Potentiometric titration of monodisperse polystyrene latexes

Potentiometric titration of monodisperse polystyrene latexes

J. Electroanal. Chem., 64 (1975) 207--218 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands POTENTIOMETRIC TITRATION OF MONODISPERSE PO...

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J. Electroanal. Chem., 64 (1975) 207--218 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

POTENTIOMETRIC TITRATION OF MONODISPERSE POLYSTYRENE LATEXES

JUHANI LAAKSONEN, J E A N C. LE BELL and PER STENIUS

Department of Phystcal Chemistry, Abo Akademz, Porthansgatan 3--5, 20500 ~ibo 50 (Finland) (Received 18th February 1975)

ABSTRACT An attempt has been made to characterize the surface groups of monodisperse latexes by high-precision potentiometric titrations followed by processing of the potentiometric data. The latexes were prepared by emulsion polymerisation in the absence of any added emulsifying agents. The polymerisation was initiated with potassium persulphate. It was found that the concentration of surface groups was too small to allow reliable separation of the effects of surface groups on the titration curves from those of minor experimental uncertainties. The possibility of determining the dissociation constants of the surface groups on latexes with higher charge is discussed.

INTROD UCTION

The preparation and characterization of monodisperse polystyrene latexes in the absence of emulsifying agents has been the subject of considerable interest in recent years [1--7], because of the importance of these latexes as model colloids. Several different methods of characterization of the surface groups on the latexes have been used, including those of conductometric titration [ 4--7 ], infrared spectroscopy [ 8], dye adsorption [ 5,6 ], electrophoretic mobility [3--7] and potentiometric titration [6,9]. Of these methods, potentiometric titration seems to be eminently suitable for determining the dissociation constants of acid and alkaline surface groups. In this paper a first report is given of the application to polystyrene titrations of the methods for determining stability constants mainly developed by Sill~n et al.

[10--13]. EXPERIMENTAL

Preparation and preliminary characterization of the latexes Monodisperse polystyrene latex (PS) was prepared by the method originally developed by Matsumoto and others [ 1--3]. The initiator used was

208 TABLE 1 Recipes for latexes used in p o t e n t i o m e t r i c t i t r a t i o n s Latex

[Styrene] /mol dm -3

103 [ K 2 S 2 0 8 ] /mol dm -3

103 [NaC1] /mol dm -3

Temperature /°C

A B C

0.87 0.87 0.87

2.76 2.76 2.76

10.0 3.0 --

70 + 1 70 -+ 1 90 + 1

potassium persulphate. Of the three latexes investigated (A, B, C), samples A and B were prepared in this laboratory and sample C in the Department of Physical Chemistry, University of Bristol. The recipes for the preparations axe given in Table 1. Latexes A and B were purified by ion exchange in accordance with the method described in ref. 5. Latex C was purified by dialysis [7]. The diameters of the latexes were determined from electron micrographs; these were calibrated with a diffraction grating (sample C) [7] or with latexes of known size (samples A and B). The diameters are given in Table 2. From the use of persulphate as an initiator, it is to be expected that there may be sulphate, carboxyl and h y d r o x y l groups on the surface of the latexes [7]. The presence of carboxyl or hydroxyl groups was investigated qualitatively by infrared spectroscopy, using a bulk-polymerized polystyrene as a reference. Latexes B and C exhibited weak absorption at 1705 cm - 1 , similar to that found by Shaw and Marshall [8] and ascribed to carboxyl groups by them. After oxidation with potassium persulphate (0.2 g per g polymer) in 10 - 5 mol dm - a AgNO3 at 90°C for 24 h [14,15], latex A also exhibited weak absorption at 1705 cm - 1 . Hence, it may be concluded that small quantities of carboxyl groups might be present on the surface of latexes B and C, while latex A carries h y d r o x y l and sulphate groups only. The total number of acid groups was determined by conductometric titration of latexes that were completely converted into the acid form b y ion exchange. Titration curves for samples A and C are shown in Fig. 1. There is no marked difference between these t w o curves; the curve of latex C may be interpreted as having two breakpoints, corresponding to neutralization of --SO4H and --COOH respectively. The total concentration of these groups and the corresponding surface charge densities are given in Table 2. The total a m o u n t of sulphur in the latexes was determined by X-ray fluorescence. From these values, it is found that a b o u t half of the - - S O 4 groups are located on the surface (Table 2); this agrees with other investigations [ 5,6].

