potentiometric titration of polyacrylic acid

POTENTIOMETRIC TITRATION OF POLYACRYLIC ACID, POLYMETHACRYLIC ACID AND POLY-L-GLUTAMIC ACID* T. N. NEKRASOVA, YE. V. ANUFRIYEVA, A. 1V[. Y E L ' Y A S H E V I C H a n d 0 . B. PTITSYI~ Institute for High Molecular Compounds, U.S.S.R Academy of Sciences (Received 23 J u l y 1964)

POTENTIOMETRIC t i t r a t i o n is a sensitive m e t h o d of i n v e s t i g a t i n g t h e s t r u c t u r e of p o l y e l e c t r o l y t c s . D e s p i t e t h e f a c t t h a t t h e course of t h e t i t r a t i o n curves is d e t e r m i n e d b o t h b y t h e m u t u a l positioning of t h e charge g r o u p s on t h e p o l y m e r chain, a n d also b y t h e ionic e n v i r o n m e n t , a n d also t h a t t h e i n t e r p r e t a t i o n o f t h e t i t r a t i o n curves m a y n o t a l w a y s b e carried o u t simply, t h e general course o f t h e curves m a k e s it vossible t o d r a w certain conclusions a b o u t t h e s t r u c t u r e of t h e m a c r o m o l e c u l e s . I n t h e p r e s e n t work, a c o m p a r a t i v e i n v e s t i g a t i o n of a n u m b e r of p o l y - a c i d s has b e e n carried o u t b y t h e m e t h o d of p o t e n t i o m e t r i c t i t r a t i o n a t v a r i o u s ionic s t r e n g t h s ; t h e poly-acids were: p o l y a c r y l i c (PAX), p o l y m e t h a c r y l i c (PMAA) a n d p o l y - L - g l u t a m i c (PGA). T h e molecules of P A X a n d P M A A , despite t h e i r similar in chemical s t r u c t u r e , differ m a r k e d l y in a n u m b e r of p h y s i c a l p r o p e r t i e s (see, for e x a m p l e , [1-4]), w h i c h t h e a u t h o r s explain b y t h e presence of i n t r a m o l e c u l a r h y d r o g e n b o n d s in P M A ~ a n d t h e i r a b s e n c e in P A X . P G A r e p r e s e n t s a t y p i c a l s y n t h e t i c p o l y p e p t i d e , w h i c h h a s a helical configuration in t h e w e a k l y ionized condition. EXPERIMENTAL MATERIALS AND METHOD

The samples of PAA and PMAA that were investigated, were obtained by photopolymerization of the distilled monomer with a radical initiatbr. PAA was separated into five fractions by the method of fractional precipitation from a 4% solution in methanol. Ethyl acetate was used as the precipitant. The first and fifth fractions were investiga,ted; these had mean molecular weights M w of 1.3 x 10e and 4.0 x 10s respectively, determined from the intrinsic viscosity of PAA solutions in dioxane [5]. PMAA was separated into 10 fractions by the same method, by means of the addition of a mixture of ethyl acetate and acetic acid (9 : 1 by volume) to a 3% solution of PMAA in methanol. The first and tenth fractions with .M w of l-0x 10e and 1.2 × 104 respectively, as determined from the intrinsic viscosity of PMAA solutions in 0.002 M HC1 [6], were investigated. The sample of PGA (in the form of its sodium salt) was kindly presented to us by P. Dory. Titration was carried out using a multiscale millivoltmeter EM-60 and a glass electrode. The electrode had been calibrated by buffer solutions with pH of 4.01, 7.00, and 9-18. The determination of pH was carried out with an accuracy of 0.03. The concentration of the poly-acid was usually 0.005 mole of the monomer unit per litre. Titration was carried out * Vysokomol. soyed. 7: No. 5, 913-921, 1965. 1008

Potentiometric titration of polyacrylic acid

1009

with 0.05 :~ NaOH (10 ml of solution were used. in one experiment, and therefore the volume change during titration may be neglected). The ionic strength was varied from 0-01 to 2 mole/1, by adding l~aC1; the contribution of the polymer's own counter-ions to the overall ionic strength was very small, and we did not take it into account. All the measurements were carried out at room temperature (approximately 20°C). With the aim of investigating the effect of ionic strength on the ionization constants, titration of aqueous salt solutions of the following dibasic acids was carried out: succinic, glutaric and adipic acids, at acid concentrations of 0.0025 molc/l. The ionization constants were calculated by the method suggested in reference [7]. RESULTS AND DISCUSSION

