Precipitation during Electromigration of Ions Joris Deman Kliniek voor Radiotherapie en Kerngeneeskunde, Akademisch Ziekenhuis, University of Ghent, Belgium
A separation method is described that makes use of exchange reactions between ions in solution and those bound in precipitation products. In order that differences in solubility products should result in separation, the ions in solution must be displaced. This is done by the a plication of direct current. The present paper is chiegy devoted to theoretical considerations. It is shown that the method is different from chromatographic methods for two reasons: The material (;.e., the precipitate) with which exchange occurs, is formed in situ during electromigration; and the change in “concentration” of the bound ion i s not accompanied by a parallel change in concentration of the free ion.
IONIC srEc1E-swhich precipitate each other are introduced into different regions of a gel column. When direct current is applied, the ionic regions move toward each other and begin to precipitate on contact. A region containing the reaction product is formed with one side bordered by a moving reaction front. Precipitation actually occurs only at this front, which occupies a very thin section of the gel column. Because of the movement of the front, the length of the product region increases steadily. When different ionic species with charges of the same sign are brought into the column, they all must migrate through the product region before they precipitate. During this passage they exchange with the ions that are bound in the precipitate. Obviously a separation effect will result, and it can be expected here that the differences between the solubility products and the mobilities of the “separation ions” will prove to be responsible for the effect. From this brief description it is apparent that the method cannot be called truly chromatographic. There is no true stationary phase because the second phase is formed by a chemical reaction during the electromigration of the ions. Also neither physical nor chemical adsorption nor affinity for a solvent is involved. The exchange reactions are occurring with chemical compounds and are due to the dynamic nature of chemical reaction. The method can be thought of as a technique which uses exchange reactions in a continuous manner. Besides precipitation reactions, many other kinds of reactions might be used in the way described. However we found that precipitation reactions were best suited for theoretical treatment. In a previous study ( I ) , this has been pointed out more extensively. In that paper the phenomena accompanying the formation of a reaction front are treated. The equations that are important to the separation process will be presented in this paper. The main purpose here, will be to derive the equation which describes the change in concentration distributions resulting from the exchange reactions. Also the way in which the method can be put in practice will be given. In later publications we intend to describe a separation of rare earth metals and an elution procedure. SYMBOLS
cJ = concentration of ions of species J , expressed in gram ~ equiv per cm3 of electrolytic solution; c ~is , the uniform concentration at which the ions precipitate at the front. (1) J. Deman and W. Rigole, J. Phys. Chem., in press.
E
= electric field strength, defined as i/qK, where i = current, q = cross sectional area, K = specific conductivity. The column is supposed to have a constant q and the
field strength is constant and uniform owing to the presence of a nonreacting electrolyte in large excess. mJ = effective mobility taking into account adsorption of the ions to the gel; it is regarded as a constant and its dimensions are cm*/sec. Volt. VJ = E mJ = velocity of ions in cmjsec. ut = velocity of the reaction front in cmjsec. P = precipitate concentration. Because in the gel medium the precipitate is very finely dispersed, the term “concentration of precipitate” appears allowable. This concentration is denoted by the symbol P, and is expressed in gram equiv of either the cationic or anionic species present in the precipitate per cm3 of gel. In the computations which follow we make use of an x-axis which points in the direction in which the positive ions move. Consequently, velocities acquire the appropriate sign according to the direction of movement. The solubility product of the reaction: IAa+
+ aL1-
=
A&,
is expressed by means of the concentrations in gram equiv per cma, i.e.
K A L = C A ‘ CL’ (1) When we designate molar concentrations with square brackets then: K8 = [Aa+]b [LL-]“ = a-1 .[-a. 103(1+n) . K A L REACTION FRONT
It is assumed that at both sides of the front uniform concentrations and cL,oexist. It is only at the front that precipitation occurs. The ions Aa+ and L’- which are left in solution and have continued their path across the front, assume concentrations which are in equilibrium with cL,0 and c ~ ,respec~ , tively, according to the constraint of Equation 1 , When the solubility product is considered negligible with respect to c ~and, c ~~ ,then ~ , the amount of an ionic species precipitated at the front per unit time, is equal to the difference between the velocity of the ion and that of the front, multiplied by the ionic concentration. (VIAE
- vi) C A , O =(mLE f- vf)cL.o =
.P
where mA
CA.0
- mL cL,O
+ cL,O
E
(2)
P = i (mA f mL) C A . 0 cL,O mACA.0 - mLCL.0
(3)
Vf =
cA,O
and
From Equation 2 it follows that the velocity of the front and its direction of movement depend upon the concentration CA 0 AO mL When C= -, the front does not move ratio 2. CL,O CL,O mA (vf = 0), and all precipitate accumulates at the initial section of meeting (numerator zero in Equation 2). ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
321
+ O
F
Figure 1. 0 is the section of initial contact between An+ and LZ-,F the reaction front. Between section 0 and F i s the product region
We will describe here a separation between positive
Now consider a product region where two ionic species A'+ and P+have been precipitated as A&, and BzLa,respectively. The concentrations PA and PB are not necessarily uniform nor are the concentrations in solution, as was the case for a single precipitate. The ratio of the mean mobilities at a given section of the product region is:
ionic species, Consequently, the ratio %9 must be greater CL,O
than 5 so that the front will move in the same direction as the mA
positive ions. The region containing L", the common precipitating ion, is assumed to be long, whereas the region containing the ions to be separated is short. The separation process will be considered complete when all positive ionic species have been precipitated by Lz- which reacts in a homogeneous concentration c ~ , Figure ~ . 1 gives the situation when the separation is in progress. Only one positive ionic species is represented.
