8/2/2019 A Chain Model for Polyelectrolytes

1/7

5070 MITSURU AGASAWAND STUART. RICE Vol. 82[CONTRIBUTION FROM THE DEPARTMENTF CHEMISTRY AND INSTITUTE FOR THE STUDY OF METALS, UNIVERSITY OF CHICAGO,

CHICAGO 37 , ILLINOIS]A Chain Model for Polyelectrolytes. V. A Study of the Effects of Local ChargeDensity1

B Y MITSURU AGASAWAN D STUART A. RICERECEIVED A R C H , 1960

A series of copolymers of a difunctional acid an d a neutral monomer have been synthesized. By determination of thetitration curve and extent of counter ion association it is shown that the local charge density dominates the behavior of th edissociating carboxyl group, bu t the over-all charge density app ears more impo rtant for ion-binding. On the other handthe experimental results indicate tha t t he mean electrostatic field act ing on a fixed charge is dominated by neit her th e over-allcharge distribution nor the nearest neighbor charge but that both effects are of comparable importance. A derivation of th eKern equation for the titrat ion curve of a polyacid is given wit hout an y assumption abou t uniformity of charge distribution.I. Introduction

From the extensive research on polyelectrolytesin recent years three sets of facts emerge.(1) As the ionic strength of the medium in whicha polyion is dissolved is lowered, the polyion ex-pands.(2) In any process involving the translational orrotational motion of the polyion, a large fraction ofthe counterions to the polyion are intimately as-sociated with it.(3) The activity of t he counterions to a polyionis markedly lower than the concentration, whereasthe activity of t he byions is relatively unaffected.For the case of Na+ as the counterion, the activitycoefficient increases as the ionic strength is in-creased.A number of theories have been proposed to ac-count for the observations cited. The various the-ories differ chiefly in two respects: the retention oromission of the connectivity of t he polymer skele-ton and the method of handling ion association. Inprevious paperslb a chain model for polyelectro-lytes has been proposed which has had moderatesuccess in semiquantitatively interpreting both thethermodynamic and configurational properties ofthe polyion. In dealing with the phenomenon ofcounterion association it has been suggested thatthe major par t of the binding mechanism consists ofthe formation of ion-pairs, similar to but not neces-sarily identical with the ion pairs originally sug-gested by Bjerrum. The phenomenology of thebinding was handled through an assumed dissocia-tion constant, a representation of our ignorance ofthe true interactions at the molecular level. It isour opinion that there are still many unsettled as-pects of the na ture of the ion binding, particularlyquestions related to the difference between ion-binding an d the dissociation of weak acid groups.Although all current theories compute the electro-stat ic free energy of the polyion as if the charge dis-tribution were uniform, it is the local charge dis-tribution which may be expected to affect the dis-sociation of carboxyl groups and t he possible forma-tion of ion pairs. Studies of polyelectrolytes withnon-uniiorm charge distributions are therefore per-tinent to the understanding of ion association andproton dissociation.

(1) (a) This research was supported by a grant from the National(b) F. E. Harris and S. A. Rice,cience Foundation, NSF G5117.J . Phyr . Chem.. 68, 725, 733 (1954).

It is the purpose of this paper to discuss the prop-erties of copolymers of maleic acid and non-ioniz-able monomers. Although a few studies of 1 1 co-polymers have been re p ~ r t e d , ~ - ~his is the firstsystematic study of copolymers of variable ratio.11. Preparation of Copolymers

