J. Phys. Chem. 1988, 92, 3905-3910 surfactant concentration, mol/cm3 oil concentration, mol/cm' protein concentration, mol/cm3 tracer concentration, mol/cm3 water concentration, mol/cm3 water concentration in the reference state reverse micelles number density before the uptake empty reverse micelles number density filled reverse micelles number density NO/("PN) Ne/(npNl Nr/(nfl
rP Sa
4
elementary charge Iq12xaIzlI1 / 8 * d Trp water core radius of the empty reverse micelles after the uptake, A water core radius of the filled reverse micelles negative tracer ion radius protein counterion radius positive tracer ion radius surfactant counterion radius reverse micelle water core radius before the uptake protein radius surface of the surfactant polar head, A2 mean protein surface for ionized residue absolute temperature, K 4~rp2IzaI/SaIz1I 4~rp21zpl/Spl~,l
protein volume, A' water volume, A3
3905
water/AOT molar ratio water/AOT molar ratio in the filled reverse micelle na/Gnp rs/rp rf/rp
absolute value of the surfactant polar head charge absolute value of the negative tracer ion charge absolute value of the protein counterion charge absolute value of the positive tracer charge absolute value of the surfactant counterion charge absolute value of the mean charge of a protein residue absolute value of the corrected protein counterion charge absolute value of the corrected surfactant counterion charge free energy change for the protein inclusion, kcal/mol G"I(Nk7'); reduced free energy reduced form of the electrostatic energy contribution to the free energy reduced form of the counterions mixing contribution to the free energy reduced form of the reverse micelle mixing contribution to the free energy reduced form of the electrostatic entropy contribution to the free energy dielectric permittivity dielectric constant of the water layer near the protein and at the inner surface of the reverse micelle protein surface charge density, q / A 2 Registry No. RNase, 9001-99-4; AOT,577-1 1-7; lysozyme, 90016 3 - 2 ; chymotrypsin, 9004-07-3; cytochrome c, 9007-43-6.
Permittivity of a Suspension of Charged Spherical Particles in Electrolyte Solution. 2. Influence of the Surface Conductivity and Asymmetry of the Electrolyte on the Lowand High-Frequency Relaxations Constantino Grosset Instituto de Fisica. Universidad Nacional de Tucuman, (4000) San Miguel de Tucuman, Argentina, Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina, and Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 191 04 (Received: June 1 , 1987; In Final Form: November 9, 1987)
A theoretical treatment is presented of the dielectric properties of suspensions of charged spherical particles in electrolyte solution. It is based on a simple model of counterion polarization, which was first developed for the case of highly charged particles in symmetric electrolytes. This model is now extended to the general case of particles with arbitrary charge in nonsymmetric electrolytes, and to the entire frequency spectrum. Analytical expressions are deduced for the low- and high-frequency relaxation parameters. The predictions of the theory agree with available experimental data.
1. Introduction T h e dielectric behavior of suspensions of charged micron-sized particles in aqueous electrolyte is characterized by two relaxations. A t low frequencies (kilohertz), a n extremely high amplitude relaxation is found, with permittivity values reaching hundreds or even thousands of dielectric A t higher frequencies (typically tens of megahertz) there is a m u c h smaller relaxation with a n amplitude of a few dielectric ~ n i t s . ~ . ~ These phenomena have been theoretically studied, with most attention given to t h e large dispersion a t t h e low-frequency part of t h e spectrum. T h e observed behavior was first interpreted as due to the diffusion of bound counterions moving along the surface of the particle^.^^^ Recent studies show, however, t h a t t h e mechanism controlling this relaxation is t h e diffusion of ions in t h e bulk electrolyte around t h e particle^.^-'^ Address for correspondence: The Catholic University of America, Department of Physics VSL, 620 Michigan Av. NE, Washington, DC 20064. 0022-3654/88/2092-390.5$01.50/0
Due to their mathematical complexity, these theories a r e usually limited t o t h e case of large particles in symmetric electrolytes, (1) Schwan, H. P.; Schwarz, G.; Maczuk, J.; Pauly, H. J . Phys. Chem.