209

0. o

o_ •

~i1¢

0

-,~o0

I 0 0

~ ~

o

o~.

r.~

r-. co o

I 0 0

0 ~

~ 0

~o~ o~

~,~

o~o~ I',~

o

0

r-. ' ~ e~

o. ~. ~.

0

,d oo• coo o~° 0t.~o

oo qD co

cq

0., 0

210

a< Z

~. o~..

o

t

,

i

I

o

i

'

I

1o P

o

!

zo

°°

i

i

I

I

3o

¢o

10"~moi dn~ NoOH cm 3

Fig. 1. Conductometric titrations of latex A (o) and C (e).

Solutions

The purified latex suspensions contained about 8% (dry weight) latex. They were diluted with 0.2 mol dm - 3 NaC1 to give an ionic strength of 0.1 mol dm - 3 . The NaC1 was dried Merck suprapur quality. The water (conductivity 0.5 pS cm - 1 ) was doubly distilled and ion-exchanged in the same way as the latex suspens]ons. All vessels were cleaned by soaking in 50% aqua regia for 24 h, followed by rinsing with 10% KOH in ethanol and large amounts of distilled water. All solutions were protected from CO2 by flushing the vessels with nitrogen and the use of soda lime protection tubes. Potentiometric titrations

The potentiometric titrations were carried out either volumetrically or coulometrically. The construction of the titration vessels and an earlier version of the titration apparatus has been described in detail elsewhere [ 14,15]. The reference electrode and the bridge solution can be written Ag, AgCl13 M KC1 (satd. with AgC1)I6M KC1 The reference electrode was prepared by a m e t h o d slightly modified from that of Brown [16]. The half-cell in which the titration was performed can be written IPS (cs), HC1 (c~i), NaC1 (0.1 M -- c~i -- CN)lglass electrode Here, CN is the concentration of sodium ions introduced by the latex and

211 c~ the c o n c e n t r a t i o n of added HC1 (see below). To keep t he ionm strength as constant as possible at 0.1 mol dm - 3 t h r o u g h o u t the titration the initial sGlution was titrated (a) volumetrically (samples A and B) by adding a latex suspension (latex O c o n c e n t r a t i o n cs), in which the c o n c e n t r a t i o n of NaOH was Con and the cono centration o f NaC1 was 0.1 mol dm - 3 - - c N - - C o n ; (b) coulometrmally (sample C) by discharging hydrogen ions from a platin u m cathode in the solution. The anode was a silver rod in a separate electrode chamber, c o n n e c t e d to the solution by a bridge containing 0.1 mol dm - 3 NaC1. A R a d i o m e t e r G 202 B glass electrode was used. The e.m.f, was recorded with an e l e c t r o m e t e r amplifier, t y p e AD 311K connect ed t o a Data Precision 2520 A1 digital v o l t m e t e r with an Addo-X printing device. T he zeropoint drift of this system was < 10 pV per 24 h. The e.m.f, generally stabilized within +-20 pV (that is, the noise level of the glass electrode at 25°C) within a b o u t 3 min after each addition on the acid side of the equivalence point. A b o u t 30 min were required on the alkaline side; very close to the equivalence p o in t it was generally impossible to achieve a stability bet t er than + 100 pV. The titrations were p e r f o r m e d automatically by a programmable control unit th at alternated between recording the e.m.f, and volumetric or coulometric addition at pre-set time intervals. Volumetric additions were made with a Metrohm Dosimat motor-driven burette. Coulometric additions were made with a Metrohm E 303 coulometer, controlled by a digital clock. The time required for each titration was 16--20 h. CHOICE OF EXPERIMENTAL CONDITIONS AND PROCESSING OF EXPERIMENTAL

DATA Since the concentrations of the surface groups to be investigated are extremely small, great care should be taken to eliminate or control all factors, o t h e r than the dissociation of the surface groups, that could affect the potentiometric results.

Activity coefficients By working at constant ionic strength and constant c o n c e n t r a t i o n of PS the variations in the activity coefficients in a titration can be assumed t o be negligible. Hence, concentrations m ay be used instead of activities in all calculations.

Interaction between surface groups The addition o f ca. 0.1 mol dm - 3 NaC1 compresses the diffuse doubl e layer almost completely. Hence, variations in the apparent dissociation constant o f the surface groups due to changes in double layer thickness with the

212 degree of neutralization [ 17] may be assumed to be negligible. Moreover, the average distance between surface groups on the particles with the surface charge densities given in Table 2 is of the order of 20 nm. Hence, it can be assumed that the surface carries two independent types of dissociating groups: --SO4H, which all have the acidity constant ~A, and --COOH, which all have the constant/3 B.

