FREDERICK T. WALLAND THOKW J. SWOBODA
50
The well-known variation of r],,/c with c leads to the sa,me qualitative conclusion. To obtain more precise information from viscosity measurements two contributions to the value of qsp/c must be eliminated so that that portion due only t o polyion size can be evaluated. The first contribution is the electroviscous effect, that is, the augmentation of qap/c by (he counterion atmosphere. The fact that size determinations based on extrapolation to infinite dilution where the effect of the gegenions should be maximal are consistent with those from light scatteiing indicate that the electroviscous effect is unimportant. Measurements of this effect in the serum albumin system, to be published later, show likewise that the effect, although important a t low viscosities as in protein solutions, is negligible in polyelectrolytes of high molecular weight. MTe conclude that the observed values of vBP/cfor solutions of polysalts is due to the size of the polyions and their interactions; the effect of the gegenions directly is negligible. Therefore, only the effect of intemctions must be taken into account. On the basis of preliminary experiments it appears that this may be done a t least to a good approximation, by making isoionic dilutions from various points on the vRP/c versus c curve for the polysalt. Further investigation along these lines by both viscometric and light scattering measurements will probably clarify the problem of the concentration dependence of the polyion size. It may be useful to remark a t this point that the approximate equation success of FUOSS’S E! = c
A 1+Bd/c
~
(7)
to represent the viscosity of many polyelectrolyte
Vol. 56
solutions is consistent with the views outlined here. This is readily seen by comparing this with the corresponding equation for ordinary electrolytes
In the later case vsp/c increases without liniit upon dilution. This is consistent with the assumption that the size of the counterion cloud, which is in this case solely responsible for the increased viscosity over that of the solvent, varies inversely with the square or cube root of the concentration and thus reaches infinite size a t zero concentration. V7itjhpolyelectrolytes on the other hand, ~ , , / capproaches a finite limit of A with decreasing concentration. This is consistent with the size of the polymer ion being the controlling factor, the value of -1. reflecting the limiting size to which the polyion expands. Finally mention should be made of three ot,her reports of light scattering observations on polymeric ele~trolytes~6~~~~28 which have appeared recently. In all of these the diminution of Rsowith increasing charge was observed and in one casez8the dissymmetry showed the characteristic minimum similar to that in Fig. 2. However, the essentially qualitative nature of these observations and their restriction to relatively high concentration prevents further comparison. Acknowledgment.-The authors wish to thank the Research Corporation for financial support which made this work possible. (26) W. W.Cashin, J . Colloid Sei.,6, 271 (1951). (27) R. M. Fuoss and D. Edelson, J . Polymer Sei., 6, 767 (1951). (28) P. T. Wall, J. W. Drenan, M. R. IIatfield and C. L. Painter. J . Chem. Pliys., 19, 585 (1951).
ELECTROLYTIC INTERACTION OF NYLON WITH AQUEOUS SOLUTIONS OF SODIUM HYDROXIDE BYFREDERICK T. WALLAND THOMAS J. SWOBODA~ Noyes Cheni ical Laboratory, University of Illinois, Urbana, Illinois Received Auouel SO, 1061
Theoretical equations have been derived to describe the interaction of fibrous nylon suspended in aqueous acids or bases. To test the theory, experiments have also been carried out using undrawn nylon fibers with aqueous sodium hydroxide. Good agreement is observed between theory and experiment, and the results have been used te calculate equilibrium constants for the ion absorption and neutralization processes. The numbers of carboxyl and amino groups within the ~ylori are also calculated and the results are found to be in good agreement with titrations carried out in solution.
Introduction When an insoluble substance containing ionizable groups is placed in an aqueous solution of an electrolyte, ion absorption or ion exchange generally occurs. In particular, if the substance is a polymer like nylon, whose molecules contain carboxyl and amino end groups, one can expect marked interactions with acids and bases. Indeed it is presumed that acid dyes attach themselves to nylon through salt formation with the amino end-groups.2 Since nylon provides a relatively simple model of a solid (1) Chemical Department, E. I. d u Pont de Nemours and Company. Wilmington 98, Delaware. (21 McGrew and Schneider, J . Am. Chem. Soc., 72, 2547 (1950).
