Potentiometric titration of poly(α-D)galacturonic acid

J. Visserand A.G.J. Voragen(Editors), Pectins and Pectinases 9 1996Elsevier Science B.V.All fights reserved.

609

P o t e n t i o m e t r i c t i t r a t i o n of p o l y ( a - D ) g a l a c t u r o n i c acid D.Rudan-Tasi5 and C. Klofutar

Department of Food Science and Technology, Biotechnical Faculty, University of Ljubljana, Jamnikarjeva 101, SI-61000 Ljubljana, SLOVENIA

Abstract A commercially available sample of poly(a-D)galacturonic acid, i.e. pectic acid, was characterized according to the size and shape of its molecule through the volumetric and transport properties of its aqueous solutions. Thus, the average molecular weight of polygalacturonic acid and its average degree of polymerization were estimated on the basis of viscosity measurements. The length-to-diameter ratio, calculated by means of S i m h a ' s equation, strengthened the assumption that pectic acid is a fairly rigid, rod-like molecule. By potentiometric titration of aqueous solutions of poly(a-D)galacturonic acid with several alkaline and tetraalkylammonium hydroxides, the effects of the size and nature of the counterion on the degree and extent of dissociation of the polymeric acid were estimated. In evaluation of the potentiometric curves the treatment proposed by M a n d e l for weak polyacids not exhibiting a conformational transition during titration was used. In addition, the nonelectrostatic character of polyion-counterion interactions was confirmed by the application of the cell m o d e l to the polyelectrolytic solute investigated.

1. INTRODUCTION

In the course of studies on the physicochemical properties of natural polymers in aqueous solution, attention has been drawn to pectic acid, i.e. poly (a-D)galacturonic acid as a potential model of a rigid polysaccharide. Extensive data are given in the literature for the potentiometric titration of polymer acids which may be used to study the behaviour of polyelectrolyte systems under different conditions. For poly(a-D) galacturonic acid there are few data of this kind, especially in connection with the occurrence of a conformational transition induced by pH variations, or with the effect brought about by the addition or the exchange of counterions. Since for a polyacid not exhibiting a conformational transition in the course of titration, p K a ( K a denoting the apparent dissociation constant) increases monotonously with degree

610 of dissociation,a, it is possible to represent this functional dependance by a converging series expansion of pK a in a [1]. The purpose of this study is to consider in more detail the influence of the size and n a t u r e of the counterion on the degree and extent of dissociation of poly(a-D)galacturonic acid already discussed in a previous paper [2], particularly to check the effect of screening the charges on the polyacid in the presence of different counterions.

2. E X P E R I M E N T A L

Solution preparation Commercially available poly(cz-D)galacturonic acid (PGA) was purchased from F l u k a Chemie. To obtain an aqueous solution of the polyacid, insoluble PGA was converted to its soluble sodium salt and then percolated through a cationexchange resin in the H-form [3].

Density measurements Density m e a s u r e m e n t s were carried out using an A. Paar digital densimeter (model DMA 100) at a temperature of 298 K over the mass concentration range 0.75- 6.00kgm-3 -The densimeter was calibrated with water [4] and dry air [5].

Viscosity measurements The viscosities of aqueous solutions of PGA were determined with an Ubbelhode capillary viscometer at 298 K in the same concentration range as the density measurements. The temperature of the water bath was maintained to + 0.05K.

Degree of esterification The degree of esteritication of the methyl ester of PGA was determined acidimetrically after hydrolysing the ester with sodium hydroxide [6].

Potentiometric titration Potentiometric titrations of aqueous solutions of PGd with some alkali hydroxides (LiOH, NaOH, KOH)and tetra-n-alkylammonium hydroxides, e.g.

(CH3)4NOH and (C4H9)4NOH,

were performed in three parallel determinations

in a titration vessel at 298 K using a Radiometer pH meter (type pH M4d) and a combined glass electrode (type GK 2501 C) [2] . The pH meter was standardized with six s t a n d a r d buffers (pH range 3 -10). The end point in the potentiometric titrations was determined using Gran's procedure [7].