Calibration of the electrode system The standard potential of the electrode system was determined separately for each titration by the addition of a known excess of hydroxide ions after the equivalence point, as described in refs. 18 and 19.

Diffusion potentials At constant ionic strength, it can be assumed [18] that the diffusion potential is a linear function of [H] and [OH] :

Ej =Jac[H] +Jalk[OH] =Jac[H] +KwJalk/[H ]

(1)

where Jac and Jalk are constants and Kw is the ionic p r o d u c t of water. Generally, Jac ~ 10--20 mV mo1-1 dm 3 and Jalk ~ 10 mV mo1-1 dm 3. Thus, Ej ~ 0 for 3 < p H < 11.

Determination o f the equivalence point In each titration, the equivalence point was determined using Gran plots [20] for the points on the alkaline side of the equivalence point. These yielded straight lines that allowed determination of the total a m o u n t of O H - added at the equivalence point within + 0.05%.

Acid or alkaline impurities The presence of acid or alkaline impurities was checked by blank titrations of HC1 with NaOH, using procedures reproducing those in the titrations of PS as closely as possible. The concentration of weakly acid or basic impurities may then be estimated from the difference in the equivalence points indicated by the Gran plots for the acid and the alkaline parts of the titration curves respectively [21].

Systematic errors and determination o f the stability constants The final evaluation of the experimental titration curves was made using the ETITR version of the c o m p u t e r programme L E T A G R O P V R I D developed by Sill~n et al. [11--13]. The function of this programme in the present case is as follows:

213 The two independent acidity constants for --SO4 H (A) and --COOH (B) are defined by ~A = [H] [ A ] / [ H A ] ; ~B = [H] [B]/HB]

(2)

[A], [B] are the concentrations of dissociated and [ H A ] , [HB] the concentrations of undissociated --SO4H and --COOH groups in the solution. The total concentrations of these groups are given by cA = [A] + [HA] = [A] + [H] [A]/flA

(3)

CB = [B] + [HB] = [B] + [H] [B]/~B

(4)

Hence, the total analytical concentration of hydrogen ions in the solution is given by CH = [H] + [HA] + [HB] = [H](1 + ~ X [ A ] +fi~l[B])

(5)

However, if there is an acid impurity DH (total concentration CD) present, which is assumed to be monobasic with acidity constant riD, CH is given by CH =

[H](1 +/3-~AI[A] + t3-~BI[B] + fiDI[D])

(6)

where [H] may be calculated from the experimental values for E using the Nernst equation E = E ° - - R T F - 1 In [HI + E,

(7)

Ei is given by (1) and E ° is a constant for each titration. Hence, if flA, fiB, f/D, CA, Cm CD, E ° , j a c , J a l k and K w are known, c~ may be calculated for any experimental point. On the other hand, since the initial total concentration of hydrogen ions, c~, is known from the equivalence point, cH may be calculated from CH = ( C H V 0 - - CT V T ) / V t o t

(9)

where Vo is the initial volume of the solution, VT is the volume of sodium hydroxide added (concentration c~) and Vto t = Vo + V T . For a coulometric titration, (9) becomes O

CH = CH - - QT / F V o

(9')

where QT is the quantity of electricity added and F is the Faraday constant. However, there may be a small error in the equivalence point (fill0) or in CCH(SHT), in which case CH is given by CH = ( c ~ V 0 - - C T V T ) / V t o t 4- ~Ho + ~ H T

(10)

If the titration curve is defined by a large n u m b e r of points on the titration curve, the parameters in eqns. (6) and (10) may be determined by adjusting them to give a minimum in the sum of squares of errors for all experimental points

214

u =

(c'.,,-

2

(11)

!

where c~ is given by (6) and c~ by (10). It is, of course, n o t feasible to determine all these parameters simultaneously. However, several of them can be neglected or determined in independent experiments (see below). RESULTS AND DISCUSSION

In Figs. 2 and 3 ordinary titration curves for latex B (volumetric titration) and latex C (coulometric titration) are shown. Both curves are typical curves for the titration of a strong acid with a strong base and from the alkaline parts of them E ° can be determined within +0.02 mV [18,19] (Fig. 4). All the latexes were titrated twice and one of the titrations was chosen for further treatment. From the blank titration preceding each titration of a latex, the concentration of acid impurity was found to be approximately 12 pmol dm - 3 in volumetric and approximately 30 pmol dm - 3 in coulometric titrations. These concentrations were used as starting values for CD in the LETAGROPVRID processing. In our experience, it is extremely difficult to achieve impurity levels below 10 pmol dm - 3 in titrations as slow as these. Since the most likely impurity is small amounts of carbon dioxide, the acidity constant for HCO~ was taken as flD (P/3D = 10.33 [22]).

