POLYCATION-POLYANION REACTIONS IN DILUTEAQUEOUS SOLUTION
1447
A Conductometric Study of Polycation-Polyanion Reactions in
Dilute Aqueous Solution
by Alan S. Michaels, Leon Mir, and Nathaniel S. Schneider Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts (Received March 9, 1964)
Reaction of the strongly ionized, oppositely charged polyelectrolytes sodium (polystyrenesulfonate) and poly(vinylbenzyltrimethy1animonium chloride) leads to the formation of a compact precipitate over the entire range of relative concentrations. Conductometric studies show that the reaction is stoichiometric and that the pairing of ionic functions in the complex is complete for the reaction in salt-free solutions or even in 10-2 iV KaC1. Addition of divalent-univalent salt, e.g., CaC12, results in deviations from stoichionietry but only on one side of the equivalence point. Reaction of the polyacid and polybase, even in the presence of electrolyte, results in deviations from stoichiometry on both sides of the equivalence point and film fragments rather than the usual discrete particles. The deviations from stoichiometry in the first case can be related to the more tightly coiled configuration of one of the polyions in the presence of its divalent counterions and in the second to the rapid reaction of acidic and basic functions which results from neutralization of the counterions. This suggests that two requirements for the unusual stoichiometric reaction are an open-chain conformation and the moderating effect of salt-type counterions.
Introduction The mixing of oppositely charged polyelectrolytes leads to the formation of a complex whose composition, in general, is sensitive to such reaction conditions as the composition of the reaction mixture, the order of mixing, and the polyion concentration a t which the reaction is carried out. Under these circunistances the complex is frequently stabilized by incorporation of a larger than stoichionietric proportion of one component and, therefore, precipitation may occur only in a narrow range near the equivalence point. In contrast, studies of the interaction of the strongly ionized polyelectrolytes, sodium (polystyrenesulfonate) (NaSS) and poly(vinylbenzyltrimethylanimoniuni chloride) (VBTAC1), have revealed a remarkable specificity in salt-free solutions.' A compact precipitate is formed over the entire range of relative reactant concentrations, the coniplex contains the oppositely charged polyions in stoichiometric balance irrespective of their concentration in solution, and the virtually complete release of the previously associated counterions indicates that a one-
to-one pairing of ionic functions exists within the complex. Previous work on the dilute solution reaction was restricted to salt-free solutions.' This paper reports the results of a conductometric study of the effect of a nuniber of variables, such as the t,ype of counterion and the concentration and type of added salt, on the stoichiometry of the reaction. The results offer considerable insight into the factors which control the specificity of interaction and should be of interest not only as an extension of the more classical area of polyelectrolyte studies which deal with the interactions of the polyion with microions, but also as a model systeni sharing features coninion to the important ionically-mediated interactions between proteins.
Experimental The polyelectrolytes supplied by the Dow Chemical Co. had been polymerized froin the corresponding sty(1) A. S. Michaels and R. G. Miekka, J . Phys. Chem., 6 5 , 1765
(1961).