1962, 66, 2626.
(2) Ballario, C . ; Bonincontro, A.; Cametti, C. J . Colloid Interface Sci.
1979, 72, 304.
(3) Springer, M. M.; Korteweg, A.; Lyklema, J. J . Electroanal. Chem. 1983, 153, 55.
(4) Lim, K.-H.; Frances, E. I. J . Colloid Interface Sci. 1986, 110, 201. (5) Ballario, C.; Bonincontro, A.; Cametti, C. J . Colloid Interface Sci. 1976, 72, 304. ( 6 ) Sasaki, S.; Ishikawa, A,; Hanai, T. Biophysical Chem. 1981, 14, 45. (7) Schwarz, G. J . Phys. Chem. 1962, 66, 2636. (8) Grosse, C.; Foster, K. J. Phys. Chem. 1987, 91, 6415. (9) Dukhin, S. S.; Shilov, V . N. Dielectric Phenomena and the Double Luyer in Dispersed Systems and Polyelectrolytes, Halsted: Jerusalem, 1974. (IO) Fixman, M. J . Chem. Phys. 1980, 72, 5177. (11) Chew, W. C.; Sen, P. N. J . Chem. Phys. 1982, 77, 4684. (12) Fixman, M. J . Chem. Phys. 1983, 78, 1483. (13) O'Brien, R. W. Adu. Colloid Interface Sci. 1983, 16, 281.
0 1988 American Chemical Society
3906 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 such as KCl. Thev also cannot be extended to cover the entire frequency range, except by matching the limiting behaviors of different models.” In a recent study,I8 we presented a simple model for the dielectric properties of suspensions of charged particles in electrolyte solution. Due to the initial assumptions used, the results pertained only to the low-frequency part of the spectrum and are only valid for highly charged particles in symmetric electrolytes. Nevertheless, they agree well with experimental data without the use of any adjustable parameter. Due to the simplicity of the model, these initial assumptions can be removed. W e extend its validity to the general case of particles with arbitrary charge in nonsymmetric electrolytes, and to the entire frequency spectrum.
2. Model A charged particle in an electrolyte is surrounded by a layer of ions of predominantly a single sign. Because of this, the field-induced motion of the two types of ions from the bulk electrolyte is different. When a counterion approaches the particle, it encounters a region of high counterion density along which charge can be rapidly transferred to the opposite side. A co-ion does not have this highly conductive path, so that it must either remain on the original side of the particle or move around it under the action of electric and diffusive forces. Therefore, a charged particle, together with its counterion layer, essentially behaves as a conductor as far as the motion of counterions is concerned, and as an insulator, as judged by the motion of co-ions. In the model presented in ref 18 the counterions bound to the particle are represented by a thin layer characterized by a surface conductivity. This layer is in electrical contact with the flow of counterions in the electrolyte, but insulated from the flow of co-ions. It is further considered that the charges and mobilities of the two types of ions have the same value and that the surface conductivity is infinitely high. This last assumption reduces the frequency response of the system to a single low-frequency relaxation. Because of this, the analytical expression for the permittivity can be obtained without making any further assumptions regarding the relationship between the particle size and the Debye screening length. In what follows, we shall extend this formalism to the general case where the charges and mobilities of the two types of ions can have any value. We shall also consider that the surface conductivity which characterizes the counterion layer has a finite value. This last generalization leads to the appearance of an additional high-frequency relaxation. Both relaxations are well separated in frequency only when the radius of the particle is much greater than the Debye screening length. In this extended model this is the only case when an analytical expression for the permittivity can be obtained. We shall use the following nomenclature for the system in the presence of an applied field Eo exp(iw2). The charged particle has a radius R and is composed of a material whose relative permittivity is e*, independent of frequency. It is surrounded by a conducting layer which has a surface conductivity X and bears a field-induced surface charge density p exp(iwt) cos (e), where 0 is the polar angle relative to the direction of the applied field. The electrolyte of relative frequency independent permittivity e , contains two types of ions characterized by their charge *e+-, mobility u+-, and equilibrium density N+-. Its generalized conductivity is K, = u, iweoem,where u, = N+e+u++ N-e-uis the frequency independent conductivity and to is the absolute permittivity of free space. We shall consider that the particle is negatively charged, so that the counterions are positive.
