I
ANTHONY T. DI BENEDETTO and EDWIN N. LIGHTFOOT Chemical Engineering Department, University of Wisconsin, Madison, Wis.
Ion Fractionation by Permselective Membranes Factors Affecting Relative Transfer of Glycine and Chloride Ions Report of preliminary work of a long-range research program on ion exchange presents information helpful in recovery and purification of fine chemicals. It gives original data on a complex transfer process and includes a mathematical approach to ion fractionation by permselective membranes.
A L T H O U G H the possibility of ion fractionation has been known for 4 or 5 years, little information is available on the behavior of actual systems or the relative importance of the factors influencing the transport phenomenon. The study reported was undertaken to test the feasibility of such separations, preliminary to a fundamental investigation of the factors controlling electrodiffusion rates. Mixtures of amino acids are of particular interest because of their amphoteric nature and the attractiveness of a simple separation. To obtain a clearer picture of the behavior of amino acids in a n ion fractionator, a very simple system was chosen for study-glycine and sodium chloride. All experimental data were taken at pH 6.3 to 12.0, so that the ionic system under consideration was the transport of gIycine ion relative to chloride ion through an anion exchange membrane. An ion fractionator can be constructed by alternating anion exchange and cation exchange membranes between the electrodes of an electrolytic cell. Ionic fluxes that occur upon the passage of current are shown in Figure 4. The behavior of this system is best characterized by the transport numbers of the individual ions, determined by the behavior in the solution phase, a t the membrane-solution interface, and in the membrane. I n the solution phase, the ionic fluxes due to the potential and concentration gradients built up across a thin laminar film adjacent to the membrane are considered. For engineering purposes, the ion transport in the membrane phase can be exemplified by the behavior of ions adjacent to the interface. The membrane concentra-
tion ratio, x A / x B , at the interface is assumed to be proportional to the transport ratio, t ~ / t ~The . interfacial phenomenon is considered as adsorption and desorption of ions between phases.
balanced by the effect of the potential gradient.
($ + CZmF x ")dz
AD,
Theoretical Development Turbulent Flow, Two 1-1 Electrolytes Sharing Same Cation. TRANSPORT NUMBERS IN MEMBRANE PHASE. The relative transport numbers of two ions to be separated, A- and B-, are the same for all cross sections of the membrane. I n a monomolecular layer adjacent to the solution, a definite fraction of exchange sites, XA, is occupied by species A. The average residence time of A- ions depeqds inversely on their migration velocity, UA, which is dependent on the potential gradient (assumed constant throughout the membrane). Mathematically, this is expressed as :
(%-
-ZA = A D A - -
where =
rA/rA
+ r~
TRANSPORT O F IONS XN SOLUTION PHASE. This situation is analogous to normal electrode polarization and leads to a limiting current through the membrane. I t is assumed: All concentration change occurs in a thin laminar film adjacent to the. membrane surface. As the film is thin, few migrating ions originate in it. I t can be assumed that there is no net movement of the nonmigrating ions. The membrane is ideally selective. The system is a t constant density. Diffusivities are constant. Water transport is grouped with the transport of the migrating ions. There are no pressure or temperature gradients across the film. Consider the anions to be the migrating ions. At steady state the free diffusion of cations caused by the concentration gradient across the film must be
CA
")
ZF R T X dz
(4)
Equations 3, 4, and 5 may be solved simultaneously. When the boundary condition, c = c' at z = 0, is used, c =
CO
- bz
(6)
where
and 6.4
+
CB
Thus a linear total concentration gradient with a limiting current, as in electrode polarization, is obtained. cA and cB are not known individually, as is desirable for predicting relative transport, but may be calculated by adding Equations 4 and 5 to obtain the total current and solving in terms of one component to give :
The relative transport number may then be expressed as:
- tg
(3)
A similar equation may be written for the anions, except that the two gradients reinforce each other and the sum of their effects equals a membrane current:
6
t~ = 1
= 0
CA
=
CA'C'
- z(ZA/ADA)(C' - b z / 2 ) c0
- bz
(7)
The relative concentration a t the interface is then given by:
E? = 4 _ A YB
=
CB
co + c
'
(-)(%)@
cAo
-
cBo
- (T)($)($)
co + c
(8)
We now have an expression for the solution concentrations at the membranesolution interface. What is needed, however, is the membrane concentrations a t this interface, which are directly related to the over-all transport (Equation 2). The interfacial phenomenon that occurs must therefore be considered. A simple thermodynamic equilibrium such as proposed by Gibbs and Donnan VOL. 50, NO. 4
APRIL 1958
691
(4) cannot be assumed here because of the disturbance caused by the current density. Continuous removal of ions through the membrane should disturb this equilibrium, in proportion to the magnitude of the current density. The interfacial phenomenon is considered simple adsorption and desorption of ions between the phases. The sorption processes are controlled by two driving forces : concentration potential and electrical potential. It is assumed:
An "apparent" equilibrium is maintained at the interface. Total current is carried by the anions. Sorption rates have a linear dependence on concentration and current. The rate of adsorption of ion A is controlled by two driving forces acting in the same direction : TA
+
kiyi
=
Concentration potential
k ~ y 4 ( ~ 4 )X6
Electric potential
Z (9a)
U
Figure 1 .