The copolymer samples were made by the poly-merization of maleic anhydride or diethyl maleatewith vinyl acetate or vinylpyrrolidone. As is wellknown, maleic anhydride and/or diethyl maleatewill not polymerize with themselves and thereby acopolymer containing more than 50 mole 70maleicacid cannot be made. It should be noted how-ever, that a 50 mole % copolymer of maleic acidand neutral monomer has the same linear chargedensity a s polyacrylic acid. Copolymers of less than50 mole yo maleic acid content can be made byproper choice of init ial conditions and the resultantpolymers will never have adjacent maleic acidmonomers. All monomers were purified by vac-uum distillation : maleic anhydride b.p. 89-90'(-15 mm.); diethylmaleate b.p. 100" (-11 mm.);vinylpyrrolidone b.p. 97" (-15 mm.); vinyl ace-tate b.p. 72". Solution polymerization methodswere employed, with the polymerizations termi-nated at about 20% conversion to insure polymeruniformity.1. Maleic Anhydride-Vinylpyrro1idone.-Thepolymerization was carried out in thiophene freebenzene in an atmosphere of Nz at temperatures be-tween 70 and 80" with 0.2% benzoyl peroxide asinitiator. The polymer precipitates from the ben-zene solution, is separated from the supernatant andpurified by precipitation with ethanol from acetonesolution. The purified polymer is a white powder.All the copolymers were dissolved in water andheated at 80-90" for 48 hr. before use. The copoly-mer composition was determined by potentiometrictitration with the first break taken to correspondto the neutralization of the primary carboxyl group(see subsequent discussion). The reactant ratiosand resultant copolymer compositions are shownin Table I.As can be seen, the composition of the copolymer

(2) E. R . Garrett and R . L. Guile, T H r s JOURNAL, 73, 4533 (19.51).(3) J. D. Ferry, 1).C. Udy, P.C. W u, G. F. Heeker and D. B.

Fordyce, J . Colloid Sci. , 6 , 429 (1851).(4) J. D. Ferry, L. D. Grandine, Jr., and D. C.Udy, i b i d . , 8, 529

(1953).

8/2/2019 A Chain Model for Polyelectrolytes

2/7

Oct. 5, 1960 POLYELEC TROLYTE SLOCALHARGEDENSITY 5071is sensibly independent of the reactant ratio. Thismay be due to the formation of a molecular coin-plex between the monomers, an explanation whichis suggested by a yellow color in the monomer mix-ture and the marked increase in the solubility ofmaleic anhydride in the presence of vinylpyrroli-done.

TABLEMALEICNHYDRIDE-VINYLPYFUZOLIDONE

Reactan t ratio, CopolymerSample MA/VP composition MA/VPB1 3/1 1/1.293 1/1 1/1.364 1/2 1/1.232 2/1 1/1.11

5 1/3 1/1.222. Maleic Anhydride-Vinyl Acetate.-For thesepolymerizations we used as the solvent benzeneand as the initiator CY,a'-azodiisobutyronitrile attemperatures between 70 and 80". During thecourse of the polymerization the product precipi-tates from solution. The polymer was dissolvedin acetone and hydrolyzed with NaOH. As thehydrolysis proceeds the polymer precipitates. Theprecipitation was completed after 24 hr. of hydroly-sis by the addition of ethanol. The sample wasthen again dissolved in aqueous NaOH to completehydrolysis and again purified by precipitationwith ethanol. The solution of purified polymerwas deionized by passage through ion-exchangecolumns (Amberlite IR-120, IR-4B). The sampleswere stored in the refrigerator in solution. Com-bustion of sample polymer with HzS04 on aplatinum plate verified the absence of excess smallions. The reac tant ratios and copolymer composi-

tions are listed in Table 11.TABLE1

MALEIC NHYDRIDE-VINYLCETATESample Reactant ratio,MA/VA Copolymercomposition, MA/VAC 1/32 1/2.35D 111 1 / 2 . 7 7E 1/35 113.13

3. Diethyl Maleate-Vinyl Acetate.-This sys-tem was suggested to us by Professor A. E. Wood-ward of Pennsylvania State University. Theprocedures were similar to those cited for thecase of maleic anhydride plus vinyl acetate exceptth at a sun lamp was used to accelerate polymeriza-tion, and the temperature was only 60". Thepolymer is soluble in benzene from which it may beprecipitated by petroleum ether. It was then dis-solved in ethanol and hydrolyzed with NaOH in amanner analogous to that already described. Itwas found that 5-7 days were necessary to carrythe hydrolysis to completion. The hydrolyzedpolymer was purified by precipitation with ethanoland finally deionized with ion exchange resins.