W i t h t h e a i m of investigating the influence of the p o l y e l e c t r o l y t e c o n c e n t r a t i o n on t h e t i t r a t i o n curves for PA_k a n d PMA&, t h e t i t r a t i o n of P_A_k was carried o u t a t c o n c e n t r a t i o n s c f r o m 0.1 t o 0.0025 mole of t h e m o n o m e r u n i t per litre, a n d t h e t i t r a t i o n of P M A A f r o m c = 0 . 0 2 5 t o 0.0025 mole of t h e m o n o m e r u n i t per litre. W i t h i n the c o n c e n t r a t i o n interval i n v e s t i g a t e d a t an ionic s t r e n g t h of 0.1, t h e t i t r a t i o n curves coincided. I n t h e literature, t h e r e h a v e b e e n d a t a (see, for example, [8]) on t h e independence of the t i t r a t i o n curves of t h e molecular weight of t h e samples. T h e investigation carried o u t b y us confirmed this conclusion for a wider r a n g e of molecular weights, s t a r t i n g f r o m M w - 104. T h e t i t r a t i o n curves for t h e e x t r e m e fractions of P2~_& a n d PM_A_&are s h o w n in Fig. 1. As m a y be seen f r o m t h e Figure, a change in molecular weight b y t w o orders in neither case leads t o a n y m a r k e d change in t h e course of t h e curves.

p /( (ct)

5"5 pM

07

7"0

0"2

8.0 0

d'O

0'5 !

&5 J'O 5.0 ~'0 3"0

l

Y" J

FIG. 1

I

ct

/'0

4"5

j

I

0

0"5

cc

/'0

Fro. 2

FIG. 1. Titration curves for PMAA fractions with _Mw of a) 4.0 × 104; and b) 1.3 × 106; and for PAA with _Mw of c) 1.2 × 10', and d) 1.0 × l0 s. F I 6 . 2 . Dependence of pK(~)=pK0~-ApK for PAA on ~ at various ionic strengths/l.

1010

T. N. NEKRASOVAet a/.

The titration curves for PAA, PMAA and PGA are shown in Figs. 2, 3 and 4 respectively in coordinates pK(~)--pH--log[a/(1--~)] and a, where ~ is the degree of ionization.* The selection of these coordinates arose from the fact that the titration of poly-acids is described by the equation [9]

pH ~-pK 0-Flogl-~a-F ApK(a),

(1)

where p K o is the negative logarithm of the dissociation constant (at the given ionic strength) of the ionized group, isolated from its neighbouring charged groups, and ApK(a) is a term which arises because of the interaction of the charged groups of the chain and is equal to (0.434[kT)OF/Ov,where a$']0v is the change in free energy of the macromolecule for one more charge on it at the given (v----an, where n is the degree of polymerization). The data shown in Figs. 2, 3 and 4 are in good agreement with the data of other authors [8, 10-12]. Titration curvesof l~olyacrylivacid. As may be seen from Fig. 2, the titration curves for PAA at all ionic strengths/~ have a similar characteristic form: a sloping part for pK(a) at small degrees of ionization, and then (for a>0.3) a linear increase in pK(~). At the present time there are two groups of theories about

$'0 ~

y -o.0/ 0"02

~

~.o

0

.

pxt#) 8.o

j

p = o.oi

.x,5-x--X-~ --~

I

/ ~--

/'0

X

/

/ ~ o.ls

5 "0

Z.o

x~..x.,,.x/X,,.x.~..,x'"

5"0 f

0

0"5 FT~. 3

ot 1"0

0

0.5

a

/.0

Fr6. 4

FI6. 3. Dependence of p K ( ~ ) = p K o + ~ p K for PMAA on ~ at various ionic strengths/~. FIG. 4. Dependence of pK(~)~pK0~-zipK for P G A on ~ at various ionic strengths/~. * F o r ~>0.1, the degree of ionization coincides with the degree of neutralization, determined from the amount of alkali added.