300 200 100 E__

mV

0 -100 -200 -300 I 25

I 50 __

I 75

I 100

v,

mt Fig. 2. E l e c t r o m o t i v e force as a f u n c t i o n o f the added v o l u m e o£ s o d i u m hydroxide in a p o t e n t i o m e t r i c t i t r a t i o n o f l a t e x A.

215

3oo! 20O

100

0

E

mV -100

-200 -300 t

~ . 20

0

L, ,

I. 40

_..

~

J 6O

l

_l 80

J

_

.¢ C

Fig. 3, Electromotive force as a function of the added quantity of hydroxide ions (expressed as quantity of electricity) in a coulometric titration of latex C,

In order to determine its acidity constant, at least i 0 % of an acid should be undissociated at the beginning of a titration. In the latex suspensions, cA ~ 100 pmol dm - 3 and flA ~ 0.05 {Table 2). Hence, the titration should start at pH ~ 2. Then [Hi ~ 1000 × [HAl; moreover, [HA] will be of the

46t

E% ~+E~

450.00*0.02

mV

460

mV

t 459

,,I 0t5

....

t

tO

I. . . . . . . .

1.5

!

2,0

2,5

z, AHOUNT OF OH A00ED IN EXCESS/mmo~.

Fig. 4. Determination of the standard potential of the cell used in the titration of latex C. The quantity E ° + E) ~- E + R T F - - I In [OH] is plotted against the quantity of hydroxyl ions added. Extrapolation to [OH] = 0 yields E °, since according to eqn. (i), Ej = 0 at this point.

216 same order of magnitude as the concentration of impurities. At lower pH values the diffusion potentials become appreciable. For this reason, it was considered impossible to determine the dissociation constant of the sulphate groups; their influence was assumed to be negligible and the term/3AI[A] was left out of eqn. (6). As mentioned above, Jae and Jalk are negligibly small for 3 < pH < 11. Since the titrations were made within this range, Ja~ and Jalk were set equal to zero in all calculations. For CB the values determined in conductometric titrations were used as starting values for latexes A and C; a guess of the same magnitude was made for latex B. The acidity constant for benzoic acid (10 -4"2°1) was used as a starting value for fiB. The value for Kw in 0.1 mol dm - 3 NaC1, 1.0156 × 10 -14 [23], was used as a starting value in all calculations. For 5H0 and 5HT the m a x i m u m value was assumed to be 0.05% of c~a, as judged from the Gran plots. Thus, fairly reliable first estimates for all parameters could be used in the attempts to minimize U. The main parameters adjusted in the computer treatment were fiB, CB, CD and riD" The effect on U of these variations was compared with the effects of small changes in ~H0, 5HT and E °. Attempts were first made to minimize U w i t h o u t the introduction of any impurity acid; then the presence of an impurity was assumed, and finally, small errors in E °, c~ and CT were introduced. For all titrations it was found that (a) w i t h o u t introduction of impurities, a minimum in U was f o u n d that was strongly influenced by small changes in E ° and c~, but only slightly influenced by changes in CB and ~B; (b) if an impurity was introduced, this generally lowered U by a few per cent, but U was very little influenced by changes in eD and ~D of a b o u t 50%; (c) if it was assumed t h a t impurities were present, but the influence of the PS surface groups were neglected, the concentration of impurities was somewhat increased by the computer (typically, from ~ 20 to ~ 40 pmol dm - s ) and the minimum value of U was only ~ 1% higher than that found in (b), (d) if the influence of impurities and surface charges were both neglected (CB, eD = 0), U was increased by a few per cent, but it was still possible to obtain reasonable agreement with experimental data (standard deviation in CH ~ 5%) w i t h o u t assuming errors in the equivalence point or E ° greater than 0.1% and 0.05 mV respectively. Thus, it was concluded that it was n o t possible to make a significant distinction between the effects of the - - C O 0 - or --SO4 groups on the binding of hydrogen ions from small uncertainties in the equivalence point, the concentration of impurities or the diffusion potentials. Several methods of improving the possibilities of characterizing the surface by potentiometric titration may be envisaged. (i) One might start from a latex in completely acid form. When this is suspended in water, most of the hydrogen ions dissociate. Hence, the argument concerning the --SO4H groups given above still holds. A titration will yield a

