NEW DIALYSIS MEMBRANE Y O S H I O O D A , A K l R A N I S H I H A R A , H l R O S H l H A N I , A N D T A D A S H I Y A W A T A Y A Research Laboratory, Asahi Glass Go., Ltd., Yokohama, J a p a n
A new synthetic membrane has been developed for industrial applications of dialysis. The membrane, weakly basic anion exchanger with a high ion exchange capacity, is mechanically strong and acid-resistant. The behavior of the membrane to dialysis of the various solutions containing an acid and its salt was investigated. The membrane has been shown to function efficiently for the separation of an acid from its mixture, except for the system in which the strong formation of complex ions occurs. The high separation by the membrane is attributed to the fact that the ion-exchange capacity of the membrane is large, and the diffusivity of hydrogen ion is very high compared with that of other cations. As an example of practical application of the membrane to dialysis process, the separation of sulfuric acid from the mixture with nickel sulfate is described, and the efficient removal of the acid is demonstrated, as a unit operation has recently attracted attention to industrial applications ( 7 , 751, along with the development of new dialysis membranes. One of them is a plastic film like Nalfilm (73) and Hi-Sep membrane. Vromen (15) ha5 suggested the possibility in commercial application of Hi-Sep membrane to the systems where dialysis separation was considered impossible a few years ago. This membrane shows no demonstrable ion-exchange properties. O n the other hand, attempts were made to use ion-exchange membranes. A cation-exchange resin membrane ( 7 ) was studied with respect to the function of separating electrolytes and nonelectrolytes. The use of an anion-exchange membrane as a dialysis diaphragm was proposed (5, 72) by Japanese investigators to separate an acid and electrolytes or nonelectrolytes from their mixtures by dialysis. The proposal has b-en based on the fact that the anion-exchange membranes exhibit high permeability to acid compared with cation-exchange membranes. A new membrane (8), Selemion DMT (Asahi Glass Go., Ltd., Japan), has been developed for commercial uses in dialysis. This is a weakly basic anion-exchange resin membrane with a high ion-exchange capacity’and, in this respect, differs from the dialysis membranes which have been reported so far. A high degree of separation in dialysis process is achieved by the use of this membrane. In the dialysis of a solution containing sulfuric acid and nickel sulfate, for example, the ratio of dialysis coefficients of Hi-Sep 70 membrane is reportedly 11 to 13 (3, 73), whereas the corresponding value of D M T membrane is 60, although the condition of dialysis operation is not always the same. Such a high value is hardly expected by the use of a noncharged membrane in ordinary dialysis operations. Among many industrial applications of D M T membrane to dialysis processes, the separation of sulfuric acid and glucose in the process of manufacturing glucose from wood (72) and the separation of sulfuric acid and nickel sulfate in the process of electrolytic refining of copper are now under development. From a practical viewpoint, two important factors are involved in dialysis process, one of which is the transfer rate of substances through the membrane and the other the degree of separation. In any commercial operation, the separation of two components by dialysis and the capacity of dialyzer should be as high as possible. Nevertheless, as the degree of separation generally decreases with rise in the rate of dialysis, a compromise on the two competitive factors should be accepted in preparing the membrane and in dealing with the practical dialysis systems. IALYSIS