Volume 69, Number 5
M a y 1966
1448
rene monomers. Substitution was completely para for the polyanion but the polycation was essentially a copolymer of ortho and para isomers in the ratio of 35: 65. Determination of the equivalent weights gave values close to the theoretical values of 206 g./equiv. for NaSS and 212 g./equiv. for VBTACl, confirming the fact that the polyniers were essentially Completely substituted. The viscosity-average molecular weights were 760,000 for NaSS and 300,000 for VBTAC1. Since the samples were used without fractionation it was assumed that the ratio of the weight- to number-average molecular weight was 2 in calculating the nuniberaverage degrees of polymerization, 1350 for NaSS and 700 for VB'I'ACl, for use in later calculations. Solutions of the polyelectrolytes a t 4% concentration were passed through a mixed ion-exchange column. The conversion of SaSS to HSS was completed on a Dowex 50 column and a Dowex 1 column was used for the VBTAOH. The various salt forms NaSS, CaSS, or VBTACl, VBTASOl were prepared from standardized solutions of the polyions by adding the calculated titer of the appropriate base or acid. Conductivities were measured in Jones Bollinger cells with bright platinum electrodes a t four decade intervals froni 0.1 bo 100 kc. using a General Radio Co. Type 1650 comparator. I n almost all cases, the variation in conductivity over the full range of frequencies was below 0.3% and most of this change occurred between 0.1 and l kc. However, under one set of reaction conditions, that for mixtures of HSS and VBTAOH in salt-free solutions, the variation with frequency sometimes exceeded 1% and these results were extrapolated to infinite frequency to remove the polarization effect. The behavior appeared to result from suspended particles since the conductivity of the supernatant after a brief centrifugation showed the nornial insensitivity to the frequency of measurement. I n the standard mixing procedure the concentration of polyelectrolyte and added salt in the polyanion solution was the same as that in the solution of the polycation. The reaction was carried out by slow dropwise addition wii hout stirring and the reaction niixture was agitated only after addition was complete. Conductance nieasurenients were made after 2 days to allow for any transitory phenomena. I n frequent checks of the conductivity of the reaction mixtures after removal of the precipitate by centrifugation at 2000 r.p.ni. the differences froni the uncentrifuged solutions were negligible except as noted above. The degree of stoichiometry attained was assessed by coniparison of the conductivity of the reaction mixture with that of a control solution made up to the composition expected for stoichiometric reaction and complete counterion release. The Journal of Phyeical Chemistry
A. S. MICHAELS,L. MIR, AND N. S. SCHNEIDER
As an example, in the reaction of 3 parts of AT VBTACl and 7 parts of N SaSS the composition of the control solution would be 4 X N in NaSS, the final concentration of excess polyion, and 3 X N in NaC1, the concentration of microion that would be released in a one-to-one pairing of oppositely-charged polyion functions. If the conductivity of the reaction mixture were found to be less than the value for the control solution the difference could be attributed to incomplete microion release and would furnish a measure of the departures froni stoichiometry subject to the assumptions discussed in the next paragraph. The use of conductivity nieasurements to examine the reaction between the polyions depends on the change in concentration of species of different equivalent conductance. In the reaction of salt f o r m of the polyions, e.g., VBTACl and KaSS, there is a marked increase in conductance since the equivalent conductance of the released microions is about threefold higher than the polyions which are removed In the reaction of the polyacid and polybase there is a marked decrease in conductivity due mainly to the loss of the counterions, H + and OH-, which have an exceptionally large equivalent conductivity. The prior study of the reaction in salt-free solution' involved the deterniination of both the residual concentration of polyelectrolyte (viscosimetrically) and the release of the counterions (argentometric titration of the chloride ion). I t was thus possible to state that the reaction was stoichiometric and coniplele in the sense that the two coniponents were incorporated in a one-to-one equivalence ratio and that thc ionic functions were completely reacted. With the conductometric determinations alone it is not possible to make this distinction. In the reaction of VBTACl and NaSS the release of niicroions furnishes a direct measure of the fraction of ionic groups which have reacted. A coniplete reaction presumably would also be stoichiometric, but the low equivalent conductivity of the polyion makes the method less sensitive to departures from stoichiometry than to incomplete niicroion Table I : Equivalent Conductivities and Estimated Counterion Binding" Polyion
NaSS S'BTAC1 CaSS VBTASOi HSS S'BTAOH a
Equivalent conductivities, (ohm om.) -'/equiv. cc.
38.5 41.0 12.5 11.7 141 85
Fraction of bound counterions
0.40 0.44 0.84 0.88 0.60 0.60
Polyelectrolyte concentration 10-3 'V; salt-free solutions.
