- Email: [email protected]
The permselective coefficient of inorganic ions on reverse osmosis membrane
Dtwlmarion. I7 ( 1975) 257-265 @ Eisevicr Scientific Publishing Company.
THE
PERMSELECTIVE
REVERSE
OSMOSIS
M. IGAWA.
S. YOSHIDA.
InsIilutc uf Inhstrial
Amsterdam
COEFFICIENT
OF
- Prmted in The Netherlands
INORGANIC
IONS
ON
MEMBRANE
Sciwcc.
T. YAMABE Uniwrsity
AUD
N. TAKAI
of Tok_w . X-1
Roppolrgi.
7 chonre. M~nufo-krr.
Tokyo,
106 lfapun)
(Rcccited
May 30. 1975; in rc\ iscd form October 3 I. 1975)
Although many investigations on the rejection of inorganic ions in reverse osmosis were carried out for single-solute systems. their measurements could not be compared exactly with each other because of the change of the membrane property with time. In this paper. the permselective coefficient in reverse osmosis was defined similarly to eiectrodialysis, and those of various ions for mixed-solute systems were measured. From the results, an approximately linear relationship exists between charge-to-radius tive coefficient
a logarithm of the permselective coefficient of each ion and the ratio. The influence of experimental conditions on the permselecwas studied.
There are many papers on the degree of rejection of many inorganic ions. In general. rejection increases with the increase of the charge number of ions and with the decrease of crystal ion radius. The order of the rejection is as follows. Sr’ + > Ba’+ > Lit > Na’ > K’ (I) Mgzf > Cal+ > Naf > K+ (2) However. these results are obtained with a comparison of independently measured rejection. In this paper, the permselective coeffkient in reverse osmosis was defined similarly 20 electrodialysis (3) and then these coefficients were measured by using a mixed solution which consisted of Na+, another cation and a common anion, C I -. The permselective coefficient is defined in Eq. (I),
where Tt is the permselective coefficient of two cations (or two anions), A and B, and A is the sodium ion and B is the other cation in this paper, J is the ion flux across membrane and C is the ion concentration of a raw solution. In the stationary state,
J,
JB = J,. x C;,
= J,. x C-:,.
(3
where J,- is the solution flux and C’ is the solution From Eqs. (I) and (2). the following
ion concentration of the equation is obtained:
permeate
(3) When
salt rejection.
p
_’ - &I
R [:= (C -
C’)/C
x 1001, is used,
Eq (3) becomes
Eq.
(4). . = .I
1 -
ASra\\al in aqueous prediction
and
Sourirajan
becomes
The equation
(3) \\ ho studied
= s,
of inorganic
coefiicient
is rewritten
as follows:
JB = sB f J”H
(3 system
N hose
concentration
is Co mol/l,
c/j = _KB.CO
- co,
salts
more precise.
Jo is the ion flux for the single-solute and s is mole fraction. C,
the permeability
a mixed solute with a common ion. made an exact Using their method. the meaning of the permselec-
of the permselective
= x., - J:.
J,
(4)
solution containing of the permeability.
tive coefficient
.
’ .
R,
(6)
Then Eq. (1) becomes T,”
=
~&z_
(7)
x., - J’j I
So I,” is the ratio of ion flux for the single-solute
systems.
ESPERI.\lENT4L
The
branes method
membranes
developed (6). Casting
diacetate. formamide brane was annealed
used were cellulose
in our laboratory solution
acetate
membranes
and 6-nylon
mem-
(5). They
of cellulose
\+ere prepared by the Manjikian acetate membrane consisted of cellulose
as additive and acetone as solvent. After casting, in water at 8O’C for five minutes. Casting solution
the memof S-nylon
membrane consisted of &nylon, formamide as additive and formic acid as solvent. After casting. the membrane was annealed in boiling water for ten minutes. Memrrernent of tile pernmdectiw COt$kklli The apparatus used for the measurement
was a flow-type
shown
in Fig-l.
PERXISELECTIVE
COEFI-ICIENT
OF INORGANIC
IONS ON RO hlEXfRRANE
259
Stalnfe-ss steel Porous
plate
Membrane Feea
out
c-
Desavlng
Feed I”
cell
FIN. I. Flow sheet
of test nppantus and desalting cell. A-Storage rank for fed solution. C-Apirdror. D-Volumcrric pump. E-Safety val\c, F-Pressure indicator. H-De~l~ingccll. I-Messcylmdcr. J-Prcssurc regulator. K-N? gas homb, L-Flow meter.
