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The determination of stability of macrocyclic ether complexes by use of 13C dipole-dipole relaxation time measurements.
Journal o[ Molecular Liquids, 37 (1988) 107-115
107
Elsevier Science Publishers B.V., A m s t e r d a m - P r i n t e d in T h e N e t h e r l a n d s
THE
D E T E R M I N A T I O N OF
ETHER
STABILITY
COMPLEXES B Y U S E
RELAXATION TIME
OF * = C
OF MACROCYCLIC DIPOLE--DIPOLE
MEASUREMENTS.
P a r t . I V . D e t e r m i n a t i o n o f f r e e e n e r g y o f complex f o r m a t i o n o f L i ÷ : Ca2÷ and M9~ -
w i t h 1,4,7~10-tetraoxacyclododecane,(12.Crown.4) in
methanol_~ and D0H s o l u t i o n s cx~
Cakil ERK, ¢÷~
Dicle University, Faculty of Apts and Sciences, Department
of Chemistry,Diyarbakir,281~l,TURKEY.
(Received 21 April 1987) ABSTRACT
In o r d e r t o d e t e r m i n e t h e s t a b i l i t y
of
t h e complexes o f
m a c r o c y c l i c o l i 9 o e t h e r s with a l k a l i n e and a l k a l i n e e a r t h c a t i o n s we have r e c e n t l y developed a NMR method which determined t h e e q u i l i b r i u m c o n s t a n t s o f complexin9 s o l u t i o n s by measurin9 t h e ~=C d i p o l e - d i p o l e r e l a x a t i o n times o f now r e p o r t
t h e m a c r o c y c l i c e t h e r s in c a t i o n i c s o l u t i o n s . We
t h e e q u i l i b r i u m c o n s t a n t o f 12.crown.4
complexin9 w i t h Li ÷
in methanol-~ and f r e e e n e r g i e s o f complexin9 o f Li ~ in methanol_d and Ca=÷ and M9=÷ in D0H which were determined by t h e aid o f 9iven method. E x p e r i m e n t a l r e s u l t s were discussed from t h e view o f o'own e t h e r complexation and t h e b a s i s o f
t h e r e l a x a t i o n times c o n c e p t .
INTRODUCTION
In p r i n c i p l e t h e complexation s t a b i l i t y
and t h e r e f o r e t h e
e q u i l i b r i u m c o n s t a n t s could be determined in many ways . However we
(X). P a r t . I l l , ref.14.b. (+). P r e s e n t a d d r e s s , T e c h n i c a l U n i v e r s i t y o f I s t a n b u l , F a c u l t y o f Science,Department o f Chemistry,Levend,80626~Istanbul,TURKEY.
0167-7322/88/$03.50
© 1988 Elsevier Science Publishers B.V.
108 now s u 9 9 e s t a method t o o b t a i n t h e e q u i l i b r i u m c o n s t a n t s and t h e f r e e energies f o r
t h e complexation by t h e use o f r e l a x a t i o n r a t e s
o r i 9 i n a t e d from t h e d i p o l a r i n t e r a c t i o n o f h e t e r o n u c l e i o f {~H}-~=C. In d e m o n s t r a t i n 9 t h e analo9y between t h e chemical exchange and t h e r e l a x a t i o n r a t e in s y s t e m s composed o f two n o n e q u i v a l e n t spins A and B i n d i c a t i n 9 t h e uncomplexed and complexed li9and m o i e t i e s r e s p e c t i v e l y , t h e McConnel e q u a t i o n s f o r l o n 9 i t u d i n a l m a g n e t i z a t i o n s could be 9iven with Equ.l,2.(l-3) Those r e l a t i o n s h i p s may be 9iven in
dM=A/dt = (M==A--M=A)/TIA--M=A/t~+M=D/t~