The reactant ratios and resultant copolymer com-positions are shown in Table 111.TABLE11

DIETHYLALEATE-VINYL CETATEReacta nt ratio, CopolymerSample DM/VA composition, DMM/VA

F 1/10 1/4.84G 1/20 1/18.3H 1/40 1/14.0III. Properties of the Copolymers

1. General Comments.-The polymers de-scribed in Section I1 are almost colorless, exceptfor occasional samples hydrolyzed a t higher tem-peratures. These latt er samples had a yellowcolor, but there was no detectible difference inproperties between these and the colorless poly-mers. While polyvinyl alcohol is soluble in water,copolymers of vinyl alcohol and maleic acid arenot always soluble in water when not neutralized.In fact, copolymers which have an acid content ofless than about 3 mole % are insoluble, probablybecause these polymers salt themselves out of solu-tion. The degree of neutralization at which th epolymer becomes soluble in water is shown in Fig. 1.As the content of maleic acid decreases the polymerbecomes less soluble. All solutions of copolymersexhibited some viscoelasticity.2. Potentiometric Titrations.-Potentiometrictitrations were carried out with a Beckman GSpH meter. Typical curves are shown in Fig. 1.Sample B has a titration curve similar to tha t of amaleic acid-styrene copolymer, as reported b yGarrett and Guile2 and Ferry and co - ~o rk er s. ~The neutralization point of the secondary carboxylgroup is smeared out and lies in a very alkaline re-gion. Th e composition of copolymer B was deter-mined by assuming tha t the break a t pH 8 corre-sponded to the dissociation of the primary carboxylgroup. Since the equivalence point of the secondcarboxyl could not be determined, the questionarose as to whether this point is indeed correctlyidentified. Garrett and Guile have demonstratedfor the case of maleic acid-styrene copolymers tha tthis point coincides with th e phenolphthalein end-point of the primary carboxyl group as determinedin a non-aqueous solvent by the volumetric titr ationmethod of Morgan and Siegel.3The tit ration curves of the other copolymers arevery unusual. Th e neutralization point of the pri-mary carboxyl group is not a t the center of the ti-tration curve but is displaced toward t he neutrali-zation point of the secondary carboxyl group. Inparticular, it is interesting to note that the titra-tion curve approaches the titration curve of a poly-monobasic acid and the characteristic features of adibasic acid disappear as the content of maleicacid decreases. This is in contradiction with thenaive expectation that the titration curve shouldapproach t ha t of the maleic acid monomer as thecontent of maleic acid decreases. As can be seenby examination of Fig. 1, the experimental results

(5 ) M. K. Morgan and E. F. Siegei, THIS OURNAL, 69 , 1457 (1947).

8/2/2019 A Chain Model for Polyelectrolytes

3/7

5072 MITSUXU AGASAWANDSTUART. RICE Vol. 82are just the opposite. It is easy to verify th at th ebreak at CY = 1 is the stoichiometric equivalencepoint of the secondary carboxyl group because itoccurs at an almost constant pH for all the copoly-mers and this pH is the equivalence point of t hesecondary carboxyl of the monomer.

i.-?-I I

IA I 1rI 1A- I 1-

G2 -8 -

PH . -I I0.5 Q! I 0 0.5 a!0.5 Q! I I I0 0.5 a! I

Fig. 1 -Potentiometric titration of copoi3mers (2.5') :Copolymermole ratio Initial(.M.A.: soln.,other erl.Code Sample monomer) -COOH NaOH,N

Aq Monome rR B-1C cD DE EF FG GH H

. . . 0 . 0 51:1.2n .01991:2.36 , 1 1 11:2.ii .1301:3 .13 ,01031 : 4 . 8 4 ,06521:14.0 .07491:16.3 , 0161

0.0981080,

1.000.096i,967.967,967

.o m2

To explain the phenomena described it seemsnecessary to invoke changes of molecular configura-tion accompanying the changes of composition.That is, the dissociation constant of a carboxylgroup in a polyelectrolyte molecule is determinedby the local electrostatic potential, the relationshipbetween p H , a and KaOein$m7