B-Hwrer
and cooler,
G-Filter.
M -Thcmmometer.
Unless
stated otherwise.
pressure of 40 h&m’.
0.025
IV; and
permselective a tked rate
temperature
25X.
coefficients
were
measured
of 28 1,Ihr. a feed concentration Perm se - 1ec t ive coefficients were
at an operating
of ions A and 6 calculated from
Eq. (3) or (4). Permselective coefficients of various ions were measured for both cellulose acetate membranes and 6-nylon membranes. When the influence of experimental conditions on the permselective coefficient was studied, the feed solution used was a mihed solution of NaCl and M&I2 and the membrane used was only cellulose
acetate membrane. The ion concentrations in the feed solution and the product solution were determined by a flame photometer for alkaline metal ions and by an atomic absorbance photometer for other metai ions. RESULTS
AND DlSCUSSlON
Refatimsirip
bernecw rhe pernweiectire
The permselective
coefficients
coeficient
(T) measured
and rlre radius of tile hydrated iort are shown
in Table
I. Permselec-
-
\I. IGAWA, TABLE
I
PERhtSELEClWE
COEFRCIEhTS
_.-..--
___--__--loft __
S. YOSHIDA, T. YAMABE AND N. TAKAI
___..___-_-._.-
-.-.
6-n_v/on nrcrnbrane -..---------
-._
-..
.._.--_.
-.-.._
-._--.
_ -... ._..- .-
---___
1.1 0.061
K’ Mgl_‘-
0.97 0.47
Nj’
(-U? r
0.40 0.54
Pb’Cd?I=$r\13+
1.06 0.59 0.97 0.11
0.054 0.044 0.0&J 0.26 0.15 0.17 -
0.45
I
._.-..-._.
-_ coefficients of alkaline metal ions are about unity, but those of multivalent ions are smaller than unity. The permselective coefficient of cellulose acetate membrane was smaller than that of 6-nylon membrane in the case of the same metal. It was considered that ion flux increased with the decrease of rhe radius of the hydrated ion. Of course. the hydrated ion radius increases with the increase of numbers of hydration, but for the same ion the numbers of hydration measured by various methods are much different from each other. However, the number of hydration increases with the increase of electric charge (z) and the decrease of crystal ion radius (r). A convenient criterion for the estimation of the complexing ability of metal ions is the charge-to-radius ratio (7). Therefore we attempted fo use z/r to estimate the number of hydration of the ion and compared T with z/r. tive
L
-
lmm 0 m 0 0
pcrt~ol m0l01 volume compressibility trcnspca-t l-urnentropy
0 0
0
0
0
Electric
:horge/Ian
rod~us
Fig. 2. Number of hydration (measured by many methods)
VS. electric charge/ion
radius.
PERMSELECTIVE
COEFFICIENT
OF INORGANIC
chargelion
Electrtc
Fig. 3. Pa-mselcc!ive co&icient. Of-
3
n
m
”
RejectIon
02
0
Mg Fig. 4.
a4 -
Tzf.
I 1
MgC12
06 Feed
RO hlEMBRANE
rocl,us
VA.electric charge/ion radius.
U oi
IONS ON
08
composhon
R and TE? vs_ feed composition.
10 NO
261
\l.
262
IG4WA,
S. YOSHIDA,
T. YAMABE
AND
33. TAKAI
Fig. 2 shows the relation between the number of hydration measured by many the relationship between log Tzx and -jr methods and z/r, and Fig. 3 shows respectively. In Fi_g. 3. an approximately linear relationship exists between log T:t and z/r in both the cellulose acetate membrane and the 6-nylon membrane, except for Fe3+ ion. From Fig. 3, we can say that the permselective coefficient is estimated by the value of
z/r.
lnfltrertce of lhe esperitnedd co,tditiotts INI rc$vtioJt and p&WJJSekrtiW coe$iri~wt Rejection and permselective coefficient VS. feed composition In this ekperirnent. the total molarity of the raw solution was 0.020 111. From Fig. 4, the influence of the feed composition on the permselective coefficient is The value calculated from Eq. (7), negligible for cellulose acetate membranes. 7-T = Jz/J,“, is 0.061. and this value is nearly equal to the value calculated from (1)
Eq. (3) for mixed-solute
system.
