J. Phys. Chem. 1984,88, 420-424
420
sodium, or binary combinations of the cations. A few of these are summarized in Table 11. It should be noted that only crystals containing lithium ions have v 1 mode frequencies above 1000 cm-l, suggesting that the interaction of the lithium ion with the oxygen atom of the sulfate ion stiffens the stretching force constant of the sulfate ion, leading to a somewhat higher v 1 frequency. In this regard the three frequencies of v 1 reported here for the LiN a S 0 4 crystal are particularly interesting. The six sulfate ions in a unit cell of LiNaS04 are distributed with two pairs on Wyckoff b sites and one pair on Wyckoff a sites. The resulting coordination of a lithium ion by the oxygen atoms of nearby sulfate ions is not a perfectly regular tetrahedron as in the case of LiKS04. In LiNaS04 the lithium ion-oxygen atom distances range from 1.872 to 2.087 A. The higher frequency v, component at 1026 cm-l may, to a greater extent, involve sulfate ions which are closer to lithium ions than the lower frequency v1 components. Of course (14) V. Ananthanorayanon, Ind. J . Pure Appl. Phys., 1, 58 (1963).
(15) J. Hiraishi, N. Taniguchi, and H. Takahashi, J . Chem. Phys., 65, 3821 (1976).
each v 1 component contains some contribution from the intramolecular motion of each sulfate ion since the Wyckoff a and b sites have the same point group symmetry (C,) and hence each contribute to the AI factor group vibrations. However, this view is consistent with the striking temperature dependence of the high frequency v 1 component and the previously mentioned study of the external optic modes.s As described earlier, an A, mode at 63 cm-' attributed to the librational motion of the sulfate ions appeared to soften with increasing temperature. This would require large sulfate ion vibrational amplitudes which primarily consist of oxygen atom motion. The lithium ion-oxygen atom interactions are strongly perturbed by the increasing oxygen atom motion, and this would be reflected most strongly in the internal mode most dependent on those interactions, namely, the highest frequency A, component of the v 1 vibrational multiplet.
Acknowledgment. This material is based upon work supported by the National Science Foundation under Grant No. DMR8001666. Registry No. LiNaS04, 13568-34-8; LiKS04, 14520-76-4.
Particle Adhesion and Removal in Model Systems. 10. Effect of Chelating Species on the Hematite/Steel System C.-C.Lo, E. MatijeviL,* and N. Kallay Department of Chemistry and the Institute of Colloid and Surface Science, Clarkson College, Potsdam, New York 13676 (Received: June 22, 1983)
With small amounts of properly chosen additives such as EDTA (ethylenedinitrilotetraacetic acid), DFOB (desferrioxamine B, a trimeric hydroxamic acid derivative), and Co(bpy),(ClO& the deposition of monodispersed spherical hematite (a-Fe203) particles on stainless steel can be enhanced under the conditions which otherwise allow for little or no adhesion. In some cases, nearly maximum rates of deposition are secured at concentrations of the added chelating agents or metal chelates considerably smaller than the critical concentrations needed, if indifferent electrolytes are used. Detachment of adhered hematite particles from the same substrate is found not to be affected by the elution of the packed bed with EDTA solutions in strongly alkaline media.
Introduction Using the packed column technique, systematic studies on deposition of monodispersed colloidal particles (a-Fe203, flFeOOH, and Cr(OH),) onto solid surfaces (steel, glass) and on their detachment from these substrates have been carried out in this laboratory'-' over the past few years. It has been reported that the optimum uptake occurs when the particles and the adsorbent are of opposite charge. When both surfaces carry the charge of the same sign and of large magnitude the adhesion is prevented, as long as the ionic strength of the medium is low. In the latter case deposition can be induced either by adding an inert electrolyte in sufficiently high concentration or by adsorbing on one of the surfaces ionic species that can reverse the original charge. It has also been shown that adhered particles can be ~~~~~~~
~
~
~
(1) J. E. Kolakowski and E. MatijeviE, J . Chem. Soc., Faraday Trans. 1, 75, 65 (1979).