acid-base system, we have carried out quantitative studies of its interactions with aqueous alkali. The experimental results have also been compared with a simple theory based on mass action considerations. Gilbert and Ridea13have already treated theoretically the interactions of wool with electrolytes and have compmed their conclusions with the experimental results of Steinhardt4-g and others? Since wool is presumed t o have equal numbers of acid and base groups, the theoretical equations assume quite (3) (4) (5) (6) (7)
Gilbert and Rideal, Proc. Ror. Soc. (London), 1B2A,335 (1944). Steinhardt and Harris. Bur. Stand. J . Res... 44.. 335 (1940). . , Steinhardt, ibid., 28, 191 (1942). Steinhardt. Fugitt and Harris, ibid., 30, 123 (1943). Speakman and Stott, Trans. Faraday Soc., 31, 1425 (1935).
..
Jan., 1852
INTERACTION OF NYLOX WITH AQUEOUSSODIUMHYDROXIDE
simple forms. Nylon, on the other hand, can have almost any ratio of acid to base end-groups; hence, it provides a more drastic test of the theoretical considerations involved. Suppose that a certain nylon fiber, which is to be immersed in a solution of an appropriate electrolyte, contains all total An carboxyl groups and Bo amino groups. Let us further suppose, for the sake of our present discussion, that Ao is greater than Bo. Then since the proton affinity of an amino group is greater than that of the carboxylate ion, we can expect that the fiber will initially contain approximately Bo positive (-NHs+) and BOnegative (-COO-) groups as well as An - Boun-ionized carboxyls (-COOH). If the fiber is now placed in a solution of sodium hydroxide, for example, we can expect the following over-all reactions to occur -COOH
and -NHj+
+ Na+ + OH- --+ --CW-Ka+ + HsO
+ -COO- + S a + + OH- + -COO-Na+ + -NHg + H20
By the symbol -COO-Na+ we shall mean a sodium ion attached to the fiber, presumably in the neighborhood of a negatively charged carboxyl group. The reactions written above imply that both fiber and solution remain electrically neutral; of course this will not be exactly the case, but it will be very nearly true for fibers that are large compared to colloidal sized particles. It is evident that if appreciably different amounts of positive and negative ions were taken up by the fiber, a prohibitively large fiber potential would be set up; hence it will be assumed that equivalent amounts of positive and negative ions react. In any event, the interaction of the fiber with alkali will take place in two distinct stages, t,he first involving un-ionized carboxyls and the second involving pairs of ionized groups. Therefore, we can predict (as is verified experimentally) that the base titration of solid nylon (with A n > Bo)will be accompanied by a break occurring approximately after the completion of the first reaction and before the start of the second. Theory Although our experiments were carried out only with sodium hydroxide acting on nylon with excess acid end-groups, it would seem appropriate to deal theoretically with six different possibilities. These involve,titration with either acids or bases of nylons with Ao > Bo, An = Bo, and Ao < B,. The theory is a generalization of that developed by Gilbert and Ridea13 who made use of Fowler's8 statistical methods and also took cognizance of the possible existence of an electrical potential on the fiber. Certain assumptions concerning the nature of the fiber and of the absorption processes will be made in the development of the titration equations; these assumptions can be summarized as follows. The acidic and basic polymer end-groups, which are presumed to be randomly distributed throughout the fiber, are the specific sites occupied by absorbed ions. All carboxyl sites are assumed to be identical with respect to their interactions with ions, irre(8) Fowler and Guggenheiin, "Statistical Merlienics," Cambridge University Press, 1939, p. 428.