dM=m/dt = (M==m-M=m)/T~B-M==/tB+M=~/t~
t h e Equ.3,4 in terms o f e f f e c t i v e l i f e
times t~A and tim o f
the
s e p a r a t e spins o f f r e e and complexed ligands r e s p e c t i v e l y . ( 1 )
1/t~a = 1 / T ~ + 1/tA
1/t~m = 1/Ti= + 1 / t ~
4
Some o f t h e a u t h o r s have a l r e a d y applied t h e above 9iven c o n s i d e r a t i o n s and made some assumptions t o u t i l i z e them f o r r a t h e r simple c a l c u l a t i o n s in t h e range o f measureable exchan9e r a t e s . ( 1 - 5 ) In t h e o t h e r hand t h e r a t i o
of effective life
times o f
the
s o l v a t i o n s h e l l and t h e f r e e ligand sphere could 9ive t h e energy o f solvation or
t h e complex f o r m a t i o n f r e e energy,Equ.5.(6,7)
t l a / t ~ m = exp(-E=/RT)
However, iT t h e r e i s no exchan9e t h e e q u a t i o n s for" t h e l i f e
times o f
ligand s i t e s could be c o n s i d e r e d t h a t 1/t~=0 and 1/t==0 then Eqs.6,7 a r e obtained,
6
1/T~ = 1/t~
7
1/T~ = 1/ti=
T h e r e f o r e t h e complexation f r e e ener9y~ E= i s now 9iven with Equ.8. which i s c o n s i d e r e d as an energy b a r r i e r between t h e f r e e and
109 complexed li9ands in an e q u i l i b r i u m .
= T~IT~
t~/tlm
= exp(-E=IRT)
Accordin91y , such r e s u l t s could be p a r t i c u l a r l y explained in terms o f ion p a i r s t h e o r y . ( 6 - 8 ) In t h e o t h e r hand in a complex s o l u t i o n t h e r e l a × a t i o n time o f
t h e spins o f chemically exchangin9 ligands a r e
a l s o ei~pressed in terms o~ mole f r a c t i o n , Pm o f
t h e complexed iigand
sites,Equ.9.(9)
9
I / T ~ = ~ . - I / T ~ = P~(I/T~m-I/TsA)
I(~
T~A/T~o~.
-I = F'~(T~a/TI~ -1>
11
T~A/TI=b~
-i
= P=Zexp(-E=/RT)-I]
The e x p e r i m e n t a l r e l a x a t i o n time o f a ligand i s 9iven as T,=~. in c a t i o n i c s o l u t i o n s . In t h e case o f a s t r o n 9 s o l v a t i n 9 ligand t h e Pm comes t o o c l o s e t o u n i t y (P--~I) and t h e r e f o r e E~u.ll becomes,
12
T,a/T,=b. = P=
13
In(TIA/T~=b,) = inP~ - E=/RT
The a c t i v a t i o n e n e r g y f o r
exp(-E=/RT)
complex f o r m a t i o n ,E= i s
therefore
a d e q u a t e l y o b t a i n e d by measurin9 t h e T i ~ / T i = = . r a t i o t e m p e r a t u r e s where TIA i s
t h e r e l a x a t i o n time o f
at various
t h e f r e e li9and ,
Table.1 and Fi9.1,2. On t h e o t h e r hand t h e e q u i l i b r i u m c o n s t a n t s could be measured accordin9 t o o u r e a r l i e r r e p o r t s as i t
is b r i e f l y
discussed below, Equ.14-18.(1~,12) In 9 e n e r a l t h e e q u i l i b r i u m c o n s t a n t o f 1:1 r a t i o
o f a complex i s
9iven as f o l l o w s .
14
A*
+ C ~- A*C
15
K . = [A÷C]/[A÷][C]
Accordin91y t h e mole f r a c t i o n s o f
t h e complexed ligand P= and
complexed c a t i o n Pc a r e 9iven w i t h t h e PD=[A*C][Co] and
ii0 T a b l e . l Complexin9 p a r a m e t e r s o f
1,4,7,1~-tetraoxacyclododecane
b i n d i 9 w i t h L i ÷ , C a =~ and M9=÷ i n
CATION
SOLVENT
ION CONC.
solutions
ETH.CONC.