( 2 ) R.J. Kuo and E. MatijeviE, J . Chem. SOC.,Faraday Tram. I , 75,2014 (1979). (3) R. J. Kuo and E. MatijeviE, J . Colloid Interface Sci., 78,407 (1980). (4) N. Kallay and E. MatijeviE, J . Colloid Interface Sci., 83, 289 (1981). ( 5 ) J. D. Nelligan, N. Kallay, and E. MatijeviE, J . Colloid Interface Sci., 89, 9 (1982). ( 6 ) N. Kallay, J. D. Nelligan, and E. MatijeviE, J . Chem. SOC.,Faraday Trans. I , 19, 65 (1983). (7) G. Thompson, N. Kallay, and E. MatijeviE, Chem. Eng. Sci., 38, 1901 (1983).
0022-3654/84/2088-0420$01 S O / O
released without the application of appreciable hydrodynamic forces if the composition of the surrounding solution is properly altered. The kinetics of particle removal has been analyzed in terms of one-, two-, and three-population models by taking the topology of the substrate surface into consideration. Obviously, colloidal forces play an important role in the control of the deposition and detachment processes. So far, most of the work has concentrated on the effects of such parameters as pH, ionic strength, particle size, flow rate, and temperature. Less attention was placed on the adsorption of solute species which may have a profound influence on the surface chemical properties of the interacting materials. In the present work, three different chelating agents or metal chelates were added in very small amounts to modify surface characteristics of hematite particles at appropriate pH values (below and above the isoelectric pints of hematite and steel). The conditions were chosen under which little or no uptake of dispersed solids was observed in the absence of such chelating agents (as long as the ionic strength was low) in order to evaluate the effects of these additives on particle adhesion. Attempts have also been made to elute the adhered particles in the packed bed by solutions of a chelating agent at various pH. The enhancement in deposition is relevant to a number of practical problems, especially to metal corrosion or deep bed filtering. In the latter case significant improvement can be achieved with media that fail to produce efficient filtration by 0 1984 American Chemical Society
Chelate Effects on Adhesion of Hematite on Steel altering the chemistry of the system rather than by merely changing the conventional parameters, such as particle size, flow rate, bed depth, or pH.
Experimental Section Materials. Spherical 316L stainless steel beads, having a diameter between 74 and 105 pm, were obtained from Nuclear Metals Inc. They were cleaned by stirring in 6 M H N 0 3 followed immediately by a thorough rinsing, first with doubly distilled water and then with ethanol. After this treatment the beads were dried in air at 100 OC. Hydrosols consisting of uniform hematite (a-Fe203)particles were prepared and purified as described earlier.* The particle size distribution, determined from electron micrographs, gave an average diameter of 0.12 pm with a standard deviation of 0.01 pm. EDTA (disodium ethylenedinitrilotetraacetate) was Baker Analyzed Reagent. The methanesulfonate salt of desferrioxamine B (DFOB) was kindly supplied by Ciba Pharmaceutical Co., Summit, NJ. Tris(2,2’-bipyridyl)cobalt(III) perchlorate, Co(bpy),(ClO,),, was previously synthesized in this laborat~ry.~ All other chemicals were of reagent grade and used without further purification. Methods. 1. Deposition. The assembly and the procedure for the use of the powder-bed column were described previo~sly.~,’ Steel beads (5 g) were added into the column which was immersed in an ultrasonic bath to remove any adherent microbubbles of air. The hematite sols were then passed through the bed at a flow rate controlled by a peristaltic pump. Experiments were performed in which either the steel powder or the hematite dispersions were treated with a chosen solution of a chelating agent prior to deposition. In those cases where the steel surface was modified, the beads were soaked with 30 cm3 of the solution of a chelating agent for a desired period of time. The bed was then rinsed with 30 cm3 of an aqueous solution having the same pH as the hematite sols. The experiments were carried out by passing the hematite suspension (containing no chelating agent) through the column. The effluent was collected at several different time intervals and the particle concentration was determined in each sample. In another series, the surface properties of hematite particles were modified by the addition of complexing species at appropriate pH values. Specifically, EDTA was used at pH 3 and 4, DFOB at pH 8, and C ~ ( b p y ) , ( C l O ~at) ~pH 10. Immediately before passing the hematite suspensions treated with a chelating agent through the column, the steel powder bed was rinsed with 30 cm3 of a supernatant solution obtained separately by centrifuging a portion of the same hematite sol, containing