+
(14) 143, 1. (15) (16) (17) (18)
Lyklema, J.; Dukhin, S. S.; Shilov, V. N. J. Elecfroanal. Chem. 1983, Chew, W. C. J . Chem. Phys. 1984, 80, 4541. Mmdel, M. and Odijk, T. Annu. Reu. Phys. Chem. 1984, 35, 7 5 . 0 Brim, R. W. J. Colloid Interface Sci. 1986, 113, 8 1. Grosse, C.; Foster, K. J . Phys. Chem. 1987, 91, 3073.
Grosse
3. Solutions for the Potentials and the Ion Densities The field-induced variations of the concentrations of the two types of ions, exp(iwt), can be obtained from the continuity equations re+-iwp+- = div J + -
(1)
where J+ - are the current densities determined by J f - = -N+-e+- + u grad &, =F e+-D+- grad p + -
(2)
In this expression 0, exp(iwt) is the electric potential in the electrolyte, which is determined by the Poisson equation
V24, = -(e+p+ - e-pL-)/(eOtm)
(3)
while D+- are the diffusion coefficients for the two types of ions. These coefficients are related to the mobilities by means of the Einstein relation D + - = u + - k,T/e+(4) where kB is the Boltzmann constant and T the absolute temperature. Combining eq 1-3 gives the following equations for the ion densities V2e+-p+- - [iw/D+-
+ ( ~ + - ) ~ / 2 ] e + - p ++( ~ + - ) ~ e - + p - += / 2O (5)
x+- are the reciprocals
where
(x’
-)2
of the Debye screening lengths:
= 2N’ -e+ -u+ -/(eotmD+-)
(6)
The equations to follow are simplified by introducing a notation in which the asymmetries of the electrolyte are explicitly shown. We use the following definitions:
+ e-)/2 u + - = (1 f k)(u+ + u-)/2 e+- = (1 f j)(e+
(7) (8)
and, due to the neutrality of the electrolyte N+- = (1
T
j)(N+
+ N)/2
(9)
The solutions of eq 5 are e+p+ = [AQ(r) + W r ) ( v - j ) / ( I - j ) l cos (0) e-w- = [-AQ(r)(V-j)/(l
+j)
+ BP(r)I
COS
(0)
(10) (11)
where A and B are integration constants, while Q(r) = exp(-qxr) [(qXr)-]
+ (qxr)F21
p(r) = exp(-pxr)[@xr)-’ + @ x ~ ) - ~ I
(12) (13)
are functions of the radial coordinate r multiplied by the reciprocal of the “effective” Debye screening length x, where
x2 = (N+ + N-)e+e-/(eoe,kBT)
(14)
and of q2 = [ l
+ 2iF(1 - j k ) / ( l
+ S]/2
(15)
p2 = [l
+ 2iF(1 - J k ) / ( l - k 2 ) - S ] / 2
(16)
- k2)
The other symbols are V = -2iFQ - k ) / ( l - k 2 ) + S S2 = 1
+ 4iFjQ - k ) / ( l
- k 2 ) - 4 P Q - k)’/(1 - k2)’
(17) (18)
and F=
WCOC~/U,,,
(19)
The normalized frequency F is the frequency of the field divided by the characteristic frequency of the electrolyte.