POLYCATION-POLYANION REACTIONS IN DILUTEAQUEOUS SOLUTION
release. In the reaction of HSS and VBTAOH in saltfree solutions, the absence of a conductivity contribution by the released microions makes it impossible to determine whether all ionic groups in the complex have reacted. I n this case, any resulting differences in conductivity from that of the control solution are then due only to departures from stoichiometry. Values of the polyelectrolyte equivalent conductiviN polyion concentration ties in salt-free solutions at are listed in Table I. The fraction of bound counterions, a,listed in the third column of this table have been calculated from the equation A
=
CP(1 -
LY)(TP
+
T
~
)
where A is the specific conductance in (ohm cm.)-', Cp is the concentration in equiv./cc., and T P and rm are the equivalent conductivities of the polyion and counterion in (ohm cm.)-'/equiv. cc. Two assumptions were made in employing this equation to calculate 0 : (1) that additivity of equivalent ionic conductivities holds with the value for the free microion unaltered by the presence of the polyion; (2) that the equivalent conductivity of the polyion could be approximated as 15 (ohm cni.)-l cc. mole-', the value determined by transference measurements on 80% neutralized polyacrylic acid.2 For HSS, the degree of proton bonding thus calculated agrees very well with the concentration invariant value determined by Mock and Marshall from pH measurement^.^ The reduced specific viscosities of polyelectrolyte N polyion concentration, determined solutions a t in a Couette viscometer at a shear rate of 15 set.-', are recorded in Table 11. Although these values a t finite concentration will be affected both by hydrodynamic and coulombic interactions, the results should serve as a loose measure of the relative polyion extension under most of the conditions used in the reaction studies.
Results and Discussion Reaction between Salt Forms of the Polyions, NaSSVBTACI. Figure 1 presents a comparison of the conductivities of SaSS-VBTACl reaction mixtures and control solutions for two sets of conditions: (a) 10v3 N polyion concentration in salt-free solution ; (b) 1X N polyion concentration in the presence of N added NaC1. For all proportions of the reactants the conductivity of the reaction mixture is equal to that expected for a stoichiometric reaction involving complete release of the counterions. The same behavior, although not shown, was observed in the reaction of the polyions in salt-free solutions a t 10-2 and 2 X IO+ N polyion concentration. These
1449
Table I1 : Reduced Specific Viscosity of Polyelectrolyte Solutions" Salt concentration, N 0.5 x 10-2 1.0
r
Polyrner/dt
0
NaSS/NaCl CaSS/CaC12 VBTACl/NaCl VBTAS04/Na2SOa
110 16.0 15.1 4.00
34.7 7.65 4.87 1.48
Polyelectrolyte concentration cosity, dl. /g.
x
10-9
28.5 7.52 3.27 1.41
N ; reduced specific vis-
results confirm the conclusion reached in the earlier study, by somewhat less elegant methods, that reaction of VBTACl and NaSS in salt-free solutions is complete. Further, the present results show that the specificity of interaction is preserved even in 10-2 N NaC1 despite the more contracted polyion dimensions indicated by the fourfold reduction in specific viscosity compared to salt-free conditions (Table 11). At higher salt concentrations (0.1 M NaBr) it is known that the reaction is no longer stoichiometric.] It seems reasonable to postulate that the quantitative pairing of ionic functions depends on the ability of long portions of the oppositely-charged polyion chains to come into juxtaposition, on the rearrangement of rotational conformations to bring the reacting groups close enough to form stable links, and possibly on local realignment to correct short-range errors in the pattern of ionic pairing. The first, requirement is met by the open extended conformation of the polyion chain in salt-free solutions or in the presence of only a low concentration of salt. The high local concentration of microions and the slow diffusion of released microions from the sites of reaction should assist in moderating the electrostatic interaction of approaching ionic groups of the polyions, thus permitting the readjustments necessary to ensure efficient pairing. The importafice of both the polyion conformation and the nature of the counterions is convincingly demonstrated by the results obtained under the other conditions which are treated in the sections which follow. By electron microscopy, the polysalt fragments appear to be agglomerates with a well-defined spherical substructure that is also a characteristic feature of the samples formed a t other concentrations. These spherical particles have a rather narrow distribution of diameters mostly in the range 200-400 K.,which is (2) F. T. Wall,
J. Polymer Sci., 20, 477 (1956). (3) R. A. Mock and C. A. Marshall, ibid., 13, 263 (1954)
Volume 69, Number 6
May 1966
A. S. MICHAELS, L. MIR, ASD N. S. SCHNEIDER
1450
190
180
I70
160
150
140
130
120
110
.I
,2
.3
Eq.
.4 NaSS/Eq.