244
I & E C P R O D U C T RESEARCH A N D D E V E L O P M E N T
In this work, the characteristics of Selemion D M T in dialysis of various systems were investigated and a mechanism for the high degree of separation was discussed. Dialysis Coefficient
In the dialysis process, the transfer rate of substances through a membrane is considered to obey Fick‘s law on the assumption that an ion-exchange equilibrium is established between the phases of membrane and solution. It is then given by the following equation which is similar to Fick’s diffusion equation (6, 7 )
W = U,,.A.Cm
(1)
where W(mole/hour) is the transfer rate of a substance through a membrane, A(sq. meter) the effective area of the membrane, U,(mole/sq. meter.hour.M) the over-all dialysis coefficient of the substance, and C,(M) the logarithmic mean bulk formula concentration difference across the membrane over the whole period of a run. A change in unit of U,from mole/ sq. m e t e r . h o u r . M to cm./min. is easily made by dividing the value of U, by GOO. When two dissolved substances are present, the separation factor, Sba,for them is defined as
These relations assume that no water transfer occurs through the membrane. According to the knowledge of mass transfer, the over-all rate of dialysis includes an element of rzsistance owing to the stagnant liquid films a t interfaces of the membrane and solution. Thus, the over-all dialysis coefficient (6) can be considered as the following combination
l/uo=
-+ 1 / u ,
l/um
(3)
where Urn is the membrane dialysis coefficient, and U L the combined liquid film transfer coefficient which is remarkably affected by flow conditions of solution. Experimental
Membranes. For dialysis experiments, Selemion D M T membrane with a standard porosity (DMT-1) was mainly used, the dialysis coefficients of which were measured by a method of bath experiment. Samples for the measurements were taken from one sheet of commercial standard-size DhlT membrane, 88 X 88 cm. The membrane is composed of an
~~
Table I. Properties and Functional Behaviors of Selemion DMT-1 Membrane Nitrogen content for wet membrane, meq./100 sq. cm. 5.2 Ion exchange capacity in chloride form For wet membrane, meq.jl00 sq. cm. 4.0 For dry resin, meq./gram 4.3 Water content for resin, 96 0.5.W MgC12 In solution of 1M HC1 35 In solution of 1.M H2S04 0 . 5 M ZnSO4 29 Ion concentration inside membrane, mole/gram of HzO In solution of l.M HC1 0 . 5 M MgClz Ion Species Ratio R+a C1H+ Mg+z H+/Mgf2 In solution, molehiter ,.. 2.00 1.00 0.50 2.0 Inside membrane, obsd. 8.02 9.15 0.82 0.16 5.1 Inside membrane, calcd. 8.02 8.32 0.24 0 . 0 3 8.0 In solution of 1.M H2S04 0 . 5 M ZnSO4
++
+
+
In solution, calcd., mole/liter Inside membrane, obsd. Inside membrane, calcci.
...
1.26
8.64 8.64
5.27
0.24 2.43
4.03
2.45
1.5
1.6 4.6
0.05
Acid Solutions H2SOd H3P0,
-.
HF
B-SO1Hb
0.17
0.15
0.17
0.14
0.18
0.894
0.189
0 , 0 7 1 0.123
~~
HCl
Thickness of swollen membrane in 1 M solutions, mm. Clonductance of membrane in O.lAT solutions. mho,'sq. crn. (25' C . ) Concentration potentiale across the membrane in concentration chain of 0.05 niole/l.O mole, mv.
0.50 0.41
0.74
0.67 0.23
- 39.9
+13.4
.,,
...
4.0
14 85
0.026 , . .
(25'C.) a
Fixed ionic groups.
b
Berirenesul/oriic acid.
c
T h e sign ofpotentials is shown on the side o/ more dilute solution.
