May, 1956
PREPARATION OF SULFOSTTRENE CATION EXCHANGE RESINS
533
SULFOSTYRENES.1 PREPARATION OF VARIABLE CAPACITY SULFOSTYRENE CATION EXCHANGE POLYMERS FROM STYRENE/ SULFONAMIDOSTYRENE COPOLYMERS BYRICHARD H. WILEYAND SAMUELF. REED Contribution from the Department of Chemistry of the College of Arts and Sciences of the University of Louisville, Louisville Kentucky Received October 88, 1066
pSulfonamidostyrenehas been copolymerized with styrene in varying ratios by a modified bulk technique and hydrolyzed with nitrous acid to give a series of variable capacit cation-exchange resins. The nitrous acid h drolysis has been shown to be substantially corn lete under conditions (15') wLre little, if any, atructural chaage in the porymer can take place. The capacities of twelve iydrolyzed copolymers prepared at 85-136" with varying ratios of monomers are, with one exception, 96100% of the theoretical value based on the monomer ratios. Swelling and solubility data indicate the copolymers to be cross-linked.
The first studies2on the selectivity coefficients of access of the reagent to the group on the chain a series of variable capacity, sulfostyrene-type being modified. In the other, recognized copolycation-exchange resins disclosed an unexpected merization phenomena will determine the distribualteration in selectivity coefficients. The co- tion of the two monomers, and hence the ionic efficients for the sodium-hydrogen exchange de- groups, in the polymer chain. Depending on the creased as the capacity of the resin was decreased particular reaction conditions involved, in the from 5.1 meq./g. to 2.52 meq./g. Furthermore, a first type, or on the copolymerization characteristics complete reversal of selectivity was observed with of the two monomers, in the second type, rather the way from a close the resin of lowest capacity. It has been suggested extreme variations-all that these effects are attributable to variations in bunching a t separated intervals to a random charge densities. These very unusual observations distribution with maximum separation of individual have established the possibility that additional units-in the distribution of charges, and hence the studies on exchange .resins varying structurally charge density, along the polymer chain can be only in the number of exchange groups on the recognized as possible. In the evaluation of an polymer chain will lead to a distinct advance in effect which is to be attributed to variations in our understanding of the fundamental behavior of charge density it is apparent from this that alteraion-exchange resins. Such resins have received tions in the manner of preparing the exchanger very little study and are not readily available. will possibly alter the type and extent of the It is their preparation that is to be considered in variations in selectivity coefficients. The preparation of a copolymer from two monthis paper. . The objective in the preparation of an otherwise omers one of which is to serve as a source of ionic structuraily uniform ion-exchange resin of variable groups, while the other does not, requires the capacity is that of varying the frequency a t which a development of new modifications in standard given ionic group occurs along a given polymer polymerization techniques. Those monomers chain. This objective can be achieved by either of which contain ionic groups-such as sulfostyrene4two different routes. A preformed polymer with are not soluble in or miscible with those monomers suitable exchange groups can be subjected to a --such as styrene-which do not contain such reaction which will remove or introduce ionic groups nor are common solvents for such pairs groups in varying proportions. This procedure obvious. .This makes the direct copolymerization has been used2 to decrease the capacity of sulfo- of such a pair of monomers by any obvious modinated polystyrene by the hydrolytic removal of fication of aiiy of the usual copolymerization sulfonic acid groups and to decrease the capacity techniques an unusual event One obvious way of an acrylic acid polymer by partial e~terification.~to avoid this impasse is to copolymerize a comThe alternative procedure involves the prepara- patible pair of monomers one of which contains a tion of a series of copolymers of varying composition functional group convertible by some mild reacone of which provides the exchange unit.@ The tion, which will not otherwise alter the nature of alternative methods will lead to materials dissimilar the polymer chain, to an ionic group. Several in the manner of distribution of the charges on the possibilities of both types are under study in polymer. I n the former the distribution of charges our laboratories and we wish to describe a t this will be determined statistically in terms of the time our results on the preparation of a series of exchange resins of varying capacity prepared by (1) Presented at the Southeastcrn Regional Meeting of the American the hydrolysis of a series of styrene-sulfonamidoChemical Society, Columbia, 8. C., November 3-5, 1955. Previoua paper in this series: Richard H. Wiley, N. R. Smith and C. C. Ketstyrene copolymers. terer, J . A m . Chem. Boc., 7 6 , 720 (1954). The basic premise which makes this route rational (2) G. E. Boyd, B. A. Soldano and 0. D. Bonner, T ~ r aJOURNAL, is that the sulfonamide group can be hydrolyzed 68, 456 (1954). to the sulfonic acid group by the action of nitrous (3) H. Deuel, K. Hutscheneker and J. Solms,2. EZektroohsm., 67, 172 (1953). acid under very mild conditions.b It was believed, (38) Such a procedure has been used for the hydrolysis of copolymem of divinylbenaene with varying amounts of alkyl p.styrenesulf6 nates; I. H. Spinner, J. Ciric and W. F. Graydon, Can. J . Cham. 8P, 143 (1954).