.5 .6 NaSS + VBTACi
Figure 1. Conductances of reaction mixtures and control solutions: (a) salt-free solutions; (b) 10-2 N NaSS-10-2 N VBTACl in 10-2 N NaC1.
far smaller than the 4000 A. extended length of a (number-average molecular weight) NaSS molecule. There is evidence that the spherical particles are not artifacts arising in preparation for the electron niicrographs but are formed in solution. If it is valid to regard these entities as the primary polysalt particles which are initially formed in the reaction and later aggregate, then this implies that the reaction is accompanied by an enormous degree of coiling of the reacting polyions. This coiling would be favored by the resulting increase in contacts between hydrophobic portions of the chain as well by the increase m conformational entropy. Presumably the coiling is mediated by the accumulation of released counterions in the neighborhood of reacting groups. The over-all process might be described as a molecular syneresis accompanied by expulsion of released counterions. A second conclusion suggested by the small size of the primary particles is that the reaction does not occur by random cross linking of molecules in the bulk solution since this would yield highly ramified The Journal of’ Physical Chemistry
,7
.8
,9
1.0
N NaSS-10-3 N VBTACl,
giant molecules or a continuous gel structure. Assuming a bulk density of 1.5 g./cc., the average particle would contain only about 5 NaSS and 13 VBTACl molecules. The volume containing the equivalent number of monomer units is approximately that occupied by an average NaSS molecule extended to onehalf its contour length. This implies that the reaction is localized to the interfacial region of contact between the added droplet and the solution and occurs within the domain that can be ascribed to one or two of the larger reacting polyion species. A t concentrations higher than those used here a stable interfacial film can be formed indicating that now the longer chains participate in a reaction that extends into the neighboring regions to form an interconnecting network. I t is interesting that the thickness of this film is 200-300 A. and shows a granular substructure of a scale comparable to the diameter to the primary polysalt particles. * Reaction of the Divalent Salt Forms of the Polyions, CaSS-VBTACI and NaSS-VBTAS04. Mixing the
POLYCATION-POLYANION REACTIONS IN DILUTEAQUEOUS SOLUTION
1451
120
100 u)
0
0) 0
- 40 0
a
D 0
0
20
0
0 - Reoction
-
X 1
I
I
I
I
I
1
Mixtures Mixtures, Centrifuged Supernotont I l
- Reoction
-
Figure 2. Conductances of reaction mixtures and control solutions: (a) N CaSS-10-2 N VBTACl, iY CaSS-2 X N VBTACl, salt-free solution. salt-free solution; (b) 2 X
salt-free solutions a t a concentration of less than N again results in complete reaction, as shown by the N CaSS-VBTAC1 in Figure 2. Comresults for plete reaction of the polyions under these conditions is rather surprising in view of the higher degree of binding of the divalent counterions and the resulting compression of the chain dimensions. No definitive comparison is available for assessing the direct effect which increased counterion binding might be expected to have on the pairing of polyiori functions. With respect to the decrease in polyion extension it may be noted that the specific viscosities of CaSS and of VBTASO,, although far lower than the values for saltfree solutions of SaSS and VBTACl, are comparable to the viscosities of the latter polyions in 0.01 N NaCI, where complete reaction has been shown to occur. When the concentration of CaSS-VBTACl solutions is increased to 2 X N or when the reaction is carried out at N with the addition of N CaC12, differences in conductivity occur, but as shown in Figures 2 and 3, only on the side of the equivalence
point where CaSS is present in the smaller amount. The reverse behavior is observed with N NaSSVBTASO, in N NatS04,the deviations now occurring when VBTASO, is present in less than the equivalence ratio (Figure 3). These results indicate that a certain fraction of the ionic groups have not reacted in forming the polysalt. The asymmetry of the deviations rules against an explanation based on the direct competition between binding of the divalent counterions and reaction of the polyion functions. However, the results are readily explained in terms of steric restrictions arising from the more tightly coiled conformation of one of the polyions in response to the higher concentration of its divalent counterions. When the proportion of CaSS is less than that of VBTACl complete release of microions demands the reaction of all ionic groups belonging to CaSS. Apparently the tightly coiled conformation of (4) R. G. Miekka, Sc.D. Thesis, Massachusetts Institute of Technology, Department of Chemical Engineering, 1961,
Volume 69, Sumber 5
M a y 1965
A. S. MICHAELS, L. MIR, A N D N. S. SCHNEIDER
1452
Eq. vBTASO,/Eq.
