J . Chem. Sac., Faraday Trans. I, 1988, 84(11), 40434047

Diffusion Coefficients and Effective Charge Numbers of Lignosulphonate

Influence of Temperature

Anna-Kaisa Kontturi Helsinki University of Technology, Laboratory of Physical Chemistry and

Electrochemistry, Kemistintie 1 , SF-02150 Espoo, Finland

The effect of temperature on the diffusion coefficients and effective charge numbers of a polydisperse polyelectrolyte, lignosulphonate, has been studied. The measurements were carried out in 1.Og dm-3 sodium lignosulphonate dissolved in 0.1 mol dm-3 NaC1. The temperatures studied were 10, 20, 29, 38 and 53 "C. The diffusion coefficients increase with increasing temperature and the molecules behave as compact spheres in the temperature range studied. The effective charge number of the ligno- sulphonate molecules decreases slightly in the temperature range 10-29 "C, but drops suddenly to zero at ca. 38 "C , which means that the molecules are neutral at this temperature.

The lignosulphonate molecule is a branched, net-like macromolecule, which is very polydisperse. Lignosulphonate is also a typical polyelectrolyte. It has two kinds of ionizing groups: sulphonate groups (pK, < 2) and phenolic OH- groups (pK, = 10). In addition to giving information about the mobility of the ion, the ionic diffusion coefficient also tells us about the shape and size of the macromolecule. In previous work' it has been shown that lignosulphonate molecules (molar mass < 50000 g mol-l) are spherical in acidic, neutral and alkaline solutions. The effective charge number of lignosulphonate molecules has been determined at different pH values. 1-3 The effective degree of dissociation was almost zero at pH 1,2&30 % at pH 5 and 35-80 YO at pfl 1 1 . These measurements were carried out at 20 "C.

The temperature dependence of the ionic diffusion coefficients and the effective charge numbers of lignosulphonates have not been studied, although they are interesting from the practical point of view. For instance, Forss and Pirhonen4 have shown that the degree of extraction of lignosulphonates with aliphatic amines increases with increasing temperature.

The methods presented in the literature for the determination of the ionic diffusion coefficients of polyelectrolytes are based on a non-stationary diffusion process. For lignosulphonates techniques such as the solution-to-gel m e t h ~ d , ~ porous plate method,6 sedimentation method' and free-boundary method' have been used. The effective degree of dissociation of lignosulphonates has been determined by Lindstrom and Soremarkg with the aid of Donan equilibrium measurements, and also by Rezanowich and Goring,lo who estimated the degree of dissociation by viscosity measurements. However, all of these methods demand prefractionation of the polyelectrolyte, and in order to obtain the ionic diffusion coefficients and the effective charge numbers as a function of molar mass several measurements have to be made. Furthermore, the fractionated samples are never monodisperse, even though in the measurements and calculations they have to be treated as if they were monodisperse.

A method for determining the ionic diffusion Coefficients' and the effective charge numbers2' of polyelectrolytes has been presented recently. This method is a modification

4043

Publ

ishe

d on

01

Janu

ary

1988

. Dow

nloa

ded

by Q

ueen

s U

nive

rsity

- K

ings

ton

on 2

6/10

/201

4 11

:57:

12.

View Article Online / Journal Homepage / Table of Contents for this issue

4044 Diflusion Coeficients of Lignosulphonate

M I

a I P I/

V 0 v 5 pi I

I

V a

Fig. , A schematic drawing of the membrane cell. The system consists of two electrolyte solutions (a and p) separated by a thin membrane (M). The solutions a and B are kept homogeneous by stirring. Inside the membrane the local concentration gradients are determined by the Nernst-Planck equations with constant ionic fluxes. These fluxes can be determined from the concentration in the a compartment, V" and the surface area of the membrane ( A ) with the aid

of the balance equation 4 A = -c"V"; i = 1,2, ..., n.

of the diaphragm-cell method'' and is based on a stationary convective diffusion process across a thin porous membrane instead of the original non-stationary diffusion process. When the diffusion process reaches the stationary state, it is easy to study the effect of various parameters (pH, temperature, solvent etc.) on the ionic diffusion coefficients and on the effective charge numbers. Furthermore, with the present method the prefractionation of the polyelectrolyte is unnecessary because the molar mass distribution of the polyelectrolyte can be determined in the steady state as described earlier.

