Enthalpy of Ionization of Polycarboxylic Acids ly observed, while for the heavier metals a(M) is 10-510-6 M' in agreement with the observation that dilute solutions of these metals may be prepared. Similarly, the trend for the amines is well reproduced in the calculated solubilities. Neverthe Less, the calculated solubilities for NH3 are about 2 orders of magnitude lower than the rneas u r d ones. The success of this comparison between the metal chlosuggests that ride and metal solutions, except for "3, the saturated metal solutions are salt like and consequently composed of ion pairs. These ion pairs cannot be between metal cations and solvated electrons because other properties of the solutions rule out this possibility.35 The only reasonable alternatives are M+.M-. This conclusion is in agreement with indications from measure-
539
ments on electrical conductivity36 and optical spectra37 of alkali metal amine solutions that the metal anion is an important constituent of these solutions. Acknowledgments. This work was supported in part through a grant from the National Science Foundation. The authors are grateful for many helpful discussions and suggestions by Professor Sidney Golden. (35) Dilute solutions often show propertbs attributable to solvated electron, but other species grow in importance as metal concentration increases. See, for example, R. R. Dewald and J. L. Dye, J. Phys. Chem.. 68, 121 (1964). See also ref 32 and 34. (36) R. R. Dewald and J. L. Dye, J. Phys. Chem.. 68, 121 (1964). (37) S. Matalon, S . Golden, and M. Ottolenghi. J. Phys. Chem., 73, 3098 (1969).
A Comparative Study of the Enthalpy of Uonization of Polycarboxylic Acids in Aqueous Solution rescenri," F. Deiben, F. Quadrifoglio, and D. Doiar' lnsfifute of Chemistry. University of Trieste, Trieste. Italy
(Received September 78, 79721
Calorimetric data are reported on the enthalpy of dissociation of the maleic acid-ethylene copolymer, the maleic acid-propylene copolymer, and of the maleic acid-ethyl vinyl ether copolymer, together with additional data for poly(acry1ic acid), in water at 25". These data with the aid of potentiometric ones afford a rather complete thermodynamic description of the ionization behavior of the four polycarboxylic acids in dilute aqueous solution. In the case of the maleic acid copolymers our present results (from the unchargled state to half-neutralization) point out the strong influence of chain substituents on value and sigu of the enthalpy of dissociation. A simplified approach is attempted to account for the fraction of the total observed enthalpy due to the buildup of the charge density along the polyelectrolyte chains.
Introduction In previous papers from this laboratory, enthalpy of dissociation data for two polycarboxylic acids, namely poly( methacrylic acisl)2a and the maleic acid-butyl vinyl ether copolymer2b in water, have been reported. The calorimetric results >were essentially employed to derive, in conjunction with potentiometric data, a thermodynamcoil conformational transition ic picture of the glohule which the two polyacids mentioned above undergo upon increasing their degree of dissociation in dilute aqueous solution. We wish to report here a set of enthalpy of dissociation data for other polycarboxylic acids which are assumed gradually to expand and solvate upon increasing charge density along the chains and which therefore may provide an insight into the energetics of proton ionization from weak polyacids devoid of complications due to conformational transitions. The ultimate aim of our research is that of descrrbing with the aid of direct microcalorimetric measurements how free energy changes associated with the ionization of weak polyacide are built up by enthalpy and entropy con-
-
tributions, a basic type of physicochemical information which is lacking in the realm of polymer solutions. Data reported here represent to our knowledge the first attempt in this direction. Polymers considered are poly(acrylic acid), maleic acid-ethylene copolymer, maleic acid-propylene copolymer, and maleic acid-ethyl vinyl ether copolymer. The results of the microcalorimetric measurernents indicate that nature of side chains, extent of hydration, and charge density of polyions would be the main factors controlling the absolute value and sign of the enthalpy of dissociation of polycarboxylic acids. The interplay of such factors whose relative entity depends on the degree of neutralization, as typical of any property of polyelectrolytes, is difficult to grasp, however, on the basis of our limited number of data. Difficulties encountered in the (1) Chemistry Department, University of Ljubljana, Ljubljana, Yugoslavia. (2) (a) V. Crescenzi. F. Delben, and F. Quadrifoglio, J. Polym. Sci., Part A-2, 10, 357 (1972); (b) V. Crescenzi, F. Quadrifoglio. and F, Delben, paper presented at the 9th IUPAC Microsymposium on Macromolecules, Prague, Sept 1971; J . Polymer. S c i , Part C, in press. The Journal of Physical Chemistry, Vol. 77, No. 4, 1973
V.