Kc
InKo
(varied)
Li ÷
CH~OD
0.66
~.66
M92÷
DOH
0.50
1.00
25.969~
3.257
-1.954
Ca =+
DOH
0.50
1.00
5.884~
1.772
-1.063
1:1 r a t i o
of
i n 1/mole and f r e e
of
1:2 r a t i o
of
1:1 r a t i o ,
,66
.62
.58 o I--p-
c
.50
.46
1000/°K
.42
-1.313
ener9y in
0.788
kCal/mole
(#). The c o m p l e x i n 9
o b t a i n e d f r o m Equ.18.
.7 0
.54
-0.633x
c o m p l e x i n 9 which was o b t a i n e d f r o m Equ.13.
(*). The c o m p l e x i n 9 c o n s t a n t constant
0 . 2 6 9 "~
1.054
E=
CH=OD
for
2.870~
30=C
Li ÷
(X). E q u i l i b r i u m c o n s t a n t
(varied)
at
3.1
3.3
3.5
3.7
3.9
I
I
I
I
I
111
.5
,4
.3
.2
.1 Mg2 +
.0 lOO0/eK
2.9 I
I
3.1 I
3.3 I
I
I
3.5 I
I
3.7 I
I
Fi9.2. The r e l a t i o n s h i p b e t w e e n t h e In(T~a/T~=b.) and i n v e r s e t e m p e r a t u r e in DOH s o l u t i o n s oT Ca=÷ and M92÷ (0.50 m o l e / l ) w i t h 12.crown.4 (1.0~ m o l e / l ) , t h e s l o p e = - E = .
Pc=[A÷C]/[A~] r e l a t i o n s h i p s in which t h e i n i t i a l c o n c e n t r a t i o n i s d e n o t e d a s [C=] and i n i t i a l
cyclic li9and
cation concentration is
d e n o t e d a s [A~]. In o u r e x p e r i m e n t a l c o n d i t i o n s t h o s e a r e k e p t identical for
various concentrations of
the s o l u t i o n s , t h e r e f o r e
a p p l i c a t i o n o f Equ.15 i n t o Equ.9 9 i v e s t h e f o l l o w i n 9 s t a t u s a n a l y t i c a l model o f
t h e 1:1 complexin9 r a t i o
for
s i n c e t h e [C=]=[A&],
Egu.16-18.
Fi9.1. The r e l a t i o n s h i p b e t w e e n t h e In(T~a/T~===)
and i n v e r s e
t e m p e r a t u r e in CH=OD s o l u t i o n o f Li+/12.crown.4 (0.66 m o l e / l ) , the slope=-E=.
the
any
112 16
K.=PB[C=]/{[C=]-[A÷C]}{[A~]-[A÷C]}
17
I/K=[A+--] + 2 = P m + 1/P=
18
I/K.[A+~] + 2 = (I/Ti=bu-I/TiA)/(1/Ti~-I/Ti~)
+
(I/TIm-1/TIm)/(I/T~°b.-I/T,m)
However, in t h e p r e s e n t e d work t h e TIp v a l u e o f c o m p l e t e l y complexed ligand i s c a l c u l a t e d by t h e s i m u l a t i o n o$ t h e probable v a l u e s on Equ.17,18 which 9ave t h e b e s t f i t
with a s t r a i g h t line o f
t h e slope o f 1/K.. The e x p e r i m e n t a l r e s u l t s a r e now displayed on Fi9.3 f o r
Li ÷ complexin9 with 12.Crown.4 in CH~OD.
~5
3~)-
2~.
(llrnole) 1.0 I
2.0 I
1/[Co] 3.0 i
Fi9.3. The dependence o f mole T r a c t i o n o f Li ÷ complexed 12.crown.4 t o the inverse cation concentration, [I/A= +] o b t a i n e d from t h e r e l a x a t i o n time o$ complexed ligand, T~=b. accordin.9 t o EHu.IS in CH~OD
at
RESULTS
3~=C.