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3907
Dielectric Properties of Suspensions 1
,.;, -
----_ _ _ _ _ - - - . -,- _ ,_--
,e+-/---
-6
-7
-5
-3
-4
-2
-1
I
E
Log F 3
4
Figure 1. Real (broken lines) and imaginary (full lines) parts of the dipolar field coefficient as a function of the normalized frequency. The curves were computed from eq 44 for Z = 1000, and different values of
L. The expressions obtained for the ion densities make it possible to solve eq 3 for the potential in the electrolyte. This leads to +m
=
[-
A ( V + 1)Q(r) - B(V- l)P(r) eo',,,( 1 + j ) x 2 q 2 eoem( 1 - j ) x 2 p z
C +- Eor r2
1
Figure 2. Real part of the permittivity minus the infinite frequency limit, as a function of the normalized frequency. The curves were computed from the sum of eq 52 and 55 for Z = 1000, u = 0.01, and different values of L.
where po is the equilibrium surface density of ions in the counterion layer. Assuming that the mobilities in the two regions are essentially the same, eq 26 can be written as
cos ( 8 ) (20)
The potential inside the particle, from the solution of the Laplace equation, has the form +p = -Kr cos (e) (21)
For large values of the surface conductivity, this condition reduces to the simple form used in ref 18
In the above expressions C and K are integration constants.
while, in the limit when the surface conductivity tends to zero, it states that the surface charge density must vanish. In this last case, eq 24 reduces to the same form as that of eq 25, leading to a symmetrical behavior of the two types of ions. The system of eq 22-25, 27 becomes
4. Dipolar Field Coefficient In order to determine the unknown constants A, B, C, K , and p , we shall generalize the boundary conditions used in ref 18. I. Continuity of the potential: +,(RJ) = &(R,e)
(22)
11. Discontinuity of the displacement: (V
2x1 -
+ l)G
(V- l ) H X , - EX3 - X4 x5 = -1 2(1 + j)q22, 2( 1 - j ) p T
111. Continuity of the surface charge density: -imp cos
(e) = -We'd-
:lR :d
dp+l
- e+D+-
dr
- 2xK cos
R
(e)
IV. Value of the radial component of the current density of negative ions. Since the negative ions are excluded from the counterion layer, the radial component of the current density of these ions must vanish at r = R:
V. Value of the density of positive ions at r = R. This condition is not obvious since the positive ions can freely exchange with the ions in the counterion layer. In the absence of an applied field, this layer is in equilibrium with the surrounding electrolyte. This state is characterized by the densities of the positive ions in the two neighboring regions. In order to preserve this equilibrium when a field is applied, the relative change of the ion density on the two sides of the boundary must be the same P+(R,O)/N+ = P cos ( O ) / P o
(26)
2(1
iFG + k ) X , + -X2 q2z2
x, -
- 2Lx3
2(1 ~
+ 2iFX4 +
+ k )x4 + -x5 V-j
L
1- j
iF( V - j ) H
x5 = (1 - _j )_ p W -(1 + k) (31)
=0
(33)
3908 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 G = [(qZ)2 + 2 q z
+ 2]/(qZ + I) = [(pZ)2+ 2pZ + 2 ] / @ Z + 1)
(39)
H
(40)
E = ep/e,
(41)
L = 2X/(Ru,)
(42)
Z = xR
(43)
Grosse where e(m) is the permittivity at a frequency intermediate between the low- and high-frequency relaxations. For values of F of the order of or greater than one, the dipolar field coefficient reduces to
E-1 E+2 3 E+2
XI =
Equations 29-33 lead to the following solution for the dipolar field coefficient in the case of a symmetric electrolyte E-1 XI = E+2 2H -E(L iFE) ( L - E ) C I -(L - E)(G E ) 3 Z2L 2H E 2(L iFE) + ClC2+ -[GC2 - 2(L - E ) ] Z2L (44)
-+ L Z Y ( L - E ) - 2E
+ 4( 1 + i
F
2
+
+
+
+
where
+
where
C2 = L
e(@)
+ iF(G + H )
(45)
+ 2 + iF(E + 2)
(46)
C1 = H
+ W)(1 + iW) l+W+iW = Z2F/2
3V€,
+ w)/4]/[(X+
[3Z2(1
2(x+
2)2(1 + 2 W + 2w?) + 2 ) ( x + 1 1 ~ +3 (x+ 1 ) 2 w 4 1 (52)
(19) Garcia, A,; Grosse, C.; Brito, P. J . Phys. 139.