epoxy resin cured with amines and is reinforced with a synthetic fiber cloth of poly(ethy1ene terephthalate). T h e thickness of the swollen membrane is 0.015 cm. in 1M solution of sulfuric acid. Mullen burst strength of the wet membranes is 5.5 kg./sq.cm. Properties and functional behaviors of DMT-1 membrane are given in Table I. Chemicals. All the chemicals used were of guaranteed reagents. Analysis. Hydrogen ion was titrated by standard sodium hydroxide solution. Ferrous ion and other metal ions were titrated with potassium permanganate solution and EDTA solution, respectively. Acid in the mixture with its salt was determined either by direct titration of hydrogen ion or by the calculation of the difference in amount betlveen the total solute and the salt, the former of which was determined by the titration of hydrogen ion gained by passing the mixture through a column uf cation-exchange resin in hydrogen form. X quantitative analysis for benzenesulfonic acid was made by the titration of hydrogen ion and by the ultraviolet absorption method using Hitachi recording spectrophotometer
ET'S-?. iMeasurements of Dialysis Coefficients. The cell for batch dialysis experiments consists of two half cells made of Lucite with a clipped u.indow of 3 X 5 cm. on one side ivall, two stirrers, and a press device, An assembly of the cell was made by interposing a sample membrane between t\vo half cells and by clamping it with the press device. Prior to the experiment, the sample membrane was equilibrated with a solution to be dialyzed. Effective area of the sample membrane was 3 X 3 cm. The cell assembled was dipped into the water regulated at a given temperature in a thermostat and each chamber was filled with 60 ml. of the solution to be dialyzed and of water, which ivere regulated a t the same temperature. The n v o liquids were stirred mechanically a t about 500 r.p.m. as qccasion demanded. .4fter a dummy dialysis run for 1 to 1.5 hours, the solutions
in both chambers were renewed and the dialysis run was consecutively resumed exactly for 1 hour. From the transferred substances which were obtained by chemical analysis of the solutions after and before the run, rhe dialysis coefficients were calculated by Equation 1. The dialysis coefficients were shown with the average values for two runs a t least. The accuracy in the dialysis coefficient for acids and salts is about i 4 % and &lo%, respectively. Measurements of Water Transfer through the MemDIFFERENCE ACROSS THE MEMBRANE brane. CONCENTRATIOS (OSMOSIS). The measurement of osmosis was made by use of the cell which was attached with a horizontal capillary tube to read the small change in volume of solution. Two chambers on both sides of the membrane tvere filled with the solutions of different concentration or the solution and water, which were renewed after about half an hour. After a certain time elapsed, a linear relationship between the readings of the movement of solution head in the capillary tube and the time was observed, from which the rate of osmotic tvater transfer was calculated. STATIC PRESSURE DIFFERENCE ACROSS THE h f E M B R 4 K . E . The same cell and almost the same procedure mentioned above were used. After applying a pressure difference across the membrane with the water column on one side of the solution, the movement of solution head in the capillary tube was read against time. Similarly, the rate of \vater transfer through the membrane \vas calculated from the linear relationship obtained under a steady state. General Characterization Procedures. THICKYESS. The thickness of membranes was measured by a micrometer. ION-EXCHANGE CAPACITY A S D L4BSORPTIOY O F SOLUTES (DOYSANSORPTION). The ion-exchange capacity of the membrane was determined in chloride form by a method used for weakly basic anion exchangers (4)-i.e., a sample membrane converted into chloride form was rinsed with methanol, and then the chloride ion exchanged with sulfate ion was VOL. 3
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S E P T E M B E R 1964
245
titrated. For comparison, the nitrogen content of the membrane was measured by the Kjeldahl method. An acid and its salt imbibed in the membrane in a solution containing the acid and its salt were determined in the following proc'edure. For the Membrane Equilibrated with a Solution Containing Hydrochloric Acid and Magnesium Chloride. T h e equilibrated sample membrane was washed quickly with methanol to remove the acid solution on the membrane surfaces, and then was leached with sodium sulfate solution of 0.LV. T h e chloride and magnesium ions in the leachates were titrated with silver nitrate and EDTA solution, respectively. 