(4) R. H. Wiley, N. R. Smith and C. C. Ketterer, J . Am. Chem. SOC. 16, 720 (1954): G. J. Moralli, Bull. BOC. chim. France, 1044 (1953). (5) 0 . Hinsberg, Bar., P7, 598 (1804.)
534
RICHARD H. WILEYAND SAMUEL F. REED
however, that additional study of this reaction should be made to see if it were applicable to the hydrolysis of polymers and, if so, under what conditions and to what extent hydrolysis could be achieved. A variety of nitrous acid hydrolyses were run on the bulk polymer prepared as previously described6 to determine the effect of temperature, mole ratio of nitrous acid to sulfonamide groups and time on the yield of evolved nitrogen. At 50" gas is evolved rapidly but contains brown fumes which undoubtedly result in part from the decomposition of the nitrous acid. After correction for this side reaction on the basis of blank runs, the amount of evolved gas indicated that hydrolysis to the extent of 60 to 75% had taken place. The reaction was then studied a t lower temperatures to avoid this decomposition. At 0" no reaction takes place. At 25" hydrolysis was 80-929/'0 complete and at 15" the amount of nitrogen evolved, corrected for a blank, gave reproducible values indicating 96-97% hydrolysis. Other experiments indicated that hydrolysis was more nearly complete using a ratio of 2 moles of acid to 1 mole of sulfonamide than it was with equimolar mixtures and that at least two 24-hour reaction periods, with an additional equal quantity of nitrous acid added prior to the second, were necessary to complete the reaction. The theoretical vs. observed exchange capacities, given in Table I, indicate that this procedure gave substantially complete hydrolysis. For only one copolymer was the observed capacity less than 94% of theory. On this basis it was decided to hydrolyze all of the polymers and copolymers to be used in this study by treating each three times with a 2/1 mole ratio of nitrous acid a t 15" for 24 hours. TABLE I Wt. loss TheoTemp. on Degree retioal of vacuum of oaCom osition pol., drying/ slyell- pacity m o l 8 SAS/S O C . g. ing meq./g.
100/0 75/25 50/50 25/75 100/0 75/25 i0/50 25/75 100/0 75/25 50/50 25/75
Total capacity
136 0.118 26.2 5.43 5 . 1 2 , 5 . 1 1 136 .059 16.6 4.58 4.03,4.05 136 .OS1 4 . 8 3.47 3.43,3.37 136 .111 1 . 3 2.03 1.97,1.94 .086 14.1 5.43 4.91,4.94 110 110 .096 18.3 4.58 4 . 2 7 4 . 2 9 ,116 7 . 4 3.47 3.36,3.37 110 ,083 2 . 0 2.03 1.97,1.99 110 ,076 . . 5.43 5.15,5.11 85 85 ,166 24.4 4.58 4.22,4.25 85 ,098 9 . 5 3 . 4 7 3.47,3.45 85 ,113 2 . 3 2 . 0 3 1.O5,1.96
Titration ca-
pacity
5.18 3.99 3.35 1.96 5.12 4.37 3.44 2.03 5.18 4.43 3.44 2.03
The polysulfonamidostyrene used in these preliminary hydrolysis experiments was prepared by bulk polymerization from the molten state using no added initiator. The monomer, even though recrystallized carefully several times from benzene and finally from ethanol just before polymerization and even when carefully protected from the atmosphere with a blanket of nitrogen, polymerized without added initiator when melted (m.p. 138140").
The problem of preparing polymers and co(0) R. H. Wiley and C. C. Ketterer, J . (19FZ3).
