3451
ollal Volumes of Polyelectrolytes in Aqueous Solutions by CC, Tmdre and R. Zana* CNRS, Centre de Recherches sur les MacromolBcules, Straabourg, France
(Received May 12, 1978)
Using a precision densimeter, the densities of a series of carefully prepared and purified aqueous solutions of polyelectrolytes of accurately known concentrations have been determined. The following polyeIectrolytes have been investigated : poly(methacry1ic acid) (PMA) samples of various molecular weights, carboxymethylceliuloses of various substitution degrees (acid form and tetramethylammonium (TMA) salt), poly(acry1ic acid) ( PAA), poly(ma1eic acid-methyl vinyl ether), polyphosphate, poly(ethylenesu1fonnc acid), and poly(styreriesuifonic acid). Measurements of densities have also been performed on the alkali metal and TMR salts of che last five polyelectrolytes. The densities have been used for the calculation of the apparent molal volumes @cp, I n the concentration range investigated the plots +cp = f(concentratior1) have been found to be linear and the values of aPcP have been extrapolated to zero concentration to give the @GPO’s. For PAA and PMA, @,c$ s+howspractically no dependence on the polymer molecular weight. The *cpo’s have been found to be nonadditive, in contradistinction to what is observed with simple electrolytes. This result gives an additional rxpt3rimental evidence to the so-called counterion “site binding.” The volume changes B ssociated with this process have been determined for various counterions and found to present large differences, according to the nabure of both the polyion and the counterion. Finally for polycarboxylic acids simple assumptions have perm i t l d the determination of the contribution of electrostrktion to the apparent molal volume of the polyion at Infinite dilution and of the fraction of bound counterions with total dehydration.
.
Introduction
We have shown that this excesfi absorption is due to the “specifi~’~ or “site” binding of counterions by polyThe appment molal volumes at infinite dilution ions. Ultrasonic absorption measurements should 0) of simple electrolytes in aqueous solutions have then be capable of providing informations on the kin the subjcct of extensive studies, recently reviewed netics of site binding processes, particularly the values by Nillcro.~ Tbe +20 values of a large number of However, preliminary measureof the rate constants. dectrolytes are now known with great accuracy. For ments’O have shown that counterion site binding is a instance, two ~ e r i e s of ~ ! independent ~ determinations multistep process, chracterized by a large number of of the Wis for tho alkali chlorides showed differences unknown quantities (rate constants, volume changes, of only a few hundredths of crn3/moI. Such accurate As will be shown in results have dernons*rated the additivity of the azo’s. concentrations of the species). the Discussion, the measurement of the apparent On the other hand, the values of the ionic apparent molal volumes of polyelectrolytes permits the evnluamolal volurnes at infinite dilution have been used to tion of the total volume change associated with the obtain informations on the interaction between ions site binding of the counterion and thus helps greatly Iing water mo1ecules.l It would be the thorough analysis of the ultrasonic absorption tam the Ramp kind of informations data. with polyelectrolytes, Unfortunately the situation is much less favorable than €or simple electrolytes as indicated by irzc paucity of the apparent molal volume data found in thc iiterature4-8 and by the large dis(1) F. Millero, Chem. Rev.,71, 147 (1971). (2) F. Vaslow, J . Phys. Chem., 70,2286 (1966) crepancies ivhAchclxist between the results of the var(3) F. Millero and W. Drost-EIansen, J . Chem. Png. Data, 13, 330 ious workers. For. Instance values as different as (1968). 33 and 37 cm3/moP have been reported for the (azo (4) N. Ise and T. Okubo, J . Amer. Chem. Soc., 90, 4527 (1968); of sodium ~ o l y a c r ~ Also ~ ~ Ise ~ ~and ~ .Okubo4 ~ , ~ results Macromolecules, 2,401 (1969). (5) B. Conway, J. Desnoyers, and A. Smith, Phil. Mag., 256, 359 for poly(cthylenc~u6fonicacid) and for poly (styrene(1964) ; J. Lawrence and B. Conway, $1.Phys. Chem., 75, 2353, 2362 sulfonic acid) are incompatible as will be shown below. (1971). Moreover, these workers reported that the additivity (6) M. Rinaudo and C. Pierre, C. R. &ad. Sei., 269, 1280 (1969). also applies te the W‘ of polyelectrolytes in contradic(7) P. Roy-Chowdhury, J . A p p l . Polym. Sci , 12, 751 (1968); 14, 2937 (1970) ; J . Polym. Sci., Part A - 8 , 7 , 1451 (1969). tion with &e p r c w ~ tideasS on counterion -polyion (8) 9. Friedman, A. Caill6, and H. Daoust, Macromolecules, 3, 700 interactions. The abovc facts alone would have been (1970). iquficient to motivate new and more accurate detcr(9) G. Manning, J . Chem. Phys., 51,924 (1969). ininations of the apparent molal volumes of poly(10) C. Tondre and R. Zana, Abstracts, IUPAC Symposium on Macromolecules, Vol. I , Leiden, 1970, p 387; J . P h y s . Chsm. 75, elcctroly tes Our interest however also arose from 3367 (1971). the state of our curi*mt studies of the excess ultrasonic (11) R. Zana, C. Tondre, M. Milas, and M . Rinaudo, J . Chirn. Phys., ihbsorption obs~rvedin polyelectrolyte solutions.’Os1l 68, 1258 (1971). The Journal
of
Physical Chemistry, VoE. 76,N o . 25, 1072
C. TONDRE AND R. ZANA
3452