540
type microcalorimeter. For the study of MAP, an LKB, flow-type microcalorimeter was used. The procedure followed with the batch-type calorimeter has been described elsewhere.2a With the flow-type apparatus a polyelectrolyte solution (mp = 0.200; see Figure 1) at a given initial degree of neutralization ( a l ) was allowed to flow through the apparatus at a constant flow rate and was first mixed with water (to determine the heat of dilution of the polyelectrolyte) and then with a 2.5 x 10-3 N HC1 solution, both flowing a t a rate half of that of the polyelectrolyte solution. All flow rates were controlled by weighing. The output of the calorimeter was amplified using a Keithley Model 150B microvoltmeter and recorded with a Perkin Elmer Model 165 pen recorder. Electrical calibrations were performed routinely before and after each run. Corrections were made for the heat of dilution of HCl.* The recorded heat exchange, q&$dl obtained by adding m H +moles of hydrogen ions to the solution of the partially neutralized polyelectrolyte, was in all eases corrected for the heat of dilution of the polyelectrolyte and of HC1 to calculate the heat of dissociation, qdiss
MAEVE e-
-----0.1
E 0.2
6.3
d4
0.6
0:s
0:7
0:s
OS
interpretation of the enthalpy of dissociation data are discussed. Finally, an estimate of the contribution of electrostatic interactions to the observed ionization behavior of four polyacids considered is attempted.
Experimental Section (a) Materials. Poly(acry1ic acid), PAA, was a conventional sample prepared and characterized as previously specified2a ( M , =e 3 X lo5). Maleic acid-propylene copolymer, MAP, and maleic acid-ethylene copolymer, MAE, samples were received from the Monsanto Chemical Co. (M, 105) The maleic acid-ethyl vinyl ether copolymer, MAEVE, was a high niolecular weight sample obtained from Professor IJ. P.Strauss. Aqueous solutions of the three maleic acid copolymer were prepared following essentially the procedure outlined by Bianchi, et aL3a Solutions of the sodium salts of the copolymers were dialyzed, passed through a cation-exchange column in the W f form, dialyzed again, and concentrated under reduced pressure a t ca. 40“. The titre of the polyacids stock solutions was determined by means of potentiometric titrations in ca. 0.1 M NaC1. ]In these experiments as well as in the preparation of the (salt-fret?) polyelectrolyte solutions for the calorimetric measurement B standard NaOH solutions were used. ‘The concentralion of polyelectrolyte is given as the number of moles of repeating units (or monomoles) per liter of solution, m p ,at 25”. All the copolymers used are of the 1:1 alternating type.3a,b In view of ihe free radical process of synthesis they are believed to be essentially “atactic.” ( b ) Microcaberimetric Experiments. The experiments w r e carried out at 25” using an LKB Model 10700 batchThe Journal of Physical Chemistry, Vol. 77, No. 4, 1973
qdiss
t:O
Figure 1. Dependence of the enthalpy of dissociation, AHdiss (see text), upon the degree of neutralization cy, for aqueous solutions of: 0 , poly(8cryiic acid), PAA; m p = 4.3 X lo-*; 0 , maleic acid-propylene copolymer, MAP; mp = 1.3 X lo-*; e , maleic acid-ethylene copolymer, MAE; mp = 1.7 X lo-*; @, maleic acid-ethyl vinyl ether copolymer, MAEVE: mp = 1.7 X 10-2.
-
Crescenzi, F. Delben, F. Quadrifo~lio,and D. Dolar
E
- { qobsd - qdilPo’ - gdilHCi
The change of degree of neutralization from a1 to a2 was not greater than 0.06 in each experiment. The qdiss thus obtained was recalculated per niole of hydrogen ions giving the enthalpy of dissociation as function of di
where 6 = (a1 4 a2)/2. In the range of a values between 0.1 and 1.0 the true degree of dissociation a d i s s of the polyelectrolytes considered in our study may be taken with good approximation as equal to the degree of neutralization, a , Appropriate a [€-+]/m,resulted in small corrections using oldiss shifts of both the A H d i s s and CY values which were within experimental error. (c) Potentiometric Titrations. Potentiometric titrations were performed at 25” using a Radiometer PHM4d pM meter with Radiometer “combination” electrodes, GK2301 6.