+ 0.434f$- C YPH PKso - og-Y

with + the mean electrostatic potential. If the con-tent of maleic acid is small, the molecule will behighly coiled even when CY = 1. In this case amodel with all charged groups uniformly smearedthroughout the polymeric domain, such as th at ofHermans and Overbeek,8 leads to the expectationthat the electrostatic potential is approximatelyconstant throughout the molecule. Thus, withmany of t he charged groups much closer togetherthan anticipated from the linear charge density anda mean electrostatic potential essentially inde-pendent of charge location, the net effect is the sup-pression of th e influence of the nearest ionizedgroup relative to the influence of o ther charges inthe polymeric domain. A41though he equivalencepoint of the primary carboxyl group of maleic acidis at the center of the t itrat ion curve (essentially allprimary group are titrated before the secondarygroups star t to ti tra te) , in the coiled copolymer theelectrostatic field keeps some primary carboxylgroups undissociated even after the initiation of t hetitr ation of th e secondary carboxyl groups.

AS an extension 01 frie preceding argument, wlienthe maleic acid content is large and the polyion ex-tended it is to be expected that the characteristicfeatures of the dibasic acid tit rat ion curve will berecovered. Of course, when the maleic acid con-tent is large, interactions between colinear difunc-tional groups will tend to smear the tit ration curve,bu t the field of the first neighbor should remaindominant so long as there are few internal longrange polymer-polymer interact ions. This ex-pectation is confirmed as is the predicted spreadingof the primary carboxyl end-point when sal t isadded. Typical data are represented in Fig. 2(sample C).We must conclude that a non-uniform chargedistribution has an important influence on the dis-sociation of carboxyl groups, especially when thepolymer is extended.Finally, it is interesting to examine the empiricalrelationships between the apparent dissociationconstant and the pK or the degree of dissociationoriginally suggested for polymonobasic acids. Ifthe apparent dissociation constant K s defined bythe relation

then for a polyelectrolyte K s no t a constant butbecomes a function of the pH or a. The empiricalequations reported are(Kern@) pK = pK, + B p H ( 3 )(Kagawa, et ~ 1 . ~ ~ )K = p K , - z log(e)4)

(Katchalsky, et uZ.11) pH = p K , + n log(e)5 )(6) J. Th. . Overbeek. Bu ! l . SOC .Chim. Belpes, S7 , 252 (1948).(7) A. Katchalsky, N. Shavit and H. EiFenberg, J . Po l ymer sei,1 3 , 69 (1956).(8) J. J. Hermans and J. T h . G. Overbeek, Rec. f r a c . chi in. , 67, 76 1(1948).(9) W. Kern, Z. hy s i l : . C'hcm. ( L ~ i 3 : : g ) , 181, 20 9 (1938).

8/2/2019 A Chain Model for Polyelectrolytes

4/7

Oct. 5, 1960 POLYELECTROLYTESLOCALHARGEENSITY 5073where PKo, PK,, P K a , B, m, n are constants. Theseequations are equivalent, the relationships amongstthe constants being

B 1

In Fig. 3 we have compared Kern's equation 3 withour experimental results. The over-all agreementsuggests tha t i t is likely tha t the empirical equationof Kern holds for all polyacids and is independent

I

10'I I

0 0.5 Ia .Fig. ,".-Effect of added sa lt :

Initial s o h , NaCl,Sample N N NaOH,N

C C 0.130 0 0.0802I C 0.065 0 . 5 0 0x02

of the distribution of fixed charges. The extrapo-lated value of pKo is in good agreement with theprimary dissociation constant of maleic acid (pK1=1.921). On the other hand, equations 4 and 5 dono t represent our da ta satisfactorily. In view ofthe equivalence of eqs. 3, 4 and 5 , this suggests tha tB is not exactly constant, and a variation in B is ex-aggerated in m and n because B is not far fromunity.3. Counterion Mobility.-The mobility of thecounterions to a polyion is conveniently deter-mined by measurement of the tracer diffusioncoefficient, a method first used by Huizenga, Grie-ger and If the observed decrease of themobility of the counterions due to the presence ofthe polyelectrolyte is attributed to ionic associa-tion, a measurement of counterion mobility isequivalent to a determination of the extent ofcounterion binding. I f f is the fraction of ionizedgroups occupied by ion pairs, then