PI. Experimental Section a. Density Measurements. The density of the solution was measured by means of a digital precision densimeter D \/%A02 designed by Stabinger, Leopold, and Kratky.l! The density is determined from the measiirement of the resonant frequency of a mechanical oscillator filled with the solution. The oscillator is a U-glass tubinp; placed within a temperature controlled metal block. The electronic part provides an excitation of the owillator and allows a precise measurement of the oscillator frequency within a short time T (typically 2 min). An ultrathermostat attached to the instrumcnt controls the temperature a t 25 i 0.002” The mcbasurements are performed once the sample solution has reached a constant temperature. The time T read on the apparatus is the time required for a numnber A7 of oscillations. The apparatus is calibrated by measuring the values Toand TI for water and air whose densities do and dl are known. The apparatus constant A. and tJhe difference between the density d of the solution and that of water (taken as 0.997044 g/cm3) arc then obtained from A = (To2 - Tl”/(dO - d,) d
-”
c/o =
(T2 - To2)/A
(1) (2)
The appareut niollal volume %P of a polyelectrolyte CP solution with a concentration c (in mole of monomer per liter) was obtained from the density d of the solution accordiiig to
(3) \chew M M IS the molecular weight of the monomeric unit of the pol3,elcctrolyte under study. The results were corrected for atmospheric pressure changcs when such changes occurred during the measurements.’I The precision of the density measureg/cm3. The overall ments was about 1 to 2 X accuracy of the apparatus was checked by measuring the apparent mold volumes of a series of alkali chlorides as a [unction of concentration. Extrapolation to zero concentration yielded the following values of the apparent molal volumes a t infinite dilution: 16.88, 16.62, 26.66, 21.73 and 39.1 cm3/mol for LiC1, NaCl, KC1, RbCI, :Lnd @sC1, respectively. These values are in good agreement (dz0.2 cm3/mol) with those previously For the polyelectrolyte solutions the accuracy on the apparent molal volumes is likely to be not as good since, as will be seen below, other causes of error are introduced in the making of the polyacid and polysalt solutions. The duplication of some exper mentn led us to estimate the accuracy on @CP as i O . 5 cm3/mol or f1% depending on whichever the larger. h. Materials. Measurements of density have been perlormed on the following polyelectrolytes : polyThe Journal of Physical Chemistry, Vol. ‘76,No. I S , 1978
(acrylic acid) (PAA), poly(methacry1ic acid) (PMA) with various molecular weights, carboxymethylcellulose (CMC) with various substitution degrees, alternate copolymer of maleic acid and methyl vinyl ethcr (MA-MVE), poly(ethylenesu1fonic acid) (PESA), poly(styrenesu1fonic acid) (PSSA), and polyphosphate (PP). The origin of the CMC, MA-MVE, PESA, PSSA, and PP samples has been previously given.1° PAA was purchased from K and K Laboratories (CaIif.) as a 25% aqueous solution free of ionic impurities and was found to have a molecular weight of 120,000. PIMA was prepared in our laboratory by a bulk polymerization of the purified monomer under uv irradiation. The resulting polymer was fractionnated using methanol as solvent and benzene as precipitant. The fractions were purified as described below and the molecular weights determined by means of vi~cosity.’~ c. Purification and Preparation Procedures. The major sources of discrepancies among the values of the apparent molal volumes reported by various workers are likely to be found (I) in the purity of the samples, (2) in the accuracy on the values of the concentrations of the polyacid stock solutions and, (3) in the preparation of solutions of polysalts of accurately known concentrations and free of ionic impurities. These three points will be now examined in detail. 1. PuriJication of the Polyelectrolytes. Several of the products used in this work as well as in previous studies4,5~8 were of commercial origins and may have contained sizable amounts of ionic and nonionic impurities. The classical method of polymer Purification, Le., dissolution and precipitation, k i n g inoperant for ionic impurities, the following procedure was adopted. Aqueous solutions oE the raw materials were first extensively dialyzed against distilled water m order to remove most impuritics of low molecuiar weights. A further purification was achieved by passing the polyelectrolyte solutions through anion and cation exchange resins and filtering them. Ttiesc purified polyelectrolyte solutions, in the acid form, had concentrations between 0.2 and 0.4 equiv/l. They wcre used as stock solutions and stored below 5” to avoid a bacterial contamination which was found to occur a t room temperature with polycarboxylic acid solutions. 2 . Determination of the Concentratton of the Polyacid Xtoclc Solutions. Two methods were used for the polycarboxylic acids (PAA, PMA, CMC, and MA-RIVE) : potentiometric titration and dry content measurement. The determinations were performed on a weighted sample of the stock solution (about ml), the density of which had been measured thus yielding the value of the (12) H. Stabinger, H. Leopold, and 0. Kratky, “Digital Densimeter DMA 02,” Institute for Physical Chemistry, University of Graa, Austria. (13) J. Francois, R. Clement, and E. Franta, @. R , Acad. Bci., Ser. C, 273, 1577 (1971). (14) A. Katchalsky and € Eisenberg, I. J . Polym. Sci., 6 ,145 (1951).
