J. Phys. Chem. 1987, 91, 4827-4830
4827
Proton Association-Dissociation Kinetics of the Hydrogen Sulfate Group on the Surface of Monodisperse Latex Particles Studied by the Electric Field Jump Method Minoru Sasaki, Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan
Tadaomi Inoue,* Faculty of Engineering, Kinki University, Kure 737- 10, Japan
Tatsuya Yasunaga, Research Institute for Science and Technology, Kinki University, Higashi- Osaka 577, Japan
and Z . A. Schelly Department of Chemistry, The University of Texas at Arlington. Arlington, Texas 76019-0065 (Received: January 27, 1987)
Single relaxation of the order of microseconds was observed in an aqueous suspension of monodisperse polystyrene latex by using the electric field pulse technique with conductivity detection. The electric field intensity dependence of the relaxation amplitude could be interpreted by Onsager's theory for dissociation field effect. The dependence of the relaxation time on electrolyte concentration and pH shows minima. From the static and kinetic results obtained, the relaxation was attributed to the association-dissociation of the proton of the hydrogen sulfate group on the surface of the latex particles. The intrinsic association and dissociation rate constants were determined to be (8 f 1) X lo5 mol-' dm3s-l and (9 f 5) X lo4 s-I, respectively, at 25 "C. The former value was well interpreted by Astumian and Schelly's theory for the reduction of association rate constants in heterogeneous systems, and the latter value revealed that the hydrogen sulfate group acts as a weak, solid acid such as TiO,, Fe203,and Fe304.
Introduction The dynamic properties of solid surfaces are of great importance in many fields, such as soil chemistry, environmental engineering, materials science, and colloid chemistry. Kinetic studies of fast reactions at solid-liquid interfaces have been performed by the present authors using chemical relaxation techniques, and much interesting information on detailed mechanisms of the reactions involved have been obtained.'-I0 Very recently, Astumian and Schelly have pointed out that the association rate constants of reactions in heterogeneous system are extremely reduced compared to those in homogeneous systems because of the reduction of dimensionality at interfaces." According to their theory, the association rate constant in heterogeneous systems is a function of the radius of the solid particles involved. The need for a quantitative test of their theory has motivated us to carry out a kinetic study of a fast reaction, in a well-defined and uniform-sized particle system such as polystyrene latex. Monodisperse polystyrene latex particles form an ordered state in extremely dilute electrolyte solution and their suspension shows a beautiful iridescence caused by diffraction of visible l i g h ~ l ~ - ' ~ (1) Ashida, M.; Sasaki, M.; Kan, H.; Yasunaga, T.; Hachiya, K.; Inoue, 219. (2) Hachiya, K:; Ashida, M.; Sasaki, M.; Kan, H.; Inoue, T.; Yasunaga, T. J . Phys. Chem. 1979, 83, 1866. (3) Ashida, M.; Sasaki, M.; Hachiya, K.; Yasunaga, T. J. Colloid Interface Sci. 1980, 74, 572. (4) Astumian, R. D.; Sasaki, M.; Yasunaga, T.; Schelly, Z. A. J . Phys. Chem. 1981.85, 3832. (5) Ikeda, T.; Sasaki, M.; Hachiya, K.; Astumian, R. D.; Yaunaga, T.; Schelly, Z. A. J . Phys. Chem. 1982, 86, 3861. (6) Sasaki, M.: Mikami, N.; Ikeda, T.; Hachiya, K.: Yasunaga, T. J. Phys. Chem. 1982,86, 5230. (7) Sasaki, M.; Moriya, M.; Yasunaga, T.; Astumian, R. D. J. Phys. Chem. 1983.87, 1449.
T.J . Colloid Interface Sci. 1978. 67.
(8) Mikami, N.; Sasaki, M.; Kikuchi, T.; Yasunaga, T. J. Phys. Chem. 1983, 87, 5245. (9) Hachiya, K.; Sasaki, M.; Nabeshima, Y.; Mikami, N.; Yasunaga, T. J Phvs. Chem. 1984.88. 1623.