+
=R~/D
(56)
This value is almost independent of the surface conductivity, Figure 2, showing that this relaxation is governed by the radial diffusive motion of ions in the bulk electrolyte around the particle, rather than by the tangential flow of counterions near its surface. The amplitude of the broad low-frequency relaxation
YVtmZ4L4 GLF =
16[ZL(L
+ 1) + 212
(57)
is usually very large. It attains its maximum value for high surface conductivities ( L >> l), in which case eq 57 reduces to the simple result deduced in ref 18. The dielectric increment only becomes a function of the surface conductivity when L 5 I , Le., when the value of surface conductivity divided by the radius of the particle is comparable to the conductivity of the electrolyte. In this situation the amplitude of the relaxation rapidly decreases with diminishing L. The conductivity of the suspension, in contrast, is much more sensitive to changes in L. Its value can be derived from the dipolar field coefficientI8
(50)
-
3
'TLF
The permittivity e(@) of the suspension can be now deduced by using the general expression valid for low values of the volume fraction v of the particles:
e(@) - 4 m )
[ ( L- E ) / ( L + 2)12 (55) E + 2 I + [F(E 2 ) / ( L + 2 ) J 2
+-
6. Discussion ( a ) Effect of Finite Surface Conductivity. The mean relaxation time of the broad low-frequency relaxation is approximately
(49)
The final result for the low-frequency relaxation in symmetric electrolytes is
E-1 E +2
=-
This result corresponds to the simple Maxwell-Wagner relaxation for a suspension of insulating particles covered by a conducting layer.20 The complete relaxation spectrum, obtained by adding eq 52 and 5 5 , is represented in Figure 2. It consists of a broad highamplitude relaxation at low frequencies, and a single time constant low-amplitude relaxation at high frequencies. While in most experimental studies only the low-frequency relaxation has been in~estigated,'-~ this general behavior is in qualitative agreement with the few studies in which measurements were performed over a wide frequency range.si6
5. Low- and High-Frequency Relaxations For low values of F, the dipolar field coefficient, eq 44, reduces to H(l - X / 2 ) - 1 XI = (47) H(l + X ) + 2 where
2(1
- em
3ue,
The general behavior of the real and imaginary parts of XI as a function of frequency, is shown on Figure I . This figure shows that the system undergoes two relaxations: (1) a low-frequency relaxation corresponding to a frequency such that Z2F is of the order of unity; and ( 2 ) a high-frequency relaxation which occurs at a frequency such that F is of the order or greater than unity (the actual condition depends on the value of L ) . These two relaxations become independent of one another when their characteristic frequencies strongly differ, that is, for Z2 >> I . Since this is the only case when an analytical expression for the permittivity can be deduced, we shall assume in all the forthcoming calculations that this condition is fulfilled. The low-frequency relaxation disappears in the limit of vanishing surface conductivity. Equation 44 reduces then to the result deduced in ref 19 for the case of suspensions of noncharged insulating particles.