3453
volunie of t,hc sarnplr with great accuracy, a t 25". The two resultii usuzrlly agreed to better than 0.7% and the avcrage va:ue oi the concentration was used in the Eolo.vvlng. Accurate mducas of thc dry contents of PSSA, PESA, and PP sohatnone cou'ld not be ohtained as these compounds u ere Suund to retain water even under vacuum arid zit tentprrateir?J wlme decomposition occurs. Hon ever the 'v z r y t.dmrp change of pN corresponding to the neutralization of PE A and PSSA permitted an aceurai,e ~ ~ ~ of their e ~ ~ ~ For n concentration. PP a special proceduc "im necessary. lo Attempts to obtain the concentration of alkali metal and ~ ~ t miurn ~ ~(TMA) ~ salts e of tthe poly~ ~ eje(+mlyLes lrom dry content measurements have been umueciessfiil as all these salts have been found to retizirt water. ,S ,Solutions of Polysalts with Known following procedure has been le polyelectrolytes but the PP salts. *B knocvn volume iP, 609 * 0.005 cm3) of metal hydioxidr solutmt whom concentration is known to within is iritrodincd into a 25-ml volumetric flask with a caiiioratetl prjnet. Then is added a mass of the ptA7i.iaa d stock soiutiort (of known density and conci>n~rn [ion) c.ali:uEated as to neutralize the hydroxide aird 'Iravcs a srnall ainount of free polyacid (I t o 2O/oO). Bi'indly water is added to reach a final volume of 25 rnl al, 25". An excess 01 polyacid was used as both calculatioris and rxpiwmmts showed that for heavy dkali mctak (cwentially Rb and Cs) free hydroxide introdiices a substantial error on %P. On the contrary a slight excesii of polyacid has practically no inflrzenee on thc result ILZ this proccdurc the concentration of the poiysalt is readily obtained from that of the hydroxide and from the ratio of thc volumes of the hydroxide and of the volumetric dask. Moreover, this procedure avoids both evaporatnori a n d €ormation of carbonate which occur i n the potcntiornrtric preparation of polysalts if sp~cialprecautionq ere not takcn. The presence of carbonate in lhr metal. hydroxides used to prepare the polysdts is thought 1 0 have been one of the major sou~~ccs of disagrcemcn t between the various workers. In t h i c ; work t h r h y h x i d e s were thoroughly decarbonated by pacsing Lhrm through an anion exchange resin, The oprration was performed under nitrogen. The stock solutAonUS aneta1 hydroxide was titrated and stored hinder ~ierogen. The titration curves determ i n d before and sftcr the ion exchange showed that the carbonate h a d brei? completely removed. The above rnpthod 101preparation of polyqalts could not 'UP uqed ior the polyphosphate salts a9 depolymerization occur^^ nhen I T in: in the acid form. Therefore a IZPP solution was prepared and passed through a cal ion excbangc rnqln prc4ously neutralized by the cbown metal hi d r m d e . The concentration of the
I
'
~
~
~
~
~
~
~
,
4
~
~
1
~
~
Figure 1. Variation of @CP with c for polyaerylic acid ( X ) and for its Na(O), Li( f), K(O), Rb(A), Cs( and TMA(V) salts.
120t
0
0.05
0.1
0.2
Figure 2. Variation of @cp with c for MA-MVE in the acid form ( X ) and for its Na(O), Li(+), M(n), Rh(A), Cs(O), and TMA(V) salts.