Rejection
increase with the increase of the Na”
that
the smaller
its rejection
the relative
of Na’
and the permselective coefficient result agreed with the fact of the more permeable ion the lower
mole fraction. This
concentration
(8).
100 Remron
of
MgC12
I
I
007
01
Feed cuncentmtlon
Fig. 5. R and Tzz
vs. feed concentration.
PERMSELECTIVE
COEFFICIENT
OF ISORGANIC
IONS ON
263
RO LIEWRRANE
(2) Rejection and permselective coefficient US. feed concentration in this experiment, the molar ratio of the feed solution was 1: 1. In Fig. 5, the permselective coefficient hardly changes with tked concentration. of the rejection
osmotic
in the high
concentration
region
was caused
and the decrease
by the
increase
of
pressure.
(3) Rejection and prmselectike coefficient Z-S.feed rate In this experiment. feed rat, was chaqed from 4 I/hr to 30 I/hr. The increase of tkd rate decreases the concentration polarization on the membrane surface and consequently increases the rejection. influenced by the feed rate. (4)
But the permselective
coefficient
was hardly
Rejection and permselective coefficient ti.g. I,lAP
In this experiment, AP is the pressure on the gauge (kg/cm*). and AP was As shown in Fig. 6, the permselective changed from 90 kg/cm” to IS kg/cm’. coefficient increases with the decrease of the reciprocal of pressure. The reason that IjAP was used as the abscissa is that when l/AP becomes infinitely small, salt rejection shows the reflection coefficient. 6 (9). We see that the o of NaCl and
I
004
002 IIAP
Fig. 6. R and Tzz vs. II&‘.
006
I
264
51. IGAWA, S.
in the cellulose M&I, tively. The permselective
YOSHIDA, T. YAYABE AND N. TAKAI
acetate membrane are about 0.95 and coefficient increased with AP.
> 0.996 respec-
(5) Rejection and the permselective coefficient CCLoperating temperature In this experiment, the operating temperature \vas changed from 8°C to4O”C. This experiment was carried out by batch-type apparatus because it is very difficult tc keep the temperature of the flow-type apparatus constant. Both ion flux and volume flux increase with operating temperature btit rejection is constant and then the permselective coefficient is constant. (6) Rejection and the permsc!ecti\e coefficient LX annealing temperature This experiment was carried out in order to study the influence of the membrane porosity on rejection and the permselectivc coefficient. As shown in Fig. 7, the membrane annealed at low temperature and. consequently. having large porosity. showed low rejection and a high permselective coetlkient. It was thought that the difference of variation between NaCl rejection and MgCl r rejection was caused by the variation of the ratio of the hydrated ion radius to the pore size of the skin layer of the membrane_ 100
6-ok
e-or
76-c Anneahng
Fig. 7. R and Tz!
vs.
temperature
annealing temperature.
PERMSELECTIVE
COEFFICIENT
OF lNORGI\NIC
265
IONS ON RO MEIWRANE
REFERENCES
I. 3 ;: 4 5. 6. 7. 8. 9.
S. S. T. J. S. S. F. p. T. S.
SOIJRIRAJAN.
Id. Eng. Chet~~. Frrdunwn~~ds. 2 (1963) 51. H. YA.HA.UOTO AVD H. SAITO. Nippun Kaisui Cakkuishi, Y~UAHE AYD M. SESO. Im E.vchunge .Wem&runes. Giho-do. 1964. P. AGRAWAL A&D S. SOURIRAJAS. Inch. Eng. Chem. Process Design YOSHIDA. N. TAKAI xsc T. YAIIAEC. Nlpport Koisrri Gd-kaishi. 26 MASJIKIA~, Id Eng. Chem. Prod. Res. Drvrf~p., 6 (1967) 23. BAWLO AUD R. Jorrssou, Cuorrlraufron Chenrislr_v. W. A. Benpmin. 122. G. H~DGSOS. Desalinufiun. 8 (1970) 99. KILWRA, Proc. Fourth Inrrrt~ S_~mp. on Frerir Water front lhe Seu.
OKAUOTO.