Am. Chem. Soc., 16, 4519
Vol. 60
polymers of styrene and p-sulfonamidostyrenewhich are mutually insoluble-by a process which would give matefials suitable for study as variable capacity ion-exchange resins was solved by devising a modified bulk polymerization technique. The two monomers were combined with the minimum sufficient quantity of dimethylformamide to provide a homogeneous molten reaction mixture a t the beginning of the polymerization. Dimethylformamide was selected as superior to several other third components tried in preliminary tests. Using 0.5 ml. of dimethylformamide per 1.56 g. of the monomer mixture a series of polymers and copolymers was prepared containing 100, 75, 50 and %yo sulfonamidostyrene a t 136 and 110" using 0.01% l-butyl peracetate as initiator and at 85" using 0.01% of benzoyl peroxide as initiator. The reaction mixtures were agitated to see that a homogeneous molten state was established during the first few moments a t reaction temperature. The cooled solid polymer was pulverized and sized to 40-60 mesh. A vacuum treatment (at 76" and 12 mm.) to constant weight, as a means of removing the N,N-dimethylformamide, was customarily given each polymer prior to hydrolysis. One experiment indicated that the formamide was a t least partially washed out during hydrolysis to give a product which, on the basis of a slightly lower capacity-4.8 meq./g., may not have been completely freed of inert material. This vacuum treatment gave a weight loss corresponding to the removal of about one-half of the added dimethylformamide. A considerable portion of the solvent also volatilized and condensed onto cooler portions of the flask during the polymerization. The vacuum treated resin was hydrolyzed with dilute aqueous nitrous acid for 72 hours, washed and dried. The swelling characteristics were determined by a previously described displacement method.7 The total capacity determinations were made by the method of Topp and Peppers and the titrations on the resins were run by the method of Kunin and Myers.g Typical data are given in Table I1 and Fig. 1. The capacity data indicate that the resins have 87-100~0of the capacity theoretically possible based on the monomer mixture used. There are several reasons for believing that these polymers are cross-linked. They are completely insoluble in all solvents tried including aqueous sodium hydroxide and pyridine which are excellent solvents for a high viscosity emulsion polymer prepared from p-sulfonamidostyrene. The hydrolysis is almost always incomplete indicating that some of the nitrogen may he left in the polymer as non-hydrolysable imide linkages. The swelling data also seem to indicate cross-linkage. Because it is of considerable importance to have materials in a known and controlled state of cross-linkage, this problem is receiving further study. The selectivity coefficient characteristics of these resins are to be studied by Dr. G. E. Boyd. Acknowledgment.-This research completed under contract, AT-(40-1)-229 between the Univer(7) H. F. Walton, THIEJOURNAL, 47, 371 (1943). (8) N. E. Topp and K. W. Pepper, J . Chem. Soc., 3299 (1949). (9) R. Kunin and R. J. Myers, "Ion Exchange Rrsinn," John Wilcy snd Sons, Inc., New York, N. Y.,1950, p. 150.
1
May, 1956
PREPARATION OF SULFOSTYRENE CATIONEXCHANGE RESINS
535
sity of Louisville and the Atomic Energy Commission, The authors acknowledge this support with appreciation.
Experimental The p-sulfonamidostyrene used in the following expcriments was prepared as previously described,' recrystallized several times from benzene, and finally, just prior to use, The styrene was distilled from ethanol, m.p. 138-139'. at reduced pressure just prior to use. The N,N-dimethylformamide was carefully fractionated through a helixpacked column with a partial take-off head and that fraction boiling at 152.5-153' separated for use in the polymerizations. Polymerization of Sulfonamidostyrene with Styrene The procedure used in the copolymerization will be illustrated with the details of the preparation of a 75/25 sulfonamidostyrene/styrene copolymer at 110'. Other copolymers were prepared by the same procedure, with the modifications indicated, using different monomer ratios a t 85 and 136'. The copolymers prepared a t 85' were initiated with 0.1% by weight of benzoyl peroxide. Five and twenty-four one hundredths g. (0.0286 mole) of p-sulfonamido-styrene, 1.0 g. (0.0096 mole) of styrene and 2.0 ml. of N,N-dimethylformamide (0.5 d. per 1.56 g. of monomers) containing 0.624 mg. (O.Ol'% of the monomer weight) of t-butyl peracetate were placed in a 125ml. erlenmeyer flask. The flask was flushed with nitrogen, freed of oxygen by washing with alkaline sodium anthraquinone-b-sulfonate