+
Results The results of the microcalorimetric measurements on aqueous solutions of PAA, MAP, MAE, and MAEVE are reported in Figure 1. In the case of the maleic acid copolymers, a = 1 is defined to correspond to half-neutralization. The data lead to the following conclusions. (1)In general, AHd,,, depends upon a. The dependence is particularly strong in the case of PAA, while only slight in the case of MAE. (2) For PAA, MAP, and MAE the difference between A H d l s s and Aff’dlss (the extrapolated AHd,8svalue for a -- 0) becomes more negative with increasing a . In analogy with the conventional treatment of the free energy of ionization of polyions, we shall designate this difference as the excess enthalpy of dissociation. E. Bianchi, A. Ciferri, R. Parodi, R . Rampane, and A. Tealdi, J. fhys. Chem., 74, 1050 (1970); (b) P. L. Dubin, and U. P. Strauss, ibid., 74, 2842 (1970). (4) D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey, and R. H. Schumm, Nat. Bur. Stand. (U. S.) Iech. Note, No. 270.3, 27 (1 968). (3) (a)
Enthalpy of Ionization of Polycarboxylic Acids
541
TABLE I: Thermodynamics of Dissociation of Polycarboxylic
Acids in Water at 25"
-AS&,('.".) 36 35 34
PAA 0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.7 0.8
0,O -0.61
- 0.96
4.40 5.10 5.46
-1.15
5.71 5.91
-1.30
- 1.29 - 1. I
6.11 6.30 6.48 6.64
0.13
3.80
0 10 0 07
4.24
- 1.25
-1.32
6.00 6.95 7.44 7.78 8.06 8.34 8.60 8.84 9.06
20.1
33.
25.4 28.2 30.0 31.3 32.4 33.3 34.0 34.4
32
5.18 5.74 5.92 6.05 6.14 6.20 6.25 6.28
17.0 19.0 19.6 20.2 20.6 20.9
4.77 5.35 5.58 5.73 5.84 5.95 6.01 6.06
16.0 18.7 20.1 21 .o 21.5 21 .% 22.0 22.0
4,773 5.577 6.136 7.082
15.8 18.4
31
30 29
A% 0.0 0.1 0.2
0.3 0.4 0.5 0.6 0.7
0.04
0 00 -0.02 -0.06 -0.09
4.34 4.44 4.50 4.55 4.58 4.61
MAEVE MAE MAP
(a)
21.2 21.4
MAP
0.0 0.1 0.2
00 - 0 22
- 0.40
0.3
-0.51
0.4 0.5
-0.56
0.6 0.7
-0.56
- 0.53
-- 0.49
3.50 3.92 4.09 4.20 4.29 4.36 4.41 4.44
0
0.2
0.4
0.6
0.8
1.a
Figure 2. The entropy of dissociation of poly(acry1ic acid), PAA, of poly(methacry1ic acid), PMA,*a and of the maleic acid copolymers (see text and Figure 1) in water at 25'.