AND
D I S C U S S I O N S
The s t u d i e s on t h e d e t e r m i n a t i o n o f ~=C d i p o l e - d i p o l e r e l a x a t i o n time o f m a c r o c y l i c ligands e s t a b l i s h e d r e a l l y i n t e r e s t i n 9 r e s u l t s due
113 t o the f a c t
t h a t t h e e f f e c t i v e c o r r e l a t i o n times o f r e l a x i n g n u c l e i
i s d i r e c t l y governed by t h e m o l e c u l a r motions. T h e r e f o r e any kind o f i n t e r a c t i o n with the demonstrated nuclei e f f e c t e d the dipole-dipole rela~,'ation time o f for
t h e spin systems.The d i p o l e - d i p o l e r e l a x a t i o n time
an i n t r a m o l e c u l a r i n t e r a c t i o n o f
t h e methylene group o f a c y c l i c
backbone could be e x p r e s s e d w i t h t h e f o l l o w i n g e q u a t i o n where T , d ~ i s given f o r
t h e d i p o l a r r e l a x a t i o n time o$ t h e *=C n u c l e i o f
m a c r o c y c l i c ligand which i s e x p e c t e d t o r o t a t e
the
a n i s o t r o p i c a l l y in t h e
e x t r e m e narrowing conditions,Equ.19.
19
I l T ~ , ~ =2/3 h=~%r~t=~Ir~w
U s u a l l y t o p r e d i c t a s p e c i f i c chemical e q u i l i b r i a amon9 t h e i o n s and t h e s o l v a t i n 9 d i p o l e s i s d i f f i c u l t
due t o t h e random s t r u c t u r e
of
s o l v a t i o n o r c o o r d i n a t i o n medium. However, m a c r o c y c l i c c a v i t i e s complexin9 by c h e l a t i o n o r w i t h c a v i t y e f f e c t caused u s u a l l y ratheruniform s t r u c t u r e s which s t r i c t l y
reduced the c a t i o n exchange r a t e
and t h e s k e l e t a l - m o l e c u l a r motions o f a m a c r o c y c l i c ligand which i s in f a c t q u a n t i t a t i v e l y dedected in o u r study.(1~-12>
C o n t r a r i l y the
p o l a r b u t small molecules have no such a s p e c i f i c i n f l u e n c e even in t h e i o n i c - e l e c t r o l y t e - s o l u t i o n s due t o
t h e domination o f
the
t r a n s l a t i o n a l motions on t h e e f f e c t i v e c o r r e l a t i o n times. (5,7-9) R e c e n t l y , we t r i e d some f o r m u l a t o o b t a i n t h e e q u i l i b r i u m c o n s t a n t s , K= in s i m i l a r ways a l t h o u g h t h e y were somewhat c o n c e n t r a t i o n dependent which i s a c t u a l l y common t o a l l a n a l y t i c a l methods. However, t h e p r e s e n t e d f o r m u l a i s capable t o s u r v e y q u i t e a l a r g e c o n c e n t r a t i o n range by computing the mole f r a c t i o n , P o f t h e complexed species,Equ.14-18.(14,15>
This i s even remarked a t
Table.l.