In this work we have used the above mentioned method and measured the ionic diffusion coefficients and the effective degree of dissociation of lignosulphonates at five temperatures and in one supporting electrolyte system (0.1 mol dm-3 NaCl).

Theory The theoretical details of the method for the determination of both the ionic diffusion coefficients and the effective charge numbers of polydisperse polyelectrolyte have been described previously. 1-3 These methods are based on a stationary convective diffusion process across a porous membrane, using the polyelectrolyte as a trace ion, i.e. added to the system of a supporting electrolyte in a small amount. The theoretical analysis is based on the Nernst-Planck transport equation. The cell arrangement is shown in fig. 1, for which the caption explains the situation to be modelled.

When determining the ionic diffusion coefficients the concentration of the supporting electrolyte is maintained homogeneous throughout the system and thus the gradient of electric potential present in the Nernst-Planck equation is equal to zero, i.e. dq5/dx = 0. Therefore the charge numbers (zi) of different species of the trace ion disappear in the transport equations, and it is possible to determine D, without knowing zi. The equation for the determination of diffusion coefficients is presented in ref. (1). In order to determine z, the concentration of the supporting electrolyte is made non-homogeneous, which in turn gives a non-zero value for d@/dx, and thus preserves z, in the Nernst-Planck equations. The experimental situation is analogous to that in fig. 1 , except that instead of the supporting electrolyte, pure water is fed into the 01

compartment. Now d@/dx can be solved from the Nernst-Planck equations written for the supporting electrolyte ions, using the condition of electroneutrality and the boundary values ci(x = 0) = c: and c,(x = 1) = 4. When this value of $/dx is substituted

Publ

ishe

d on

01

Janu

ary

1988

. Dow

nloa

ded

by Q

ueen

s U

nive

rsity

- K

ings

ton

on 2

6/10

/201

4 11

:57:

12.

View Article Online

A-K. Kontturi 4045

into the Nernst-Planck equations for the trace ions and integration is performed across the membrane we obtain the solution:2

cf - exp(pcl/AD,) cf (@/ca) z,(D/D+ - 1) - -

where D = 2D+O-/(D+ + D-). Eqn (1) is valid in the system where a 1-1 electrolyte is used as the supporting electrolyte, the ionic diffusion coefficients of which are D, and D-, respectively. From eqn (1) the charge numbers z, can be calculated by iteration.

Experimental A detailed description of the experimental set-up and the details of the analytical methods for lignosulphonate have been described previously.

Measurements

The concentration of the supporting electrolyte (NaCl) in the p compartment was 0.1 mol dm-3 in each case. The temperatures used in the measurements were 10, 20, 29, 38 and 53 "C. The concentration of the lignosulphonate in this compartment was 1 g dm-3 for all measurements. The convection was adjusted so that the concentration ratio (c/c was reasonable (i.e. so that c: was not too low) and the total concentration of the supporting electrolyte did not diminish below ca. 0.08 mol dm-3.

Because the concentration of the supporting electrolyte changes relatively little it can be assumed that the diffusion coefficients are independent of concentration. To avoid the growth of micro-organisms, all solutions were saturated with toluene. The potassium ion was used as an internal standard, therefore it was also added to the solution of the p compartment in small amounts. The system was deduced to have reached a stationary state when the concentration of lignosulphonate remained constant in the flow V". The values for A/Z and V c were approximately the same as those reported previously.'