MAEVE 0.8 0.1 0.2 0.7
0.05 0.09 0.14
0.52
3.500 4.090 4.500 5.193
20.722.0
Interpolated or extrapo ated from the curves drawn in Figure 1
-
(3) For PAA a flat minimum in the plot of ARdlSs against a occurs at around a 0.6. A very slight minimum may also be noticed in the case of MAP. (4) The absolute value and sign of A&ss (as well a$ the trend of AH^,,, with increasing a ) depend in a striking manner on the chemical structure of the polymer. (5) Among the polycarboxylic acids studied so far, only MAEVE is characterized by > 0 over the entire range of a. To make more complete the thermodynamic characterization of the dissociation behavior of the different polycarboirylic acids, we take recourse to a number of potentiometric data obtained working with the same polymer solutions used 1x1 the microcalorimetric experiments. From these data, with the aid of the potentiometric equation
-
each given a value
where KOis the limiting value of the dissociation constant of the polyelectrolyte for a 0 and AGexc is the change of the excess free energy (electrostatic, conformational, etc.) when the charge on every polyion is increased by one, one readily obtains for the total free energy of dissociation for
Combined use of the microcalorimetric and potentiometric data, which are also reported in Table I, finally yields a set of entropy of dissociation values ASdm
=
AHdiss
- AGdiss T
l _ l -
which are reported in Figure 2 (see also Table I). Data of Figure 2 clearly show that the entropy of ionization is distinctly more negative for PAA than for the maleic acid copolymers at least for a 5 1. (The data for poly(methacry1ic acid), PMA, were calculated from microcalorimetric and potentiometric results already reported in the literature.2a) This fact should be at least in part connected with a stronger water molecule inimobilization during the charging process of PAA (and oE PMA) than for the copolymers in the range of values considered so far. This hypothesis appears in agreement with the results of dilatometric experiments recently reported by Begala and Strauss5for MAE and PAA.
Discussion The interpretation of the ionization behavior of polymeric carboxylic acids in water is fraught with a number of difficulties additional to those encountered in the rela(5) A. J. Begala and U. P. Strauss,J. Phys. Chern., 76,254 (1972).
The Journal of Physical Chemistry, Val. 77, No. 4, 1973
V. Crescenzi, F. Delben, F. Quadrifogiio,and D. Dolar
542
0,
PAA
@
MAE
0 MAP 63 PMA
n
8 MAEVE
L-,
414
16
18
20
22
24
26
28
30
32
34
- A ~ , . j i (e.u.1 ~~ 36
38
40
Figure 3. Free energy-entropy of dissociation relationship for poly(carboxy1ic acids) (see Figures 1 and 2 and text) in water at 25" The data for PMA are from ref 2a.
tively simpler case of mono- and dicarboxylic acids considered so far in the literature.6,7 We refer in. particular to the fact that polyions in dilute aqueous solution are highly charged species each of which may be thought of as a local very high concentration of carboxylate residues'* The energy required for the ionization of each carboxylic group will thus depend on the number of fixed charges already present along the chain and on their relative distances. These, in turn, are a function of the stoichiometric degree of neutralization the chain-backbone flexibility and its more or less favorable interactions with water. Furthermore, the specific influence of nonionizable chain substituents on value and sign of A H d i s s may be very important, as already shown in the case of substituted dicarboxylic a.cjds7 and as also dramatically demonstrated by the difference in behavior exhibited by the maleic acid copolymers (see Figure l). Chain substituents will in fact influence the conformational distribution of polymeric electrolytes, and thus the mean distance between ionized groups, as well as their hydration, and will diversely control also the local effective dielectric constant. In other words, the observed (AHdiss - AHodiss) values may be thought as made up by different contributions arising from changes in (a) the electrostatic enthalpy, '(b) the hydration, and (c) the conformational energy of the chains and from changes in the extent of interaction of the polyions with sodium conterions, upon varying a. The associated different,ial enthalpy changes are difficult to evialuate and may be of course of different relevance passing from one polyelectrolyte to another. Pending more experimental data which might furnish all quantitative ,informat,ion necessary for an evaluation of the different enthalpic terms mentioned above (for each given polyelectrolyte), we shall confine attention on a possible estimate of the contribution of electrostatic interactions to the ionization behavior of polyelectrolytes studied in .this work. ( I ) Let us first consider that we may express the electrical free energy of polyion ionization in water by The Jountal of Physical Chemistry, VoI. 77, No. 4, 1973
where r, are the distances of the ionic charges from a carboxyl group undergoing ionization. (eo is the unit charge and D is the dielectric constant of the medium.) We have then, by straightforward manipulation of eq 2, the following expressions for the electrostatic entropy, ASel, and the electrostatic enthalpy, AH,,, respectively
(3)
If the d In Q/dT and T d In Q / d T t,erms are neglected, eq 3 and 4 reduce to the well known relationships derived by Bjerrum8 for simple polyprotic acids, which lead to a linear plot of AG,, against AS,, with a slope equal to -217°K a t 25". A plot of AGdiss against A s d i s s using our experimental data is reported in Figure 3 . It is seen that the experimental points reported for different polyacids, in steps of 0.1 a unit for each, may be fitted with reasonable approximation by a single line (with the exception of the data for MAEVE) having a slope equal to -222"K, quite close to that; predicted by Bjerrum's theory . These results would reinforce the hypothesis that the interactions involved in proton ionization for the polyacids studied by us are primarily electrostatic. This is no proof, of course, that the d In Q/d In T term is indeed negligible, the qualitative correlation depicted by the plot of Figure 3 being possibly somewhat fortituous. Calculation of absolute AHel values on the basis of eq 3 would require, besides a knowledge of the d In Q/d In T (6) J. J. Christensen, R. M. Izatt, and L. D. Hansen, J. Amsr. Chem. Soc., 89, 213 (1967). (7) J. J. Christensen, M. D. Slade, D. E. Smith, R. M. Izatt, and J. Tsang,J. Amer. Chem. Soc., 92,4164 (1970). (8) E. J. King, "Acid Base Equilibria," Macmillan, New York, N. Y . 1965,p211.