51
spective of whether or not neighboring sites are occupied; similarly, all amino sites are identical. Each site can interact with only one ion, which then makes this site unavailable for further absorption. When nylon fibers are suspended in an aqueous solution of either a monovalent acid or monovalent base, two or more of the following reactions can t,ake place
+ H+
-COO-
__
-COOH
-coo- + B+ 1J -COO-B+ -NHs -NHs+ H+
+ H + -NH3+ + A-J--NHa+A-
+ OH-
HtO
(1) (2) (3 1 (4)
(5)
In these equations, -COOH and -NH2 represent the carboxyl and amino end-groups, respectively, within the nylon fiber, and B+ and A- represent the cation of a base and the anion of an acid. The significance of the remaining symbols obviously follows. As suggested earlier, let us define Ao and Boas the total concentrations of carboxyl and amino endgroups in the fiber, t o be expressed as moles per gram of fiber. We can therefore assert that Ao = [--COO-]
and Bo
+ [-COOHI + [-COO-B+] + [-?SH3+A-]
+ [-",+I
VI"-[
(6) (7)
where the bracketed terms represent the concentrations of the enclosed end-group species, likewise expressed in moles per gram of fiber. Certain fractions, el, 02, 83 and B4 are further defined by the eqiiations [-COOHI [-COO-B+] [-NHx+]
= BlAo
(8)
= BtAo
(9) (10) (11)
[--NHI+A-] [-COO-I [-NHJ
=
e&
=
e4B8
= (I = (1
- el - &)A0
- 83 - e4)Bo
(12) (13)
Equations expressing the free energy changes accompanying reactions (1) through (5) can now be written in terms of the quantities just defined. API = AIL?
Ap3 =
+ RTln
+ R T In I - ea - e4 - RZ'In [H+] + F $ + RT ln eae-! - RZ'ln [A-] - P$
ArJ"
A p , = Aw;
Awb = A&
- e, - - RTIn [H+] + F$
e3
- R T In [OH-]
- R T In [H+]
(14)
(16) (17) (18)
Api represents the free energy change per unit of reaction concerned, while ApP is the corresponding standard value. The last term in each of equations (14) through (17)is the contribution to the free energy of reaction which can be attributed to the charge on the fiber.S The quantity $J is the electrostatic potential of the fiber, and F is the value of the faraday. It will be necessary to subdivide the subsequent development into the several aforementioned cases. These cases will include separate treatments of the absorption of acids and of bases subject to a further
FREDERICK T.WALLAND THOMAS J. SWOBODA
52
breakdown according to the relative numbers of acidic and basic end-groups within the fibers. A. Titration with Acid.-It is obvious in this instance,
where no base is involved, that 82 = 0 . Now let us consider in order three possibilities, namely, A0 < BO,A0 = Bo, and A0 > BO. Case 1. A0 < Bo.-Before reacting with a solution, praFtically all of the carboxy! groups in a fiber with A0 < Bo will be ionized to carboxyl ions and an equivalent number of amino groups ionized to ammonium ions. Thus when acid is added to the solution, the protons find two possible absorption sites available, namely, the carboxyl ions and the un-ionized amino groups. Obviously the amino groups of the nylon are the sites preferred by the protons, so it will be assumed that the amino groups become completely saturated with protons before absorption of protons by the carboxyl ions begins. The absorption of acid by these fibers is thus divided into two regions corresponding to o < e d < - - Bo - - Bo - = e.? and 0: < 0, < 1. These regions must be treated individually. Subcase (a). 0 < 04 < Bo = Bt.-As protons are BO absorbed by the amino groups, an equivalent number of acid anions must also be absorbed. These anions form salt linkages with the alkyl ammonium ions, thus contributing to the followingover-all reaction which is a combination of reactions (3) and (4) -K"z H + A-"*+A(19)
+
+
After sufficient time, the fibers will come to equilibrium with the solution in which they are suspended. A t equilibrium Aps
Hence ApP
+
Apr"
+ RT In
+ AM = 0
tons takes place at the carboxyl ion sites of the fiber giving rise t.0 the over-all 4 0 0 - -"s+ H + A - s 4 O O H -"*+A(28) Proceeding in the same manner as before, we have a t equilibrium
+
+
-+
- - e, -
Equat,ion (21) can then be rewritten with [A-] and 8, eliminated and the natural logarithm converted to a common logarithm 2.303 er = 2 log [H+] - -( A p ; Apf) log 1 - A - " - e 4 RT Bo (25) Further simplification leads to
+
The quant#itya1 is a constant a t any given tem erature. Thus the desired titration equat.ion, which relates &e pH of the acid solution to a function of the amount of acid absorbed, has been obtained for the condition that 0 < 0, < e f . Subcase (b). Bo = e: < e4 < I.-For this abBO sorption region, the acid concentration. of the suspending solution has been increased to a point where all of the amino sites are covered with protons. Further absorption of pro-
+
%T ln[H+][A-] =i 0 (29) Here again the electrostatic potential terms have cancelled, Besides equation (22), the following additional equalities hold Making use of these relationships, equation (29) can be reduced to the desired expression in terms of pH and ed.