PP salts were then determined potentiometrically as previously reported.'O This procedure resulted in a lesser accuracy (about 1%). The water used throughout this work was first deionized by means of a mixed-bed ion exchange resin and then distilled. 111. Results Figures 1-4 show the apparent molal volumes as a function of concentration (in mole of monomer per liter) for PAA, MA-JIVE, PESA, and PSSA and for the alkali metal and T M A salts of these polyacids. The results relative to samples of PM4 with molecular weights M , ranging from 44,000 to 370,000 arc- givcn in Figure 5 . Figure 6 is plotted relative to the acid forms and the T M A salts of Cl\IC with substitution degrees (SD) 0.98, 1.3, 2.1, and 2.65. For most of the polyelectrolytes studied in this work the concentration8 inThe Journal of Phgsical Chemistry, Vol. 76, N o . 25, 1972
C.TONDRE AND R. ZANA
3454
-Q---+-.
54
V
c
-I
.--!--"--.Q,OS
0
c (MIL) 6
0,lS
081
Figure 3. Variation of *CP with c for PESA( X ) and for its Li(+), Na(Q), K(El), Rb(A), Cs(O), and TMA(V) salts.
0
0,OS
0,15
0,1
0,2
Figure 5 . Variation of *CP with c for poly(methacry1ic acid) samples of molecular weights 44,000(0),76,000(0), 97,50O(A), 184,00O(U), 275,00O(V), and 370,000( X ).
--e
a 0
140 r
0
0,02
0804
0,O6
0,oe
Figure 4. Variation of @CP with c for PSSA( X ) and for its Li(+-), Na(O), K(o), Rb(A), Cs(O), and TMA(V) salts.
vestigated ranged lrom 0.04 to 0.25 N . In this limited range all of the plots @CP = f(c) were found to be linear, and, as c wm incrcased, @CP either remained constant (sec C;\'IC's, TX'[A-CR'IC's, PMA's, PAA, TRIAAPES, and MA-AWE) or increased linearly. Similar linear i n c r e a ~ sof C ~ C Pwith c have been previously reported by Conway, et ~ 1 . and ~ 5 Ise and Okubo4 for various polyeiectrolytes. Such a behavior has been interpreted in terms of an overlapping of the hydration shells of the polyioos as c increases. This results in a lesser electrestrictive eff cct per polyion and therefore, in a positive slope for the plots @CP = f(c). These lincw plots led UR to a tentative estimate of the apparent molal volumes a t zero concentration (@GPO) from the extrapolation of @cp to zero concentration. The values of @,z$ obtained from the results on Figures 1-6 and also from our results on PP which were not The Jozirnal of Physical Chemistry, Vol. 76, N o . 23, 1972
132. 131
0
-0-
0.05
"
0.1
,
0.15
c (MIL)
,
0.:
Figure 6. Variation of *CP with c for carboxymethylcellulose samples with substitution degrees 0.98(0, ), 1.3(V,f), 2.1(0,B), and 2.65(A,A). The symbols 0, V, 0, and A refer to the acid form of the CMC's while 0, f, B, and A are relative to the TMA salts.
shown are given in Tables 1-111 together with the values of @cp0reported by other workers. The comparison of these results shows points of excellent agreement (PSSA, PAA, PMA), of fair agreement (NaPP, PAA, and PSSA salts), and of strong disagreement (PESA and PESA salts). The latter case requires special consideration because the two sets of data are clearly incompatible. The difference between the @GPO values for PSSA and PESA represents the apparent molal volume of a phenyl ring minus two H atoms. This volume is found t o be 125 cm3/mol in Ise and Okubo work while our results yield the value 65 cm3/mol. On the other hand this volume can be eval-
Table I : Apparon?, Mold Volumes of Polyelectrolytes PAA-MA-MVF:
Acid form Li salt Na salt M salt Rb salt cs salt TlMA salt From ref 7 ,
a l
l
_
30.8 aei . 3 49. A 54.5 120.8 b
From ref 4.
_
_
46.7a
47.gb 33b
28.8
37a
33" 436
38.2 41.4 4'9.6 113.3
$7.4,
~
46,7 28. I
_
-
c -
This work
Other results
This work
44.9 43.8 45:4 54.6 59.3 85.1 132.3
-13.2b
110.3 107.5 108 7 119.5
1186
-l o . @
I
Other results
121b 213b
220
100.1
Prom ref 5. I
~
~~
~~
Polg(metha,crylic Acid), Effect of the Molecular Weight 44,000 59.4
p/Pw @GPO,
17.6 18.8 28.4 30.3
1106 108.P
___l__p___l________-__I
Table HE:
%his work
Other resiiltu
llOb
126
131.9 197.4
.--.