611 3. R E S U L T S A N D D I S C U S S I O N

3.1.Transport

properties

of poly(~-D)galacturonic

acid

The mole fraction of polygalacturonate d e t e r m i n e d on the basis of potentiometric h y d r o g e n ion titrations was found to be 0.85. The degree of esterification of the m e t h y l ester of PGA was d e t e r m i n e d to be 5.34 per cent. The density of the investigated solutions is given by d - do - ac~ + bc~

where a a n d fl are empirical constants characteristic of the solute a n d the t e m p e r a t u r e , d e t e r m i n e d by the m e t h o d of least squares on the basis of the d a t a in Table 1. Their values a m o u n t to a = 0.427 andfl = -4.490. The e x p e r i m e n t a l viscosity data were analysed according to the relation 2

3

17-- 17o -- a l c 2 h - a 2 c 2 d - a 3 c 2

where ~ is the absolute viscosity of the solution ( k g m -1 s'l), 1]0 is the absolute viscosity of the solvent a n d a l , a 2 a n d a 3 are empirical coefficients ; their calculated values a m o u n t t o a I - 9.588x10 -5 , a 2 - -3.649x10 -6 and, a 3 - 6.929x10 -7 . The intrinsic viscosity was calculated as

[17] - a___~,= O.10769m3kg -1 r/o The viscosity average molecular weight of PGA was d e t e r m i n e d using the M a r k - H o w n i k - S a k u r a d e equation with the necessary constants from ref. [8] --b

[1"/]- a M v -

4.368xl

0- 7 ~1

Mv

8737

a n d was found to be M v - 30115. Thus, the average degree of polymerization was calculated to be 146. The a p p a r e n t specific volume was d e t e r m i n e d from the density m e a s u r e m e n t s via the relation [9]

1E

qgv = ~o 1

c2

1

where do is the density of the solvent a n d c2 is the m a s s concentration of the

612 solute (gcm 3) and the value of ~Ov*-0.574cm3g-1 was calculated at very low reference concentration, c2 = 3.75x10-4 gcm -3 For comparison, the value of the partial specific volume at infinite dilution for D-galacturonic acid is @o _ 0.554cm 3g-1. The viscosity increment was determined as v - B / v ~ - 172.7 ( ~ 2.5 for spheres) where B is the viscosity coefficient characteristic of a given solue-solvent --o

pair, and amounts to (9.91 + 0.24)x10 -zm3kg -~ for PGA in aqueous solution, v2 is the partial specific volume of the macromolecular component equal to (p: at v a n i s h i n g c2 . The length-to-diameter for P G A was then estimated via S i m h a ' s relation for elongated ellipsoids [ 10] and its value amounts to (a / b) = 49.6.

Table 1 Densities and viscosities (experimental and calculated) of aqueous solutions of P G A at 298 K in the concentration range studied.

C2 / kgm -3

d / kgdm -3

17xl 03 / kgm-ls -1

~L~l~xl 03 / kgm -~s -~

0.75

0.997390

0.9581 __+ 0.0012

0.9581

1.50

0.997700

1.0266 __+ 0.0012

1.0269

3.00

0.998287

1.1657 __+0.0014

1.1646

3.84

0.998629

1.2420 __+0.0015

1.2434

4.80

0.999020

1.3409 __+0.0014

1.3402

6.00

0.999462

1.4835 __+0.0017

1.4836

3.2. P o t e n t i o m e t r i c titration of poly(a-D)galacturonic acid

The degree of dissociation, a, was calculated from the electroneutrality condition

a

= Cp

613 where [BOH 1 is the number of moles of base added per dm a of solution, [H+]and

[OH-] are the molarities of free hydrogen and hydroxyl ions and c; is the concentration of polyacid in monomol dm 3. The apparent dissociation constant of the polyacid, pK a , was calculated by the relation

pica

- pH

+

log (1- a) a

3.2.1. For the systems investigated, the increase of pKawith expressed by a second degree polynomial according to Mandel [1]

pKa = pK ~ + qbla + r where pK~ and r and r

a

could be

2

~ - l i m p K a ) ~ ~ is the intrinsic dissociation constant of the polyacid are the regression coefficients. As an example the dependence of