the same chelating species. This was done in order to minimize sudden changes in the aqueous environment of hematite particles, Le., not to change abruptly the equilibrium condition of the adsorbed chelating agents on the hematite surface. In all cases, the treatment took 0.5 h. The hematite particle number concentration was kept at 2 X lo8 particles/cm3 and the ionic strength at 1 X M. The concentration of the particles in the dispersion was determined by measuring the ratio of scattering intensities of vertically polarized blue light (436 pm wavelength) at an angle at 45’ relative to the intensity of the incident beam. This ratio was found to be linearly proportional to the number concentration of hematite for dilutions of interest in this work. 2. Detachment. Two methods for the preparation of samples of steel beads with adhered hematite particles have been used. In one series of experiments, 50 cm3 of a dispersion of known hematite concentration was passed twice through 5 g of steel powder bed at pH 5.8, which procedure took 1 h. Light scattering tests showed that the particle removal from the suspensions was essentially quantitative. Electron micrographs indicated that -95% of the deposited particles were attached to flat surfaces of steel as singlets. Subsequently, the bed was rinsed with 30 cm3 ~
~
~~~
(8) E. MatijeviE and P. Scheiner, J. Colloid Inrerfuce Sci., 63, 509 (1978). (9) E. MatijeviE and N. Kolak, J . Colloid Inrerfuce Sci., 24 441 (1967).
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 421
-
me 2
I
I
HEMATITE- STEEL (EDTA) CEDTAI
I
~(crn’t
I
Ib)
(01
I
~(crn’)
Figure 1. Left: Plot of the number of hematite particles deposited per gram of steel pretreated with EDTA solutions of two different concentrations as a function of the volume of the sol passed through the bed at pH 4. Triangles give the results in the absence of EDTA. Right: The same data plotted in terms of the percentage of the dispersed particles remaining in the effluent. Concentration of the sol: -2 X IO8 particles/cm3;flow rate: -2 cm3/min;steel used: 5 g.
of an aqueous solution of pH 5.8 to remove any particles entrained in adsorbent interstices, but no particle detachment was detected. In the second series, the steel beads were first added to water in a plastic bottle and immersed in an ultrasonic bath to eliminate air bubbles. A well-dispersed hematite sol of a predetermined concentration was then added to the steel suspension. The pH of the mixture was adjusted to 5.8 by the necessary amount of a dilute base. The sample was carefully capped and inverted gently for 20 min to assure proper mixing and uptake of hematite on steel. The amount of adhered particles was determined by light scattering and the nature of the deposit ascertained by electron microscopy. So that the desorption of attached particles could be studied, -5 g of steel beads was transferred into the column, and the bed rinsed with 30 cm3 of a solution of pH 5.8 to remove any loosely trapped solids. Detachment experiments were then carried out by continuously passing through the column at a constant flow rate a solution of the chelating agent of a given concentration and pH. The ionic strength of the elution solution was always kept at 1 X lo-) M. The effluent was collected at several different time intervals and the particle concentration was determined in each sample. The time that elapsed between the end of the deposition procedure and the beginning of the detachment step was about 1 h. 3. Electrophoresis. Electrophoretic mobilities were measured with the Rank Brothers Mark I1 microelectrophoresis apparatus using a cylindrical thin-walled (- 50 pm) van Gils cell. For each measurement at least 20 particles were timed in both directions. The electrokinetic properties of steel were determined on a sample of submicron particles separated from the bulk material with which the column bed was packed. It is assumed that the fine particles had the same surface potential as the powder employed in this work.
Results Deposition. The effect of the adsorbed EDTA complex anion on the steel surface on the uptake of untreated hematite sols at pH 4 is illustrated in Figure 1. The left-hand side of the diagram shows the number of deposited a-Fe203particles as the sol is passed through the column of steel beads pretreated with an EDTA solution at different time intervals. Obviously, the adsorption of this complexing species onto the steel beads enhances particle adhesion; the effect is more pronounced if the steel bed is treated with a higher concentration of EDTA for a longer time. The right-hand side of the same figure presents these data in terms of the particle concentration remaining in the effluent. It is
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
422
H E M A T I T E IEDTAI- STEEL
I
I IEDTAII
I
/(a1
012
I b 1”1o-*Y I .