Case2. A0 = Bo.-!Cheeimilarityofthiscasetotheupper absorption region, 0: < 0, < 1. of Case 1 is obvious. Thua equahons (28) .and (29) also a ply here. However, since A . = Bo, equation (30) 1s mod&d to @a = (1 e,) = (1 - 01) (33) and the finsl titration equation becomes
-
(34)
(20)
RT In[H+][A-] = 0 (21) I t will be noticed that the two electrostatic otent.ia1terms present in the parent equations (16) and (17pdo not appear in equation (21). This cancellat~ionoccurs, of course, because the two terms are of equal magnitude and opposite sign. Since the solution contains only acid, and since protons and anions are absorbed in equivalent amounts, it follows that [H+] = [A-] (22) It is obvious, under these particular circumstances, that 81 = 0 (23) and ea = Ao (24) Bo
~
Vol. 56
This is precisely the titration equation developed by Gilbert It should be noted that in t+ instaqce, one and Rid+.* equation 18 sufficient to describe the absorphon of acid from zero to total saturation. Case 3. AO> &.--In this case, all amino and an equivalent number of carboxyl groups are initially ionized with the excess carboxyl groups un-ionized and taking no part in the reaction. Therefore, the absorption is described by a single titration e uation which shares some of the simplicity of Case 2. %e over-all reaction is given by equation (28) and the corresponding free energy expresenon by equation (29). E uations (30) also hold, although the relative magnitudes o?Ao and Boare, of course, reversed. Thus the ha1 equation obtained is
-
where 0: is still defined as (BO Ao)/B0but is now a negative quanhty. Remington and Gladdingo offered a similar equation in their recent work on nylon fibers. B. Titration with Base.-When a simple base, such aa sodium hydroxide, is added to the solution in which nylon fibers are suspended, the driving force for the absorption process is supplied by the tendency of the hydroxyl ions to stri protons from the end- ups of the fiber and to react wit[ them to form water. %w it is evident that the protons should first be removed from the carboxyl sites, after which they are taken away from the ammonium groups. Any tendency of the fiber to take on a prohibitedly high negative charge by means of proton remaval is counteracted by the absorption of an eqwvalent number of sodium ions which become associated with the negatively charged carboxyl end-grou s. Thus the net effect is the stoichiometric absorption of &OH by the fiber followed by the elimination of water. Since no acid is now involved, it is obvious that 0, = 0 . Here too it is necessary to consider the three possjbilities, A0 < Bo, A0 = BOand A . > BO. Let us now consider the denvation of titrahon equations for the various fibers. Case 1. AO < Bo.-In the normal fiber (with AO< the transfer of protons from the carboxyl groups to an equivalent number of amino groups is complete. Since the excess amino groups remain un-ionized, they will not take part in the subsequent absorption of base. Therefore, the absorpt,ion process involves the removal of protons from the
BO)
(9) Remiogton and Gladding, J . Am. Chcm. Soc., 79, 2553 (1950).