Namely,the t h e r m a l dependence o f energy b a r r i e r determinations,EHu.!3 has e x h i b i t e d somewhat d i f f e r e n t r e s u l t s as compare t o
the r e s u l t s
o b t a i n e d from c o n c e n t r a t i o n dependent mole f r a c t i o n d e t e r m i n a t l o n s , Equ.18, e x h i b i t i n g t h e r o l e o f c o n c e n t r a t i o n l i m i t a t l o n s on t h e well known a n a l y t i c a l methods. (14.a-c) Regarding t h e e v a l u a t i o n o f t h e e x p e r i m e n t a l r e s u l t s as t h e thermodynamic p a r a m e t e r s Table.1 e a s i l y e x h i b i t e d t h e r o l e o f t h e s o l v e n t p o l a r i t y as w e l l as t h e o t h e r medium eTfects.(lO,12,14,15) The K . v a l u e f o r
t h e complexing o f 12.crown.4
w i t h L i ÷ o b t a i n e d in
CH=OD according t o p r e s e n t e d methods i s q u i t e a g r e e a b l e with o u r e a r l i e r results,Equ.18.(1{),14) I t
is i n t e r e s t i n g to note t h a t
the
114 complexin9 o f
L i ÷ i o n w i t h 12.Crown.4
expected since
the ionic r a d i u s o f
t h e 0.12 nm t i n 9 s i z e o f
is
n o t so f a v o u r a b l e as i t
was
0.&0 A= might be e x p e c t e d t o
t e t r a o x a t i n 9. S i m i l a r r e s u l t s
fit
h a v e been
r e p o r t e d w i t h c a l o r i m e t r i c complexin 9 e n e r 9 y measurements.(11.b) t h e o t h e r hand i t studies partly
is
now p r o v e d t h a t
t o d e t e r m i n e t h e c a t i o n bindin9 p r o p e r t i e s o f d i s c r i b e d in
In
the dipolar r e l a x a t i o n r a t e
t h i s work seem r e a l l y
cyclic ethers
i n f o r m a t i v e . Accordin91y ,
t h e l a r 9 e r atomic number o f a l k a l i n e and a l k a l i n e e a r t h c a t i o n s were much more a t t r a c t e d
by t h e c y c l i c e t h e r dependin9 on t h e s o l v e n t
polarity.(10b,c,14a,b) The o b s e r v e d r e s u l t s t h e c a t i o n exchan9e r a t e electrostatic
reflected
the p a r t i c u l a r
contributions of
and i n t e r n a l m o t i o n s as w e l l as
the involved
and c o n f i 9 u r a t i o n a l i n t e r a c t i o n s . They a r e , h o w e v e r , a l l
computin 9 t o each o t h e r in t h e c a s e o f 12.Crown.4
of smallest size o f
crown e t h e r . More d e t a i l e d d i s c u s s i o n s a r e , h o w e v e r , g i v e n i n o u r r e c e n t work.(14c)
E X P E R I M E N T A L
The 1 , 4 , 7 , 1 0 - t e t r a o x a c y c l o d o d e c a n e o b t a i n e d a c c o r d i n 9 t o o u r earlier
method was r e p u r i f i e d by d i s t i l a t i o n
at
low p r e s s u r e .
(10a,15a) The s o l v e n t DOH was p r e p a r e d from D=O and CH=OD o f
the
Merck p r o d u c t . The 10 mm p y r e x NMR c a p i l l a r i e s were loaded w i t h t h e complex s o l u t i o n o f
t h e m a c r o c y c l i c e t h e r and c a t i o n o f a p p r o p r i a t e
molar c o n c e n t r a t i o n s t h e n de9assed by c o o l i n 9 in l i q u i d n i t r o g e n under
10- =
tort
and t h e n s e a l e d .
~=C d i p o l e - d i p o l e r e l a x a t i o n time measurements were t r i e d pulse s p e c t r o m e t e r o f
method s u p p l i e d as a s t a c k i n 9 program w i t h a l e a s t calculation of
squares f i t
field frequency at
in
t h e ran9e o f
0,05 -
6,00 sec p u l s e
times.
The NOE measurements were t r i e d
at
c o m p l e t e l y decoupled and p u l s e
modulated decoupled c o n d i t i o n s w i t h 10.0 sec o f and t h e below 9 i v e n f o r m u l a was used f o r c a l c u l a t i o n s , Equ.20.(16,17)
20
2000 Hz
a c o n s t a n t p r o b e t e m p e r a t u r e and 180= and
90 ~ p u l s e sequences were t r i e d interval
for-
TI values.(10c,12,14a-c)
The e x p e r i m e n t s were c o n d u c t e d on t h e s p e c t r o m e t e r - a t of
on a
JEOL, model FX-60Q, w i t h t h e i n v e r s i o n r e c o v e r y
Tidlp = T i = b .