In the Lucite cell electrolyte flows continuously into four chambers
where k is a constant. The rate of desorption is likewise controlled by two driving forces, acting in opposite directions : RA
- k 4 x 4 ( ~ 4 I) ~
= kax.4
U
J TANKS
(9b)
Assuming an apparent equilibrium between adsorption and desorption, r.k/rR = li.&/R~, and using Equation 2 : X
J A / ~ B = ,+(I) ( U B / U A ) R
t.i/tR
I
(10)
where
f f
[k6
'('I
= [kl
kS(UB)S kZ(UA)S
11 [k3 - k l ( U . 4 ) R 11 21 !k7 - k 8 ( U B ) R I ]
Combining Equation 10 with Equation 8 and expressing in terms of t k : g(c$l,z)LA2
f [&Bo - g(c,l,z)ltA
LBECKYAN pH-METER
t
=
g(C,l,Z) = (c'
+ c/2c0)(lZ/A) [ ~ / D -B (1lD.4)
(UA/UB)R(l
/'( 1I))
and = 1 -
(Z/A)(1/4c0)(t.4/D.4
+
C. F.
As (Z/A)+ t ~ l t (~U A / U B ) R
0 ,f ( 2 )
-+
K
( 1 / K ) CA'/CB'
H I
N
(2) UB
6
Anode compartment Cathode compartment Feed compartment Product compartment
The relative transport is: therefore, proportional to the ionic mobility ratio in the solution phase; a t high current densitji the membrane loses its selectivity. Experimental Methods
(12)
whem K is a true thermodynamic equilibrium constant. As (I/A)+ a limiting current
2
P.
tB/DB)
Equation 11 is the general equation describing the transport of two 1-1 electrolytes sharing the same cation. The equations describing the limiting conditions are :
692
l
SIGMA DISPLACEMENT PUMP Figure 2. Complete flow system A.
+ c/2co
and
l
i
where
ca
I
Equipment. The experimental data were taken in a Lucite cell in which there was a continuous flow of electrolyte into four chambers (Figure 1). Rubber gasket sheets a t all adjoining sections ensured a watertight seal. The two electrodes were made of platinum gauze and had a surface area of 16.2 sq. cm. They were made to fit the center hole cut through the Lucite, which fixes the transport area. By alternating Amber-
INDUSTRIAL AND ENGINEERING CHEMISTRY
plex C-1 and A-1 membranes (Rohm Kr Haas). the cell is broken up into four compartments: an anode, product, feed, and cathode compartment, Figure 2 shows the complete flow system. Valves a t the entrances of the chambers regulated the flow rates, which were measured by a graduated cylinder placed a t the break near the exits of the chambers. A Beckman p H meter, Laboratory AIodel G, with a standard flowmeter attachment, placed in the feed line between the head tank and the cell entrance, measured the p H of the feed. The anolyte and catholyte were run into the same head tank to neutralize any acid and basic materials formed. The electrical system is pictured in Figure 3. The two rheostats were used
ION FRACTIONATION
r
D.C. SOURCE
+-
ELEGTROLYTfC CELL
ANOLYTE Figure 4.