(IO) I. Kagawa and K. sumura, J . Chem . SOC.afian ( I n d . Ch em .(11) A. Katchalsky and P. Spitnik, J . Po l yme r Sci., 2 , 432 (1947).(12) J. R. Huizenga, P. H. Grieger and F. T. Wall, THISJOURNAL,

Sect.) 67,437 (1946).

72 , 4228 (1950).

l - f = F * (7 )where D* s the self diffusion coefficient of thecounterion in an ordinary electrolyte solution hav-ing the same ionic strength as the polyelectrolyte

8t BAFig. 3,-Eramination of the empirical relationship of

B, calcd, from B in Fig. 1,0 80 ; G, calcd.

Kern between p K and PH:n = 0 95 ; C , calcd. from C in Fig. 1, nfrom G i n Fig. 1, n GZ 0.58.solution. As always, the contribution of the poly-ion to the ionic strength is neglected. Previous ex-periments have shown that 1 - f is almost inde-pendent of polymer concentration.In our experiments a sodium salt solution of acopolymer with NaZ2abeling of the counterions isplaced in contact through a fine glass frit with thesame sample solution without Na22. The self dif-fusion coefficient of Na then is calculated easilyfrom the rate of exchange of Na between the twosolutions. We have used eq. 6 in the paper ofHuizenga, Grieger and Wa1112 for the purposes ofcalculation. After evaporation of an aliquot ofthe sample solution, the activity of the isotope isdetermined in a proportional counter. All diffu-sion experiments were conducted by tumbling thecell in a large 25" water thermostat. The reproduc-ibility of our measurements was good bu t over-allslightly poorer than that reported by Huizenga,Grieger and Wall. This we att ribut e to the use ofseveral different cells rather than only one cell.The results of the experiments are shown inFigs. 4 and 5 . Also plotted are t he dat a points ofHuizenga, et al., for sodium polyacrylate. I n Fig.4, f is plotted ne rw s 01 and in Fig. 5 f for severalcopolymers, all at a stoichiometric degree of neu-tralization of 0.95, is plotted versus the reciprocalaverage distance between neighboring chargedgt-oups. It is seen readily that there is no markedMe re nc e between the effects of primary and sec-ondary carboxyl groups. We may therefore con-clude that the non-uniform local distribution ofiixed charges does not uniquely affect the mobilityof th e counterions but th at the total charge den-sity of the polyion is a factor of primary importance.

8/2/2019 A Chain Model for Polyelectrolytes

5/7

5074 MITSURUNAGASAWAND STUART. RICE Vol. 82IV. Discussion

Let the polymer chain be composed of Z acidicgroups. We divide the free energy, A , of the poly-electrolyte solution into three par ts, one of hich,AI, describes th e free energy of the free hyc .ogenion and counter ions eligible to take part in bind-

0 (2.5 I.oa.Fig. 4.-Relationship 01 ion-binding of copolymers t o th e

degree of neutraiization:Equivalent concn.Code Sampie polymer ( N )

3 Polyacrylate 0.0378b B .(I168C C .OlMd G ,0110

ing and neutralization phenomena. (Note th atthe free energy is expressed as energy per polyelec-tro lyte molecule.) The remainder of the free en-ergy will then be the contribution of the polyion it-self. The first portion of this free energy, AS, willbe the electrical interaction free energy of the netcharge of the polyion, regarding the ion-pairs as un-charged sites completely equivalent to un-ionizedgroups. The remainder, A I , includes the chemicalfree energy of dissociated, undissociated andcounter ion paired acid groups, which are assumedto behave independently. In A z , two kinds ofelectrostatic interactions must be taken into ac-count; one is the interaction amongst the fixedcharges of t he polymer in equilibrium with theouter solution only through the exchange of hy-drogen ions and counter ions. The other is theelectrostatic effect on the polymer molecule of otherpolyions and the small ions (ionic atmospheres).If the former is denotedAd and the latter A6