F-------PP-------
F-----PSSA---
~PESA--------
Other results
ThiB work
56.3
I
cn3/moi
76,000 59.6
87,000 59.6
185,000 59.1
270,000 59.0
370,000 59.3
Gao ,0000 60.0
From ref 7,,e :> 0.1 livl~
uated in two different ways, (1) from an ultrasonic vibration potential study of monocarboxylic acid@ arid (2) from the B'CFO values for CH8PhS03Na1 and CK3S0@Ja (obtained by extrapolating the data of Corkill, et aE.16). Given the approximations involved in these calculatioxis the average value 58 cm3/mol compares well with that obtained in this work and shows that h e and Oliubo data4 for PESA and PESA salts cannot be taken into consideration.
Table III : Cal.bor;ymethylcelluiose, Effect of the Substitution Degree 0.98
GMC acid I r m
SD 2.1
1.3
7
2.65
2.5a
131.4 140.8 172.4 193.2 190.5
%Po
~ F O ,
TMA CMC cm3/molb
A V O , cm3/moBc ATT0/8D, cm3/equiv
208.9 239.7 332.0 371 126.4 130.2 155.2 147.9 10.3 17.6 28.5 69.7 10.5 13.6 13.6 22.5
From ref 6. Q>p0 = @PO - VBOSD,
@T~~A-CII$
-
@TAIA~SD.AVO =
Qla-cRrco --
l _ _ l l l _ _ / _ _ _ _ s l - _ l . l ~ - , ~ -
Figwe 7 shiows that for PMA @GPO does not depend on M , . This resiilt is discussed in the next paragraph. On the other hand, Figure 8 shows a linear increase of Q&I with $343 for CMC'x in the acid form. For CMC-TMA's, &PO aTw increase linearly with SD up to SD 2.1. Above thiri value there is a departure from linearity which is explained in part IVd of this paper. I1 i$ noteworthy thaL the two curves @cp0= f(SD) relative to CMaYs in the acid form and CMC-TMA's extrapolate at, SD == 0 to the same value, ( 3 ~ p ~ ) s D = ~O =L
95 cm3/mol. This result which represents the apparent molal volume of the cellulose nionorner appears as a rather original one when it is pointed out that celhilose is insoluble in water.
IV. Discussion As said in the Introduction the results reported in the 1it)erature show strong discrepancies. In particular, contradictory results have been reported for the effect (1) of the polyelectrolyte molecular weight M , and (2) of the concentration e, a t c < 0.05 h' on the value of @cp for polycarboxylic acids. These two points will be examined first as they condition in part the rest of the discussion. The separation of the @ccpo'sof polyelectrolytes into those of their ionic coniponents (polyion P and counterion 6)wili be then examined. It will be shown that, as expected from ultrasonicl0,l1 and d i l a t o m e t r i ~ ' ~studies, ~'~ the additivity does not hold for the apparent molal volumes of polyelectrolytes because part of the counterions are bound by the polyions. Finally a method for the evaluation of the contribution of electrostriction to the apparent molal volumes of polyions will be presented and applied to polycarboxylic ions" a. Efect qf the Polyelectrolyte Molecular Weight. Highly charged polyelectrolytes can be approximated by charged ~ylinders.5,~This model predicts that for sufficiently long polymer chains, i.e., \$--henA!!n7 is large enough, the @GPO per monomer becomes independent of (15) R. Zana and E. Yeaper, J . China. Phys., 6 5 , 467 (1968). (16) J. Corkill, J. Goodman, and T. Walker, Trans. F Q ~ u Sac., ~ u ~ 63,768 (1967). (17) Y. Po Leung and TJ. Strauss, J . Amer. CXcm. rSoc., 87, 1476 (1966). (18) A. Begala andU. Strauss, J . Phys. Chem., 76,254 (19'7$!), The Jooztrnal of Physical Chemistry, Vol. 76, AVO.$3, 1972
3456
48 47
I
Figure 7 . Effect of the polyelectrolyte molecular weight on the value of @ c p o for BRlA (curve 1) and PAA (curve 2). The results on curve 2 have been taken from ref 4(A), ref 7 ( + ) , ref 8(0),and this work ( X ). (- - - -) curve is given in ref 8.