543
Enthalpy of Ionization of Polycarboxylic Acids term, which is related to the temperature coefficient of polyion dimensions, the evaluation of AG,, values. Consistent with the line of reasoning schematized in a previous paragraph for (AHdlss- AHodlss),the excess enthalpy of ionization, we assume that AG,1 represents only a portion of the total excess free energy of ionization as derivable from potentiometric (PIC, - pKo) data (see eq I), and consider it ail an entity not yet unambiguously derivable from experimental data. (2) Let us now consider the rod-like electrostatic model for the p o l y i ~ n s ,a~ model , ~ ~ which has been applied with considerable success also to the interpretation of heat of dilution of polyelectrolytes.1I The macroions are thus assimilated to rods of fixed radius a , in contact with a medium (containing the counterions) of dielectric constant D invariant with the charge density on the rods. R dilute solution of a polyelectrolyte may be formally divided into parallel cylindrical domains of radius R, each containing a macroion and its counterions. For this cylindrical cell the Poisson-Boltzmann equation has been s o l ~ e d giving ~ - ~ ~the electrostatic potential as a function of distance from the axis of the polyion, $(TI. LJsing this model, we shall have to calculate the enthalpy AH,, of tile process
in which a proton ir; removed from an already broken OH bond on a partially ionized rod-like polyion (6) and brought to a drstance R where the electrical force of the macroions vanishes. For process ( 5 ) the free energy change would be
which according to theory for rod-like macroions in water becomes
AG,,
=
RT 'in {e"[(X
- 112- ,@]/(1-@">I
(7)
where X = aeo2/DKTh = charging parameter = aXo and b is the length of the monomer unit. In eq 7 p is a constant, related to X and y by eq 9, and y is the concentration parameter
y
-. -$In
( 1 0 3 / ~ a 2 b ~-AIn )
rnp]
(8)
where N A is Avogadro's number and m p is the concentration of ,the polymer in moles of monomer units per liter.
The expression for AHel may then be derived from eq 7 according to the Gibbs-Helmholtz relationship. The final equation reads
where all symbols have their previously defined meaning and where Vis the volume of the solution. Use of eq 7 and 10 requires that we adopt appropriate values of both the charging parameter Xo and the socalled concentration parameter y (see eq 8 and 9). Calculations of AHe1 and AG,1 have been carried out for different sets of ho and y values, neglecting the derivatives with respect to temperature of the parameters a and b and taking for the terms
RT (1
-+
s-); RT---dln V d In T
the values -220.4 and 44.9 cal/mol, respectively, i,e., those for pure water a t 25" ( D = 78.54). In Figure 4 three representative AHe, against a plots, according to eq 10, are reported for two Xo values. These two values (A0 = 3.0 and 1.5) use b = 2.52 A and b = 5.0 A, which correspond to the spacing of nearest-neighbor carboxyls in PAA and next-to-nearest-neighbor carboxyls in the maleic acid copolymers if the polyions chains are represented in the all trans conformation, The associated y values were also chosen consistent with the structural parameters of the polymers and experimental concentrations (y 3 for all polymers considered assuming a common value for a equal to 3 A). Other curves calculated for higher X O values are not drawn in Figure 4 since it was found that an increase in i o beyond 3 only moderately influences the AHel values and in the same time shifts the minimum in the AH,,-a plots to lower a values. comparison with the experimental f ! d & ~ ~us. s a curves of Figure 1 shows that the trend exhibited by the data for MAP and MAE happen to fall within predictions of the approximate electrostatic theory outlined above. One could then be led to assume that the differences & ! between calculated AH,, values and experimental & values