A AI + Az + At = AI + Ad + A6 + A I ( 8 )Let a be the stoichiometric degree of neutralizationof the polyacid, A a the degree of dissociation of car-boxyl groups and f the fraction of the dissociatedsites occupied by bound ion pairs. The net frac-tional charge of the polyion, a, will thus be ( a +

A a ) ( 1 - fl and the fraction of bound sites, p , re-ferred to th e total number of sites of the polymerwill be (a + A c Y ) ~ . Thusa = a + A a - 9 (9 )

A1 can be expressed easily in terms of th e chemi-cal potentials of the free hydrogen ions and counterions

A i = ZAcrc~~r+ Z ( a - B)pc+ (10)A , is a function of the net charge, ZCY,f the poly-mer only, and As is a function of a,A a , p and the

1.0

f .0.5

0 0.5 I .oFig 5.-Relatioiiship of ion-bind ing of copo!yiners t o the

reciprocal average distance between two ticighboriiigcharges :

Concu., DeareeCode Sample N neutraliz.-- IPolyacrylate 0.0378 . . .h Maleic acid ,0300 0.95C G ,0300 .9 5d F .0300 .9.5e E .03r)0 .9 5f C .0106 .%[ extrap. fromg B ,0148 .95{ Fig. 4.

polymer concentration.A3 may be written Corresponding to eg . 10

A 3 = Z ( l - a - A ~ ) M C O O Hwhere P C O O H , COO- and c ( c o o - c t are the chemicalpotentials of COOH, COO- and COO-C+ groups,respectively. Substitution of the above into eq. 8givesA = AI(^, B ) + Ad ( ~ y )+ A&u , A a , 8, Cp ) +

A d a , A a , 8 ) (12)

8/2/2019 A Chain Model for Polyelectrolytes

6/7

Oct. 5, 1960 POLYELECTROLYTESLOCAL HARGEENSITY 5075The equilibrium hydrogen ion activity can be de-termined by minimizing A with respect to ACY,holding CY and 0 onstant

Performing the indicated operation we find

from which@Ht [Coo - l = K ~ ~ -b A4 + As) ( 15 )k l baa[COOH]

or

if CY >> ACY. The third term on the right side ofeq. 16 has been calculated by several investigatorsfor the case of a uniform charge distribution.Herein we shall evalua te b A c / b A a by a method dif-ferent from that discussed in ref. 1. Our intentionis to obtain a relation similar to t he empirical eq. 3without the assumption of a uniform charge dis-tribution. To proceed, let the absolute activitiesof the hydrogen ions and the counter ions be AH+and XC+. Then the grand partition function forthe system may be written

with N H + , c+ he numbers of hydrogen ions andcounter ions, and Q(NH+, c+) he canonical par-tition function. For our purposes it is convenientto evaluate the double sum of eq. 8 by replacingthe sum by its maximum term, E m , determined by

(19)E+ = Z ( l - a - A a )NC+ = ZB

whereupon

and- k T In Q(NH+,No+) = Ad(a' ) ( 21 )

Substitution of 5 into eq. 17 with eq. 20 and 21gives

or

since

Th e calculation of A6 in sal t free systems will not bediscussed in this paper. However, the followingqualitative deduction can be made from eq. 24.Since Ab must be a smooth function of its argu-ments, the empirical equation of Kern, eq. 3, mustbe insensitive to the non-uniformity of the chargedistribution with B probably near to unity, assuggested by t he d ata plotted in Fig. 3.13If we assume that the ion association can be de-scribed simply by a dissociation equilibrium, then(13) Th e previous statements may be verified in greater detail by

consideration of a simple model. Consider a copolymer in whichthe doubly charged groups are dilute with respect to the non-iouizablegroups. I n this case, each difunctional group may be considered to beindependent of other difunctional groups. If with each site we associ-ate a state variable v i , i - 1,1',2,2', , , . 2,Z' where the sites arenumbered consecutively along the chain, and the 'l i take on the twovalues 0 or 1 corresponding, respectively, to uncharged and chargedsites, then the semi-grand partition function of the system becomes

where X is the absolute activity of the charged group, x the interactionenergy between the two charged groups of the difunctional monomerand S ( a ' ) is the entropy associated with tbe distribution of chargedand uncharged groups. When the free energy of expansion and ofbuilding ion atmospheres is negligible relative to the other contribu-tions and th e mixing of ion-pairs and un-ionized groups is taken t o berandom, it may be shown th at these relations are approximately valid