'The amount of chloride ion imbibed in the membrane was obtained as the difference in amount between the determined chloride and the chloride equivalent to the ion-exchange capacity. T h e imbibed acid, in this case: amounts to the difference between the imbibed chloride ion and the magnesium ion. For the Membrane Equilibrated with a Solution Containing Sulfuric Acid and Zinc Sulfate. The imbibed acid in this system is difficult to determine directly, because both sulfate and bisulfate are ion species in counter ions inside the membrane. An indirect determination of the imbibed acid, however, will be allowed by the following procedure and calculation, assuming that a n equilibrium among sulfate, bisulfate, and hydrogen ions in solution applies even inside the membrane, the amount of fixed ionic groups is the same in both sulfuric acid and hydrochloric acid solutions, and the salt of the fixed ionic groups fully dissociates. T o obtain the sum of the sulfate and the bisulfate inside the membrane, the equilibrated sample membrane was leached with 0.jAt7sodium hydroxide solution, and the total sulfate in the leachates was determined by the gravimetric analysis. For the imbibed zinc ion, another equilibrated sample membrane was rinsed with water, and then the zinc ion was titrated with EDTA solution. T h e concentration of the sum of the sulfate a n d the bisulfate inside the membrane, [TI, the dissociation eqcilibrium of the bisulfate, and a n electroneutrality condition inside the membrane are expressed by Equations 4, 5 , and 6 :
[TI = [HSOa-]
+ [S04-2]
K z f = [ H + l [S04-'1 [HSO,-]
system with magnesium chloride where chloride ion is a single counter anion. In the system containing sulfuric acid. the existence of both sulfate and bisulfate as counter ions indicates that the Donnan equilibrium as well as an equilibrium among sulfate, bisulfate, and hydrogen ions is involved in ionexchange equilibrium process. Such an equilibrium among the hydrogen ion and the counter ions seems to enhance the concentration of the hydrogen ion as compared with the system with hydrochloric acid. T h e observed ion concentration is high compared Lvith that calculated from the ion concentration in surrounding solution using the Donnan relarion and an electroneutrality condition. One reason for this is that the association of ions and the activity coefficient of ions are disregarded in these calculations. The calculation for the system Lvith sulfuric acid does not always satisfy the equilibrium among sulfate. bisulfate, and hydrogen ions inside the membrane. Dialysis Coefficient of Single Electrolyte. Dialysis coefficients of D M T for acids and salts under various conditions are listed in Table 11.
Table II. Temp.,
O
C.
Dialysis Coefficient in Single Solution .&ids ( 7M Solution/Membrane IH2O:D.MT-7) HCl H ~ S O I H3P04 HF B-SOSH' 3.63 1.87 0 . 6 9 1.39 0.16 5.24 2.48 1.11 1.74 0.34 4.2 2.20 0.92 1 . 6 4 0.30 7.79 4.15 1 . 7 3 2.59 0.61
13 25 25b 40 Activation energy for diffusion inside membrane, kcal./ 5.3 5.7 4.3 8.2 mole 5.2 c',, mole/sq. meter/ hour, M (25'C.) 21 19 11 28 ... Diffusion coefficient in solution, sq. cm./ sec.(20°C.) X lo6 2 . 6 1.8 0.9 , , , ... Salts and Glucose (0.5MSolution/Membrane/H~O:DMT-I) T e m p . , ( h'H~q)zSO4 ZnSO 4 CuSO 'Vis0 Glucose O
c.
25
0.37 0.07 0.07 0.05 Bentenesulfonic acid. b Under quiescent condition. the membrane was dyed w i t h color of cupric sulfate solution. a
c
0.07 In this case
(4)
Dialysis coefficient of acid depends strongly upon the nature of the acid, and the variation in dialysis coefficient is seen to [R+] [H+] 2[ZnA2] = [HSOI-] 2 [ S 0 4 - 2 ] (6) correspond to that in membrane conductance, referring to the results of Table I. T h e organic acid is less dialyzable than the where [ R + ] is the concentration of the fixed ionic groups obinorganic acid. tained from the ion-exchange capacity and water content: and T h e combined liquid film transfer coefficients: are calK P ' the apparent second dissociation constant of sulfuric acid. culated by Equation 3 from the difference bet\ceen the dialysis I t is related to K Pin the equation: K n = K 2 ' ~ H + . ~ J 0 4 - 2 ~ ~ H S O a coefficients under stirred and quiescent conditions, and also G 0.01 and the values adopted for Kz' in solution and inside are given in Table 11. These are large compared with the the membrane are 0.1 and 0.3 (77), respectively. These membrane dialysis coefficient equations can be solved. Thus, the concentration of the hyT h e activation energy for diffusion inside the membrane can drogen ion and other ions \vas obtained from these equations be determined from the slope of the line obtained by plotting by the determination of [R-1. [TI, and [ Z n f 2 ] . the logarithm of the membrane dialysis coefficient against the ~ V A T E R CONTENT,CONDUCTANCE, A N D CONCENTRATION reciprocal of absolute temperature. It is noteicorthy that the POTENTIAL.These were measured by routine methods. less dialyzable organic acid provides higher activation energy for diffusion inside the membrane. Results and Discussion Dialysis coefficient of sulfate salt is much smaller than that of Ion Concentration inside the iMembrane. Table I gives sulfuric acid, the concentration of ions inside the membrane. An apparent diffusion coefficient (sq.cm:'sec.) can be calT h e Donnan equilibrium excludes co-ions, in this case, culated from the membrane dialysis coefficient using the folcations. T h a t is. the concentration of co-ions is smaller lowing equation, inside the membrane than in surrounding solution. An exclusion of bivalent cation occurs Iehich is rzmarkable ichen compared with that of hydrogen ion, especially in the
+
246
l&EC
+
(5)
+
PRODUCT RESEARCH A N D DEVELOPMENT
a re. NO
. .