SO 5C!j----------
I’
2
L
3
Figure 8. Effect of the substitution degree on the &PO CMC’s in t’ie :wid E o m ( 0 ) and for TMA-CMC’s(+),
for
XT*.This concluqjon has been verified for NaPP5 and polyethyleneimine -HBr.5 The situation is more complicated for weakly charged polyelectrolytes, &.e., for polyearboxylic acids, whose conformation is close to that of a coil with a radius of gyration I ~ qlightly G larger than in the uncharged state. €Io15 ever, T a n f ~ r dhas ~ ~ shown that the intrinsic volume of the polymer chain represents less than 1% of the volumLeof the sphere of radius R G , the rest being solvent. Moreover thP hydration shell is then mainly the rcwlt of Aort-range forces since the polymer chain bears only a amall charge. Thus, the amount of water within tht. polymer coil appears sufficient to ensure a complete hydration of each part of the polymer chain, indcpcndently of the others parts of the chain in the Immediate vicinity. One should therefore expect @cp0to be independent of M, when M, is large enough. This prrdiction has been verified for uncharged polycthyleneimine.6 Also, for PlLIA, the rcsul ts of RohThe Jorlrnol o j Physzcel Chernisliy, Val. 76,
ZS, lA72
Chowdhury7 together with those obtained in this work in the range 44,000show no effect of M , on %PO 680,000 (see Table I1 and Figure ’7). On the contrary, Friedman, et a l l 8observed for PAA a decrease of cpcPO However it can be seen on Figure for increasing M,. 7 that if the results reported by these workers (four PAA samples) are plotted on the same graph than the result of Roy-Chowdhury’ (PAA ~ ~ , and ~ Othat~ ob) tained in this work (PAA 120,000), a straight line with a very small negative slope can be drawn which goes very close to four of the six experimental points. Two results are left out, one which has been taken from Xse and Okubo work14whose results have been found systematically too large (see above and in rcf 5), the other is from the Friedman, el al., study.8 In terms of concentration the departure of this last result from the straight line (curve 2 on Figure 7) corrcsponds to a 3% error on the concentration. The small negative slope of curve 2 may be explained by the rc catalyst in the preparation of thew PAA ~ r t m p l e s . ~ ~ ~ ~ ~ This catalyst remains bound t o the polymer by a covalent bond and is impossible to eliminate. As usually each macromolecule bin;ds one catalyst molecule thk relative effect of the catalyst on &p0 should decrease as M , increases. It is noteworthy that the P l I A samples of curve 1 on Figure 7 were catalyst free and showed no dependence on llfns. From the above it can be safely concluded that fW, has no influence on @Cpo a t least for M , sufficiently large, i e., above ~ 0 0 0 to 10,000. For lower values of M,, a dependence of @c)Cp0 on iMv should appear, as indicated by a c @cp0values for the monomer alone ( same monomer included into a polymer. These values, given in Tables 1Va and PVb, show that polymerization results in a sizable decrease of apparent molal volume and suggest a possible use of apparent molal volume measurements for the determination of M , for oligomers. The results in Table are rdative to weak polyelectrolytes and oonpolyclectrolytes. They show that the ratio AVW/MX (where AVItla= @C;lro and Mat is the molecular weight of the monomer) is independent of Mbl , within experimental accuracy. Table IVb is relative t o strong polyelectrolytes. aMO and @Po represent respectively the apparent molal volumes of the monomeric ion alone and included in the polyion. The values of @Po and %In have been evaluated as indicated in the footnote in Table bVb, arid in part c of the Discussion. I n this case L I V ~ ~ de~ / J ~ ~ ~ creases for increasing 1 4 4 ~ . This result i 9 examined in part IVd. b. Eeect of Concentratioiz on ihe Partial Molal Volume of Polycarboxylic Acids. For concentrations (19) C. Tanford, “Physical Chemistry of Macromolecules,” Wiley New York, N . Y., 1961, p 178.
3457
a. W&'~nlc Polyelectrolytes itletiiacrylic
Aery!ic acid
Monomer
acid
Acrylamide
Polymer
61.'P PA.4
78,@ PILL4
65.5" Polyacrylamide
@0P0
46.P
59.4ib
50.9"
MW i
72.08
AVW = @on? .- *CP" AVnrp/Mii
15
86.08 19.2
71.1 14.6
@ c 110
0.223
0.20S
0.205
Methacrylamide
81" Polymethacrylamide 62.5" 85.1 19.5 0.226
b. Strong Polyelectrolyte Monomer
51 .!7 I"A29.1a
*g?,o
Poly ion @Po
AVm = +?,I" &!