200
I
I
I
NaSS 1
+
VBTASO, I
I
170
I
I
160
150
140
130
120
110
100 X -Reaction Mixtures, Centrifuged Supernotont
90 ,I
42
.3
-4
.5
,6
.7
.8
.9
Ix)
Eq. CoSS/Eq. CoSS + VBTACl
Figure 3. Conductances of reaction mixtures and control solutions: (a) loe2 N CaSS-10-2 N VBTACl in 10-2 N CaClz; ( b ) 10-2 ,V NaSLS-10-2 N VBTASOa in N NatSOa.
CaSS renders a fraction of its ionic groups inaccessible for reaction. On the other side of the equivalence point the complete reaction of all the ionic groups of VBTACl can be satisfied by the excess CaSS except near the equivalence point where this amount is less than the number of groups blocked from reaction. Analysis of the conductivity differences, with the same assumptions used to estimate the degree of counterion binding, indicates that the fraction of divalent counterions which are not released is about the same in all three systems, essentially independent of the proportion of the reactants, and amounts to about 8%. Reaction between the Polyacid and Polybase, Salt-Free Solutions. Whereas particle formation was typical of the reaction between salt forms of the polyions, the reaction of HSS arid VBTAOH in salt-free solutions characteristically resulted in the formation of a film at the added droplet-solution interface. Prolonged shaking was required to break up these film fragments to obtain a dispersion suitable for the conductivity measurements. As shown by the curves for the The Journal of Physical Chemistry
reaction a t low2N polyion concentration in Figure 4, the equivalent conductance of the reaction mixture was less than that of the control solution on both sides of the equivalence point. These conductivity differences can only result from the removal of a larger than stoichiometric fraction of the excess polyelectrolyte, the only conductive species remaining in solution. Accordingly, the conductivity differences in the region of HSS excess have been converted to equivalents of HSS lost. In the lower curve of Figure 5 the results appear as the ratio of the equivalents of HSS to the equivalents of VBTAOH in the complex. The ratio is essentially independent of the composition of the reaction mixture and is about 10% higher than the stoichiometric value. The results obtained on the VBTAOH side of the equivalence point were similar but more scattered, possibly as a result of adsorbed atmospheric carbon dioxide, despite efforts to prevent such an effect. The distinctive feature of the present reaction system is that the counterions H + and OH- disappear from
POLYCATION-POLYANION
REACTIONS I N
DILUTEAQUEOUS
160
A Control Solutions
0 Reaction Mixtures VBTAOH Into WSS
x Reoction
140
Mmtures HSS Into VBTAOH
120
LT
2
-
Y
I
130
'€
r(
-I.
80
5 0
2 6
60
0
'10
80
0 B q . HSS/Eq.
HSS
+
VBTAOH
Figure 4. Conductance of reaction mixture and control solutions, N HSS-10-2 N VBTAOH, salt-free solutions.
- HSS 0 Son Free Condition, 10% PE Cmc
VBTAOH
0 In 0 I M or 0 5 M NoCi, 2
'
dl
'
OIZ
'
d3
'
I
I@N
PE Cone
d 4 ' d 5 ' d6 eq V B T A O H l e a HSS
'
d7
'
ole
'
dS
'
1'0
Figure 5. Polysalt composition in the complex formed from HSS-T'BTAOH: upper curve, lo-* N polyelectrolyte concentration, salt-free conditions; lower curve, 2 X N polyelectrolyte concentration, in 0.1 or 0.5 M NaC1.