0 0
4
t-
-
mr.
. .
-1
-0
N t-
en m
. .
e
b0
N
Lnmm
. .
d 0
m
n m
e.-. N O
d 1
. .
t-*N
. .
-4.0
NO
Ln Q\
N
t-m
99 m 0
W c\
G I
I
t-
- 0 0
c\
.
0-0
.
N O 0
1
N
N
mm
99
m
N O
N
e
Ln
y?
2g
P
3
e n
NO
m
m W i0 n
. . d e
NO
*
t m- 0 e
. .
m
NO
W Q
mN
t-mm
999 NO0
m OI
6
D
t-r-
m d m
??e
N O 0
m N
where 6 is the thickness of swollen membrane in centimeters. Orders of apparent diffusion coefficients are l o p 6 for sulfuric for its salts, and they are small compared acid and lo-' to with that of the diffusion coefficients in solution. LrE19o4of DMT-1 membrane converted into the unit of 0.41 and can be compared with cm./min. X l o 2 is 0.37 that of Hi-Sep membrane, 1.3 (75). Separation of Two Electrolytes from Their Mixture by Dialysis. The experimental results for the various systems containing two electrolytes, one of which is sulfuric acid or hydrochloric acid, are tabulated in Tables I11 and IV, respectively. The measured separation factors, S, for their mixtures are so large that the excellent function of D M T membrane in practical dialysis operation is expected. The separation factor for the system with ammonium sulfate is small compared with that for the systems with 2 : 2 electrolytes because the diffusivity of ammonium ion is higher than that of other metal cations concerned. The separation factor for the system containing HzSO4 and Fe2(S04)3 is a little low among the systems with 3 : 2 electrolytes, which fact will be explained as a result of the complex ion formation between S01-2 and Fe+3. Probably the contribution of complex ion such as Fe(S04)2- ion (76) to the diffusion process inside the membrane takes place to a considerable extent, as compared with two other systems. A similar case is observed to occur to a remarkable extent in the system containing HC1 and ZnClz where the formation of complex anions such as ZnCl3- and ZnC14-* (9)has been known. Separation factor for this system as shown in Table IV is 2.5, which is much smaller than that, 67, for the system containing H z S 0 4 and ZnSOd under the same conditions as shown in Table 111. The system containing HC1 and CuC12 appears to reveal a similar tendency. The formation of complex ion implicates the relation of the transfer rate of a substance through the membrane to the driving force for each ion species and, therefore, makes ambiguous the meaning of U or S obtained from the simple expression of Equation 1 or 2 by formula Concentration. Membrane dialysis coefficients in the system with zinc sulfate or ferric sulfate were obtained under different concentration conditions where the concentration of acid was varied to 2 M and 3 M , keeping the concentration of salt constant, or, in one case, the acid solution was used in place of water on one side of the membrane, maintaining the concentration difference of 1M across the membrane. As shown in Table 111, the rise in concentration of the acid results in the decrease in dialysis coefficient of the acid, while the dialysis coefficients of salts appear to change in a rather complicated way. T h e replacement of water with acid solution on one side of the membrane decreases the dialysis coefficients of salt in two cases of ZnSO4 and Fea(S04)~. T h e over-all dialysis coefficients of sulfuric acid or hydro-
W t-
Table IV.