1 I
Ib l
II
I I HEMATITE-STEEL
I
E L U T I N G S O L U T I r 1110-*C E D T I
Lo et al.
o12b I
1 I 1 I 0 E L U T I N G W I T H EDTA SOLUTION E L U T I N G W I T H AQUEOUS SOLUTION ALONE ~
1
1
W 0
g 008
W
z
5
S t
e
W -1
2
40
004
2 0
V(cm3)
Figure 2. The percentage of the number of hematite particles remaining in the effluent as a function of the volume of the sol pretreated with EDTA solutions of different concentrations passed through the powder bed at pH 4 (a) and at pH 3 (b). Circles give the data in the absence of EDTA. Concentration of the sol: -2 X lo8 particles/cm3; flow rate: -2 cm’/min; steel used: 5 g.
100
80
r
u
8 W U
F: a
40
40
2
t
4 -4
0
160
PH
Figure 4. Left: Fraction of or-Fe203particles removed from steel by eluting the bed with 1 X lo4 M EDTA solution as a function of the volume of solution passed through the powder bed at various pH values. The initial number of particles adhered: -9 X lo9 per gram of steel; pH of deposition: 5.8; flow rate: 2 cm3/min. Right: The total fraction of particles removed by rinsing the bed with 1 X lo4 M EDTA solution as function of pH (0)and when aqueous solutions of different pH in the absence of EDTA were used for elution ( 0 ) . given as the number of released particles divided by the total number of initially deposited hematite particles. The dependence of this quantity on the pH is given on the right-hand side of the figure, which also includes previous data3 obtained with rinse solutions containing no chelating agents. Similar results are and 1 X 10” M EDTA over the same range obtained with 1 X of pH values. Essentially the same behavior is observed with samples of steel beads to which hematite particles were added in the column or by the “batch” method (adhesion occurred outside the column). No dissolved iron was detected in the effluent solutions by either the thiocyanate test or by the atomic absorption method under conditions used in this work.
2
’z 100 W 2 k 80
eo v~crns)
Vlcrn’)
80
160
VlcmJl
Figure 3. The percentage of the number of hematite particles remaining in the effluent as a function of the volume of the sol pretreated with different concentrations of (a) DFOB solutions at pH 8, and (b) Co(bpy),(CIO& solutions at pH 10 which were passed through the steel bed. Circles give data in the absence of EDTA. Concentration of the sol: -2 X 10” particIes/cm’; flow rate: -2 cm3/min;steel used: 5 g. observed that little enhancement in adhesion is detected when the steel beads are pretreated with 1 X 10” M EDTA for a period of 1 h before deposition. The importance of this finding will be discussed later, The attachment at pH 3 indicates a similar trend but the increase in the uptake is less pronounced. No effect is detected when the experiments are performed at pH 8.0 i 0.3. The attachment of hematite particles, pretreated with EDTA from dispersions of pH 4 and 3, onto steel is shown in Figure 2. The concentration of EDTA in the sol as low as 1 X lo-’ M at pH 4 shows a noticeable effect on the adhesion process, while -90% of particles are removed by deposition at an EDTA concentration of 1 X lo-* M. The enhancement efficiency is less in more acidic systems (pH 3). At pH 8.0 i 0.3 essentially no influence of EDTA is detected at concentrations up to 1 X
M. Figure 3 presents the effect on uptake of hematite particles on steel by treating the former with various concentrations of DFOB at pH 8 (a) and of Co(bpy),(C104), at pH 10 (b). Detachment. Figure 4 shows the detachment of adhered hematite particles from steel surface by eluting the bed with 1 X lo4 M EDTA solution of different pH as a function of the volume of the solution passed through the bed. The fraction removed is