1.99/rich
pulse i n t e r v a l
time
t h e d i p o l a r r e l a x a t i o n time
115
ACKNOWLEDGEMENT
Prof.H.G.Hertz (Karlsruhe-Germany) i s acknowled9ed due t o his kind discussions a t t h e i n i t i a t i o n o f t h i s work and Prof.W.M.-Warmuth (Munster-Germany) i s acknowled9ed due t o the experience o f the a u t h o r in his l a b o r a t o r y a t Munster.
REFERENCES
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107
Elsevier Science Publishers B.V., A m s t e r d a m - P r i n t e d in T h e N e t h e r l a n d s
THE
D E T E R M I N A T I O N OF
ETHER
STABILITY
COMPLEXES B Y U S E
RELAXATION TIME
OF * = C
OF MACROCYCLIC DIPOLE--DIPOLE
MEASUREMENTS.
P a r t . I V . D e t e r m i n a t i o n o f f r e e e n e r g y o f complex f o r m a t i o n o f L i ÷ : Ca2÷ and M9~ -
w i t h 1,4,7~10-tetraoxacyclododecane,(12.Crown.4) in
methanol_~ and D0H s o l u t i o n s cx~
Cakil ERK, ¢÷~
Dicle University, Faculty of Apts and Sciences, Department
of Chemistry,Diyarbakir,281~l,TURKEY.
(Received 21 April 1987) ABSTRACT
In o r d e r t o d e t e r m i n e t h e s t a b i l i t y
of
t h e complexes o f
m a c r o c y c l i c o l i 9 o e t h e r s with a l k a l i n e and a l k a l i n e e a r t h c a t i o n s we have r e c e n t l y developed a NMR method which determined t h e e q u i l i b r i u m c o n s t a n t s o f complexin9 s o l u t i o n s by measurin9 t h e ~=C d i p o l e - d i p o l e r e l a x a t i o n times o f now r e p o r t
t h e m a c r o c y c l i c e t h e r s in c a t i o n i c s o l u t i o n s . We
t h e e q u i l i b r i u m c o n s t a n t o f 12.crown.4
complexin9 w i t h Li ÷
in methanol-~ and f r e e e n e r g i e s o f complexin9 o f Li ~ in methanol_d and Ca=÷ and M9=÷ in D0H which were determined by t h e aid o f 9iven method. E x p e r i m e n t a l r e s u l t s were discussed from t h e view o f o'own e t h e r complexation and t h e b a s i s o f
t h e r e l a x a t i o n times c o n c e p t .
INTRODUCTION
In p r i n c i p l e t h e complexation s t a b i l i t y
and t h e r e f o r e t h e
e q u i l i b r i u m c o n s t a n t s could be determined in many ways . However we
(X). P a r t . I l l , ref.14.b. (+). P r e s e n t a d d r e s s , T e c h n i c a l U n i v e r s i t y o f I s t a n b u l , F a c u l t y o f Science,Department o f Chemistry,Levend,80626~Istanbul,TURKEY.
0167-7322/88/$03.50
© 1988 Elsevier Science Publishers B.V.