Dialysis Coefficients for Mixtures Containing Hydrochloric Acid and I t s Salts
, 7&Hglt]l / Mem branel HzO, 25
m
Concn.. M HC1' Salt
D ___ M T -1
C.:
HCI FeC12
HCl MgCl2
HCl ZnCll
HCl CuCl2
1.12 0.49
0.91 0.50
0.74 0.55
0.73 0.47
7.70 0.04 190
1.36 0.55 2.5
7.28 0.22 33
8.18 0.07 120
Under stirred condition WTCl
U d ., S
VOL. 3
NO. 3
SEPTEMBER
1964
247
Water Transfer through DMT-1 Membrane Osmotic Water Trans,fer Rate, l . / s q . meterlhour -0.12 HC1, 1MIO.05M -0.08 HSP04: l>M/O.05M B-SO3H6, 1M/O, 05M -0.05 -0.12 Na2SO.. l M i H z O Glicose; lM/H;O -0.13
Table V.
Rate, l . / s q . meterlhour
+ O . 30 -0.10 -0.06 -0.17 + O . 15
W a t e r Transfer under Pressure Difference of 70 Cm. of HzO across the Membrane Rate, 1.lsq. meterlhour Rate, 1 . l s q . meterlhour
HaSO,, lM/l.M
0.12
0.5M/O.5 M 1M I 0 .05M 1'M/ 1M
*
HCl! 1M/O. 0 5 M
0.05
Na2S04,0 , j M / O . 5 M Glucose, 0 , 5 M / O . 5 M
7.9
0.26
0.16 0.14 Pressure difference of 20 cm. of HzO.
2.6
Bentenesulfonic acid. b Positive signs show the increase in volume of more Concentrated solution.
0
chloric acid in the presence of their salt become lower, or higher, than that in a single acid solution, depending upon the nature of the salt. The dialysis coefficient of DMT-2 membrane is larger than that of DMT-1 membrane, and the rise in dialysis coefficient of the acid is accompanied by the decrease in separation factor. This indicates that the structure of DMT-2 membrane is more porous than that of DMT-1 membrane. A filter-press-type dialyzer which was incorporated with DMT-1 membrane (a total membrane area of 24.3 square meters) was operated by the continuous duplicating flow system in the dialysis of mixtures of HzS04 (413 grams per liter) and NiSOi (24.5 grams per liter). The results obtained for ordinary operation in which about 50 to 80% of the sulfuric acid was recovered showed that the dialysis coefficient of sulfuric aiid and separation factor for the dialyzer were almost the same as those obtained for the small batch dialysis experiment under quiescent condition-that is, the average values of L'HtSOa and S a t 25' C. were 2.0 and 63, respectivdy. During the operation, water transfer was observed to occur from the dilute solution to the more concentrated one through the membrane, and its rate was about 0.1 liter/sq. meter hour under the operational condition for 76% recovery of sulfuric acid. Mechanism for High Degree of Separation by Ion-Exchange Membrane. A function of an ordinary dialysis membrane, such as a cellophane membrane, has been explained by the capillary theory which is based on the bundle of capillary tubes acting mechanically ( 6 ) . For the function of D M T membrane which is an ion-exchange membrane, however, a different mechanism must be considered. A plausible explanation for the behavior of D M T membrane as shown in Tables I11 and IV is based on the fact that the diffusivity of hydrogen ion is much larger than that of competitive metal ions and that the Donnan equilibrium excludes the multivalent cations more than the hydrogen ion owing to the high concentration of fixed ionic groups inside the membrane. The steady-state flux of ions through a membrane is represented by the refined Nernst-Planck equations in the following form (2) :
where
-
=
D -t
=
ZI
=
ci= 248
flux of ion i diffusion coefficient of ion i inside membrane concentration of ion i inside membrane charge of ion i
I&EC PRODUCT RESEARCH A N D DEVELOPMENT
Ti = activity coefficient of ion z inside membrane (o
= electric potential
Y
= flow rate
For the diffusion process inside an anion-exchange membrane, a set of flux equations is subjezt to the restrictions of an electroneutrality inside the membrane and no electric current.