INTERACTION OF NYLON WITH AQUEOUB SODIUM HYDROXIDE
Jan., 1952
ammonium groups and the absorption of the cations of the base by the carboxyl groups 400"-a+ B + OH-COO-B + -NHn He0 (36) Noting that el = e, = 0, we have a t equilibrium
+
+ +
+
+
RT In[B.+l [OH-] = 0 (37) Here again the two electrostatic potential terms of the parent equations do not appear because of their equal magnitudes and opposite signs. Since only base is added to the solution and the absorption of cations by the fibers is accompanied by the formation of water, it follows that [B+] = [OH-] (38) This equation, in combination with equation (18), can be used to eliminate both [B+] and [OH-] from equation (37). ThereTisrthen obtained, after simplification and a change to common logarithms
The following relationship exists between e, and Bo Ao
e3 = (1 - e,)
(40)
so equation (39) becomes where
(43) and
ea* is a negative quantity similar to 0: of case 3 for acid titration. Case 2. AO = Bo.-This example is similar to the previous one, differing only insofar as no un-ionized amino groups are present. Since these groups do not participate in the absorption, their absence results in simplification of the titration equation. Thus, because A0 = Bo,e: becomes equal to zero and the titration equation becomes ez
= PH
+
(44)
Case 3. A0 > Bo.-Here all the amino groups and an equivalent number of carboxyl groups are ioruzed, but there still remains an excess of un-ionized carboxyl groups. Thus, for this fiber there are two distinct absorption stagea, one inA volving the 0 < & < = !I, and *,the second ocAo curring in the range e,* < en < 1, where e,* is now positive. Each of these regions must be considered separately. A -Bo = @.-The over-all reSubcase (a). 0 < 02 < L-..-Ao action for this subcase is -COOH B + f OH-COO-B+ HZ0 (45) A t equilibrium
eo
+
-ArP
+
4-&a" 4- A& 4RT In e, - RT el
In [B+][OH-] = 0 (46)
Here again the electrostatic potential terms of the parent equations cancel out. We also note that ea = 1 and Bo (1 - el - e,) = (47) Ao With the additional help of equations (18) and (38),there L obtained upon simplification
ez log e? - ee 2pH
+
a4
53
where a4
3
- 2.303 -(RT -Ap?
+ Ap; - A p t )
(49)
- e; < e, < 1.-This subcase Subcase (b). & - B o 4 0 bears a close resemblance to Case 1. At the start of absorpt.ion in both instances, the fiber contains an equivalent number of carboxyl and alkyl ammonium groups for participation in the subsequent absorption. Thus, the over-all reaction for both cases is given by equation (36) and the free energy by equation (37). Here again, el = 0 and equations (38) and (40) apply, except that the relative magnitudes of AOand BOare reversed. Proceeding aa we did in Case 1, we obtain the titration equation
Experimental In the theoretical section of this study, equations have been derived which should describe the absorption of either a monovalent acid or a monovalent base by nylon fibers. Two of the cases considered have already been subject to experimental investigation; one involved the absorption of acid by nylon fibers for which AO> BO,^ and the second waa concerned with the absorption of acid by fibers with A0 = Bo, except that wool instead of nylon actually was used.*0.11 The foregoing analysis of the effect of various end group ratios on the absorption pattern for nylon fibers has in&cated that in certain instances the absorption should differ significantly from that observed in previous studies. The absorption of acid by fibers with A0 < BOor the absorption of base by fibers with A O> BO,should manifest two distinct regions. The experimental portion of the present study has been devoted to an investigation of the absorption of base by nylon fibers for which A O> BO. The two stages of absorption involved in this case provide the opportunity for a more rigorous test of the theoretical develo ment. The nylon used in this work consisted of unxrawn fibers of the so-called 66 variety (polyhexamethylene adipamide) which contained about 82 X 10-6 mole of carboxyl endgroups and 42 X lo-' mole of amino end-groups per gram of polymer as determined by the titration method of Waltz and Taylor.', These fibers were allowed to come t o equilibrium with solutions of sodium hydroxide, the concentrations of which were so chosen that the absorption varied from approximately zero to total saturation of the fibers. When the concentration of the equilibrium sodium hydroxide solution was between 0.01 and 0.2 molar, which corresponded to the upper portion of the absorption region, the following procedure was used. Three to five grams of nylon fibers and 50 to 75 ml. of sodium hydroxide solution were placed in a 100-ml. Pyrex weighing bottle equipped with a tightly fitting cover which was greased and held firnlly in place with rubber bands. The vessel was laced in a 25' constant temperature bath for at least 100 iours to permit the attainment of equilibrium. At the end of this period samples of the equlibrium solution were withdrawn for chemical analysis. Knowing accurately the weight of nylon, the volume of solution, aa well as the initial and equilibrium concentrations of the solution, the amount of sodium hydroxide absorbed by the fiber could be calculated. Carbonate-free sodium hydroxide solutions were used throughout this work. In all phases of the work, the solutions were protected from air by an atmosphere of nitrogen. Dry nylon fibers absorb water from the air so rapidly that it was found necessary to determine the moisture content by weighing samples of the fibers before and after heating in a 75' oven for six hours. Chemical analyses of both the initial and equilibrium sodium hydroxide solutions were obtained by titrating samples of these solutions with standard potassium acid phthalate. When t,he volume of solution available for analysis was small and the concentration low, microtechniques were employed. In the lower portion of the absorption region for the nylon fibers, the concentrations of the equilibrium solutions and (IO) Gilbert, Proc. Rov. SOC.(London), 1838, 167 (1944). (11) Lamin and Viakerataff, J . SOC.Duma and Colourista, 65, 405 (1947). (12) Walt5 and Taylor, Anal. Chem., 19,448 (1947).