21 (1968) 245. p_ 139. Develop., 9 (1970) (1973) 279. New York,
4 (1973)
N.Y..
197.
18.
1964.
THE
PERMSELECTIVE
REVERSE
OSMOSIS
M. IGAWA.
S. YOSHIDA.
InsIilutc uf Inhstrial
Amsterdam
COEFFICIENT
OF
- Prmted in The Netherlands
INORGANIC
IONS
ON
MEMBRANE
Sciwcc.
T. YAMABE Uniwrsity
AUD
N. TAKAI
of Tok_w . X-1
Roppolrgi.
7 chonre. M~nufo-krr.
Tokyo,
106 lfapun)
(Rcccited
May 30. 1975; in rc\ iscd form October 3 I. 1975)
Although many investigations on the rejection of inorganic ions in reverse osmosis were carried out for single-solute systems. their measurements could not be compared exactly with each other because of the change of the membrane property with time. In this paper. the permselective coefficient in reverse osmosis was defined similarly to eiectrodialysis, and those of various ions for mixed-solute systems were measured. From the results, an approximately linear relationship exists between charge-to-radius tive coefficient
a logarithm of the permselective coefficient of each ion and the ratio. The influence of experimental conditions on the permselecwas studied.
There are many papers on the degree of rejection of many inorganic ions. In general. rejection increases with the increase of the charge number of ions and with the decrease of crystal ion radius. The order of the rejection is as follows. Sr’ + > Ba’+ > Lit > Na’ > K’ (I) Mgzf > Cal+ > Naf > K+ (2) However. these results are obtained with a comparison of independently measured rejection. In this paper, the permselective coeffkient in reverse osmosis was defined similarly 20 electrodialysis (3) and then these coefficients were measured by using a mixed solution which consisted of Na+, another cation and a common anion, C I -. The permselective coefficient is defined in Eq. (I),
where Tt is the permselective coefficient of two cations (or two anions), A and B, and A is the sodium ion and B is the other cation in this paper, J is the ion flux across membrane and C is the ion concentration of a raw solution. In the stationary state,
J,
JB = J,. x C;,
= J,. x C-:,.
(3
where J,- is the solution flux and C’ is the solution From Eqs. (I) and (2). the following
ion concentration of the equation is obtained:
permeate
(3) When
salt rejection.
p
_’ - &I
R [:= (C -
C’)/C
x 1001, is used,
Eq (3) becomes
Eq.
(4). . = .I
1 -
ASra\\al in aqueous prediction
and
Sourirajan
becomes
The equation
(3) \\ ho studied
= s,
of inorganic
coefiicient
is rewritten
as follows:
JB = sB f J”H
(3 system
N hose
concentration
is Co mol/l,
c/j = _KB.CO
- co,
salts
more precise.
Jo is the ion flux for the single-solute and s is mole fraction. C,
the permeability
a mixed solute with a common ion. made an exact Using their method. the meaning of the permselec-
of the permselective
= x., - J:.
J,
(4)
solution containing of the permeability.
tive coefficient
.
’ .
R,
(6)
Then Eq. (1) becomes T,”
=
~&z_
(7)
x., - J’j I
So I,” is the ratio of ion flux for the single-solute
systems.
ESPERI.\lENT4L
The
branes method
membranes
developed (6). Casting
diacetate. formamide brane was annealed
used were cellulose
in our laboratory solution
acetate
membranes
and 6-nylon
mem-
(5). They
of cellulose
\+ere prepared by the Manjikian acetate membrane consisted of cellulose
as additive and acetone as solvent. After casting, in water at 8O’C for five minutes. Casting solution
the memof S-nylon
membrane consisted of &nylon, formamide as additive and formic acid as solvent. After casting. the membrane was annealed in boiling water for ten minutes. Memrrernent of tile pernmdectiw COt$kklli The apparatus used for the measurement
was a flow-type
shown
in Fig-l.
PERXISELECTIVE
COEFI-ICIENT
OF INORGANIC
IONS ON RO hlEXfRRANE
259
Stalnfe-ss steel Porous
plate
Membrane Feea
out
c-
Desavlng
Feed I”
cell
FIN. I. Flow sheet
of test nppantus and desalting cell. A-Storage rank for fed solution. C-Apirdror. D-Volumcrric pump. E-Safety val\c, F-Pressure indicator. H-De~l~ingccll. I-Messcylmdcr. J-Prcssurc regulator. K-N? gas homb, L-Flow meter.