ZZrG
+R
zz,at
=
=
0
(9)
0
(10)
where R is the concentration of fixed ionic groups. In the case of a system containing hydrochloric acid and magnesium chloride, where there is no evidence of the formation of complex ions, the chloride ion is only a common anion in the simultaneous diffusion of the electrolytes. ,4s shown in Table I, the concentrations of co-ions---i.e.. hydrogen and magnesium ions-are much lower than that of the chloride ion in D M T membrane. These cationic co-ions diffuse competitively The ratio of the fluxes of the tMo electrolytes is obtained from Equation 8, and also is related to the experimental result-Le., the value of the separation factor in Equation 2. T h a t is, @H +
~- -
%fg+z
where y o is the rate of osmotic flow, and p and v0 depend on the concentration of the co-ions as well as the chloride ion. In an example of the system: 1 M HCI 0.5.M MgCl?/membrane/HzO, the calculated and observed ratios _ _ are - compared. The first approximation gives DH+/Dyg+2CH+/CM,+2 as the ratio of the fluxes by disregarding the effect of terms other than that of concentration gradients. Figure 1 illustrates a sketch for concentration profiles of the ions inside D M T membrane (weakly basic anion-exchange membrane) in steady-state diffusion for the system, in comparison with that of a noncharged membrane. The ratio. ' DH+/DYgLz. of diffusion coefficient of magnesium ion to that of hydrogen ion may be calculated to be 13 from the data on the limiting molar conductivity in solution. The value is, however, expected to become to a certain extent larger than the calculated one,
+
piem brane
Membrane
I t
c1-
-
H+
(a)
Figure 1 , branes a.
b.
IMHCL
1
tb)
Profile for concentration gradients inside mem-
For noncharge membrane For weakly basic anion-exchange membrane in steady state of diffu-
sion A linearity of concentration gradients and a constancy of f i x e d ionic groups a r e assumed
because the retardation effect on the mobility of the magnesium ion \vith large hydrated diameter would be larger owing to the interaction \sith the matrix of the membrane. The concentration ratio of the t\\ro ions is 5.1, which is obtained from the measurement for Donnan sorption of the electrolytes. Thus, the value of the flux ratio in D M T membrane amounts to 66 as the product of the ratios, while the observed value is 190 X 2 = 380. The calculated value is still considerably smaller than the experimental result. This indicates that terms other than that of concentration gradients also affect to a considerable extent the flux of the ions. ‘The electric potential will cause to a different extent an acceleration, or a retardation of the ions in a simultaneous diffusion process. Such phenomena were demonstrated for diffusion in solution ( 7 4 ) and in a noncharged membrane (75). In the system, the diffusion of hydrochloric acid or hydrogen ion is observed to be accelerated, as compared with that in a single acid solution. T h e diffusion of sulfuric acid in a system containing sulfuric acid and aluminum sulfate also is accelerated. For the system containing sulfuric acid and zinc sulfate, the similar calculation of the flux ratio of the two co-ions presents the value of 1 3 X 1.6 = 21, while the experimental result sho\vs the much larger one of 67 X 2 = 134. The calculated value is expected to be larger, in this case, than 21, because sulfate and bisulfate exist as counter ions, one of which carries the hydrogen ion by diffusion itself. A more remarkable example is the system containing hydrochloric acid and zinc chloride. T h e formation of complex ions in the system brings about competitive diffusions between co-ions as well as counter ions-i.e., C1-, and ZnCls-, ZnC11-2, which carry the zinc ion. Therefore, the formation of such complex anions results in the decrease in separation factor. The separation factor of noncharged membrane ( 3 ) was indicated to correspond to the ratio of cation diffusivities. Then it is 1 3 for the system with magnesium chloride or zinc