After re-arrangement :
SEPARATION EFFECT
From the figure it is seen that the Aaf ions have to migrate through the product region before they reach the front. During this time, they are exchanging with the Aa+ ions which are bound chemically in the precipitate. Different kinds of mobilities must be considered. During the process of exchange the bound ion is released and continues the path of the former A a f ion. Consequently, it might appear at first sight that the A'+ ions with mobility mA are migrating as if no exchange takes place. This view applies with regard to the computation of the velocity of the reaction front. However if we look at the fate of an individual ion, it is apparent that its actual mobility will be equal to the mobility mAmultiplied by the fraction of time during which it is free. The Aa+ ions within the precipitation granules are not so readily accessible for exchange as those at the surface. The longer the time spent in the immobile phase, the lower the actual mobility of a particular ion will be. For this reason, we introduce the concept of mean mobility +iA. It is the average value around which the actual mobilities fluctuate (from zero to m.4). The value of +iA is obtained by multiplying m.4 by the ratio between the concentration in solution and the total concentration:
Insertion of (a) and (b) in the right hand term of the above equation, yields :
When denominator and numerator in the term at the left hand side are multiplied by the field strength E, we obtain the ratio between the amounts of species A and species B that are transported per square section and unit time. Hence, when it is assumed that ions Aa+ and Bb+ carry equal charges, i.e., a = 6, the condition for separation is:
(4)
The smaller the size of the precipitation granules, the less pronounced the fluctuation around the mean value fiiAwill be. In our case, we may assume that the granules are of small size owing to the presence of gel molecules which impede aggregation. For reactions other than precipitative ones, there is no fluctuation due to inaccessibility, and Equation 4 represents the common actual mobility. (We are neglecting another cause for fluctuation which will be mentioned later.) 322
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
mAKAL1"
# ??lsKeL'il
(6)
DISCUSSION
Since we deal with precipitation reactions, the ionic concentrations cAand cBare independent of PA and PB. Therefore a A variation of the ratio Pwill not be accompanied by a parallel PB
change in composition of solution. When Equation (a) is divided by Equation (b), assuming that charges are equal, the result is: = constant. CB
This means that no variation in the ratio 2 can occur, as long CB
PA
as PA and PB are present together. It is only the ratio - that PB
changes during separation. This special feature distinguishes the present method from chromatographic procedures.
Apart from the tailing effect, substances can be separated completely with chromatographic methods. In our method there always is some overlapping at the bordering section of the consecutive bands. We think this effect must be attributed chiefly to the fluctuation of actual mobilities. For example, let us take the case mAKAL’IG> mBK B L l I ‘ . The condition does not mean that all entities of species A move faster than those of B. Only the average ones do so. There are ions which, owing to a long time of immobility, have too low actual mobilities to fulfill the condition. Also coprecipitation and diffusion are factors that are responsible for overlapping. Notwithstanding this drawback, promising results have been obtained with the method (rare earth elements, isotopes). It seems to us that a field of application can be found in separations for which more common methods fail. In this connection, it appears convenient to stress that the method is not confined to precipitation reactions, but that use can be made of many other reaction types. The only condition is that ions must move through a region containing reaction products, so that exchange reactions can occur. So far we did not set up experiments of this kind. It is possible that a better separation efficiency would be obtained because the products, whether charged or not, are of molecular size. Consequently, there will be no “coprecipitation” and no mobility fluctuation due to inaccessibility. Here we mention that there exists an additional fluctuation effect of the actual mobility. The reason for it resides in the fact that the durations of the periods during which an ion exists in one state or another during electromigration, spontaneously exhibit random distribution (2,3). The phenomenon is of general nature and applies for all types of reaction product with which exchange occurs. Since the effect becomes perceptible as an enhancement of diffusion, it has been called “electrodiffusion.” Because electrodiffusion is dependent on the rate constants of the exchange reactions. Breuer (4) suggested that it might be possible to achieve separations between species differing only by those rate constants (e.g., isotopes). We will not go on further into this question, but will state that the difference in rate constants of the exchange reactions together with the difference in mJ KJL1/‘may permit separations between chemically similar species. In a following paper it will be shown that the exchange time can be prolonged at will by means of an elution technique. In it, precipitate at the rear end of the product region is brought continuously in solution again. The region containing the precipitation products is displaced along the column as a series of bands and is passed through continuously by the ions, EXPERIMENTAL RESULTS
We have worked with an agar gel column in glass tubes of 1-cm internal diameter. The concentration of the agar was 1 (wt/vol). As indifferent electrolyte, KC1 was used which was present in a 0.1Nconcentration. The length of the tubes varied from 30 cm to 80 cm. They were connected to electrode vessels into which platinum electrodes were dipped. At the electrodes, hydrogen ions and hydroxyl ions were produced which will penetrate into the tube. Therefore we take care to end the separation before these ions reach the precipitate. (2) J. C. Giddings, J. Chem. Phys., 26, 1755 (1957). ( 3 ) P. C. Scholten and K. J. Mysels, Trans. Faraday Soc., 56, 994 (1960). (4) M.M. Breuer, Nature, 194, 281 (1962).
