78 A Gel Chromatographic Study on the Interactions of Long-Chain Polyphosphate Anions with Magnesium Ions Phosphorus Chemistry Downloaded from pubs.acs.org by PURDUE UNIV on 08/21/18. For personal use only.
T O H R U M I Y A J I M A , T O S H I M I T S U O N A K A , and S H I G E R U O H A S H I Department of Chemistry, Faculty of Science, Kyushu, University 33, Hakozaki, Higashiku, Fukuoka, 812 Japan
In spite of much information available for the interactions of various metal ions with small oxoanions of phosphorus, rela tively l i t t l e information has been obtained for the complex forma tion of long-chain polyphosphate ion. This may be due to the fact that the conventional methods useful for the study of the complex formation of a relatively small ligand are not always applicable to the polyanion complex formation system. Since a gel chromato graphic method based on the same principle as the equilibrium dia lysis method has been proved to be applicable in the field of inorganic complex chemistry (1), this method has been applied to the study of the binding of long-chain polyphosphate ions to mag nesium ion. A long-chain polyphosphate ion is composed mainly of middle PO -units and two end PO -units. A middle and an end unit have a formal charge of minus one and two, respectively. Therefore, the affinity of an end unit for a metal ion is much greater than that of a middle unit. When the chain length of polyphosphate is suf ficiently long, the contribution of end units to the metal binding is small enough to be neglected. The complexation ability of middle units in a long-chain polyphosphate is expected to be dif ferent from that of middle units in a cyclic phosphate. 3
3
T h i s w o r k was u n d e r t a k e n i n o r d e r t o e v a l u a t e t h e b i n d i n g o f m i d d l e u n i t s o f l o n g - c h a i n p o l y p h o s p h a t e t o magnesium i o n f r o m a v i e w p o i n t o f t h e mass a c t i o n l a w . A sample s o l u t i o n c o n t a i n i n g m e t a l i o n , M , h i g h - m o l e c u l a r w e i g h t l i g a n d , L and t h e i r complexes i s a p p l i e d t o a g e l column conditioned w i t h an eluent containing M o f a s p e c i f i e d concentra t i o n , [ M ] Q , a n d i s e l u t e d w i t h t h e same e l u e n t . The i n i t i a l f r e e m e t a l c o n c e n t r a t i o n i n t h e sample s o l u t i o n u s u a l l y d i f f e r s from [M]Q. D u r i n g t h e e l u t i o n , h o w e v e r , t h e s a m p l e l i g a n d zone ( z o n e a ) i s e q u i l i b r a t e d w i t h t h e m e t a l s o l u t i o n o f [M]Q t o r e a c h a s t e a d y s t a t e , i n w h i c h a f r e e m e t a l c o n c e n t r a t i o n i n zone a , [ M ] , i s e q u a l t o [M]Q . I n zone α t h e d i s t r i b u t i o n o f t h e c h e m i c a l s p e c i e s i s c h a r a c t e r i z e d b y t h e f r e e m e t a l c o n c e n t r a t i o n , [M]Q. The r a t i o o f t h e amount o f bound m e t a l t o t h e t o t a l amount o f t h e l i g a n d , n , can u s u a l l y be e x p r e s s e d a s t h e f o l l o w i n g f o r m a t i o n f u n c t i o n . A
0097-6156/81/0171-0377$05.00/0 © 1981 American Chemical Society
378
PHOSPHORUS
f ¥
M
]
CHEMISTRY