54
FREDERICK T. WALLAND THOMAS J. SWOBODA
the amounts of sodium hydroxide absorbed were so small that the chemical method described above was inadeguate. Accordingly, radioactive tracer techniques were substituted whenever the concentration of the equilibrium solution lay between 0.0001 and 0.01 molar. Since the concentrations of most of the initial sodium hydroxide solutions were below the range for chemical analysis, more concentrated solutions were fist repared and chemically analyzed. Thcse solutions were tfen diluted by known factors to the desired low concentrations. A small amount of radioactive mdium (Na**)was introduced into these sohtions before transferring the re uired volume over the nylon fibers in the reaction vessel. l f t e r the required period for attainment of equilibrium, the large bulk of equilibrium solution was poured off the fibers. A count of the radioactivity of a measured volume of this equilibrium solution and also of a sample of the initial solution was made. Under the conditions of the experiment, the concentrations of the initial and equilibrium solutions were roportional to their radioactive counts, thus permitting carculation of the concentrations of the equilibnum solutions. From these concentrations it was possible to calculate the amount of sodium hydroside absorbed by the fibers and the pH of the equilibrium solution. For almost half of the reactions carried out, an additional direct determination of the amount of sodium hydroxide absorbed by the fibers waa made. At the end of the reaction, after the bulk of the equilibrium solution had been poured off, the fibers were mechanically squeeeed as dry as possible. The weight of residual solution still on the fibers y a s obtained by weighing the soaked fibers and subtracting the weight of the dry fibers. The fibers and residual solution were then dissolved in 88% phenol. The resulting viscous solution waa diluted to a convenient volume with a 1:lO mixture of 95% sulfuric acid and ethanol. The radiomtive count of this solution was then measured. Again taking advantage of the proportionality existing between radioactive count and amount of sodium h droxide, it was possible to calculate the moles of sodium iydroxide absorbed by the fibers after correcting for the radioactivc count of the residual solution clinging to the fibers. Relative radioactive counts of the various solutions were obtained by placing 25-ml. samples of these solutions into glass cells which fitted snugly around aGeiger-Mueller tube. The Geiger-Afueller tubes used were selfquencFng with a wall thickness of 30 mg./cm.* They were sensitive to beta and g a m m a emissions with energies above 0.35 mev. These tubes were used in conjunction with. a Model 163 Scalar of the Nuclear Inst,rument and Chemcal Corporation. The sodium isotope (Na”) used in this work was available aa its chloride salt in aqueous soIufion. The concentmtLtlon of salt in this solution was less than 10-7 mole per liter and only a few tenths of a milliliter was added to each 300 to 500 ml. of initial sodium hydroxide solution. Therefore no correction had to be made to compensate for the addition of this material to the solutions. The amount of Na*S added to the sodium hydroxide solutions gave these. solutions activities e r mnute. Radioactive equivalent to IO00 to 2000 counts p counts ranging from 100 to 700 per minute were obtained for the solutions of dissolved nylon. Background corrections of 40 to 50 counts per minute were applied. Coincidence correction curves for each Geiger tube used were obtained by mcans of the dilution method. Such corrections were applied to the radioactive counts whenever necessary, but they were never much greater than 1%. Duplicate counts were made involving times sufficiently long to insure a statistical error of less than 2%. Since NaS*has a half-life of 3.0years, no decay corrections were neceaaary.