t,he reaction zone by formation of water. Thus, during the approach of oppositely-charged polyion segments it, is likely t,hat counterions from closely-placed regions of the polyiori chains react, and leave these regions
1453
SOLUTION
without ionic shielding. Under these conditions reaction between the polyions must be extremely rapid without the opportunity to achieve the efficient pairing of ionic groups that is afforded by the moderating effects of the counterions in the SaSS-VBTAC1 reaction. hloreover, this rapid reaction of acidic and basic functions will occur a t a multiplicity of sites and serve to lock the chains in the extended conformation that existed in the individual salt-free solutions. At N polyion concentration the number of molecules per cc. is about 10 times the concentration at which the polyions would overlap if treated as spheres with a diameter equal to 20% of the contour length. Further, the accumulated released counterions which provide a local ionic atmosphere capable of promoting the contraction of the reacting polyions in the VBTAC1NaSS system are now missing. Thus formation of an interfacial film can be traced to the disappearance of the counterions and the consequent rapid reaction of the highly extended polyion chains. It is to be expected that the rapid reaction of acidic and basic functions which ties together segments of the polyion chains will result in an unequal number of cationic and anionic functions between the ionic cross links, leaving a fraction of the ionic groups immobilized but unreacted in the complex. However, as remarked earlier, the presence of such buried ionic fuiictions would not be detected since the counterions which are released in the reaction do not contribute to the conductivity. The departures from stoichiometry recorded in Figure 4 presuniably arise in the initial reaction but may also involve the subsequent adsorption of excess polyion mediated by the exposure of these buried ionic groups. Indeed, rapid stirring during the initial phase of the reaction results in an alniost twofold increase in adsorption of the excess polyion. However, this might also be due to the increased opportunity afforded the added polyion to react with a larger number of other molecules as it is swept through the solution. Reaction of HSS and VBTAOH in the Presence of Added Salts. When the reaction of T'BTAOH and HSS is carried out in the presence of 2 X N CaC12any unreacted anionic groups trapped in the complex will carry H + or Ca2+while unreaeted cationic groups will carry OH- or C1- as counterions. In due course Ca2f and C1- will replace the residual bound H and OH - in the complex and the latter counterions will diffuse into the solution and react. Thus the control solution in the region of a higher than stoichiometric ratio of HSS will contain only the excess HSS and added CaCI2. The conductance results for this reaction, shown in Figure 6, reveal conductivity differences which are +
Volume 69,Number 6
May 1966
A. S. MICHAELS, L. MIR,AND N. S. SCHNEIDER
1454
410
1
z
L
0
-
0 20-
+
390
Y
Y
-
e
-
2
L 0
370
IO.'N
3 50 Lo
HSS
- IO2*
0
In 2
0
In 10.2N
I
VBTbOH
1 0 2 N CoClz
No2S0,
0 * 330
-
""I
00
-
5 0
" ~
02
03
04 05 06 MOLE FRbCTlON HSS
0.7
00
09
IO
Figure 7 . Fraction of unreacted groups in complex formed from 10-2 N HSS-10-2 N VBTAOH: upper curve, reaction in 2 X lo-* N CaC12; lower curve, reaction N Na2S04. in 1 x
3 I0
(E
01
290
." 0
D
0"
270
250
2 3c 0
2
.4 Eq
HSS/Eq.
.6
HSS
.8
I
.o
+ VBTAOH
Figure 6. Conductances ot reaction mixture ana control solutions; 10-2 N HSS-10-2 N F'BTAOH in 2 x N CaCl2.
far larger than those observed for the reaction in saltfree solution. A clue to the origin of these deviations is the observation that film fragments rather than discrete particles are formed despite the relatively high concentration of added electrolyte. In terms of the discussion given in the preceding section this implies : (1) the domains of the polyions must overlap sufficiently to form a network structure; (2) there must remain a sufficient number of acidic and basic polyion functions which react rapidly, locking the network structure and preventing its collapse with further reaction; (3) it is expected that there remain trapped, unreacted ionic functions in the complex. Since virtually all of the counterions will be converted to Ca2+or C1-, departures from stoichiometry of the magnitude observed in salt-free solutions will make relatively little contribution to the conductivity differences i n the present case (the equivalent conductance of 1,/2CaC12is over ten times that of CaSS and four times that of VBTAC1). Just as in the reThe Journal of Phyeical Chemistry