Discussion Deposition. A number of stability and electrokinetic studies with silver halide,lOJ1chromium hydroxide,I2and ferric oxideL3-15 sols showed that the magnitude oi‘charge of the particles can be changed or even its sign reversed by the addition of very small amounts of a variety of chelating agents or metal chelates. For example, the isoelectric point of hematite suspensions is shifted M solution. from 6.0 to 3.3 when EDTA is added to give a 1 X It was also demonstrated that the deposition of hematite particles onto stainless steel could be increased at low pH if the dispersed particles or the substrate were pretreated with a heteropoly acid solution.I6 The enhancement in deposition was attributed to the reversal of charge of either of the interacting surfaces by adsorption of heteropoly anions under conditions that would otherwise allow for little or no adhesion. Superficially, the steel surface may be conceived as a thin layer of ferric oxide which also contains the oxides of nickel and chromium. It is then easily assumed that both hematite and steel may be subjected to the same influence of a chelating agent. However, Figure 1 shows that an EDTA solution of concentration lower than 1 X M does not have any appreciable effect on the steel surface over a period of 1 h, which is usually the time (10) D. Catone and E. MatijeviE, J. ColloidInterfuce Sci., 55,476 (1976). (11) D. Catone and E. MatijeviE, Colloid Polym. Sci., 257, 309 (1979). (12) C. G. Pope, E. MatijeviE, and R. C. Patel, J . Colloid Interface Sci., 80, 74 (1981). (13) J. Rubio and E. MatijeviE, J . Colloid Interface Sci., 68,408 (1979). (14) J. Eisenlauer and E. MatijeviE, J . Colloid Interface Sci., 75, 199 (1980). (15) H. C. Chang, T. W. Healy, and E. MatijeviE, J . Colloid Inrerfuce Sci., 92, 469 (1983). (16) E. MatijeviE, R. J. Kuo, and H. Kolny, J . Colloid Interfuce Sci., 80, 94 (1981).
Chelate Effects on Adhesion of Hematite on Steel
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 423
TABLE I: Mass Transfer Coefficients and Stability Coefficients Calculated from Eq 2 and 3 for the Deposition of Hematite Particles Pretreated with Chelating Agents or Metal Chelates on Stainless Steel
PH 4.0
8.0
chelant EDTA
DFOB
chelating agent lo6 k , concn, M m/s 0 1 x 10-5 5 x 10-5 1X 1 x 10-3 0
1X
10.0
1x 1x C~(bpy),~+ 1X 5x 1x
10-5 10-4 10-5
10-4
0.082 0.27
0.90 1.6 1.8 0.13 0.28 1.7 1.7 0.01 0.50 1.3
W 37 12 3.4 2.0 1.7 23 11 1.8 1.8 100 6.1 2.3
elapsed during the deposition experiments. Therefore, the enhancement in deposition, as represented by Figure 2, when the hematite particles are pretreated with EDTA solution at a concentration lower than 1 X lo-, M, must be solely due to the change of the hematite surface. This condition is obviously desirable as it allows the results on the uptake of particles to be attributed to the change of surface properties of only one of the interacting solids. The rate of deposition of submicron particles in a packed bed, an experimental system in which the diffusion mechanism can be assumed to predominate, can be expressed6by the mass transfer coefficient, k, as
TABLE 11: Electrokinetic Mobilities of Hematite Particles in the Absence and in the Presence of Chelating Agents or Metal Chelates PH
3.0
4.0
8.0
chelant
EDTA
EDTA
DFOB Co(bpy)33+
s-'
V 1cm
-
hematite
steel
0 1x 1x 1x 0 1x 1x 5x 1x 1x 0 1x
2.0 f 0.3 1.0 L 0.12 0.8 2 0.08 0.5 2 0.06 1.8 ?: 0.2 0.5 t 0.08 0.33 i. 0.08 0.39 t 0.08 -0.25 t 0.05 -0.82 2 0.08 -1.7 I0.2 -0.9 A 0.1 -0.84 t 0.08 -2.2 t 0.2 .-1.1 i 0.1 -1.0 A 0.1
1.8 t 0.2
10-5 10-4 10-3 10-6 10-5 10-5 10-4 10-3
10-6
1 x IO+
10.0
mobility, p m
chelant concn, M
0 1 x 10-5 1 x 10-4
1.2 t 0.2
-1.5 i 0.2 -2.0
f
0.2
from that of a high repulsive energy barrier to the condition where repulsion may be neglected, resulting in a rapid deposition rate. Previous work6 indicates that a similar trend is observed when an indifferent electrolyte is employed. However, in order to achieve the same effect the concentration of such a salt has to be much higher, especially when the charge of the counterion is low. To help clarify the effect of electrolytes on deposition, the corresponding electrokinetic mobilities of the particles in the presence and in the absence of additives are given in Table 11. It is obvious that the chelating agents or the metal chelate substantially reduce the electrophoretic mobility of the particles. The resulting neutralization or reversal of the charge indicates specific adsorption of the complex solutes on the solid surfaces. Generally, where Ci, and C,,, are the particle number concentrations in the a reasonably good correlation is found between the dependence influent and effluent suspensions. P i s the