Vol. 56
measurement of the amount of sodium in the fibers. The Concentrations of the equilibrium sodium hydroxide solutions, expressed in moles per liter, axe tabulated in the fourth column. The measurements for experiments numbered 1 through 6 were made by conventional chemical means, whereas radioactive tracer techniques were used for the remainder of the reactions. The last column in the tpble contains values for the pH of the equilibrium solution as calculated from the concentration data of column four. TABLEI SUMMARY OF RESULTS Reaction number
1
[-COO-Na +] X
Indirect
79.4 77.6 76.0 68.7 63.0
2 3 4 5 6
58.0
7
44.4
8 9 10 11 12 13 14 15 16
17 18 19
20 21 22 23 24
108
Direct
40.1 39.2
35.4 31.7 29.2 23.4 17.7 11.2 12.8 5.37 2.06 0.74 .23 .57 .14 .05 .02
30.3 18.2 11.8 5.61
0.53
{OH-]X
103
194.6 135.3 78.27 42.17 26.90 17.25 8.73 7.08 5.83 5.07 2.98 2.54 1.43 1.16 0.83 .79 .53
.40 * 35 .25
0.26 113
.24
.14 .09
,008
a
os
PH
13.29 13.10 12.89 12.63 12.43 12.24 11.94 11.85 11.77 11.70 11.47 11.41 11.16 11.06 10.92 10.90 10.72 10.60 10.54 10.40 10.38 10.15 9.97 9.87
The nylon fibers employed in this study contained a larger number of carboxyl than amino endgroups. The theoretical discussion presented earlier indicates that the absorption of sodium hydroxide by such fibers should take place in two steps subject to equations (48)and (50). This absorption pattern is qualitatively reflected in the titration curve of Fig. 1, in which the moles of sodium hydroxide absorbed are plotted against the pH of the equilibrium solution. As would be expected, the solid line curve of this graph contains two steps. The first step corresponds to the removal of protons from the un-ionized carboxyl groups, the second to their removal from the ammonium groups. The hesults and Conclusions point of inflection between the two steps occurs at Experiments involving interaction of the nylon [-GOO-Na+j = A . - Bo,,which is the number of fibers with sodium hydroxide solutions were carried excess un-ionized carboxyl groups in the fiber. This out for twenty-four different concentrations. In point, it should be recalled, also corresponds to 0: each instance, the amount of sodium hydroxide ab- of equations (48) and (50). The broken line sorbed and the concentrations of the equilibrium curves drawn on the graph in the neighborhood of solution were determined. The results of these A0 - Bo represent the hypothetical completion of measurements are given in Table I. The values the first absorption process and the beginning of given in the second column were obtained from the second. The titration equatioas (48) and (50) enable us t o measurements made on the solutions, whereas those in the third column were obtained from a direct make a quantitative interpretation of the absorp-
INTERACTION OF NYLON WITH AQUEOUS SODIUM HYDROXIDE:
Jan., 1952
55
TABLE I1 VALUESFOR a ASD r [-COO-Na+]
Indireot
X 106 Direct
[ndirect
a
Direct
7
1 101) 1 403
2.028 2 090 1.600 1 529
40.1 39.2 1.38
35.4 31.7 29.2 23.4 17.7 11.2 12.8 5.37 2.06 0.74
P H.
Fig. 1.-Amount of al~sorbedsocliuni ions plot,ted a@st of solution.
pH
tion data for the fibers studied in this: work. These equations can be written and
..: 103
0.298 .M9 696
79.4 77.6 76.0 68.7 63.0 58.0 44.4
30.3 18.2 11.8 5.61 0.53
3.57 4.53 11.44 13.15 16.25 20.51 19.11 12.88 6.04
-1.70
13.52 18.91 19.97
4.33
In Figs. 2 and 3, values of c and 7 are plotted against [-COO-Na+]. While the points are somewhat scattered, the data plotted in these t F t . 0 graphs do determine two straight lines. Thus the existence of two constants ICl and kz, as required by the theoretical analysis and defined in equations (53) and (54), is confirmed by the experimental data. The slopes of the two lines give for the equilibrium
Taking advantage of the fact that 8; = AO- BO//AO and K , = [H+][OH-] and letting kl = eu4!K$ and kz = ea3/Kt.,we obtain [-COO-Na+] = ki (53) {(Ao - B O ) [-COO-Na+])[OH-I*
-
”
and [--COO-Na+] { [-COO-?rTa+] - (.40 - Bo)] - k2 (54) {Ac,- [-COO-Na+] ]2[0H-]*
I n these expressions, kl and kz,are the “equilibrium constants” for the reactions which occur during the first and second stages of the absorption. Equations (53) and (54) can be rewritten in the forms [-COO-Na+] u = [OH-l2 - -k1[-C00-Na+]
+
h(Ao - Bo) (55)
I
I
10
I 20
30
[-COO-Na+]X
Fig. 2.-Plot
of
u
40
IO?