H=
(54)
Equation 53 shows that in the two limiting cases: L >> E or L = 0, the high-frequency relaxation reduces to a single Debye term. The permittivity expression then becomes
+
+
+ i F ) 1 / 2+ ( i F ) I / 2
Y = (I
. which leads to
o(0) 3uu,
u,
- Z L ( L - 2) - 4 - 4ZL(L + 1) + 8
(59)
This expression changes sign for a value of L close to 2 so that,
D: Appl. Phys. 1985, 18, (20) OKonski, C. T. J . Phys. Chem. 1960, 64, 605
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3909
Dielectric Properties of Suspensions for lower values of L, the particles behave as if their effective conductivity were lower than that of the bulk electrolyte. It also shows that static conductivity measurements appear to be a good method to determine the surface conductivity, at least for relatively low values of L. The difference of the behavior of eq 57 and 59 as functions of L, arises because the static permittivity is related to the charge densities near the surface of the particle, while the static conductivity is determined by the flow of ions around it. Negative ions always move as if the particle together with its layer of counterions were insulating, while the movement of positive ions strongly depends on the surface conductivity. For high values of L, their flow corresponds to a perfectly conducting particle18 while, for low values, the lines of flow of both types of ions coincide. For high surface conductivities, the value of L has no influence on the amplitude of the high-frequench relaxation GHF
=
3(L - E ) 2 ~VC,
(E + 2)(L
14
+ 2)2
Therefore, for large values of L, measurements of this highfrequency relaxation time appear to be the only sensitive method for the determination of the surface conductivity. For values of L smaller than about 1, the amplitude of the high-frequency relaxation starts to decrease rapidly, while its relaxation time approaches the relaxation time of the electrolyte 0,) *
Even for large surface conductivities, the relaxation amplitude at high frequencies is very small, despite the high value of the peak of the imaginary part of the dipolar field coefficient, shown in Figure 1. This is due to the factor 1 / F appearing in eq 51. Because of this factor, precise dielectric measurements of the high-frequency part of the spectrum are very difficult to perform (this contrasts with the conclusion in ref 17). A way of overcoming this difficulty appears to be the particle rotation technique21 in which the measured quantity is proportional to Im (XI) without the 1 / F factor. ( b ) Effect of Electrolyte Asymmetry. The parameters j and k, which characterize the asymmetry of the electrolyte, do not directly affect the high-frequency relaxation, at least for high values of L. However, this relaxation is indirectly sensitive to the nature of the electrolyte, since the surface conductivity is different for different types of counterions. These conclusions are in agreement with recent results obtained by using the particle rotation technique.22 The amplitude of the low-frequency relaxation in the general case of asymmetric electrolytes is
+ 16[ZL( 1 + j ) ( L + 1 + k) + 2( 1 + k ) 2 ] 2 9 v ~ , Z ~ L ~ ( lj)2(1 - k2)
GLF =
-3
-2
-1
0
1
Log F
3
4
Figure 3. Comparison of the exact solution of eq 44 and 51 (broken lines) and the analytical results eq 52 and 55 (full lines). The curves were computed for Z = 10, u = 0.01, and different values of L.
but does determine its relaxation time:
(eo€,/
2
(62)
This explicit functional dependence of the dielectric increment on the asymmetry of the electrolyte is further complicated by an implicit dependence through Z and L. The dependence of the relaxation amplitude on the charge of the ions can be seen from eq 14, 43, and 62. Changing the electrolyte from KCI to CaCl, 0’ = 0.33,k = 0.1l), for example, while maintaining the concentration of negative ions at a constant value, increases 2? by 50%. Therefore, the low-frequency relaxation amplitude should also increase by almost 50% if the surface conductivity is high. This increase should be lower, or
even decrease, for low values of the surface conductivity. For ions with the same charge value (j = 0) and at a constant concentration, the value of Z remains constant. An asymmetry in the ion mobilities should then always decrease the relaxation amplitude when the surface conductivity is high. But when L is low, the dielectric increment can either increase or decrease with the relative change in the mobilities. Measurements of this dependence have been reported in ref 3. Experimentally the relaxation amplitude increases by 20-40% for each member of the series in the order LiCl < KC1 < HCI. This order is opposite to that expected on the basis of the theory presented in ref 14 and 23. Our own results, assuming high values of L, appear to be in between those of that theory and experiment, since they predict LiCl < KCI and HCI < KCI when the concentration of the electrolyte is futed. Furthermore, our calculations leads to a broad low-frequency relaxation,18which is in agreement with the experimental evidence of these and other author^,^,^ but contrasts with the theory of ref 14 which predicts a simple Debye-type behavior. Other experimental results reported in ref 2 show that the dielectric increment in LiCl is about 20% greater than in KCI when the conductivity, rather than the concentration of the electrolyte, is maintained at a constant value. Under this condition we obtain 2 2
= Z&(1
-
k)
Therefore, the relaxation amplitude for LiCl (k = -0.19), should be nearly 15% greater than for KCI, in reasonable agreement with experiment.