volumetric flow rate of the degree of enhancement on the deposition and the mobility which is kept low so that a laminar flow is assured. m,, r,, and of the particles at different concentrations of the chelating agents. ps are the mass, radius, and density, respectively, of the steel beads Furthermore, if charge reversal takes place, Le., attraction prevails, used in the packed bed. The above equation is valid only during a maximum deposition rate could be achieved. Somewhat higher the initial stage of the process and when no significant detachment than expected values of mobility are observed when the hematite of particles occurs. sols are treated with 1 X M DFOB at pH 8 and with 1 X If the interaction forces do not influence the diffusion of colloidal M C~(bpy)~(ClO at ~pH ) ~ 10 although for both cases low particles toward the surface, one can employ the e x p r e ~ s i o n ~ ~ ' ~ stability ratios are obtained. Table I1 helps to explain the relative enhancement in deposition kd = 0.296(kBT/vrsrh)2/3( V/,S)ll3 at pH 3 and 4 when hematite is treated with a solution of EDTA; where kd is the diffusion mass transfer coefficient (in the absence the surface charge of a-Fe203particles at pH 3 is more positive of an energy barrier), kBis the Boltzmann constant, T the absolute than that at pH 4. temperature, 9 the viscosity of the medium, rh the radius of heDetachment. The kinetics of detachment, when the bed of steel matite particles, and S the cross-sectional area of the column. beads with deposited hematite particles is eluted with an EDTA Equation 2 is applicable to a column filled with still beads having solution at high pH, is found to be similar to the observations a void volume of 0.4 as used in this work. reported earlier4 in which the rinsing was done with pure aqueous In the presence of an energy barrier the efficiency of attachment alkaline solutions. Particle removal occurs rapidly at the early is decreased, which may be expressed in terms of the stability stage of the elution process and then it gradually levels off. In coefficient W, i.e. this work the total fraction of detached particles is relatively small and there is no shift in the peak of the maximum removal as a W = kd/k (3) function of pH due to the change in the isoelectric point of heWhen the stability ratio is near unity ( W = l ) , the effect of matite in the presence of EDTA. These results suggest that EDTA electrostatic repulsion is negligible and the rate of deposition is solutions do not have much influence on the detachment of the controlled by convective diffusion only. adhered a-Fe203particles from the steel surface. Table I lists the mass transfer coefficients and the stability ratios Possible explanations for this behavior may be as follows: calculated for the deposition onto stainless steel of hematite 1. During the elution process, EDTA anion may not be efdispersions to which chelating agents were added. It is clear that fectively slip into the narrow space between the adhered hematite and 1 X low3M EDTA for hematite sols treated with 1 X particles and the substrate surface in order to generate sufficient and 1 X solution at pH 4, with 1 X M DFOB solution repulsive forces to cause effective detachment. M Co(bpy),(C104), solution at pH at pH 8, and with 1 X 2. It has been reportedI5 that the adsorption of EDTA anions 10, the stability ratios are small and near unity. Therefore, the on sperical hematite particles in strongly alkaline media is much presence of small concentrations of properly chosen chelating less than that at low pH. Therefore, a weak adsorption may not agents or metal chelates makes it indeed possible to alter a system induce a sufficiently large change in the surface properties of the interacting surfaces to yield electrostatic repulsion necessary for the release of particles. (17) E. Ruckenstein and D. C. Prieve in "Testing and Characterization of 3 . A weak repulsion, due to the small amount of adsorbed Powders and Fine Particles", J. K. Beddow and T. P. Meloy, Ed., Heydon and Sons, London, 1980. complex ions, may only move the particles laterally on the substrate
424
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
Lo et al.