108 now s u 9 9 e s t a method t o o b t a i n t h e e q u i l i b r i u m c o n s t a n t s and t h e f r e e energies f o r
t h e complexation by t h e use o f r e l a x a t i o n r a t e s
o r i 9 i n a t e d from t h e d i p o l a r i n t e r a c t i o n o f h e t e r o n u c l e i o f {~H}-~=C. In d e m o n s t r a t i n 9 t h e analo9y between t h e chemical exchange and t h e r e l a x a t i o n r a t e in s y s t e m s composed o f two n o n e q u i v a l e n t spins A and B i n d i c a t i n 9 t h e uncomplexed and complexed li9and m o i e t i e s r e s p e c t i v e l y , t h e McConnel e q u a t i o n s f o r l o n 9 i t u d i n a l m a g n e t i z a t i o n s could be 9iven with Equ.l,2.(l-3) Those r e l a t i o n s h i p s may be 9iven in
dM=A/dt = (M==A--M=A)/TIA--M=A/t~+M=D/t~
dM=m/dt = (M==m-M=m)/T~B-M==/tB+M=~/t~
t h e Equ.3,4 in terms o f e f f e c t i v e l i f e
times t~A and tim o f
the
s e p a r a t e spins o f f r e e and complexed ligands r e s p e c t i v e l y . ( 1 )
1/t~a = 1 / T ~ + 1/tA
1/t~m = 1/Ti= + 1 / t ~
4
Some o f t h e a u t h o r s have a l r e a d y applied t h e above 9iven c o n s i d e r a t i o n s and made some assumptions t o u t i l i z e them f o r r a t h e r simple c a l c u l a t i o n s in t h e range o f measureable exchan9e r a t e s . ( 1 - 5 ) In t h e o t h e r hand t h e r a t i o
of effective life
times o f
the
s o l v a t i o n s h e l l and t h e f r e e ligand sphere could 9ive t h e energy o f solvation or
t h e complex f o r m a t i o n f r e e energy,Equ.5.(6,7)
t l a / t ~ m = exp(-E=/RT)
However, iT t h e r e i s no exchan9e t h e e q u a t i o n s for" t h e l i f e
times o f
ligand s i t e s could be c o n s i d e r e d t h a t 1/t~=0 and 1/t==0 then Eqs.6,7 a r e obtained,
6
1/T~ = 1/t~
7
1/T~ = 1/ti=
T h e r e f o r e t h e complexation f r e e ener9y~ E= i s now 9iven with Equ.8. which i s c o n s i d e r e d as an energy b a r r i e r between t h e f r e e and
109 complexed li9ands in an e q u i l i b r i u m .
= T~IT~
t~/tlm
= exp(-E=IRT)
Accordin91y , such r e s u l t s could be p a r t i c u l a r l y explained in terms o f ion p a i r s t h e o r y . ( 6 - 8 ) In t h e o t h e r hand in a complex s o l u t i o n t h e r e l a × a t i o n time o f
t h e spins o f chemically exchangin9 ligands a r e
a l s o ei~pressed in terms o~ mole f r a c t i o n , Pm o f
t h e complexed iigand
sites,Equ.9.(9)
9
I / T ~ = ~ . - I / T ~ = P~(I/T~m-I/TsA)
I(~
T~A/T~o~.
-I = F'~(T~a/TI~ -1>
11
T~A/TI=b~
-i
= P=Zexp(-E=/RT)-I]
The e x p e r i m e n t a l r e l a x a t i o n time o f a ligand i s 9iven as T,=~. in c a t i o n i c s o l u t i o n s . In t h e case o f a s t r o n 9 s o l v a t i n 9 ligand t h e Pm comes t o o c l o s e t o u n i t y (P--~I) and t h e r e f o r e E~u.ll becomes,
12
T,a/T,=b. = P=
13
In(TIA/T~=b,) = inP~ - E=/RT
The a c t i v a t i o n e n e r g y f o r
exp(-E=/RT)
complex f o r m a t i o n ,E= i s
therefore
a d e q u a t e l y o b t a i n e d by measurin9 t h e T i ~ / T i = = . r a t i o t e m p e r a t u r e s where TIA i s
t h e r e l a x a t i o n time o f
at various
t h e f r e e li9and ,
Table.1 and Fi9.1,2. On t h e o t h e r hand t h e e q u i l i b r i u m c o n s t a n t s could be measured accordin9 t o o u r e a r l i e r r e p o r t s as i t
is b r i e f l y
discussed below, Equ.14-18.(1~,12) In 9 e n e r a l t h e e q u i l i b r i u m c o n s t a n t o f 1:1 r a t i o
o f a complex i s
9iven as f o l l o w s .