the apparent dissociation constant pK a for the system PGA +(Call 9)4 NOH at 298 K is given. For an interpretation of the physical meaning of the regression coefficients, the Marcus titration equation for polyelectrolytes was combined with the Poisson-Boltzmann equation for the electrostatic mean potential, determining all charge interactions in a dilute polyelectrolyte solution. In this way it was found thatr depends on the distribution of macromolecular groups in V8 (the total electrically neutral sub-volume assigned to each polymeric ion) for the uncharged polyelectrolyte, and on the mean conformation of the uncharged macromolecule. The coefficients r are mainly determined by the expansion of the dimensions of the polyion in the course of the titration. The data in Table 2 show that 9 the values of pK: decrease with increasing size of the alkali counterion, which may be explained by the formation of contact ion-pairs between counterions and charged carboxylate groups on the chain. The extent of ionpairing depends primarly on the ionic potential, ~o, defined as ( ~ "--

charge ionic radius(A)

9 the positive and almost equal values of coefficients C1 for the investigated systems, C1 =1-616-+0.099, are related to the mean distribution of macromolecular groups for the uncharged polyelectrolyte, i.e. PGA, which is the same irrespective of the nature and size of the counterion. 9 the coefficients r are negative and decrease with increasing size of the alkali counterions, while in the case of tetraalkylammonium ions the sign of the coefficient changes from-0.151 for (CH3)4NOH to + 0.211 for(C4Hg)4NOg.

614 Table 2 Coefficients a n d s t a n d a r d deviation,s, of the l e a s t - s q u a r e s s e c o n d - d e g r e e p o l y n o m i a l r e p r e s e n t i n g t h e t i t r a t i o n curve of PGA with different s t r o n g b a s e s at 298 K.

Base

pK ~

r

r

s

LiOH

3.419 _+ 0.019

1.537 + 0.080

- 0.431 + 0.071

0.019

NaOH

3.413_+ 0.024

1.471_+ 0.099

- 0.439 + 0.091

0.018

KOH

3.327 + 0.034

1.776_+ 0.140

- 0.665 + 0.128

0.024

(CH3) 4 NOH

3.477 _+0.018

1.502 _+0.073

- 0.151 _+0.066

0.013

(C4Hg)4NOH

3.341+0.019

1.792 + 0.086

+ 0.211_+ 0.084

0.017

I

!

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

5:000

4.500

4.000

3.500

f

I

0.200

0.400 0.600 OK)O Of,

Fig. 1. C h a n g e of t h e a p p a r e n t dissociation c o n s t a n t with a for t h e s y s t e m PGA + (C4H9)4 NOH at 298 K. The curve w a s c a l c u l a t e d from t h e model given by Mendel.

615 3.2.2. The a p p a r e n t dissociation constant p K a is strongly dependent on the electrical potential on the surface of the macroion, v(a)according to the well known equation [ 11] p K a - p K ~ + ApK

where A p K - O . 4 3 4 s v ( a ) / k T . Following the cell model for rod-like ionized polyelectrolyte molecules, a generalized form of the equation which gives ApK in a polyelectrolyte solution of any composition may be written [ 12]

EvJna2h)]

ApK - log (qgpamm+ m~)

+log

1)22J} 2A

where v is the n u m b e r of charges t h a t the polyion carries, h is the effective total length of each molecular cylinder, a is the radius of the rod-like polyion stretched along the axis of a cylindrical cell with radius R, ~op is the osmotic coefficient of the salt-free polyelectrolyte solution, m,, the concentration (monomol cm ~) , m8 the n u m b e r of moles of added salt per cm 3 and 2 is a dimensionless p a r a m e t e r proportional to the n u m b e r of charges per unit length of the macromolecule 2

;~ .

VoC . .

aoc'

2

(h - Zb)

.

DhkT

DjbkT

if every jth monomer carries an ionizable group ( v - a Z / j ) , Z is the degree of polymerization, b the length of the monomeric unit, e the ionic charge, D the dielectric constant, and k T the B o l t z m a n n term. p is an integration constant [ 13] dependent on a and R. Relation 1-fl 2

D

1 + p coth(fly) connects fl with a and y w h e r e yis the concentration parameter, defined as 7 - In --R _ _1In _ _ 1 0 0 0 a

2

rla2bNA

1 In c 2

where c is the monomolar concentration (monomol dm 3) and NA the A v o g a d r o number. For the dimensional p a r a m e t e r s of PGA the values a = 7A and b = 4. 35A" from ref. [14] were used. The relation between 7" and concentration was expressed analytically in the form - 10g c - 0.8687" - 0.394

616 For a univalent counterion the charge density parameter A was found to be ~ = 1 . 5 5 1 a where a value of j = 1.06 was employed because of the degree of esterification of the methyl ester o f P G A ( 5.34 per cent). A comparison of calculated and experimental values of ( p K a - p K ~ at different degrees of dissociation is shown in Fig. 2. For p K ~ the values from Table 2 were used.