solution, stoppered and placed in an oil-bath held a t 110 i 1'. During the first 2 to 3 minutes in the oil-bath the flask was revolved to assist in the formation of a clear solution of the ingredients. The solution became viscous within 3.5 minutes. With 75% styrene the mixture was viscous within 15 minutes; with 100% p-sulfonamidostyrene within 2 minutes. At the end of about an hour the mixture was semi-solid. The heating was continued for 20 hours. During this time some li uid condensed on the upper, cooler portions of the flask. %he copolymer was obtained as a clear, light-yellow solid which was hard and somewhat brittle. The copol mers containing the most styrene were less brittle. The porymer of sulfonamidostyrene itself prepared by this procedure is a clear, brittle, insoluble, light-yellow solid. For further characterization the solids were pulverized in a mort& and pestle and sized to 40-60 mesh size. The less brittle resins were ground with dry ice. The sized particles were vacuumdried a t 76' and 12-14 mm. to remove the dimethylformamide. A 4.89-g. sample of the 75/25 copolymer lost 0.25 g. in 24 hours; 0.41 g. after 48 hours; 0.43 g. after 72 hours; and 0.46 g. after 120 hours. Sam les used in further studies were all vacuum-dried for 72 [ours. The loss in weight varied from 5-12%. Hydrolysis of the Polymers.-Preliminary experiments to determine the conditions required for completion of the nitrous acid hydrolysis were conducted as follows. The polymer was ground and sized with the 40-60 mesh size particles being used in the following experiments. Samples of ap roximately 0.25 g. (0.00136 mole) of polymer were a d d e f t o 1 X 4" test-tubes equipped with a gas outlet tube containing 0.188 g. (0.0027 mole) of sodium nitrite dissolved in 10.0 ml. of distilled water. The mixture was cooled to 0.8' in an ice-water bath and then an excess of hydrochloric acid (3.0 ml.) was added after which the test-tube was sealed with wax and placed in a constant temperature bath at the desired temperature (0-50"). The gas outlet tube was connected to a gas buret and the nitrogen evolved during the next 24 hours collected over water and compared with the calculated theoretical quantity. Blank runs were made to determine the amount of gas formed by decomposition of the nitrous acid. The series of copolymers and polymers were hydrolyzed according to the following procedure given in detail for the 50/50 (110') copolymer of p-sulfonamidostyrene/styrene. A sample of 3.95 g. of the copolymer (containing 0.014 mole of sulfonamidostyrene) was placed in a 500-ml. erlenmeyer flask, with a cold (0-5") solution of 1.90 g. (0.028 mole) of sodium nitrite in 100 ml. of water. To this was added 11.5 ml. (0.140 mole) of concd. hydrochloric acid in 100 ml. of water. The mixture was placed in a running water-bath at 15-18' and shaken frequently for 24 hours. In larger runs the mixture was stirred. During the first
PH.
.-
I
I
I
I
I
I
2
4
6
0
meq. KOH g.reun,
Fig. 1.-Titration characteristics of hydrolyzed sulfonamidostyrene/styrene copolymers polymerized at 85".
I2
IO 6
4 2
1
I
2
1
I
I
* 7
8
4
0
1
me q. KOH 9.resin. Fig. 2.-Titration characteristics of hydrolyzed sulfonamidostyrenelstyrene copolymers polymerized at, 110".
12 IO
PH. 8 6
4 2 2
6
me q .KOH/g .re sin.
Fig. 3.-Titration characteristics of hydrolyzed sulfonamidostyrene/styrene copolymers polymerized at 136'. several hours the evolved nitrogen floated the polymer particles. Later they sank to the bottom. The solution was decanted and frcsh solutions of nitrite and acid were
DONALD G. MILLER
536
added to repeat the process a second and third time. After the third hydrolysis the olymer was placed in a buret and washed a t the rate 0?1 ml./minute with a m u m u m of 3 1. of 1 N hydrochloric acid to remove the nitrite and then washed with distilled water until free of acid. The polymer was air-dried and vacuum-dried a t 55’ for a minimum of 18 hours to constant weight prior to titration. Polymer samples containing high ercentage of sulfo group8 absorbed more water and required yonger drying periods. Swelling Characteristics.-The procedure follows that previously described.’ A weighed sample (0.22-0.27 g.) of dried polymer was placed in a graduated cylinder and its apparent volume noted. Two ml. of hexane was added and the volume in excess of 2 ml. was taken as the true volume of the resin. Water was added to displace the hexane and permit swelling. The apparent volume of the swollen resin was noted and corrected by the same factor observed in the ratio of apparent to true value for the unswollen resin. The degree of swelling was taken as the ratio of the corrected volume swollcn to the true value unswollen.
