 1967. The present studies were begun with the support of the United States Atomic Energy Commission under Contract AT (45-1) 1544 with Washington State University. Division of Analytical Chemistry, 153rd Meeting, ACS, Miami Beach, Fla., April 10, 1967.
Determination of Sodium in Ultrapure Silicon and Silicon Dioxide Films by Activation Analysis James F. Osborne, Graydon B. Larrabee, and Victor Harrap Texas Instruments Inc., Dallas, Texas
The technique of neutron activation coupled with sensitive counting techniques has been used to determine sodium in sub-nanogram amounts in very thin layers of silicon dioxide films and at the sub-ppb level in silicon. Techniques are described for incrementally 0 removing thin layers of the oxide (50-200 A), measuring the thickness of the residual oxide with an ellipsometer, and analyzing the etch solution for sodium-24 content. The production of sodium-24 from other impurities was evaluated and was found to be minor in samples used in this work. Preirradiation handling and wrapping was found to be an important factor when analyzing for sodium at these levels.
ANALYSIS FOR SODIUM in ultrapure single crystal silicon and in very thin silicon dioxide films grown on this silicon has become vitally important for the new and advanced metal-oxidesemiconductor (MOS) technology. This MOS technology provides a significant departure from the usual semiconductor practice in that the silicon dioxide film becomes a n active part of the device. Figure 1 shows a schematic of a n MOS field effect transistor. The oxide film supports a thin metal film which in turn is used to supply a charge through the oxide to the semiconductor substrate. I n this manner the metal-oxide can act as a gate in the same way as a grid in a vacuum tube. The silicon dioxide film must be virtually free of any mobile ions which can drift through the oxide when a bias is applied to the metal film and thereby cause device instability. Sodium ion has been identified as the principal source of mobile ions ( I , 2) in these films. The electrical effects and distribution of sodium in oxide films have been described by Carlson et at. (3, 4) and Yon et ai. (5). Various authors have reported the determination of sodium in silicon by neutron activation (6, 7 ) but none describe the exact manner in which the quantitative measurement was made. James and Richards (8) and Erokhina et al. (9) list detection limits of 2.5-5 X 10-'0 gram of sodium a t neutron fluxes of 1-9 X 1OI2 n/sec/cm2. While this detection limit is satisfactory for the analysis of 0.1- t o 1-gram samples of 1144
ANALYTICAL CHEMISTRY
i
METAL G A T E 7
1,000-10,000 SILICON DIOXIDE FILM
7
I T
P - T Y P E SILICON
Figure 1. Schematic of a metal-oxidesemiconductor (MOS) field effect transistor silicon, it is necessary t o use higher fluxes and more sensitive counting techniques for the analysis of oxide films of a few thousand angstroms in thickness. This detection limit is even less acceptable when it is necessary to determine the :odium concentration in incrementally removed 50- to 1000-A layers of the silicon dioxide film. The total volume of each etch lap sample being analyzed is only 1.5 X 10-6 to 3 X lop5 cc and total sample weight is 3.5 to 70 pg. The production of 15-hour sodium-24 by the (n,r) reaction is controlled only by the neutron flux and time of irradiation. In this work, a flux of 1 X 10'3 n/sec/cm2 for 24 hours was (1) E. H. Snow, A. S . Grove, B. E. Deal, and C . T. Sah, J. Appl. Pkys., 36, 1664 (1965). (2) A. G. Reverz, IEEE Trans. Electron Decices, ED-12, 97 (1965). (3) H. G. Carlson, G. A. Brown, C. R. Fuller, and J. Osborne, Phys. Failure Electronics, 4, 390 (1966). (4) H. G. Carlson, C. R. Fuller, D. E. Meyer, J. F. Osborne, V. Harrap, and G. A. Brown, Ibid., 5, in press. ( 5 ) E. Yon, W. H. KO, and A. B. Kuper, IEEE Trms. Electron Deuices, ED-13, 276 (1966). (6) B. A. Thompson, B. M. Strause, and M. B. Lebowf, ANAL. CHEM., 30, 1023 (1958). (7) G. H. Morrison and J. F. Cosgrove, Zbid., 27, 810 (1955). (8) J. A. James and D. H. Richards, J . Electron. Corrrrol, 3, 500 (1957) (9) K. I Erokhina, I. Kh. Lernberg, I. E. Makasheva, I. A. Maslow. and A. P. Obukhov, Zacodsk. Lab., 26, 821 (1960).