- In h + In K.0 - In ac+ + -2 In 1 - a + 2 a f2 a f = 01 - a - 0In X - In KO + In U H+ - In2 1 - - a + 2 a f

from which the degree of binding, f , may be comp uted, if the ion-pair dissociation constant K.0 i s known. For the case of maleic acidsome values off are

x a (K,' - 10) (K.0 = 100) (K.0 - 1000)0.01 0.0098 . . . . . . . . .......1 .0833 . . . . . . . . . . . . . ..6 .250 0.0005 . . . . ......

1.0 .333 .003 .... ......6.0 * 455 .030 0.0031 ......

1000.0 .545 .4 8 0.099 ......Thus he simple model of this footnote predicts a vanishingly smallamount of binding until a > 0.5; as expected. When K.0 is as smallas 10, complete ion pairing of one carboxyl group i s predicted in thel imit a4 1.rom which it follows th at

8/2/2019 A Chain Model for Polyelectrolytes

7/7

5076 PHILIP . ELVINGN D JOSEPH T. EONE Vol. 82the maleic acid monomer should show considerableion-bonding. For, for the case of maleic acid,pK1 = 1.921,pK2 = 6.225 and the calculated inter -action energy between two charged groups, x , isS.22RT after correction for the statistical factor.If it is iurther assumed tha t th e mechanism of dis-sociation of a carboxyl group is the same as themechanism of association of a counter ion, the ratioof the dissociation constants of the primary andsecondary ion pairs would be

Therefore, even if the dissociation constant of theprimary ion pair is large (as large as in the case of1 1 electrolytes -102-103), the dissociation con-stant of the secondary ion pair would be relativelysmall. If Ks,Owere lo2, K,,O would be 0.025 andthere would be appreciable ion pairing. Howeverif Ks,Owere lo3, here would be negligible ion pairing.As shown in Fig. 5, the measured ion-binding ofthe maleic acid monomer a t 95y0 neutralization isindeed negligible. It is, in any event, likely thatthe ion-pair in a simple electrolyte solution is en-tirely different from the undissociated moleculepictured in the dissociation equilibrium descrip-tion. From the physical point of view the majorcharacteristic of the ion pair lies in the assumption(or definition) th at the ion-pair has no electrostaticinfluence on other ions. Therefore, the presentexperimental results which show that the effect of

the non-uniform distribution of fixed charges (andin particular the effect of the nearest neighboringcharge) is less important for ion-binding than forthe dissociation of the carbonyl group is not unex-pected. However, this result does not necessarilymean tha t there is no site-binding in polyelectrolytesolutions. Since the ions attrac ted to the neigh-borhood of the fixed charges by th e strong electro-static field shield the fixed charges and theseshielded charges have lit tle or a t least lessened elec-trosta tic effect om other charges, the notion of site-binding is useful for explaining many polyelectro-lyte phenomena. In this context, the interpreta-tion of site-binding is closely related to the inter-pretation of the depression of the counter ion activ-ity coefficient. The difference in description is pri-marily a difference in language.We believe the most important result of theseexperiments to be the demonstration of the com-parable importance of the near neighbor electricfield and the domain electric field. This resultclearly calls for a re-examination of the current ap -proximate polyelectrolyte theories, a problem weshall examine in a subsequent publication.V. Acknowledgments.-We wish to thank MissWinifred Huo for assistance with preliminarymeasurements and Professor A. E. Woodward of thePennsylvania State University for an informativeexchange of letters. We also wish to thank theNational Science Foundation for financial supportthrough XSF G5ll S.