Vol. 60
Capacity Measurements .-Total capacity determinations8 were made by adding 100 ml. of standard (m. 0.1 N ) sodium hydroxide to ca. 2.0 g. of dried olymer in its hydrogen form. The flask was stoppered and alfowed to stand one week with frequent shaking. Two 10.0-ml. aliquot portions were titrated with standard (ca. 0.1 N ) hydrochloric acid to the phenolphthalein end-point. Values are given in the table as meq. of base per gram of dry resin in the hydrogen form. Titrations were conducted by the procedure described previously) The resins were titrated with 0.1 N potassium hydroxide usin 12 Sam les of resin of approximate1 equivalent weiggt to whicf was added increments of 1.0 potassium chloride and 0.1 N potassium hydroxide in 1.0 N potassium chloride to give a total volume of 25 ml. The samples were sealed and allowed to stand for one week with occasional shaking on a machine. The pH of each solution was determined and plotted against meq. of base added per gram of dry resin. A series of such data for the polymers prepared a t 110’ is given in Fig. 1. The equivalence point is given in Table I in terms of meq. of base per gram of dry resin in the hydrogen form required to neutralizc.
k
AN ANALYTICAL PROOF THAT THE EXTREMUM OF THE THERMODYNAMIC PROBABILITY IS A MAXIMUM’ BY DONALD G. MILLER^ University of Louisuilb, Louisuille, Kentucky Received December $0, 1964
An analytical proof is given that the distribution found by extremizing the thermodynamic probability actually is the most probable one. The cases considered are classical statistics, Bose-Einstein and Fermi-Dirac statistics, radiation and Wall’s theory of rubber elasticity. I n these examples, the proof depends only on the form of W.
Introduction
distribution found actually is the most probable one. The argument will be given for classical statistics; and the Fermi-Dirac and Bose-Einstein system and use the most probable distribution so statistics, radiation and rubber elasticity will be obtained to determine the system’s macroscopic discussed briefly.6 SuRcient Condition for a Maximum.-As noted properties. 8 This procedure is permissible since the above, inflection points and saddle points number of particles is very large in most systems. will alsominima satisfy the necessary conditions obtained I n this event it can be shown that the most probable by the LM technique. Therefore it is desirable distribution completely dominates all the others. I n general a system is subject to various con- to have sufficient conditions which will enable one straints, such as a constant energy or a constant to decide which type of extreme is present. Fornumber of particles. Consequently the location tunately these conditions have been worked out, the following theorem on constrained extremes of the maximum of W is most conveniently handled and However may be by means of Lagrangian Multipliers. Theorem.-Let F ( q , . . ., zn) be subject to the the Lagrangian Multiplier (LM) method only leads to necessary conditions for an extreme, and it is m constraintsfi(z,, . . ., x,) = a i , 1 I imI m,where ordinarily assumed without proof that a maximum the ai are constants. Let 4 = F Xf, where is obtained. Although it seems more or less clear i=l that a maximum does result, nevertheless without X i are the Lagrangian Multipliers and are to be proof it is conceivable that a minimum or a saddle treated as constants. Let xIo,. . . xnobe the values point could be obtained. It is the purpose of this of XI, . . ., Zn a t an extreme of 4, as found by the paper to provide a rigorous analytical proof that the usual LM technique. Now form the sequence of determinants (1) Presented before the Physical and Inorganic Division a t the
A standard technique in statistical mechanics is to maximize the thermodynamic probability W of a
(v6
124th ACS meeting, September, 1953. (2) Chemistry Department, Brookhaven National Laboratory, Upton, Long Island, New York. (8) See, for example, Mayer and Mayer, “Statistioal Mechanics.” John Wiley and Sons, Inc., New York, N. Y., 1940. (4) Referenoe 3, appendix VI. (5) I. 8.and E. 8. Sokolnikoff, “Higher Mathematics for Engineera and Physicists,” MoGraw-Hill Book Co., New York, N. Y.. 1941. p. 163.
(6) At the time this work waa originally carried out. no proofs had ever been published. It han oome to the author’s attention that L. Page (“Theoretioal Phyaics,” 3rd edition, D. Van Nostrand, New York, N. Y., 1952) has independently given a, somewhat different one for classioal statistics. ( 7 ) C. G. Phipps. A m . Math. Monthly, 59, 230 (1952). (8) R. P. Gillespie, “Partial Differentiation,” Interscience Publishera, Inc., New York, N. Y., 1951. (9) T. F. Chaundy, “Differential Calculus,” Oxford, 1935.