7. Conclusion In this work, based on the simple model for the counterion polarization presented in ref 18, we develop a complete theoretical treatment of the dielectric properties of suspensions of charged spherical particles in electrolyte solution. The whole frequency spectrum is covered (for the first time to the best of our knowledge), and the most general case of particles with arbitrary charge in nonsymmetric electrolytes is considered. Analytical expressions for the relaxation spectrum are deduced for the case when the radius of the particles is much greater than the “effective” Debye screening length in the electrolyte, eq 14. A comparison between a numerical solution of eq 44 and 5 1 and the analytical expressions 52 and 55 is presented in Figure 3. This figure shows that these expressions, deduced in the limit Z >> 1, remain approximately valid down to Z = 10, as long as the surface conductivity is not too low. The results obtained are compatible with our previous calculation’* for the low-frequency part of the spectrum, and with the
(21) Arnold, W. M.; Schwan, H. P.; Zimmerman, U.J. Phys. Chem. 1987, 91, 5093.
(22) Arnold, W. M., private communication.
(23) Lyklema, J.; Springer, M. M.; Shilov, V. N.; Dukhin, S. S. J. Electroanal. Chem. 1986, 198, 19.
3910
J. Phys. Chem. 1988, 92, 3910-3914
classical Maxwell-Wagner r e l a ~ a t i o n ' for ~ , ~the~ ~ high-frequency ~ part. The predicted functional dependences of the relaxation parameters with the surface conductivity of the particles and with the charge and mobility of the ions cannot be conclusively tested until reliable values for surface conductivities becomes available. Our prediction for the change of the dielectric increment with a change in the counterion mobility does not agree with previous theoretical result^'^^^^ but is consistent with some of the experimental evidencea2 In general this work tends to confirm our previous calculation.'8 It shows that the dielectric behavior of suspensions of charged
particles depends little on the asymmetry of the electrolyte or on the charge density of the particle's surface. Except when this charge density is very small, the particle behaves electrically as if it were surrounded by a perfectly conducting layer, which is in electrical contact with the counterions from the electrolyte but insulated from the co-ions. That this simple model is adequate suggests that low-frequency dielectric measurements are relatively insensitive to the detailed ion distribution in the proximity of charged particles.
Acknowledgment. We are grateful to Dr. K. Foster for numerous discussions and suggestions about this work.
Hydrogen Adsorption on Ultraviolet- Irradiated Magnesium Oxide Tomoyasu Ito,* Ayako Kawanami, Keio Toi, Toshiaki Shirakawa, and Taneki Tokuda Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Fukasawa, Setagaya- ku, Tokyo 158, Japan (Received: June 19, 1987)
The UV-irradiation-inducedadsorption of hydrogen below r c " temperature on MgO surfaces outgassed at 723 K was studied by using TPD and EPR techniques. All the active sites for the hydrogen adsorption, including thermally generated and irradiation-induced ones, could be systematically explained in terms of the coordinative unsaturation of the intrinsic surface ions: (1) The adsorption on the surface preirradiated in vacuo easily attained a saturation value of about 3 X lOI4 molecules m-2 and adsorbed hyrogen was desorbed at 530 K forming peak IW2 in TPD. The adsorption site consists of two aggregations of four 04c2ions and of four Mg4C2+ions located apart from the former; by the absorption of a photon at the four 04c2site long-lived 0- and F: centers are formed, on which hydrogen is adsorbed with homolytic dissociation. (2) The adsorption under the influence of the irradiation also proceeded and gave a broad TPD peak IW, at 3 2 0 K as well as peak IW2. The adsorption site for IW1 consists of an 03c2ion and an Mg3c2+(or Mg4cZ+)ion which are located separate from each other; in this case, however, the 0-and F:-type centers formed by the photon absorption are very short-lived even at 77 K. ( 3 ) In the dark only a pair of 3- and 4-coordinated ions, OLC2--MgLC2+, at the nearest lattice position can adsorb hydrogen with heterolytic dissociation as already shown in our previous paper.