Results and Discussion Tables 1 and 2 show the measured ionic diffusion coefficients and the effective charge numbers of lignosulphonates calculated from eqn (1) and (2), respectively, at five temperatures. The tables also include the molecular radius (r,) calculated from the Stokes-Einstein equation and the effective degree of dissociation (a) calculated from the stoichiometric number of sulphonate groups in the lignosulphonate molecules. l2

The variation of D, with molar mass can be expressed using the Mark-Howink equation : Di = K M P b where K and b are constants characteristic of the polymer. For a compact spherical particle (Einstein sphere) b is i. Fig. 2 shows logarithmic plots of the diffusion coefficient 21s. the molar mass of lignosulphonate at different temperatures. From the slopes of these lines we obtain values for the exponent b at each temperature : b = 0.274.30. Thus it is evident that lignosulphonate molecules remain spherical in the temperature range 30-53 "C. The molecular radius (r,) does not change very much with temperature. The diffusivity of humic acid, which is a branched, cross-linked polyelectrolyte like lignosulphonate, has been measured by Cornel et al.13 as a function of temperature (1-43 "C), and was also found to remain spherical with increasing temperature.

t Note the typographical error in ref. (2).

Publ

ishe

d on

01

Janu

ary

1988

. Dow

nloa

ded

by Q

ueen

s U

nive

rsity

- K

ings

ton

on 2

6/10

/201

4 11

:57:

12.

View Article Online

4046 D iflus ion Coeficien ts of Lignosulph ona te

Table 1. Diffusion coefficients (DJ cm2 s-l) and molecular (,/A) of lignosulphonate molecules of different molar mass (M/g mol-l) as a function of temperature

10 "C 20 "C 29 "C 38 "C 53 "C

M Df ri Di ri Di ri Di ri Di ri

50 000 45 000 40 000 35 000 30 000 25 000 20 000 15000 1 0 000 8 000 5 000

0.46 34.3 0.48 32.9 0.51 30.9 0.53 29.8 0.54 29.2 0.57 27.7 0.62 25.5 0.71 23.2 0.83 21.0 0.87 19.5 0.97 17.5

0.84 25.9 0.87 24.4 0.91 23.4 0.94 22.6 0.97 21.9 1.05 20.3 1.09 19.5 1.16 18.3 1.31 16.2 1.39 15.3 1.58 13.5

0.98 28.1 1.03 26.7 1.09 25.2 1.11 24.8 1.15 23.9 1.23 22.5 1.31 21.0 1.44 19.1 1.58 17.4 1.65 16.7 1.88 14.6

1.24 27.9 1.29 26.8 1.34 25.8 1.41 24.6 1.46 23.7 1.53 22.6 1.58 21.9 1.69 20.5 1.91 18.2 2.00 17.3 2.30 15.1

1.54 29.8 1.58 29.1 1.67 27.5 1.68 27.3 1.77 26.0 1.89 24.3 1.97 23.2 2.21 20.8 2.64 17.4 2.80 16.4 3.28 13.0

Table 2. Effective charge numbers (zi) and effective degree of dissociation [a(%)] of lignosulphonate molecules of different molar mass ( M / g mo1-21) as a function of temperature

10 "C 20 "C 29 "C 38 "C 53 "C - ~ _ _

A4 2, a zi a zi a Zi a zt a

50 000 45 000 40 000 35000 30 000 25 000 20 000 1 5 000 10 000 8 000 5 000

- 26.7 -24.7 - 24.5 -23.5 - 22.0 - 18.6 - 18.0 - 16.5 - 10.5 - 8.5 - 5.5

28.9 29.7 33.1 36.3 39.6 40.2 48.4 58.7 55.6 50.6 47.8

-21.9 - 20.1 - 18.8 - 18.2 - 17.0 - 15.8 - 14.5 - 12.4 -9.1 - 8.6 -6.1

23.7 -21.2 22.9 0.2 0 24.2 -19.0 22.8 0.1 0 25.4 - 17.9 24.2 0.2 0 28.1 - 17.0 26.2 0.0 0 30.6 -15.5 27.9 -0.1 0 34.1 -13.3 28.7 0.0 0 38.9 -12.3 33.1 -0.2 0 44.1 -10.5 37.4 -0.2 0 48.1 -9.0 47.6 -0.3 0 51.2 -7.7 45.8 -0.2 0 53.0 -6.5 56.5 -0.5 0