AVmIM
Acrylic ion
22.4
Vinylsulfonic ion
Styrenesulfonic ion
7 4c PESA48. I d 25.9
133c PSSA 113.2d 19.8
107 0.241
181 0.11
@PO
71.06
0,315
a From ref 7 . This work. From the combination of results in ref I , 7 , and 16 and with the assumption that the removal of two H atoms in order t,o create a double bond C=C brings about a decrease of apparent niolai volume of 6.5 cm3/mol. This acisumption i s based on the comparison of the apparent molal volumes data from ref 7 and from E. King, J . Phys. Chem., 73, argraves, et a/., {bid., 73, 3249 (1969); and International Critical 'Tables, 'Vol. 3, McGraw-Hill, New York, N . Y., 1928. This work, as explained in part IVc.
above 0.1 Ii' She re:dts reported for PAA497*sand PAIAj97 agree with those obtained in this work for PAA, PMA, GMC, and hlA-MVE (see Figures 1, 2, 5 , and 6) In showing no dependence of @cp on e. This behavior is probably the result of the very low state of charge of these polyrners a t concentration above 0.1 N . On the contrary, conflicting results are found a t con~~~ cent>rations b e h w 0.1 M . Some ~ o r l i e r sobserved that the apparent, m o l d volume of PMA is increased by several crn3/mol a t concentrations below 0.1 N . On t h e other hand, all li'E\LA samples studied in this work sho-viedno concenlraekm effect in the range 0.05-0.15 N (sce Figure 5). Moreover, mPasuremcnts performed in the range 5.10--3--24f- I N on the PMA sample 76,000 failed to reveal any concentration dependence of @CP. This last result 'is quite similar to that reported by other . ~ r . o r k e d 'for ~ FAA.. The purity of the samples is likcly t o be the ~ ~ u r cofc th,r l conflicting results found €or PSIA because the samples used in previous studies were not as thoroughly purified as in this work. I n any case, it must be pointed out that no simple explanation can bz given for such a large increase of @cp at low concentratfons if nt Jtcre t o exiut. The results of P;alaliZ0hawe bem p m e n l , e in the Friedman, et aE.,S
paper as giving support to such an cffect. However both d i l a t o r n e t ~ i c and ~ ~ ~~~ *e f ~ a ~ : studiers ~ o ~ e ~ r ~ ~ have shown these results to be inco'rrecl, i , c , I h e apparent, molal volume decreases with increasing ionization, as it should be from the .inoreased electrostriction of the polyion ~ i@pcpa o ~of ~ o ~ znio~ Those ~ of ~ ~ ~ t e. ~ e ~ a ~ ofa the Their llonac Componenls. ~~~~r~~~~~~~~ Emdence of Counterion S i t e Binding. For simple ~lectrolytes the apparent molal volume of a salt a t infinite dilution i s equal to the sum of those of its ionic c o ~ ~ ~ For o ~ ~ ~ ~ l polysxlts this additivity &odd not hold as parl of the counterion must remain bound tcs llae polyion, rven at infinite aiihatinri.g Our @cpOdata can he used 8s Lolluvvs to give support to Chis theoretical pre the additivily of the apparent mcii finitc dilut,lon for polysalt solutioais li ads l o
~,~~~~~
&!ro
I -
@PO
-I- @c')
14)
where is the counterion apparent molal volume at zero conccntralion. AB the @c*'svalues are knosvn,1~2* eq 4 can be used t o calculate tlie value; of @pD. The results, given in 'Table v, show khat far a given polyion the value of @Po depends on the nature of the counterion. This dependence reveals that, part of the counterions must be bound to the polyion, and that -this binding is accornpairied by a positive volzinle climge associated to the releabe of eiectrostricted water molecules, 'This result confirms the ~ o i ~ c ~ u s i oofn s~ ~ ~ ~ t oand~ ~ ~ ~ ~ ultrasonic absorption'0*" studiea. %kpation 4 however is verified n7hen C+ = TllibA l- a s 1.i 'ria? been shown that a nqgligible volume ehang associated with the site binding of this large ion.lOl 'Then it can easily be demonstrated that if in a, solution of the poIysalt CP a fraction /3cP of counterion C is boarnd t o t h polyion P,the volume changc AVcpO for ti?, bindmg rcnction 5 is given by ~q 6.
c+-/-
P- --+GI>
AVcr' = GVcr/Pcr = [ ( h O ) c-
(5)
(@P~))T~IIAI/PcP (6)
I n this equation (@pO)cand ( @ ~ O ) T M A represent the apparent molal volumes of the pOlybn as obtained from eq 4 applied to the counterions C + end TAM+. I n what follows the apparent rnolai volimic of die polyion @PO is taken as (@PO)TMA. Both Pcp and N c p o are of great mterrht t o the workers involved in the study of polyclectrolgtes. I n particular these two quantities are iiaeded for the complete analysis of ultrasonic absorption data lo l J Thus, the 'PcpO values f o ~polysalts allow u3 to obtain 6Vcp which gives UR a relationship between BCP and AVcrO. (20) F. Wall and S. Gill, J . Phys. Chem.., 58,740 (1954). (21) A . Ikegami, J. Polynz. Sci., Pari A-b, 907 (1964) ; Biopolymers, 6,431 (1968). (22) R.Zana and E. Yeagor, J. Phys. Chem., 71 I 523,4241 (1967).