2.000

I

I

I

I 0

1.500

cL 1.000

0.500

-

o~176176

0.200 0.400 0.600 OE)O 1.000 et

Fig.2. A p K

of the potentiometric titration of PGA ( 0.011 monomol dm -3) with

strong base as a function of a" ( * ) theoretically calculated curve on the basis of the cell m o d e l , ( + ) LiOH , ( ~ ) (CH 3)4 N O H , and ( O ) (C4H9)4N O H .

4. C O N C L U S I O N S

On the basis of the experimental results, the following conclusions can be made: 9 The length-to diameter ratio strengthens the assumption that pectic acid is a fairly rigid, rod-like molecule and comparable to the structure of cellulose 9 The partial specific volume of the monomeric unit in PGA was found to be approximately 3 per cent higher than the value of D-galacturonic acid 9 For the investigated system the values of p K ~ can be explained by the formation of contact ion pairs between an alkaline ion and the carboxylate group

617 9 The differences in pK ~ values in the case of tetraalkylammonium ions as counterions can be explained by the size of the (CH3)4N§ ion in comparison with the (C4H9)4N+ ion and delocalization of the positive charge on the (CH3)4 N§ ion, which is probably the deciding factor for its stronger interaction with the polyion 9 The values of the coefficients r and r are directly influenced by the size and nature of the counterion 9 The theoretical potential calculated on the basis of the cell model shows that PGA is not suitable for testing a purely electrostatic theory since in this case significant specific binding of counterions to the polyion was detected. For an ion like (C4H9)4N§ this is offset to some extent by the four longer alkyl groups that protect the positive charge of the rigid sphere [ 15].

5. R E F E R E N C E S

.

2. 3. 4. .

.

7. 8. .

10. 11.

12. 13. 14. 15.

M. Mandel, Eur. Polym. J., 6 (1970) 807. D. Rudan-TasiS, C. Klofutar, Thermoch. Acta 246 (1994) 11. R. Kohn, B. Larsen, Acta Chem. Scand., 26 (1972) 2455. O.Kratky, H.Leopold, H.Stabinger, Digital Densimeter of Liquids and Gases (A. Paar K. G., A-8054, Graz, Austria). R. C. Weast (Ed.), Handbook of Chemistry and Physics, 62 Edn., CRC Press, Cleveland, 1981-1982. A. Mizote, H. Odagiri, K. T6ei, K. Tanaka, Analyst, 100 (1975) 822. G. Gran, Analyst, 77 (1952) 661. G .Y.M~dy, B. Lakatos, J. J. Kever, N.V.D.Yakonova, Acta Aliment., 21 (1992) 337. H. Durschlag, Specific Volumes of Biological Macromolecules and Some other Molecules of Biological Interest, in: Thermodynamic data for Biochemistry and Biotechnology, HansJurgen Hinz, Ed. (Springer-Verlag, Berlin, 1986) p. 45. R. Simha, J. Phys. Chem., 44 (1940) 25. A. Katchalsky, Z. Alexandrowicz, O. Kedem, Polyelectrolyte Solution, in: Chemical Physics of Ionic Solutions, Ed. 03. E. Conway, R. G. Barradas, J. Wiley, New York, i966), p.295. Z. Alexandrowicz, A. Katchalsky, J. Polym. Sci. Part A,1 (1963) 3231. S. Lifson, A. Katchalsky, J. Polym. Sci. 13 (1954) 43. J. C. T. Kwak, G. Murphy, E. J. Spiro, Biophs. Chem., 7 (1978) 379. J. Nagano, H. Mizuno, M. Sakiyama, J. Phys. Chem., 95 (1991) 2536.