Introduction Recent studies have accumulated increasing evidence that surface ions in positions of low coordination are closely linked with surface properties such as luminescence, chemisorption, and catalysi~.'-~ Most of these studies have been performed on the surfaces of alkaline-earth-metal oxides, especially on magnesium oxide, outgassed at high temperatures. The adsorption of hydrogen on the surface of MgO polycrystals is a system suitable for investigating such surface properties. We have studied this adsorption system in detail and found seven types of active sites labeled types Wz-W8.6-9 They have a common basic structure of an OLC2--MgLC2+pair (a subscript LC denotes a low coordination state), on which H2 is heterolytically dissociated. The difference in coordination number either of OLc2-or of MgLc2+ (1) Che, M.; Tench, A. J. Adu. Catal. 1982, 31, 7 7 . (2) Duley, W. W. Philos. Mag.B 1984, 49, 159. (3) Coluccia, S.; Tench, A. J. J . Chem. Soc., Faraduy Trans. 1 1983, 79, 1881. (4) Coluccia, S . ; Garrone, E.; Borello, E. J . Chem. SOC.,Faraday Trans. 1 1983, 79, 607. (5) Indovina, V.; Cordischi, D. J . Chem. Soc., Faraday Trans. 1 1982, 78, 1705. .. (6) Ito, T.; Sekino, T.; Moriai, N.; Tokuda, T. J . Chem. Soc., Faraday Trans. 1 1981, 77, 2181. (7) Ito, T.; Murakami, T.; Tokuda, T. J . Chem. Soc., Faraday Trans. 1 1983, 79, 913. ( 8 ) Ito, T.; Kuramoto, M.; Yoshioka, M.; Tokuda, T. J . Phys. Chem. 1983, 87, 441 1. (9) Ito, T.; Yoshioka, M.; Tokuda, T. J . Chem. SOC.,Faraday Trans. J 1983, 79. 2277. ~
produces the active sites different in adsorptive ability and the coordination number for each type of the active sites has been tentatively assigned.* UV irradiation changes mainly the electronic configuration of solids but not the geometric one and is known to be an alternative way to produce new active sites for the hydrogen adsorption on the surfaces of magnesium oxide.I0-l3 We already reported14 through the measurements of EPR spectra and volumetric adsorption amounts that the active sites on the MgO surfaces which had been produced by preirradiation with UV light in vacuo consist of monovalent surface anions, 0- centers,I5 in various tetragonal crystal fields in the surface region. The adsorption of hydrogen on these active sites results in the formation of F;-type centers.I4J6 It is also possible to adsorb hydrogen on the surfaces of MgO under UV irradiation in the presence of hydrogen.l0 The adsorption product in this case is also F,+-type centers. A preliminary experiment carried out in our laboratory, however, suggested that there is a large difference in the adsorption amounts between the (10) Tench, A. J.; Nelson, R. L. J . Colloid Interface Sci. 1968, 26, 364. (11) Lunsford, J. H . J . Phys. Chem. 1964, 68, 2312. (12) Harkins, C. G.; Shang, W. W.; Leland, T. W. J . Phys. Chem. 1969, 73, 130. (1 3) Shuklov, A. D.;Shelimov, B. N.; Kazanskii, V. B. Kinet. Katal.1977, 18, 413. (14) Ito, T.; Watanabe, M.; Kogo, K.; Tokuda, T. 2 Phys. Chem., N . F. 1981, 124, 83. ( 1 5 ) In this paper 0- center denotes an 0-ion itself and/or a V;-type
center, is., a hole trapped at a surface cation vacancy. (16) F;-type center denotes an:F center and/or an F:(H) center; F: is an electron trapped at a surface anion vacancy and F,+(H) is Fs+with a nearby hydrogen, and both of them give similar EPR signals.
0022-3654/88/2092-3910$01.50/0 0 1988 American Chemical Society