o (1)
1 +
^[MjJ
where
i s t h e o v e r a l l s t a b i l i t y c o n s t a n t o f an M^L c o m p l e x . I n t h i s work a m i x t u r e of l o n g - c h a i n polyphosphates having v a r i o u s d e g r e e s o f p o l y m e r i z a t i o n was u s e d as t h e l i g a n d . There f o r e , η d e f i n e d i n e q n ( l ) c a n n o t be c a l c u l a t e d . I n s t e a d o f n, t h e a v e r a g e number o f bound magnesium p e r one PO3 u n i t , m, was c a l c u lated. A v a l u e o f m c a n be o b t a i n e d by d i v i d i n g t h e amount o f bound magnesium, % g t by t h e amount o f t o t a l PO3 u n i t s , Np, e a c h i n zone a . A P e r k i n E l m e r M o d e l 403 a t o m i c a b s o r p t i o n s p e c t r o p h o t o m e t e r was u s e d as a d e t e c t o r f o r magnesium ( 2 ) . N
Ms
(2)
I t has b e e n p o i n t e d o u t t h a t t h e h i g h and v a r i a b l e e l e c t r i c f i e l d a t t h e s u r f a c e o f a c h a r g e d p o l y m e r makes t h e q u a n t i t a t i v e d e s c r i p t i o n o f i t s e q u i l i b r i a v e r y complecated ( 3 ) . I n t h i s work t h e f o l l o w i n g a s s u m p t i o n s w e r e made i n o r d e r t o c a l c u l a t e t h e s t a b i l i t y c o n s t a n t s o f t h e c o m p l e x e s o f m i d d l e PO3 u n i t s w i t h mag nesium i o n . 1) C o n c e n t r a t i o n s a r e u s e d i n p l a c e o f a c t i v i t i e s . 2) A s e t o f a d j a c e n t PO3 u n i t s , t h e number o f w h i c h i s n*, b i n d s one magnesium i o n t o f o r m a o n e - t o - o n e c o m p l e x , Mg(P0 ) . J n x
M g
+
( P 0
3 n*
W
)
° 3 K *
( 3 )
3) The b i n d i n g a b i l i t y o f e a c h magnesium i o n t o one s i t e i s n o t a f f e c t e d by t h e c o m p l e x f o r m a t i o n a t o t h e r s i t e s o f t h e same c h a i n . The amount o f bound magnesium, N , c o r r e s p o n d s t o t h e peak a r e a o f zone a. S i n c e t h e amount o f t o t a l l i g a n d c a n be o b t a i n e d by d i v i d i n g Np by n*, t h e amount o f f r e e l i g a n d i n zone α i s (Np/n* - N ) . The s t a b i l i t y c o n s t a n t o f t h e c o m p l e x c a n be d e f i n e d as f o r lows. Mg β (η*) = (4) [Mg] (N /n* N ) M
Mg
0
p
U s i n g e q n ( 2 ) , e q n ( 4 ) c a n be e x p r e s s e d
M g
as
78.
MiYAJiMA
Interactions
E T AL.
β. (η*) 1
=
Γ
of Polyphosphate
379
Anions
m -, , . =r [ M g J ( l / n * - m) Μ
(5)
Ί /
0
m
a
v
With an appropriate n* value, a constant value of β·^(η*) be obtained w i t h i n a s p e c i f i c [Mg]g range. The p a i r o f n* and β-^(η*) which accounts f o r the experimental p l o t s i n d i c a t e s that n* PO3 u n i t s b i n d one magnesium i o n t o form a s p e c i f i c complex i n the [ M g ] range. In order to estimate proper n* and (3-j.(n*) values which s a t i s fy the experimental data, a curve f i t t i n g method was employed. Q
6 (n*)[Mg] 1
m
=
1 + B (n*)[Mg] 1
1
( )
(
6
)
0