1011

the potentiometric titration of polyelectrolytes. According to the first of these, (see, for example, [13-15]) ApK(a) at large ionic strengths is connected with the interaction of neighbouring discrete charges and depends on the conformations of short portions of the macromolecule. These theories predict an S-shaped character for the dependence of pK(a) with symmetrical sloping parts at large and small a. The other group of theories [16, 17] connects ApK(a) with the change in free energy upon the formation and reorganization of an ionic "coat" made up of the counter-ions connected by the charged macromolecule; in these theories, the discrete position of the charges is not taken into account, and the macromolecule is considered as a uniform charged cylinder, so that ApK(a) depends on the charge density and on the thickness of the cylinder. According to these theories, pK(a) depends almost linearly on a if small a and/~ are not very small. At small a, the ionic "coat" is not formed, and the theories mentioned are known to be inapplicable, l~either group of theories takes into account reactions with remote charged groups on the chain; this is completely essential, since the free energy of the macromolecule may be presented in the form [18]:

F=Fo+nfnear'-t"~/~fremote

(2)

where F 0 is the free energy of the chain made up of non-interacting units; fnear and /remo~ are quantities determined by the interaction of near and remote (reckoned along the chain) monomer units. In so far as fnear and fremo~ are quantities of the same order, at n>> 1, the term ~/n×frerao~ may be neglected; this is confirmed by the fact, noted above, that the titration curves for P A ~ and PM_A2k are independent of molecular weight. The general course of the titration curves for PAA do not follow the S-shaped course predicted by the first group of theories, and are in better agreement with the theories of the second group. Also a sloping portion is observed at small a in agreement with the predictions of the first theories. Such a course is entirely natural for the curves, since at small a when the ionic "coat" has not yet been formed the principal role must be played by the interaction of neighbouring discrete charges, but at large a this interaction is masked by the stronger effects connected with the cooperative formation of the ionic "coat". The comparative role of the interactions between neighbouring discrete charges is increased with a reduction in the distance between them and with an increase in the ionic strength, and therefore the titration curves for polyvinylamide, in which the distance between neighbouring ionized groups is less than in P_A_A, are described by the first group of theories for all a (that is, they have an S-shaped character) [10], and the steepness of the initial portion of the titration curves for PA_A_falls with an increases in ionic strength (see Fig. 2). The dependence of pK(a) on the logarithm of the sodium ion activity (aNa+) is shown in Fig. 5. W e see that for a~0.3, ApK is linearly dependent on log aNa+ which is in agreement with the predictions of the second group of theorists [19]. According to the theory of Kotin and ~agasawa [16], the fraction

1012

T.N. Nv,K~AS0VA eta/.

of counter-ions which are kept in the "coat", does not depend on/~ and is determined by the formula 7----1-- const/a. If the interaction of the charged groups depends only on the total number of counter-ions in the "coat", then the entire dependence of the free energy F of the chain on/~ reduces to the dependence of the free energy of mixing of the counter-ions, coming from the "coat", with low molecular weight ions of the solvent, that is, F = E ' - - n k T a 7 In aNa+,

(3)

where aNa+ is the sodium ion activity, ~ o m which A p K = ApK'--log aNa+ ,

(4)

that is, the slope of the dependence of A p K on --log a~+ ought to be equal to unity (F' and ApK' do not depend on a~a+). As may be seen from Fig. 5, this slope in fact falls from 0.95 at a=0.9 to 0.6 at a=0.3. This means that for values of a, not very close to unity, the interaction of the charged groups in the PA_& chain depends not only on the total number of counter-ions in the "coat" but also on their distribution within the limits of the "coat". From Fig. 2, it may also be seen that the ionic strength influences not only ApK, but also pK0=lim pK(~). This effect is not unexpected, since a similar dependence was observed by us (see Table 1) for dibasic acids also. From the pK (oO pK(o~)

PgA

G4

6O o

58 ,,,p 3

eO' 5"0

57

4"g

40

I

0"2

D8 l'O -10~ ~ NnCI

Fza. 5

.,

1.4

o

i

D5

o~ lO

FIG; 6

FIG. 5. Dependence of pK(~)~pK0+LipK.for P A A on log al~a+ at various ~. Values of a: •--0.3; 2--0.4; 3--0.5; 4--0.6; 5--0.7; 6--0-8; 7--0.9. Fie. 6. Comparison of the curves for pK(~) for PAA, PMAA and PGA at ~ = 0 . 0 1 ; 0.1; 1.0.