(io) Sasaki, M.; Negishi, H.; Inoue, M.; Yassunaga, T.J. Phys. Chem.
1984, 88, 3082. (11) Astumian, R. D.; Schelly, 2. A. J . Am. Chem. Sot. 1984, 106, 304. (12) Hachisu, S.; Kobayashi, Y.; Kose, A. J . Colloid Interface Sci. 1973, 42. 342.
0022-3654/87/2091-4827$01.50/0
Very recently, similar ordered structure has also been found in very dilute solution of proteins, peptides, and t-RNA.I6-" The polystyrene latex system received much attention as a model system for the ordered structure of macromolecules in solution. The dynamic properties of ions in the electrical double layer of the solid particle may play an important role in the ordering of the particles, macromolecules, and ions. The purpose of the present study is to elucidate the kinetic properties of the hydrogen sulfate group existing on the polystyrene particles, using the electric field pulse technique with conductivity detection, and to test the Astumian-Schelly theory.
Experimental Section The electric field pulse apparatus was described previously in Polystyrene latex was supplied by Prof. N. Ise of Kyoto University and the preparation and purification was described e1se~here.I~ The mean diameter of the polystyrene latex particles was 1340 A and the surface charge density 1.04 pC cm-*. Sodium hydroxide was purified with methyl alcohol and potassium chloride was used without further purification.
Results and Discussion Single relaxation was observed in aqueous suspensions of monodisperse polystyrene latex by using the electric field pulse technique with conductivity detection. A typical relaxation curve observed is shown in Figure 1, where the direction of relaxation signal indicates an increase in the conductivity of the suspension during the relaxation. The electric field intensity, E , dependence , of the relaxation time, 7,and the relaxation amplitude, A K / Kwhere (13) Takano, K.; Hachisu, S. J . Colloid Interface Sci. 1978, 66, 130. (14) Ise, N.; Okubo, T.; Kitano, H.; Sugimura, M.; Date, S. Naturwissenschuften 1982, 69, 544. (15) Ise, N.; Okubo, T.; Sugiyama, M.; Ito, K.; Nolte, H. J. J. Chem. Phys. 1983, 78, 536. (16) Ise, N.; Okubo, T. Acc. Chem. Res. 1980, 13, 303. (17) Patkowski, A.; Kulari, E.; Chu, B. J . Chem. Phys. 1980, 73, 4178. (18) Giordan, R.; Maisano, G.; Mallamace, F.; Micali, N.; Wanderlingh, F. J. Chem. Phys. 1981, 75, 4770.
0 1987 American Chemical Society
4828
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
I\
A
0
Sasaki et al.
I
1 2 3 4 5 6 7 6 9 1 0 t , 10.~
Figure 1. Typical relaxation curve in the aqueous suspension of monodisperse polystyrene latex by using the electric field pulse technique with conductivity detection at E = 9.0 X 10' V cm-I and 25 ' C . Sweep, 10 psldiv; particle concentration, 10% v/v.
2
0
5 CKCll ,
10 mol dm-3
15
Figure 3. Plot of the reciprocal relaxation time vs. the concentration of potassium chloride added to the 10%v/v suspension of polystyrene latex. The arrow indicates the order-disorder transition point of polystyrene latex particles.
6
7'5 -
3
4
5-
0
m
P
h
0
-
v
h
I-'
u
.