to obtain finer current control. The voltage was impressed through a n external direct current source and measured by a Weston Model 280 voltmeter. Procedure. As glycine has a n isoelectric point, the concentration of glycine anion may be varied by varying the p H of the feed. At p H 6.3 glycine is completely in the zwitterion form, +NH&H&OO--. In more basic solution, glycine anion formation is favored, +NH3CH&OO-
*
GI-
0
Figure 3. A simple electrical system is employed: Use of two rheostats in parallel gives finer current control
NH2CHzCOO-
so:
f H'
Figure 4 shows the cell. When a current is passed through, anions migrate toward the anode and cations toward the cathode. T h e zwitterions, being essentially neutral, should move in the same manner as the solvent and be a relative measure of the water transport. As the center membrane is a n anion exchanger, the current passing through it is carried mainly by the anions passing from the feed to the product compartment. The cation exchanger to the left of the product compartment prevents anions from leaving. Concentrations of chloride and glycine ions in the product compartment can be measured and relative transport numbers obtained. T h e hydroxyl transport is undoubtedly negligible, except a t p H > 12, because of relatively low hydroxyl ion concentration. T h e chloride concentration was measured by a standard Mohr titration using
0.1N silver nitrate solution. The glycine concentration was found by the photometric ninhydrin method (9). The measuring instrument was a Beckman Model DV spectrophotometer. The red phototube a t a wave length of 570 mp was chosen. GIycine concentration in the feed was found from the equilibrium constant for the glycine ion in basic solution (2) : K = 1O - Q . 7 7 8 = ( H +)(NH&H2COO)--/ ( NHsCHzCOO-)
+
Assuming activity coefficients as unity and knowing p H and total concentration of feed, the concentration of glycine ion may be found. Transport numbers are found by using the definition: ~ N H ~ C H ~ C O O - tci = 1.000. The efficiency of the anion exchange membrane may be calculated using the definition: P = equivalents of negative ion/total equivalents passed. Observation through the Lucite walls showed that flow through the cell was turbulent. A true Reynolds number could not be determined because of the extremely short path length and eddying due to expansion and contraction a t the entrance and exit of the chambers. Equilibrium values for the system were also determined. Approximately 2 grams of Amberplex A-I membrane (hydroxyl form) was chopped very fine and placed in a known solution of gly-
+
PRbDUCT FEED
CATHOLYTE
Ionic flow in electrolytic cell
cine and chloride ion. T h e resin-solution system was agitated continuously for about 2 days to ensure equilibrium, then the resin was removed and air-dried. The solution was analyzed by standard methods to determine the solution concentration ratio, y ~ / y c . The resin was eluted with dilute sodium hydroxide and the elutant analyzed to determine the resin phase concentration ratio, XG/XC. T h e equilibrium constant, K = ( ~ G / ~ c ) / ( x G / x c ) ,was then determined. In view of the sources of error involved it is felt that results are accurate to 5 to 6%. Experimental Results The experimental work was designed to determine the relative importance of the g(c, I , I) and f(Z) functions of Equations I 0 and l l . By fixing chloride concentration, current density, and flow rate and varying glycinc ion concentration, the magnitude of the g(c, I , I) function can be determined. As the ratio (co c)/2cO, will not vary appreciably under the operating conditions g(c, I , I) will be a constant. A plot of t~ us. cco(l - t ~ can ) be used to determine the function qualitatively. By plotting a t various current densities, the nature of the f(Z) function may be elucidated, Tables I to IV summarize experimental data, plotted in Figure 5. For the lowest current density run, the
+
VOL. 50,
NO. 4
APRIL 1958
693
terion transport proportional to zwitterion concentration and subtracting this value from the total transport, a linear plot is obtained (dotted line, Figure 5). The intercept of the original curve, 7 to 10%, indicates that water transport is important a t higher current densities. Table I11 shows that relative transport is not affected by change in flow rate; indicating that the g(c, I, I ) function is unimportant. The theory then indicates that the slopes of these plots are equal to ( u G / u ~ l/f(Z)l/cco )~ (Figure 6, Table 11). M'hen the slopes are normalized with respect to cc0, the data bear out the fact that the slopes are a function of current only. The spread of points is unfortunate, but not much better results can be expected under the experimental conditions. The derived equations assume an ideal membrane, which is not the case here (Table I). Figure 6 indicates clearly thgt a limiting current is obtained, as predicted by theory. Table V is a comparison of the experimental and theoretical results. A value of about 20 was used for IC. This is not highly accurate (Table IV), but a more exact number is not necessary, in the present study, to interpret the overall fractionation process As no mobility data were available for a glycine-chloride system or for glycine ion, a number of assumptions were made to approximate a limiting slope (Equation 13).
1. The equivalent conductance of acetate ion (readily available) was about
Figure 5. Transport of glycine ion as a function of concentration and current density
plot is linear and almost passes through the origin. Its linearity indicates that the g(c, I, Z) function does not play a prominent role in determining the transfer characteristics of the membrane, a t least for chloride concentrations of 0.1N and greater (Equation 11). The fact that they almost pass through the origin indicates that zwitterion transport is negligible. This may be interpreted in the following way. The zwitterion passes through the membrane phase like the solvent molecules, but more slowly because of the larger size of the zwitterion molecule. I t follows that the unbound water transport is also relatively small a t low current densities. For the next higher current density the intercept with the t~ axis is somewhat higher which indicates a slightly higher water transport. For highest current density, a marked change in behavior is noticed. The shape of the curve is parabolic and intersects the tG axis at 7 to 10%. The nonlinearity of the curve should be a measure of the magnitude of the g(c, I , I ) function. However, the high zwitterion transport leads to the possibility that nonlinearity is caused by high readings for the glycine ion transport. Estimating the zwitterion transport by extrapolating the curve to zero concentration, assuming zwit-
694
INDUSTRIAL AND ENGINEERING CHEMISTRY
40
30
20
1.0
0
50
100
IS0
200'
250
300
I / A , Ma./sq. Cm Figure 6.