1013

Table it m a y be seen t h a t the ionic strength influences not only pK~--pK1, which is analogous to ztpK for poly-acids in this case, b u t also pK1, which is analogous to p K 0. TABLE 1. VALUESOF pK 1, pK,, pK=pK,--pK~ FOR DXBAS~CACIDS Acid Sueciuic H00C

-- C H , -- C H i - C 0 0 H

Glutarie H00C -- CH s -- CH s- CH~ --C00H Adipic H00C--CH --CHa--C00H

I-CH,-CH

Solvent

pK1

pK,

PKI--PK1

Wat~l 1.0 Ware1

4-22 4-00 3.85 4.39

5-67 5.30 5.03 5.50

1.45 1.30 1.18 1.11

0.2~ 1-0 Watt1

4.10 4.07 4.43

4.99 4.81 5-42

0.89 0.74 0.99

0.2 M 1-0 M

4.22 4.05

5.05 4.80

0.83 0.75

0.2M

ApK

i

I n this way, t h e course of the titration curves for PAA are well explained b y theoretical ideas relating to polyelectrolytes with flexible molecules, not having a secondary structure. This agrees with other known properties of PAA (see, for example, [2, 3]). I t follows that one m a y emphasize that its is impossible to obtain reliable information about the details of conformational chain structure from titration curves of flexible structureless polyelectrolytes, of which P A A is one. Titration curves of ~olymethacrylic and poly-L-glutamic acids. As m a y b e seen from Fig. 3 and 5, the titration curves for PMAA and PGA are fairly similar, and differ substantially from the titration curves for PAA. The majority of the curve is typified b y a sharp rise at small a, then b y a clearly defined plateau, and finally b y an approximately linear increase in pK(a), similar to that observed for PAA. The presence of the initial rise (in a number of cases, extremely sharp) means that for small a, PMAA and P G A exist in conformations in which each already ionized group makes it difficult to ionize even comparatively remote groups. With an increase in a in a narrow interval of pH, a reorganization of the structure takes place which eliminates these difficulties, and the polyelectrolyte begins to behave as on ordinary linear charged macromolecule. A more detailed comparison of the curves indicates that the similarity between the titration curves for PMA/k and PGA increases with an increase in ionic strength: at large ionic strengths, the titration curves for P M A ~ have a plateau exactly the same as the plateau in the case of PGA, which is connected with the helix-coil transition upon ionization of the macromolecnle [11, 12]. At small ionic strengths, the plateau on the curves for PMAA is reduced and the general course of the curves approximates to the course of PAA curves.

1014

T. N . NEXRAS0VA e~ aI.

This is very clearly seen in Fig. 6, where, for comparison, the titration curves for PAA, PMAA and PGA are shown at three ionic strengths (the ordinate values have been displaced in order t h a t the portions of the curves at large should coincide, when all three polyelectrolytes have evidently lost a n y secondary structure). Methods of treating the titration curves of polyelectrolytes which undergo a conformational transition (I--II), have been put forward b y Zimm and Rice [20] and b y Nagasawa and Holtzer [12]. The method of Zimm and Rice is based on equation (1), according to which the complete change in free energy upon ionization of the macromolecule (calculated for 1 mole of the monomer unit) is equal to: 1

0

(area A B C D E A in Fig. 7). This change in free energy is made up of the true energy of ionization of the chain and of the change in free energy resulting from the change in the conformation of the chain during process of ionization. I f the change in the conformation of the chain takes place over a narrow interval of pH, then these two terms m a y be graphicaily separated b y the method of extrapolating to = = 0 the part of the titration curve obtained at large =, t h a t is, above t h e region of the conformational transition. The area under this extrapolated curve (the area A C D E A in l~ig. 7) is equal to the free energy of ionization of a hypothetical chain having the conformation of the strongly ionized real chain for all =. The difference between the areas mentioned (the area A B C A in Fig. 7)