sulfate. The fact that the separation ability of DMT membrane is better than that of noncharged membranes is ascribed to the effect because of the Donnan sorption which occurs in ion-exchange membranes. Water Transfer t h r o u g h t h e M e m b r a n e . Water transfer which occurs simultaneously with the diffusion of solutes through a membrane is not taken into consideration in the batch experiments mentioned above. I n most cases of practical operation of dialysis. however. the change in volume of solutions has been observed to take place, and it influences the efficiency in dialysis operation. Table V presents the water transfer through D M T membrane for several systems where either concentration difference or hydrostatic pressure difference is applied across the membrane. The results for osmotic water transfer show the negative osmosis (70: 77)-i.e., the movement of water or solution from more concentrated solution to the more dilute one, except for the case of hydrochloric acid solution and glucose solution. Comparison of the rate of water transfer in hydrochloric acid with that in sulfuric acid solution is of particular interest! in contrast to their negative and positive concentration potentials across the membrane as shown in Table I. For the water transfer due to the hydrostatic pressure difference, a pronounced difference between the rates of water transfer in acid and neutral solutions is observed because of the difference in degree of swelling of the membrane in these solutions. T h e membrane swells 11% in thickness and 87& in length of woof-direction, when transferred from sodium sulfate solution to sulfuric acid solution with the same concentration of 1M . I n the system containing sulfuric acid and its salt, the direction of water transfer obtained in these batch experiments is inverse to that observed in the practical operation of a continuous dialyzer. This is not explainable a t present. Acknowledgment T h e authors thank H. Ukihashi for his helpful discussion, and Asahi Glass Co., Ltd., for permission to publish this paper. Literature Cited (1) Bkduneau, H., Keu. Prod. Chim. 62, 445 (1959). (2) Bergsma, F., Kruissink, Ch. A , , Fortschr. Hochpo1ym.-Forsch. 2, 307 (1961). (3) Chamberlin, N. S., Vromen, B. H., Chem. Eng. 6 6 , No. 9, 117 ( 1 959) . (4) Kunin, R., “Ion Exchange Resins,” p. 345, Wiley, New York, 1958. (5) Kuwata, T., Yoshikawa, S., Uchida, Y., Yawataya, T . (to Asahi Glass Co., Ltd.), Japan. Patent 19,463 (Oct. 16, 1961). (6) Lane, J . A , , Riggle, J. W., Chem. Eng. Progr. Symp, Ser. 55 (24), 127 (1959). (7) Manecke, G., Heller, H., Discussions Faraday Soc. 21, 101 (1956). (8) Nishihara, A . (to Asahi Glass Co., Ltd.): Japan. Patent 20,750 (Oct. 30, 1961). (9) Robinson. R. .4.,Stokes, R. H., “Electrolyte Solutions,” p. 417, Butterworths Scientific Publications, London, 1955. (10) Schlogl, R., 2. Physik. Chem. (Frankfurt) 3, 73 (1955). (11) Sollner: K., Dray, S.,Grim, E., Neihof, R., “Electrochemical Studies with Model Membranes,” in “Ion Transport Across Membranes,” H. T. Clarke, ed., p. 144, Academic Press, New York, 1954. (12) Tanaka, E., Kuwata, T. (to ilsahi Glass Co., Ltd.), Japan. Patent 3,624 (April 20, 1961). (13) Tuwiner, S. B., “Diffusion and Membrane Technology,” ACS Monograph Ser. No. 156, p. 324, Reinhold, New York, 1962. (14) Vinograd, J. R., McBain, J. b’., J . Am. C h f m . Soc. 63, 2008 (1941). (15) Vromen, B. H . , 2nd. En?. ChPm. 54, N o . 6, 20 (1962). (16) ’IYhiteker, R . A , , Davidson. N., J . A m . ChPm. Soc. 7 5 , 3081 (1953). (17) Young, T. F., Blatz, L. .4., Chem. Reu. 44, 93 (1949). RECEIVED for review January 28, 1964 ACCEPTED June 1: 1964 VOL. 3
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