217

value for the total concentration of acid groups, but it will not be possible to determine the dissociation constant. (ii) One could increase the concentration of the latex. This causes flocculation if the pH is adjusted to values sufficiently low for the determination of the dissociation constants. We have found that flocculation renders the response of the glass electrode sluggish; moreover, an increase in latex concentration which would substantially improve the possibilities of titrating the surface groups is hardly feasible. (iii) One might try to increase the accuracy of the titration procedure. This is hardly feasible with glass electrodes due to their high internal resistance. Hydrogen electrodes cannot be used since the hydrogen will react with polystyrene. (iv} The remaining way is to increase the concentration of the surface groups. This is certainly possible [ 7], probably without having to abandon the simplifying assumption that the surface groups are independent of each other. Work in this direction is in progress. We have, however, thought it appropriate to bring the difficulties encountered in potentiometric titrations of latexes to attention since we feel that the methods above very clearly indicate the care that should be taken in interpretations of results from titrations of small amounts of weak acids, as well as the possibilities of improving the results. In our opinion, the electrophoretm method described by Ottewill and Shaw [24] is probably the best method for latexes with low charge densities, since this method focuses on the particles proper and is n o t influenced by the concentration of free hydrogen ions in the solution. This m e t h o d was used to determine the P~A values given in Table 2. ACKNOWLEDGEMENTS

Professor R.H. Ottewill, University of Bristol, is thanked for discussions concerning the properties of latexes and for supplying one of the latex samples. This work was supported by a grant from the Foundation for Research into Natural Resources of Finland.

REFERENCES 1 2 3 4

5 6 7 8 9

T. Matsumoto and A. Ochi, Kobunshi Kagaku, 22 (1965) 481. A. Kotera, F. Furusawa and Y. Takeda, Kolloid-Z. Z. Polym., 239 (1970) 677. K. Furusawa, W. Norde and J. Lyklema, Kolloid-Z. Z. Polym., 250 (1972) 908. J.W. Vanderhoff, H.J. van den Hul, R.J.M. Tausk and J. Th. G. Overbeek in G. Goldfinget (Ed.), Clean Surfaces: Their Preparation and Characterization for Interfacial Studies, Marcel Dekker, New York, 1970, p. 15. H.J. van den Hul and J.W. Vanderhoff, J. Electroanal. Chem., 37 (1972) 161. J.W. Vanderhoff and H.J. van den Hul, J. Macromol. Sci., A7 (1973) 677. J.W. Goodwm, J. Hearn, C.C. Ho and R.H. Ottewill, Br. Polym. J., 5 (1973) 347. J.N. Shaw and M.C. Marshall, J. Polym. Sci., 6 A1 (1968) 449. C.C. Ho, Ph.D. Thesis, University of Bristol, 1972.

218 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

L.G. Sill~n, Acta Chem. Scand., 10 (1956) 186. L.G. Sill~n, Acta Chem. Scand., 18 (1964) 1085. L.G. Sill~n and B. Warnqvist, Arkiv Kemi, 31 (1968) 315,341. L.G. Sill4n, R. Whiteker and P. Brauner, Arkiv Kemi, 31 (1968) 365. I. Danielsson, Kemian Teollisuus, 23 (1966) 1081 W. Forsiing, S. Hietanen and L.G. Sill~n, Acta Chem. Scand., 6 (1952) 901. R. Brown, J. Amer. Chem. Soc., 56 {1943) 646. E.g., C. Tanford, Physical Chemistry of Macromolecules, J. Wiley, New York, 1961, Ch. 7. G. Biederman and L.G. Sill~n, Arkiv Kemi, 5 (1952) 425. S. Hietanen and L.G. Sill~n, Acta Chem. Scand., 13 (1959) 533. G. Gran, Analyst, 77 {1952) 61. L. Ciavatta, Arkiv Kemi, 20 (1963) 417. R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Butterworths, London, revised edn., 1965. H.S. Harned and B.B. Owen, The Physical Chemistry of Electrolyte Solutions, 2nd edn., Reinhold, New York, 1950, p. 483. R.H. Ottewill and J.N. Shaw, Kollold-Z. Z. Polym., 218 (1967) 34.