B-Hwrer
and cooler,
G-Filter.
M -Thcmmometer.
Unless
stated otherwise.
pressure of 40 h&m’.
0.025
IV; and
permselective a tked rate
temperature
25X.
coefficients
were
measured
of 28 1,Ihr. a feed concentration Perm se - 1ec t ive coefficients were
at an operating
of ions A and 6 calculated from
Eq. (3) or (4). Permselective coefficients of various ions were measured for both cellulose acetate membranes and 6-nylon membranes. When the influence of experimental conditions on the permselective coefficient was studied, the feed solution used was a mihed solution of NaCl and M&I2 and the membrane used was only cellulose
acetate membrane. The ion concentrations in the feed solution and the product solution were determined by a flame photometer for alkaline metal ions and by an atomic absorbance photometer for other metai ions. RESULTS
AND DlSCUSSlON
Refatimsirip
bernecw rhe pernweiectire
The permselective
coefficients
coeficient
(T) measured
and rlre radius of tile hydrated iort are shown
in Table
I. Permselec-
-
\I. IGAWA, TABLE
I
PERhtSELEClWE
COEFRCIEhTS
_.-..--
___--__--loft __
S. YOSHIDA, T. YAMABE AND N. TAKAI
___..___-_-._.-
-.-.
6-n_v/on nrcrnbrane -..---------
-._
-..
.._.--_.
-.-.._
-._--.
_ -... ._..- .-
---___
1.1 0.061
K’ Mgl_‘-
0.97 0.47
Nj’
(-U? r
0.40 0.54
Pb’Cd?I=$r\13+
1.06 0.59 0.97 0.11
0.054 0.044 0.0&J 0.26 0.15 0.17 -
0.45
I
._.-..-._.
-_ coefficients of alkaline metal ions are about unity, but those of multivalent ions are smaller than unity. The permselective coefficient of cellulose acetate membrane was smaller than that of 6-nylon membrane in the case of the same metal. It was considered that ion flux increased with the decrease of rhe radius of the hydrated ion. Of course. the hydrated ion radius increases with the increase of numbers of hydration, but for the same ion the numbers of hydration measured by various methods are much different from each other. However, the number of hydration increases with the increase of electric charge (z) and the decrease of crystal ion radius (r). A convenient criterion for the estimation of the complexing ability of metal ions is the charge-to-radius ratio (7). Therefore we attempted fo use z/r to estimate the number of hydration of the ion and compared T with z/r. tive
L
-
lmm 0 m 0 0
pcrt~ol m0l01 volume compressibility trcnspca-t l-urnentropy
0 0
0
0
0
Electric
:horge/Ian
rod~us
Fig. 2. Number of hydration (measured by many methods)
VS. electric charge/ion
radius.
PERMSELECTIVE
COEFFICIENT
OF INORGANIC
chargelion
Electrtc
Fig. 3. Pa-mselcc!ive co&icient. Of-
3
n
m
”
RejectIon
02
0
Mg Fig. 4.
a4 -
Tzf.
I 1
MgC12
06 Feed
RO hlEMBRANE
rocl,us
VA.electric charge/ion radius.
U oi
IONS ON
08
composhon
R and TE? vs_ feed composition.
10 NO
261
\l.
262
IG4WA,
S. YOSHIDA,
T. YAMABE
AND
33. TAKAI
Fig. 2 shows the relation between the number of hydration measured by many the relationship between log Tzx and -jr methods and z/r, and Fig. 3 shows respectively. In Fi_g. 3. an approximately linear relationship exists between log T:t and z/r in both the cellulose acetate membrane and the 6-nylon membrane, except for Fe3+ ion. From Fig. 3, we can say that the permselective coefficient is estimated by the value of
z/r.
lnfltrertce of lhe esperitnedd co,tditiotts INI rc$vtioJt and p&WJJSekrtiW coe$iri~wt Rejection and permselective coefficient VS. feed composition In this ekperirnent. the total molarity of the raw solution was 0.020 111. From Fig. 4, the influence of the feed composition on the permselective coefficient is The value calculated from Eq. (7), negligible for cellulose acetate membranes. 7-T = Jz/J,“, is 0.061. and this value is nearly equal to the value calculated from (1)
Eq. (3) for mixed-solute
system.