m values were obtained f o r v a r i o u s [Mg]Q values i n 0.1 M t e t r a methylammonium c h l o r i d e s o l u t i o n a t 25°C. The c a l c u l a t e d curves f o r n* = 3 through 7 were examined. When n* i s assumed to be 4, 5 and 6, the c a l c u l a t e d curves showed a good f i t f o r the experimental p l o t s , even though they are not s a t i s f a c t o r y i n the whole [Mg]g range. Since the c a l c u l a t e d curve f o r n* = 3 o r 7 g r e a t l y deviates from the p l o t s , the formation o f M g ( P 0 3 > * 3 or M g ( P 0 3 > * type complexes i n t h i s [Mg]g range can be excluded. The s t a b i l i t y con s t a n t s (β-j^n*)) thus obtained are l i s t e d i n Table 1. I t i s note worthy that the formation o f M g ( P 0 3 ) * _ ^ type complex was c l e a r l y observed when [Mg]g was between 10~5 and 10~4 mol dm~3. In order to compare the complexation a b i l i t y o f middle P O o u n i t s o f long-chain polyphosphate with those o f r e l a t i v e l y small polyphosphates, s t a b i l i t y constants of the magnesium complexes o f diphosphate, t r i p h o s p h a t e , tetraphosphate, tetrametaphosphate, and hexametaphosphate were evaluated by the g e l chromatographic method under the same experimental c o n d i t i o n s . The s t a b i l i t y constants of magnesium complexes w i t h l i n e a r phosphates (β-^(ηΐ)) and those with c y c l i c phosphates (g-^(nc)) are a l s o t a b u l a t e d i n Table 1. By comparing the s t a b i l i t y constants o f l i n e a r phosphate complexes one another, i t can be concluded that the a d d i t i o n o f another PO3 u n i t to a l i g a n d does not n e c e s s a r i l y c o n t r i b u t e to the b i n d i n g of the f i r s t magnesium i o n , when the degree o f p o l y m e r i z a t i o n o f the l i g a n d i s more than 3. I t i s worthwhile to compare β^ίη*) w i t h g-^(nc), because a c y c l i c phosphate i o n i s composed of only middle POo u n i t s . By comparison o f β-^4*) with β ( 4 ο ) and β - ^ ό * ) with PjAOc), i t can be concluded that β^ίη*) i s always g r e a t e r than βj, (nc) . T h i s i n d i c a t e s that the complexation a b i l i t y o f middle PO3 u n i t s of a long-chain polyphosphate i o n i s g r e a t e r than that of the corresponding c y c l i c phosphate i o n . T h i s may be a t t r i b uted to the f l e x i b i l i t y o f long-chain polyphosphate i o n . I t can be seen that the d i f f e r e n c e between β·^(η*) and β-^(ηο) decreases with an i n c r e a s e In n. The f l e x i b i l i t y o f c y c l i c phosphate i o n may i n c r e a s e with n. n
=
n
χ
n
= 7
380
PHOSPHORUS
Table
n,
n
1.
S t a b i l i t y c o n s t a n t s o f magnesium c o m p l e x e s for d i f f e r e n t types o f phosphates.
logif^inl)/
K
CHEMISTRY
3
mol-^dm )
b
)
b
l o g ^ n c ) /
)
log(B (n*)/ 1
3
mol^dm )
3
mol'^-dm )
-
2
5.57
-
3
6.53
1.80
4
6.53
3.40
5.60
5
-
-
6.03
6
-
5.50
6.22
a) b) c)
c
-
)
t h e number o f PO3 u n i t s w h i c h c o n s t i t u t e s t h e l i g a n d . I = 0.1, S u p p o r t i n g e l e c t r o l y t e ; ( C H ) N C 1 , Temp.; 25°C . obtained with i o n - s e l e c t i v e electrode ( 4 ) . 3
4
Literature Cited
1. 2. 3. 4.
Miyajima, T; Ohashi, S. Bull. Chem. Soc. Jpn., 1978, 51, 2543. Yoza, N; Ohashi, S. Anal. Lett., 1973, 6, 595. Marinsky, J . A. Coord. Chem. 1976, 19, 125. Kalliney, S. Υ., "Topics in Phosphorus Chemistry", Vol. 7, Griffith E. J. and Grayson Μ., Eds., Interscience, New York, 1967, p 294.
RECEIVED
June 30, 1981.