Effect of current density on f(l) function
350
I O N FRACTIONATION Table 111. Variation of Flow Rates (pH 11.0. CG 0.473. I / A , 61.7 ma./sq. om. Transport, %) Feed Flow Rate,
Table I.
PH
Relative Transport of Glycine and Chloride Ions Feed Flow CG, cci, G. Transport, yo Rate, G. Equiv./ Eauiv./ Cc./Min. L. L. G C1Total tG
I/A,
Ma./
Sq. Cm.
6.3 7.25 9.3 9.85 10.5 11.1 11.6 12.2 13.0
0 * 000 0.001 0.125 0.271 0.421 0.477 0.493 0.498 0.500
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
1.6 0.4 3.66 5.9 8.5 9.8 11.5 9.55 9.08
95.3 96.7 92.2 88.4 87.5 77.5 76.1 80.7 62.0
96.9 97.1 95.9 95.3 96.0 87.3 87.1 90.2 71.0
0.0165 0.0041 0.038 0.062 0.0885 0.113 0.132 0.106 0.128
140 240 280 280 280 280 300 280
7.9 8.9 9.9 11.4
0.006 0.058 0.285 0,488
0.50 0.50 0.50 0.50
0.2 1.0 2.6 5.1
96.1 94.1 91.4 87.5
96.3 95.1 94.0 92.6
0.0021 0.0105 0.0277 0.055
280 300 300 300
9.40 10.00 11.5 12.3 7.8
0.142 0.306 0.492 0.500 0.0055
0.50 0.50 0.50 0.50 0.50
16.2 23.0 30.6 27.80 7.75
69.0 63.7 56.9 51.7 83.25
85.2 86.7 87.5 79.5 91.0
0.190 0.265 0.350 0.350 0.085
310 320 320 315 320
8.0 8.85 9.90 11.0 11.8
0.008 0.053 0.285 0.472 0.495
0.25 0.25 0.25 0.25 0.25
3.65 5.30 18.45 25.80 27.60
87.4 84.4 71.8 62.8 61.4
91.0 89.6 90.2 88.6 89.0
0.0402 0.0587 0.2050 0.292 0.310
300 300 280 300 300
61.7 61.7 61.7 61.7 61.7
7.0 7.95 8.50 9.25 10.70 11.25 10.5
0.001 0.008 0.025 0.114 0.447 0.484 0.333
0.25 0.25 0.25 0.25 0.25 0.25 0.25
6.95 11.80 15.20 22.20 41.70 40.50 36.00
85.3 76.5 78.0 71.5 50.0 41 .O 54.0
92.25 88.30 93.2 93.7 91.7 81.5 90.0
0.0753 0.1335 0.1630 0.2370 0.4550 0.4970 0.400
300 300 300 300 300 300 300
327.0 340.0 334.0 334.0 334.0 334.0 334.0
9.15 10.5 11.05
0.0972 0.332 0.474
0.25 0.25 0.25
2.15 6.15 9.43
95 * 95 84.95 81.97
98.1 91.1 91.4
0.022 0.0675 0.103
280 280 300
6.2 8.3 8.85 9.2 9.9 10.9 12.05
0.000 0.015 0.052 0.105 0.285 0.465 0.497
0.10
0.10 0.10 0.10. 0.10 0.10 0.10
1.0 6.9 15.7 23.0 40.3 50.6 48.0
97.0 91.2 81.5 76.0 53.2 41.7 41.8
98.0 98.1 97.2 99.0 93.5 92.3 89.8,
0.0102 0.0703 0.161 0.232 0.431 0.548 0.538
300 320. 340 320 320 280 300
6.5 7.9 8.9 9.9 10.8 12.25 11,3
0.000 0.006 0.058 0.285 0.457 0.498 0.485
0.10 0.10 0.10 0.10 0.10 0.10 0.10
6.1 7.1 15.5 43.5 50.2 46.1 51.0
67.3 66.3 66.0 35.3 28.3 23.4 27.0
73.4 73.4 81.5 78.8 78.5 69.5 78.0
0.083
300
247
0.190 0.552 0.640 0.665 0.654
300 300 300 300 300
247 247 247 253 247
11.9 10.3 9.6
0.496 0.378 0.202
0.10
19.0 15.6 9.5
65.0 73.4 76.9
84.0 89.0 86.4
0.226 0.175 0.110
260 280 280
0.10 0.10
Table II. G. Equiv./Liter
PH
CG
cc1
11.8 11.25 12.2
0.495 0.484 0.498
0.10 0.10 0.10
From slopes of plots 11.8 11.8
0.495 0.495
0.25 0.25
...