action of CaSS and VBTACl these differences are a measure of unreacted groups in the complex which are now detectable because such groups will bind Ca2+ or C1-. The fraction of unreacted ionic groups calculated on this basis is shown by the upper curve of Figure 7 and amounts to well over 20% of the ionic functions in the complex. It is also noteworthy that the marked asymmetry observed in the CaSS-VBTAC1 system in N CaClz does not occur here, suggesting that, in the present case, there is a reduced sensitivity, to differences in polyion extension. The fraction of unreacted groups for the reaction in N Wa2S04 is shown by the lower curve in Figure 7. The consistently lower fraction of unreacted groups compared to the upper curve, where the ionic strength is twice as high, indicates the polyion extension is not completely without influence on the behavior. The behavior of the HSS-VBTAOH reaction a t higher salt concentrations cannot be followed conductometrically, but pH measurements in 0.1 and 0.5 M NaCl indicate that the specificity of the reaction is lost under these conditions. The ratio of equivalents of HSS to VBTAOH in the complex is shown in Figure 5, upper curve, for the region where the HSS concentration in the reaction mixture is greater than 0.5 mole fraction. The fraction of combined HSS in the complex appears to increase in proportion to its relative concentration in the mixture and the reaction now resembles the nonspecific interaction of VBTACl and NaSS in 0.1 M NaBr. Further Comments on the Polysalt Structure and the Reaction. The results of this study support the model developed earlier for the structure of the stoichiometric
POLYCATION-POLYA:VION REACTIONS IN DILUTE AQVEOUSSOLUTION
complex.' The complete pairing of ionic functions leaving no more than one group in fifty unreacted implies that the polyions have reacted continuously along extensive portions of the chain. This view is supported by the following arguments: (1) stoichiometric reaction occurs only when the polyions react in a sufficiently open extended conformation; (2) the alternative random pairing of segments from many different entangled molecules would make it impossible to achieve high degrees of reaction and runs contrary to the observation that the primary polysalt particles involve only a small number of molecules; (3) the reaction of one pair of segments restricts the motion of the next pair of oppositely charged segments to overlapping volumes, thus favoring the sequential reaction on kinetic grounds. Although thf. stoichiometric reaction involves virtually complete pairing of ionic functions the orientation and closeness of approach achieved in the individual paired functions must be quite variable owing to the atactic chain structure and the distribution of orthopara substitution in the polycation. One is forced to conclude that even when the ionic functions are prevented from approaching to the point of contact, sufficient neutralization of the coulombic fields occurs so as to release the bound microions. In a related connection, experiments with trimethylbenzylammonium chloride, TNBAC1, a close analog of the monomer structure, have shown that no precipitate occurs with HSS at N concentration, and the binding of TMBACl is no greater than that of S a + . On this basis certainly no reaction would be expected between CaSS and VBTACI. The contravening fact that complete reaction does occur suggests that the factor of importance in the polysalt formation is the gain of entropy in the reaction. Since the entropy of mixing for the polyion is far less than for the same number of monomer segments, the increase in entropy must be due to the fact that the released microions gain far more
1455
entropy than is lost by the polyion in forming the complex. Such an explanation makes it easier to understand why polysalt formation occurs even though steric interferences must reduce the effectiveness of the coulombic interactions far below that which could be obtained by interaction with the monomer analog. Finally, some comments can be made concerning the kinetics of the pairing reaction that occurs in the initial contact between segments of oppositely-charged polyions, which processes may account for the differences in reaction between the acid-base and salt forms of the polyion. I n the first case, the reaction is rapid due to annihilation of the counterions on close approach of the reacting segments. In the second case, the initiation of the pairing reaction is probably comparatively slow since it depends on the diffusion of counterions from the site of reaction and very likely requires the simultaneous accommodation of several segments in the proper conformation to produce a stable link. In this case, the initiation of further cross links might be unfavorable in competition with contraction of the chain as sequential pairing proceeds from the initial reaction site. Thus even under conditions of equivalent chain contraction produced by a modest amount of added electrolyte, the acid-base system leads to a multiplicity of cross links per molecule and gelation, while the salt-salt reaction probably propagates from a limited number of polycation-polyanion contacts to produce predominantly bimolecular pairs and small, dense particles. The possible importance of microion moderation in protein and nucleic acid pairing interactions is thus suggested by these observations. Acknowledgment. This investigation was supported by the National Institutes of Health, Biophysics and Biochemistry Subsection, Grants N o . RG-8288 and GlI-08288. The paper is a condensation of the doctoral dissertation of Leon A h , Department of Chemical Engineering, Massachusetts Institute of Technology, March 1963.
Volume 69, Number 6 M a y 1966