Rejection
increase with the increase of the Na”
that
the smaller
its rejection
the relative
of Na’
and the permselective coefficient result agreed with the fact of the more permeable ion the lower
mole fraction. This
concentration
(8).
100 Remron
of
MgC12
I
I
007
01
Feed cuncentmtlon
Fig. 5. R and Tzz
vs. feed concentration.
PERMSELECTIVE
COEFFICIENT
OF ISORGANIC
IONS ON
263
RO LIEWRRANE
(2) Rejection and permselective coefficient US. feed concentration in this experiment, the molar ratio of the feed solution was 1: 1. In Fig. 5, the permselective coefficient hardly changes with tked concentration. of the rejection
osmotic
in the high
concentration
region
was caused
and the decrease
by the
increase
of
pressure.
(3) Rejection and prmselectike coefficient Z-S.feed rate In this experiment. feed rat, was chaqed from 4 I/hr to 30 I/hr. The increase of tkd rate decreases the concentration polarization on the membrane surface and consequently increases the rejection. influenced by the feed rate. (4)
But the permselective
coefficient
was hardly
Rejection and permselective coefficient ti.g. I,lAP
In this experiment, AP is the pressure on the gauge (kg/cm*). and AP was As shown in Fig. 6, the permselective changed from 90 kg/cm” to IS kg/cm’. coefficient increases with the decrease of the reciprocal of pressure. The reason that IjAP was used as the abscissa is that when l/AP becomes infinitely small, salt rejection shows the reflection coefficient. 6 (9). We see that the o of NaCl and
I
004
002 IIAP
Fig. 6. R and Tzz vs. II&‘.
006
I
264
51. IGAWA, S.
in the cellulose M&I, tively. The permselective
YOSHIDA, T. YAYABE AND N. TAKAI
acetate membrane are about 0.95 and coefficient increased with AP.
> 0.996 respec-
(5) Rejection and the permselective coefficient CCLoperating temperature In this experiment, the operating temperature \vas changed from 8°C to4O”C. This experiment was carried out by batch-type apparatus because it is very difficult tc keep the temperature of the flow-type apparatus constant. Both ion flux and volume flux increase with operating temperature btit rejection is constant and then the permselective coefficient is constant. (6) Rejection and the permsc!ecti\e coefficient LX annealing temperature This experiment was carried out in order to study the influence of the membrane porosity on rejection and the permselectivc coefficient. As shown in Fig. 7, the membrane annealed at low temperature and. consequently. having large porosity. showed low rejection and a high permselective coetlkient. It was thought that the difference of variation between NaCl rejection and MgCl r rejection was caused by the variation of the ratio of the hydrated ion radius to the pore size of the skin layer of the membrane_ 100
6-ok
e-or
76-c Anneahng
Fig. 7. R and Tz!
vs.
temperature
annealing temperature.
PERMSELECTIVE
COEFFICIENT
OF lNORGI\NIC
265
IONS ON RO MEIWRANE
REFERENCES
I. 3 ;: 4 5. 6. 7. 8. 9.
S. S. T. J. S. S. F. p. T. S.
SOIJRIRAJAN.
Id. Eng. Chet~~. Frrdunwn~~ds. 2 (1963) 51. H. YA.HA.UOTO AVD H. SAITO. Nippun Kaisui Cakkuishi, Y~UAHE AYD M. SESO. Im E.vchunge .Wem&runes. Giho-do. 1964. P. AGRAWAL A&D S. SOURIRAJAS. Inch. Eng. Chem. Process Design YOSHIDA. N. TAKAI xsc T. YAIIAEC. Nlpport Koisrri Gd-kaishi. 26 MASJIKIA~, Id Eng. Chem. Prod. Res. Drvrf~p., 6 (1967) 23. BAWLO AUD R. Jorrssou, Cuorrlraufron Chenrislr_v. W. A. Benpmin. 122. G. H~DGSOS. Desalinufiun. 8 (1970) 99. KILWRA, Proc. Fourth Inrrrt~ S_~mp. on Frerir Water front lhe Seu.
OKAUOTO.
21 (1968) 245. p_ 139. Develop., 9 (1970) (1973) 279. New York,
4 (1973)
N.Y..
197.
18.
1964.