0.50
...
Transport, % G c1Total 58.2 60.6 49.9 similar t o
31.0 27.9 24.2
89.2 88.5 74.1
Figure 5
37.0 35.0
47.7 44.5 Figure 5
84.7 79.5
...
...
...
ta ta
0.653 0.686 0.673 0.685 0.500 0.175 0.437 0.440 0.480 0.315 0.0925 0.3325 0.125 0.0575
Cc(1
- tG)
3.80 4.51 4.13 3.98 2.50 0.583 1.57 1.59 1.92 0.90 0.231
1.11Q 0.250 0.1150
cc./
349 349 349 349 349
4.98 4.95 4.95 35.8 34.6 34.6 46.3 45.7 45.7 35.8
...
4.95 4.95 4.95
IIA Ma./
8s. Cm. 321.0 185.0 123.5 247.0 40.0 4.95 185.0 123.5 328.0 61.7 4.95 349.0 55.6 4.95
G
C1-
Total
to
Min.
25.8 26.3 28.4
62.8 64.5 66.5
88.6 90.8 94.9
0.292 0.290 0.301
300 200 400
the same as that of glycine ion, as both ions are of about the same size and structure. 2. T h e ratio of the conductance of glycine ion to the conductance of chloride ion (mobility ratio), does not vary appreciably with changes in relative and/or total ionic concentrations.
4.95 4.95 4.95 4.95
Plot of Transport vs. Current
From slopes of plots in
...
...
9 . .
52.5 52.2 52.5 55.0 52.0 55.0 61.7 57.5 58.7
T h e conductances of the two ions are given by Glasstone (6) as: C1- = 76.34 ohms per sq. cm. CHJC02- = 40.90 ohms per sq. cm.
~
The mobility ratio is then approximately: (UG/UC)S
40 9
2 76.3 = 0.53
T h e experimentally determined slopes approach, very closely, the slope calculated theoretically for the upper limit. T h e zero current density limit was determined by extrapolation of the three curves in Figure 6. Comparison with the theoretical value requires that (uG/uC)B = 0.5 to 0.6. Resin phase mobilities were not determined. However, the size of the glycine ion will slow it down more than the chloride ion in the resin phase. This change may or may not be balanced by the greater electrostatic attractive forces experienced by the chloride ion. A value of 0.5 to 0.6 for the resin phases mobility ratio is reasonable. The total percentage of current transferred by the anions is a direct measure of the permselectivity of the A-1 membrane. At lower current densities the efficiencies were always greater than 85% and went as high as 98% (Table I), but a t higher current densities dropped to 70 to 90%. This undoubtedly, indicates the importance of water transport a t higher current densities. The zwitterion transport, and therefore the water transport, increases with increasing current density. This is logical, as the water transport is caused by the viscous drag of mobile ions on the solvent. At high current density mobile ions are depleted a t the interface, necessitating a higher ionic velocity to maintain the flux. This, in turn accounts for a higher drag force per molecule and therefore a larger relative water transport. VOL. 50, NO. 4
0
APRIL 1958
695
transport number of ion A mobility of a given ion vA migration velocity mole fraction of ion A in memxA brane = solution mole fraction a t memy brane-solution interface 2 = valency z = distance across the laminar film, cm. ( d N / d B ) = number of diffusing ions per unit time (dcldz) = concentration gradient ( d E / d t ) = potential gradient tA
IV.
Table
Equilibrium Constant of Glycine-Sodium System
Chloride-Amberplex-AI
K=!@x?!?‘ YCI g
x
Resin W t . , G. 1.8000 1.8410 1.8998 1.8071 1.8248
= =
2G
solution concentration resin phase concentration
YG
YC I
0.0206 0.0586 0.0340 0.0933
0.0306 0.0301 0,0300 0.0296
(NaNOd
(blank)
Table V.
zG
x
zc 1
103
0.144 0.099 0.270 0.0870 0.000
...
I