0.1 0 0.2 0 0.0 0 0.0 0

-0.1 0 0.0 0

-0.3 0 0.2 0 0.0 0 0.0 0

-0.3 0

The effective charge number of lignosulphonate is relatively constant (or decreases slightly) with increasing temperature until at 38 "C its charge is suddenly lost. A small decrease of the effective charge of other polyelectrolytes with increasing temperature has also been reported by Darskus et aZ.,14 who measured the effective degree of dissociation (aeff) for polyvinyl derivatives by conductance and transference measurements in salt- free solutions. aeff decreased by ca. 3 % in the range 5-55 "C. However, Wall and D o r e m u ~ ' ~ reported that the degree of binding of Na+ ions in poly(acry1ic acid) solutions remains independent of temperature from 0 to 42 "C.

The complete neutralization of lignosulphonate molecules at higher temperatures is a very strange result. We have repeated the measurements at the two highest temperatures to ensure that it is not due to experimental error. The shape of the molecule does not change, although the charge number decreases to zero. For some unknown reason the counter-ions are not able to move freely at higher temperatures. Thus we obtain the same result by increasing the temperature as by decreasing the P H . ~ In order to elucidate this behaviour further this study is to be continued using different counter-ions such as Li+ and K'.

Publ

ishe

d on

01

Janu

ary

1988

. Dow

nloa

ded

by Q

ueen

s U

nive

rsity

- K

ings

ton

on 2

6/10

/201

4 11

:57:

12.

View Article Online

A-K. Kontturi 4047

1.6

1.4

h - 1.2 'Y)

2 5 9 l \

M s

0.0

0.61 I I I I 1 3.0 4 4.2 4.4 4.6 A

log (Mlg m01- )

Fig. 2. Logarithmic plots of the diffusion coefficient us. molar mass of lignosulphonate at different temperatures: ., 10 "C; 0, 20 "C; 0, 29°C; 0, 38 "C; A, 53 "C.

References 1 A-K. Kontturi and K. Kontturi, J. Colloid Interface Sci., 1987, 120, 256. 2 A-K. Kontturi and K. Kontturi, Acta Polytechn. Scand., 1987, 178, 143. 3 A-K. Kontturi and K. Kontturi, J. Colloid Interface Sci., in press. 4 K. Forss and I. M. J. Pirhonen, Finn. Pat. 45979 (1972). 5 V. J. Felicetta, A. Ahola and J. L. McCarthy, J. Am. Chem. SOC., 1960, 78, 1899. 6 J. L. Gardon and S. G. Mason, Can. J. Chem., 1955, 33, 1477. 7 K. Forss and B. Stenlund, Paper Timber, 1969, 51, 93. 8 W. Q. Yean, A. Rezanowich and D. A. I. Goring, in Chim., Biochim., Lignin, Cellulose et Hemi-

9 T. Lindstrom and Ch. Soremark, ColIoid and Interface Science (Academic Press, New York, 1976), vol. cellulose, Proc. Int. Symp., Grenoble, France, 1964, s. 327.

5, p. 217. 10 A. Rezanowich and D. A. I. Goring, J. Colloid Interface Sci., 1960, 15, 452. 11 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, 2nd edn, London, 1969). 12 S. Yano, M. Rigdahl, P. Kolseth and A. de Ruvo, Svensk Papperstidn., 1984, 87, R170. 13 P. Cornel, R. S. Summers and P. V. Roberts, J. Colloid Interface Sci., 1986, 110, 149. 14 R. L. Darskus, D. 0. Jordan and T. Kurucsev, Trans. Faraday SOC., 1966, 62, 2878. 15 F. T. Wall and R. H. Doremus, J. Am. Chem. SOC., 1954, 76, 1557.

Paper 8/00130H; Received 12th January, 1988

Publ

ishe

d on

01

Janu

ary

1988

. Dow

nloa

ded

by Q

ueen

s U

nive

rsity

- K

ings

ton

on 2

6/10

/201

4 11

:57:

12.

View Article Online