/CCIPiTRIRUTION PROM r HE vXlVE RSITY O F L & ~ I C H I G A ~ , N S ARBOR, hrICHIGAX, AND T H E PENNSY1,VANIA STATB U\IVEKSITY,UXIVERSITY PARK , PENSSYLVANIA]

Polarographic Behavior of Alkyl Phenyl Ketones with Nuclear and Side-chain HalogenSubstituents

RY PHILIP . ELVINGND JOSEPH . LEONERECEIVEDEBRUARY9, 1960

Several alkyl phen yl ketones with chlorine and bromine substi tuted 011 the benzene riiig and/or on t he al kyl group ha$been examined polarographically to determine the effect of structure on th e carbonyl group and carbon-halogen bond reduc-tions and to obtain further information on the mechanism for the lat ter process. Sucl ear halogen substitutio n facilitatescarbonyl group reduction, although not in the manner expected from a consideration of inductive effects; it has no apparenteffect on th e fission of side-chain halogen Addition of halogen on th e side chain ha s no effect on ca rbonyl group reductionssince the carbon-halogen bond is ruptured a t a more positive potential. In the acidic region, e.g., below pH 3 5, fission ofth e C-C1 bond is facilitated by increasing hydrogen ion concentration; this dependence probably is due to t he role of hydro-gen ion in a push-pull mechanism at th e electrode, which is likely accentuated by the decreased dissociation of hydrogenchloride in the 9.5% ethanol solutions used.Continuing th e systeniatic investigation of elec-

trochemical carbon-halogen bond fission in organiccompounds, a series of haloacetophenones, ;.e.,(1) (a) P. J. Elving. Recovd Ciiewz. P yo s r . , 14, 99 (1053); P. J. El\.inf:and C. E. Bennett; (b) Ami. Chein , 26, 1572 (1054); ( c ) J , Elrc lvo -chent. Soc., 101, 520 (1954); ( d ) THIS OCRNAL, 76, 4473 ( 1 954 ) ; ( e )P. J. Elving and C. M. Callahan, i b i d . , 77 , 2077 (1955); (f ) P. J. Elving

an d C. L. Hilton. ib id . , 7 4 , 3368 (1952); (9) . J . Elving, J. C. K o m y -athy, R. E. Va n Atta , C.A . Tang and 1. Rosenthal, A ; z n l . Clzem., 23,1218 (1951); (h ) P. J. Elring and J . T. Leone, THIS OURIAL, 79 ,1546 (1957); (i) 80 , 1021 (1!258), (j ) P. J Elving, J . 11.Markowitz andI. Rosenthal, J . Elec i voche in . S o c . . 101, l 9 j (19.51); (k) P . J Elving.I . Rosenthal and M. K . Kramer . THI S OURNAL. 3, 1717 (1951);(1) P. J . Elving, I. Kosenthal and .\. J , l i a r t in , i b i d . , 77, 5218 (1955);

phenacyl halides, and nuclear halogenated aceto-phenones and phenacyl halides, have been studied.The following general characteristics of carbon-halogen bond fission can be deduced from the behav-ior of substituted aliphatic and aromatic carboxylicP . J. Elving an d CS Tang, (m) A d . Chem . , 23, 34 1 (1951); (n )THIS OURNAL. 7 2 , 3244 (1950); ( 0 ) b i d . , 7 4 , 6109 (1952); P . J. Elvingand R. E. Van Atta, (p ) Aizal. Che f ? ? . ,7 , 1908 (1955); (4) J . Elcr -li,ochem. So c . , 103, 78 (195G); ( r ) I. Rosenthal, C. H. Albright and P.T. Elving. i b id . . 99, 227 (1952); (s) I. Rosenthal and P. J. Elving.T H I S OT:RNAL. 73,1880 (1951); f t) 1. Rosenthal, J . R.Hayes. A . JMartin and P .I.Elvinp, i b id . , 80 , 8050 (1958); (u ) I. Rosenthal,C:S. T ang an d l J. Elving, i b < d , ,74 , 6119 (1952).