D 5"5

pH 6.0 -

/

prim "

1 ~ /

/

"'/-'~'~/"

/~"//'2 • B/~///

5:0

4"0 / / / / A

4",~

E ~5 FIe. 7

1"o

3"0 0

I 0.25

I 05

I 075 oc

FIG. 8

FIe. 7. Dependence of pH-dog [=/(1--=)] on ~ for macromolecules which undergo a cooperative conformational transition (solid curve), and the dependence, extrapolated from large (portion CD) (broken curve). Ordinate axis: pH--log [~/(l--a)]. FIe. 8. Titration curve for macromolecules which undergo a cooperative conformational transition (solid curve), and the same relationships extrapolated from small ~ (portion AB) (broken curve 1) and from large = (portion CD) (broken curve 2).


1015

is equal to the change in free energy during the conformational transition in the unionized chain: 1

1

o

o 1

= 2.3RT f (p'lq--p]~,,)d~z

(6)

o

The method of Nagasawa and Holtzer [12] starts from the obvious equation, according to which the change in free energy during conformational trau.ition in the ionized chain is equal to: pH

pH

ztF=zIFo"}- f ~ (/IF) a d (p~)=/IFo--2'3RT f J~(d(pH), pH,

(7)

PHa

where L I ~ = ~ I ~ 2 is the difference between the degrees of ionization of the two conformations at the given pH, and pH o is the value of pH, for which zf~=0 (it corresponds to very small degrees of ionization). By making use of the approximate expression for the fraction of monomer units which undergo the cooperative transition I - - I I [15]

e-ndFIRT v= 1 +e "~F/~2'

(8)

(n is the number of monomer units, undergoing the transition as a unit), we obtain: pH

Z

(9)

PH,

Consequently, from the linear dependence of~ zi~d (pH) on log[8/(1--8)], it is pHo

possible to determlue the change in free energy during the eonformational transition in the unionized chain AFo (calculated for one mole of monomer units) and the cooperation parameter for the transition, ~. The quantity 8 (pH) may be determlued either from independent data (for example, in the case of PGA, from the dispersion of optical activity), or indirectly from the titration curves if it is considered that ~-----~,(1--~)+~28 from which: O--

(10)

(formula (9) is strictly valid for transitions which take place by an "all or nothing" principle, but, as a good approximation, it is true for all cooperative transitions pH

with n>> 1 [15]). The integral ~ zf~d(pH) is equal to the area between the curves PHo

1016

T. l~. NEKRASOVA st al.

pH(~l), pH(~) and the straight line p H = c o n s t in Fig. 8. If we integrate up zo p H m corresponding to ~=½, that is, ztF-----0, then pHm

ZJFo:2.3RT f A~d(pH)

(11)

(the area A B' C' A in Fig. 8). The determination of AFo from formulae (6) and (11) is theoretically equivalent, the method of Zimm and Rice being in practice more convenient, but the method of l~agasawa and Holtzer makes it possible to determine one other parameter, ~ (formula (9)). An additional difficulty of this method is necessary to extrapolate not only the curve pH(a2), but also the curve pH(al). However, it follows from the formulae (6) and (11) that the areas A B C and A B' C' in Fig. 8 are equal to each other. Therefore the equality of the areas B B' E' and E' C C' may serve as a criterion of the correctness of the extrapolation. TABLE 2. VALUES OF zIF e FOR P M A A AND P G A Material

Ionic strength,

ziF0, calories/mole from (9)

P3AAA P!~ PGA PGA

0.1 1.0 0.1 1-0

220 180 200 100

from(ll) 250 190 210 90

We have analysed of the titration curves for PMAA and PGA at ionic strengths of 0.1 and 1.0/~ by both methods. The values of ztFe obtained from formulae (9) and (11), are shown in Table 2. The values obtained by the two methods practically coincide. Our data for PGA agree with the dependence of zlFe on ionic strength established in reference [12]. The values of n, determined from formula (9) are very sensitive to the method of extrapolation of curves I and 2 in Fig. 8. However, the quantities obtained (of the order of 30 both for PGA and for PMA have reasonable values (for poly-~-benzylglutamate n ~ 7 0 [21]). SUMMARY