might be essentially a measure of others than coulombic interactions to the enthalpy of polyions dissociation, for each given a value. Our limited confidence in the accuracy of the electrostatic approach outlined above (as employed by us) which besides the inherent weakness of the rod-like model at low a values entails the choice of an adjustable parameter (ho) as well as a number of approximations, prevents us from tackling this more advanced stage of the problem. At this stage we can only qualitatively conclude that the behavior of PAA should be markedly influenced by a strong dependence of the hydration of the chains upon a , which would contribute an increasingly negative term to the observed enthalpy of dissociation, while for MAEVE ( AHd,,, > 0) the electrostatic interactions between fixed charges and the hydration of ionized groups would play a minor role with respect to the ion-dipole and/or dipoledipole interactions between side chain and ionizable groups in determining the AHd,,, values (for X 5 I). In conclusion, it appears that X~QI"E data should be accumulated before a less qualitative picture of the thermodynamics of dissociation of weak polyelectrolytes may be achieved. Data using other than calorimetric and po-
-
w.
d in
v
d In b
(9) T. Alfrey, P. Berg, and H. Morawetz, J. Polym. Sci., 7, 543 (1 951). (10) R. M. Fuoss, A. Kafchalsky, and S. Lifson, Proc. Nat. Acad. Sci. U. S.. 37. 579 (1951). (11) J. Skerianc, D Dolar. and D. Leskovsek, 2 Chern. 56, 207, 218 (1967); 70, 31 (1970).
The Journal of Physical Chemistry, Vol. 77, No. 4, 1973
Michael G . Marenchic and Julian M. Sturtevant
544
0. kilocal/mole)
0.1
0.2
0.3 0 . 4 0.6
0.6 0.
r
a8 0.13
u
dl
012
013
0.'4
015
tentiornetric techniques, in particular experiments from which reliable information on polyions hydration and on the temperature dependence of polyions dimensions and charge densities for different CY values might be derived, diould prove valuable in this context.
0.6
00
0:s
Oi9
ll0
Acknowledgments. This work has been carried out with financial support of the Italian Consiglio Nazionale delle Ricerche. The authors wish to express their gratitude to Professor H. Morawetz for much stimulating advice and many helpful discussions.
stigatisn of the Association of ses in Aqueous Media'
. Marenchic2 and dulian M. Sturtevant" Depdrrment of Chemistry. Yaie University, New Haven. Connecticut 06520 (Received September 25. 19721
PubiicaCion costs assisfed b y the National lnsfifutes of Health and the Nationai Science foundation
The thermodynamics of association of 6-dimethylaminopurine in aqueous media have been investigated by flow microcalorimetry. The presence of charges on the solute molecules a t high and low pH decreases the association, but the changes in enthalpy and entropy are both of sign opposite to that expected on the basis of simple electrostatic considerations. Results obtained with added organic solvents suggest contributions to the binding free energy resulting both from hydrophobic forces (W. Kauzmann, Adunn. Prolein Chern., 14, 1 (1959)) and from surface forces ( 0 . Sinanoglu and S. Abdulnur, Fed Proc., Fed. Rnier Soc Erp. Biol., 24, 5 (1965)). It is not, however, possible to give a fully satisfactory analysis of the data in terms of presently accepted views of solute-solvent interactions. Preliminary data have been obtakrred for five additional purine derivatives.
~
~ t ~ ~ ~ u ~ t i ~ ~ The associai;ion in aqueous solution of pyrimidine and purine bases. ;Ind nucleosides and nucleotides derived from them, has received much study because of the bearing of this association on the interactions between the The Journal of Phy.jical Chemistry, Voi. 77, No. 4, 7973
stacked wrimidine and Durine rings in helical nucleic acids. Current information on this association has been ~ and his have well summarized by T s ' o . Gill -
1
Y
(1) From the Ph D thesis of M G Marenchic