’il
. ......- .....
,
I
t
..-__. I
1
Figure 2. Ionic composition before separation Gel region I: 1 cm3 of gel containing KCl O.2N and a mixture of separation ions each in concentration 0.025N Gel region II and cathode vessel: KCl 0.2N KOH 4.10-*N Connecting tube I11 and anode vessel: KCI O.2N
+
The molten gel containing the appropriate ions is poured into the tubes. When cooled below 40 “C the solution sets. In this way we are able to prepare columns in which gel regions containing different ionic species are layered above each other, We have done a great number of experiments. For example metal ions have been separated as sulfides, ferricyanides, carbonates, and hydroxides. The anions C1-, Br-, and Iwere separated with silver ions. Here the results of experiments will be given by which we tried to verify the separation condition maKAL1/’# @ I & L ~ ~ ’ . Mixtures of metal ions are precipitated as hydroxides. In Figure 2 the initial ion distribution in the column is given. When the separation is finished, the gel column is removed from the glass tube. The different colors of the hydroxide precipitates permit them to be distinguished. The precipitation zone is cut longitudinally in several pieces and the sequence of the different metal hydroxides is determined with the aid of specific spot tests (5). The results are given in Table I. We cannot with certainty conclude that the product rnJKJL1/’ determines the separation, because the data from the table also gives support to the assumption that Kg (or KjL‘I’) alone could be the decisive factor. It is difficult to set up decisive experiments because the KJLl/’ values show differences of a greater order than those between the mobility values. We can state that our experiments have never contradicted the validity of the separation condition (6). ( 5 ) F. Feigl, “Spot Test,” Vol. I: Inorganic Applications, Elsevier
1954. (6) R. Parsons, “Handbook of Electrochemical Constants,” Butterworths, London, 1959.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
323
I
+
A&,
A&,;
v
1 %,o I
cA,o
Table I. Comparison between Sequence of Precipitate Bands and the m&&'" Values Sequence of
pptd. bands; Dissociation anode to constant K, mJ (6) cathode at 25 "c (6) K J L " ~ at 25 "C 10-30.17 10-41.69 60 Fe(OHh 10-17.19 10-26.89 38.2 Ni(OH)2 Zn(OH)2 10-16.36 10-26.0s 43.4 10-16.6 10-24.3 37.7 Co(OH12 10-14.74 10-23.44 47.7 Fe(0Hh 10-12.7 10-a*.4 40.3 Mn(OH)2
m.,KJL1I2 10- 39.9 1 10- 2 4 . 3 1 10-23.41 10-22.8
10- 21.76 10-19.8
ACCOMPANYING PHENOMENA
THEPRECIPITATE IS CHARGED. It is known that the presence of gel lowers the velocity with which precipitation particles aggregate. In some of our experiments no precipitate could be observed near the reaction front (which is visible refractometrically), but precipitation occurred 1 or 2 cm behind the front. It seems probable that in such cases an initial formation of colloidal particles occurs. Because colloids are charged, they undergo electromigration when the particles are small enough to penetrate the pores of the gel matrix. In the course of time the size of the particles increases until they are retained by the gel, DISSOLVING OF PRECIPITATE. During the reaction at the front, a slight displacement of the precipitate region occurs. Simultaneously a gradient in the precipitate concentration
324
-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
arises. The exact mathematics of the phenomenon requires extensive computations. However the process can also be described qualitatively. During the formation of precipitate the region of A'+ ions with concentration cA,o sweeps over the precipitate already formed. Since the concentrations of A'+ and Lz- in solution have to satisfy the solubility product, the concentration of LzK*LIl'
will be equal to __ as long as the A'+ ions are present. C* . ..ozla .
When the rear end of the concentration region c ~ has , ~ passed the rear border of the precipitate region, then A'+ and L'- ions will be dissolved from the precipitate in order to satisfy the solubility product (Figure 3). As a result the concentration of A"+ will be less than cA,0. This implies that when these ions reach the reaction front, this front will begin to move more slowly (Equation 2). Just behind the front the concentration of the Lz-ions will steadily increase because their concentration stands in equilibrium with a diminishing A'+ concentration. Because these ions move toward the anode, the amount of Aa+ brought into solution at the rear end will decrease. Consequently the reaction front will move still more slowly and finally will reverse its direction of movement. When over the whole product region, Lz- ions are present in concentration cL,othe process comes to an end. The result will be a gradient in the precipitate concentration which increases in the direction of the cathode. RECEIVED for review August 7, 1969. Accepted December 2, 1969.