The preseflt work has shown that the potentiometric titration curves for PAA, differ substantially from those for PMAA and PGA. The titration curves for PAA are typical of flexible structureless polyelectrolytes, and the titration curves for PMAA and PGA are typical of maeromoleeules which undergo a conformational transition when the degree of neutralization is altered. T h e nature of this transition in PGA is well known: it is the "helix-coil" transition, which is accompanied by a change in a number of other physical properties of the PGA molecule, whereby the stability of PGA helices is conditioned, not only by the hydrogen bonds between peptide groups of the main chain, but also by hydrogen bonds between uncharged side COOH groups [22].

Pot~ntiometric titration of polyacryllc acid

1017

In PMAA unionized or weakly ionized conditions there evidently also exist a considerable number of hydrogen or other intramolecular bonds between uncharged groups [1,2-4, 23-25]. Rupture of these bonds during ionization should naturally be reflected in the pK(a) curves. The large initial slope of the pK(a) curves for PMAA (see Fig. 3) may be explained from this point of view by restrictions on the ionization of carboxyl groups because of the presence of intramolecular bonds. The narrowness of the p H interval over which rupture of the intramolecular bonds takes place, ought doubtless not to be caused by the impossibility of the rupture of one bond without rupture of neighbouring bonds (as is the case in PGA). It is possible that in PMAA the intramolecular bonds are ruptured one after the other, but that the change in the free energy of the chain upon rupture of each bond depends sharply on pH. Such behaviour may take place, if the inframolecular bonds lead to the formation of rings in the chain [23], wherel~y carboxyl groups entering into the ring are positioned close to one another: this makes their ionization difficult, and rupture of each bond is accompanied by ionization of all the groups in the ring, which also explains the marked dependence of the free energy of rupture on pH. A calculation carried out by us indicated that this model correctly describes both the general course of the pK(~) curves, and also their dependence on ionic strength (if it is presumed that low molecular weight ions do not penetrate into rings). The supposition that intramolecular (hydrogen) bonds lead to the formation of secondary ring structures in molecules of unionized PMAA was originated in detail in work by Tsvetkov, Lyubina and Bolevskii [1] on the basis of viscometric and dynamo-optical measurements. Starting from values of the microform effect, these authors assessed the average number of monomer units making up a ring as equal to 30, which is in good agreement with our assessment of the average number of monomer units taking part in the transition. The authors wish to express their thanks to V. Ya. Bogomol'nyi and S. Y. Lyubina for the samples of PAA and PMAA made available. CONCLUSIONS

(1) A comparative investigation of the potentiometric titration curves for polyacrilic (PAA), polymethacrylic (PMAA), polyglutamic (PGA) acids has been made in aqueous solutions at various ionic strengths. (2) On the basis of the shape of the titration curves, the conclusion is drawn that PAIl_ molecules have no secondary structure, and that both PMAA and PGA molecules have such a structure in the unionized condition, and lose this structure in the process of ionization. (3) The hypothesis is put forward that the elements in the secondary structure of PMAA molecules are rings in the chain; this is in agreement with the results obtained by other methods. Tran~lat~ by G. MODI~

1018

V.A. RADTSI6and P. Yu. BUTYAGIN

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ELECTRON SPIN RESONANCE SPECTRA OF FREE RADICALS IN THE DECOMPOSITION PRODUCTS OF SOLID HETEROCHAIN POLYMERS CONTAINING OXYGEN* V. A. RADTSIG a n d P . Y U . BUTYAGIN Institute for Chemical Physics, U.S.S.R. Academy of Sciences

(Received 23 J~dy 1964) T H E results o f a n i n v e s t i g a t i o n o f the free radicals c r e a t e d u n d e r m e c h a n i c a l a c t i o n in s y n t h e t i c organic p o l y m e r s c o n t a i n i n g o x y g e n a t o m s in t h e principal c h a i n are p r e s e n t e d in t h e p r e s e n t article. T h e p o l y m e r s s t u d i e d were p o l y f o r * Vysokomol. soyed. 7: No. 5, 922-927, 1965.