surface into an energetically or geometrically more favorable site. Particle detachment is by no means the reverse of particle deposition. The former is a more complicated process due to a possible deformation at the point of contact, to dissolution of the solid, and to the heterogeneity of the substrate surface. Adsorption of solutes obviously exercise quite different effects on the detachment process than on the deposition process. Similar phenomena have been observed1*when the hydrodynamic shear was applied to detach TiOz particles from a glass surface in the presence of an EDTA solution. It was shown1s4that the kinetics of particle removal can be described by the expression4 In (x, - x) = In x, - k,t (4) where x and x, are the fractions of removed particles at times t and m from the beginning of their release and k, is the removal rate constant. In some cases, such as in the release of chromium hydroxide particles from glass beads, x, = 1, which means that essentially all adhered particles were able to escape. Less ideal systems (e.g., steel surface-colloidal hematite) can also be interpreted in terms of eq 4, although x , < 1. It was shown that hematite particles adhering to steel may either escape into the liquid medium or move laterally and get trapped into the crevices on the steel surface. In the latter case particles are bound irreversibly and they cannot escape. The rate constant of removal, k,, can, therefore, be expressed in terms of the probability of escape, p , and irreversible bonding pi:5
kr = P + Pi
(5)
Furthermore, the fraction of particles released at time f = m is proportional to the initial fraction of particles which can either escape or be irreversibly bound, xgS: X,
= pxo8/kr
(6)
Equations 5 and 6 allow for the evaluation of the relative probability of escape, prel:I9
Prei = P / P r e f = Xmk/X-,refkref
(7)
where subscript "ref" designates values obtained for a reference system, most conveniently selected by adjusting the pH to obtain the maximum value for x,. Although the quantity piis not easily determined, the spread of likely values is given by
The spread narrows with the increase in the value of x,,ref. Figure 5 gives such evaluation of data presented in Figure 4. The upper part shows the dependence of the probability of escape, prel,on pH as calculated with expression 7 . An increase in the pH value up to 11.5 enhances the rate of particle release. After the maximum has been reached further addition of NaOH causes a slowdown in the removal of the adhered solids. While the rate of particle deposition is the faster the lower is the maximum of
-
(18) M. Hubbe, private communication. (19) G.Thompson, N. Kallay, and E. MatijeviE, Chem. Eng. Sei., in press.
11
11.5
12
PH Figure 5. Same system as in Figure 4. Upper part. Relative values of the rate constant (probability) of detachment, prcl,as a function of pH calculated from eq 7. Numbers next to each experimental point denote values of k, = p + pi evaluated from eq 4. Lower part. The range of values of the rate constant (probability) of irreversible bonding as calculated from eq 8.
the total energy interaction function, the rate of release is not directly related to this maximum. Instead, the rate of desorption depends on the depth of the primary minimum which, according to Ruckenstein,20 is not infinitely deep. The results of this work indicate that an increase in the concentration of NaOH up to 3 X M causes a decrease in the total energy interaction minimum. The effects at still higher NaOH concentration can be explained either by the deepening of the minimum or by the redeposition of the dispersed particle^.^^^ The numbers next to the experimental points indicate the values of k , = p pi, which are random and no correlation with pH is evident. The lower part of Figure 5 gives the spread of the values of the rate constant (probability of irreversible bonding). A minimum is observed at a pH at which prelshows a maximum. Thus, the probability of irreversible bonding is the smaller, the larger is the probability of particle escape. Analogous results were obtained for the removal of rodlike P-FeOOH particles from steel.I9 No simple explanation for this effect can be offered at this time.
+
Acknowledgment. Supported by the Electric Power Research Institute Contract RP-966-2 and by the NSF Grant CHE-80 13684. Registry No. Co(bpy)3(C104)3, 14376-02-4; hematite, 1317-60-8; stainless steel, 12597-68-1; ethylenedinitrilotetraacetic acid, 60-00-4; desferrioxamine B. 70-5 1-9. (20) E. Ruckenstein, J . Colloid Interface Sei., 66, 531 (1978).