0 m
2.5-
0
2 %
5
10
3
3.5
4
E , lo3 Vcm-'
Figure 2. Electric field intensity dependence of the reciprocal relaxation time (0) and relaxation amplitude ( 0 )in the 10% v/v suspension of polystyrene latex at 25 OC. The dashed line shows the theoretical straight line evaluated by Onsager's theory for dissociation field effect. K is the conductivity, are shown in Figure 2. As can be seen from this figure A K / Kis proportional to E , while 7-l is independent of E . These tendencies are similar to those reported on the dissociation field effect in aqueous suspensions of ferric oxides.' According to Onsager's theory of the dissociation field effect for weak ele~trolyte,'~ A K / Kis expressed by
where a is the degree of dissociation, u1 and u2 are the mechanical mobilities of ions, and the other symbols stand for their customary meanings. If u2 for a charged colloidal particle is negligible, the / ~ Eeq 1 is calculated to be 6.5 theoretical value of ~ ( A K / K ) from X lo-' cm V-' with the experimental value of a = 0.298. This value is in good agreement with the value obtained from the slope of the solid straight line in Figure 2 ( 6 . 2 X cm V I ) . This agreement leads us to the conclusion that the relaxation observed is due to the dissociation field effect of some reaction on the surface of the latex. On the other hand, it has been well-known that an ordered state of monodisperse latex particles is formed under high particle concentration and extremely low ionic strength, and is drastically diminished by the addition of about mol dm-3 solution of ele~trolyte.l*~'~ Thus, the KC1 concentration dependence of 7-l was determined and the result is shown in Figure 3. As can be seen from this figure, in the range below [KCI] = 2 X mol dmw3,7-l deviates from the tendency of the major portion of the curve. In the vicinity of the salt concentration of [KCl] = 7 X mol dm-3, where 7-l shows minimum, the (19) Onsager, L. J . Chem. Phys. 1934, 2, 599.
PH
Figure 4. pH dependence of the reciprocal relaxation time in a 4% v/v suspension of polystyrene latex at E = 9.0 X lo' V cm-' and 25 OC. beautiful iridescence in the suspension caused by the ordered state of polystyrene latex particles drastically diminishes. At the higher salt concentration range, the suspension has a milky white color, where only disordered polystyrene particles exist. These facts suggest that the minimum of 7-1 is caused by the order-disorder phase transition of polystyrene particles coupled with some chemical reaction in the suspension. It should also be noted that hydrogen sulfate groups (-OS03H) exist on the surface of polystyrene latex particles which are partially dissociated. The degree of dissociation, a, depends generally on pH. Thus, the pH dependence of 7-I was determined and the results are shown in Figure 4. As can be seen from this figure, 7-I shows a minimum at pH 3.5. The association-dissociation reaction of the hydrogen sulfate group, -OS03H, is described as kl
-OSO3H + -OS03k-1
+ H+
(1)
where ki are the rate constants. According to Davis et al.'s theory,20the acidity constant, Kin a heterogeneous system is given by K=
[-OSO3H]
-
[-OSO,H]
(20) Davis, J. A.; James, R. 0.;Leckie, J. 0.J Colloid Interface Sci. 1978, 63, 480. (21) Mikami, N.; Sasaki, M.; Hachiya, K.; Astumian, R. D.; Ikeda, T.; Yasunaga, T. J . Phys. Chem. 1983, 87, 1454. (22) Astumian, R. D.; Sasaki, M.; Schelly, 2. A,; Yasunaga, T. J . Phys. Chem., to be submitted for publication,
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4829
Kinetics of OS03H on Polystyrene
I
0.5
0
0
1
o!
Figure 5. Plot of pK in eq 3 vs. cy: (0)salt free suspension; ( 0 )constant ionic strength ( I = 5 X lo").
I
I
0.5 1 (C-OSO;I+ Ch)exp(-e$)
1.5
, mol d m 3
Figure 6. Plot of i'exp(-(eqo/2kBT))vs. the concentration term in eq
4.
TABLE I: Equilibrium and Kinetic Parameters of Association-Dissociation of the Hydrogen Sulfate Group on the Surface of Polystyrene Latex at 25 OC 10-4k1int, s-l 10-5k-lint,mol-' dm s-l lopnt,mol dmA3 9f5 8 f l 1.1 f 0.6 (0.79)" a
Determined statically.
where \ko is the surface potential, the superscript "int" denotes intrinsic, and the other symbols have their customary meaning. This equation is conveniently rewritten as
The dependence of pK on the degree of dissociation, a, is shown in Figure 5. Under constant ionic strength ( I = 5 X M), linear relationship between pK and a was obtained, except for the higher a region. The difference between the results obtained under constant ionic strength and in salt-free suspension is due to a shielding of charged sites -OS03- by the cation, C+ -OSO