us. amount of thsorbed sodium ionA For first stage of titration.
and
-d~[-COO-Xa+]
+ dGAo
(56)
Thus, if u is plotted against [-COO-Na+] for the first stage of the absorption, a straight line should be obtained with a slope equal to -kl and an abscissa intercept equal to (& - Bo). Similarly for the second stage, a plot of T against [-COO-Na+] should give a straight line with a slope equal to the negative square root of kz and an abscissa intercept equal to A,. Values of u for [-COO-Na+] < (A, - Bo) and those of T for [-COO-Na+] > ( A o - Bo) are given in Table 11. It should be noted that the u plot must be made before 7 can be computed.
1
I
I
50
60
70
[-coo-
Fig. 3.-Plot
of
Ne+]
x
I
IO?
us. amount of absorbed sodium ion8 for second stage of t.itration.
T
FREDERICK T. WALL AND THOMAS J. SWOBODA
56
constants of the two absorption stages the values kl = 6.8 X lo6,and kz = 5.5 X lo3. The relative magnitudes of the equilibrium constants reflect the fact that more free energy is required to remove a proton from the ammonium groups of the fiber than from the less basic carboxyl groups. From the abscissa intercept,s of the two lines, there are obtained the values A . = 84 X 10” and BO= 47 X 10” for the mole of carboxyl and amino end-groups, respectively, per gram of fiber. These numbers compare reasonably well with the values Ao = 82 X 10“ and Bo = 42 X 10” obtained outside this Laboratory by an entirely independent method. l2 Before passing on to other considerations, a more critical examination of Figs. 2 and 3 and the data represented there is in order. In both figures, certain points occurring in the region of [-COO-Na+] = A . - Bo are represented by crosses. These points correspond to the transition from the first to the second stages of the alkali absorption and are seen in Fig. 1 as the points approximately midway betweefi t,hedashed “theoretical” curves. In Fig. 2, the values of u corresponding to [-COO-Na+] < 3 X 10” are also represented on the graph by crosses; they likewise do not conform to equation (55). However, the experimental circumstances indicate that this divergence can be attributed to inaccuracy of the work done in the low
(:I/ s
CII
0
-2
‘
0
I
10.5
II
I
0
I
I
11.5
P“ Fig. 4.--Plots of log .$ and log x 0s. pH. Straight linea have correct theoretical slope equal to 2.
Vol. 56
pH region rather than to a real deviation from theory. The fact that the solutions were substantially unbuffered is undoubtedly responsible for the difficulty. All reasonable precautions were taken to guard against extraneous depression of the pH, but these precautions obviously were insufficient to cope with the problem. Attempts were made during the course of the experimentallwork to check by direct measurement the pH values of these solutions which were calculated from the radioactive count data. These direct measurements were made with a glass electrode used in conjunction with a calomel reference cell and a laboratory model pH meter. In the upper portion of this first absorption stage, where [-COO-Na+] > 3 X lo“, the calculated and directly measured pH values were in good agreement; but in the low pH region in question, the observed values were considerably below those obtained by calculation. It is probable that neither the observed nor the calculated values are of much quantitative significance, so we can conclude that the data for experiments 18 through 24 have only qualitative meaning. Since these reactions were concerned only with the small initial absorption, it is felt that the dubious character of the data does not detract from the significance of the results obtained for the remainder of the absorption process. Another method for illustrating the agreement between the theoretical analysis of the absorption process and the experimental data involves the direct application of equations (48) and (50). For simplicity of notation, let us define Using the aforementioned values of Ao and Bo to determined*, values of log 6 and log x, respectively, have been calculated and plotted against pH in Fig. 4. According to equations (48) and (50), the points in each of these graphs should be on straight lines with slope equal to two. The straight lines drawn in Fig. 4 are lines which have the correct theoretical slope; in this respect the graphs demonstrat,e agreement of experiment with theory.