The Journal of Phygical Chemistry, Vol. 7 6 , N o . 9.9, 197'9
c. 'FONDRE
3458
---MA-MVE--
c
*(?
Hf Li '-
--;i 4 --6 5
Na+ Kk Rb CS .I.
-6 6 :i 6 8 7 15 9 84 2
+
TMAf
(*P%
61.7 43.1 42.9 43.5 40.8 38.5 36.4
Y-PESBT-
-PAAy---
-------PSSA-----
8VPC
(*P%
6VPC
(@P*)C
6VPC
25.3 6 7 6.5 7.0
52.1 34.4 35.4 34.6 32.7 31.6 29.1
23 5.3 6.3 5.5 3.6 2.5 0
50.3 50.1 52 51 50.6 49.1 48.1
2.2 2.0 3.9 2.9 2.5 1.0 0
4.4 2.1 0
(*P%
115.7 113.8 115.3 115.9 117.3 115.9 113.2
AND
,-------
sfpc
(*P%
2.5 0.6 2 1 2.7 4.1 2.7 0
R. ZANA
PP6VPC
23.9 25.4 24.8 21.6
8.0 9.5 8.9 5.7
15.9
0
(+pO)c = apparent molal volumes of polyion P- obtained from eq 4 using the values of 0cp0of Table I.
lL
~__ll----
An approximate method of calculation of PCP is given in the next paragraph. I n Table '61 are also given the values of GVCP for a series of polysalts. These values show considerable changes according to the nature of both the polyion and the counterion. This behavior has been interpreted in terms of a model where bound cations form cither an ion pair or some kind of a chelate with polyion charged sites, according to the respective values of the counterion radius and the actual distance between charged sitee.l' The b V C p values in Table V are in fair agreement nith thorc found by means of dilatometry.17s18 In thme experiments, however, the ratio (metal ion)/uit,e was always below 0.4, while in ours tbii; ratio equals 1. cl. Evaluatioqi of the Contribution of Electrostriction to the @PO'S of Por'ycarboxylates. For polycarboxylic acids the ionization is small and the fraction of bound proton? is dose to L a t concentrations above 0.1 N . Therefore 6Vprp f AVH:P@,where AVHPO represcnts the molar volumc change for the reaction
-COz-
+ 14-
-C02H
(7 1
+ AVpo
(8)
--t
One can w:.itcI 1 l V ~ p O= AVHO
where AVHO and AVpo are thc volume changes due to t h release cf electrostricted water molecules by Hf and P-. Thus AVpO represents the contribution of clcctrostriction to the apparent molal volume of the polyion (a$) rI\IA. On the other hand AVHO is t o a very good approximation equal t o 5.4 cm3/moL1 If we assume that the hydrophobic contributions to the apparent molal volume of a polyelectrolyte in the fully ionized and in the near uncharged states arc equal, then eq 8 pcrrnits the calculation of AVpO, using the AVH~Ovalwi of Table V. The results of these calculations are given in Table VI. For the CMC's the plot AVPO = f(SD) shoms a plateau for SD values betmren 1.3 and 2.1. This behavior is likely t o be the resiilt of the way in which the OH groups are substituted on the cellulore monomer, It is knownz3that a t SD below 2 the rubstitutcd OH groups are mainly those in The Journal of Physical Chemistry, Vol. 76, N o . 9.3, 1972
position 2 and 6 on the sugar ring. The ionized carboxyl groups even though on the same sugar ring are then far enough apart to act almost independently on the surrounding water molecules and thus to cause only a small electrostriction. It is only for SD 9 2 that a sizable proportion of monomers are carboxymethylated in positions 3 and 6. The corresponding -GOz- groups are then close enough to each other as to bring larger electrostrictive effects, comparable with those measured for PAA, PMA, and MA-!LIVE. This explains the departure from linearity which can be seen in Figure 8 for the result relative t o TNA-ChfC SD 2.65.
Table VI : Electrostriction of Polyioiis Polyion
AVp/mol of co2-
PAAPMAM A-M VE cn 15,000 and of the polymer concentration in the range 5.10-3-0.1Z N. For most of the other polyacids and polysalts @GP has been found to increase linearly with polymer concentration. The apparent molal volumes at infinite dilution cXiepo have then been used for the evaluation of (1) the volume change associated to the site binding of counterions by polyions, ( 2 ) the contribution of electrostrietion to the apparent molal volumes of polyions, and (3) the fractions of bound alkali metal counterions.
Acknowledgment. The authors are pleased to acknowledge Dr. J. FranGois for allowing the use of the digital densimeter.
The Journal of Physical Chemistry, Vol. 78, 'VQ. 23, 1972