14
A*
+ C ~- A*C
15
K . = [A÷C]/[A÷][C]
Accordin91y t h e mole f r a c t i o n s o f
t h e complexed ligand P= and
complexed c a t i o n Pc a r e 9iven w i t h t h e PD=[A*C][Co] and
ii0 T a b l e . l Complexin9 p a r a m e t e r s o f
1,4,7,1~-tetraoxacyclododecane
b i n d i 9 w i t h L i ÷ , C a =~ and M9=÷ i n
CATION
SOLVENT
ION CONC.
solutions
ETH.CONC.
Kc
InKo
(varied)
Li ÷
CH~OD
0.66
~.66
M92÷
DOH
0.50
1.00
25.969~
3.257
-1.954
Ca =+
DOH
0.50
1.00
5.884~
1.772
-1.063
1:1 r a t i o
of
i n 1/mole and f r e e
of
1:2 r a t i o
of
1:1 r a t i o ,
,66
.62
.58 o I--p-
c
.50
.46
1000/°K
.42
-1.313
ener9y in
0.788
kCal/mole
(#). The c o m p l e x i n 9
o b t a i n e d f r o m Equ.18.
.7 0
.54
-0.633x
c o m p l e x i n 9 which was o b t a i n e d f r o m Equ.13.
(*). The c o m p l e x i n 9 c o n s t a n t constant
0 . 2 6 9 "~
1.054
E=
CH=OD
for
2.870~
30=C
Li ÷
(X). E q u i l i b r i u m c o n s t a n t
(varied)
at
3.1
3.3
3.5
3.7
3.9
I
I
I
I
I
111
.5
,4
.3
.2
.1 Mg2 +
.0 lOO0/eK
2.9 I
I
3.1 I
3.3 I
I
I
3.5 I
I
3.7 I
I
Fi9.2. The r e l a t i o n s h i p b e t w e e n t h e In(T~a/T~=b.) and i n v e r s e t e m p e r a t u r e in DOH s o l u t i o n s oT Ca=÷ and M92÷ (0.50 m o l e / l ) w i t h 12.crown.4 (1.0~ m o l e / l ) , t h e s l o p e = - E = .
Pc=[A÷C]/[A~] r e l a t i o n s h i p s in which t h e i n i t i a l c o n c e n t r a t i o n i s d e n o t e d a s [C=] and i n i t i a l
cyclic li9and
cation concentration is
d e n o t e d a s [A~]. In o u r e x p e r i m e n t a l c o n d i t i o n s t h o s e a r e k e p t identical for
various concentrations of
the s o l u t i o n s , t h e r e f o r e
a p p l i c a t i o n o f Equ.15 i n t o Equ.9 9 i v e s t h e f o l l o w i n 9 s t a t u s a n a l y t i c a l model o f
t h e 1:1 complexin9 r a t i o
for
s i n c e t h e [C=]=[A&],
Egu.16-18.
Fi9.1. The r e l a t i o n s h i p b e t w e e n t h e In(T~a/T~===)
and i n v e r s e
t e m p e r a t u r e in CH=OD s o l u t i o n o f Li+/12.crown.4 (0.66 m o l e / l ) , the slope=-E=.
the
any
112 16
K.=PB[C=]/{[C=]-[A÷C]}{[A~]-[A÷C]}
17
I/K=[A+--] + 2 = P m + 1/P=
18
I/K.[A+~] + 2 = (I/Ti=bu-I/TiA)/(1/Ti~-I/Ti~)
+
(I/TIm-1/TIm)/(I/T~°b.-I/T,m)
However, in t h e p r e s e n t e d work t h e TIp v a l u e o f c o m p l e t e l y complexed ligand i s c a l c u l a t e d by t h e s i m u l a t i o n o$ t h e probable v a l u e s on Equ.17,18 which 9ave t h e b e s t f i t
with a s t r a i g h t line o f
t h e slope o f 1/K.. The e x p e r i m e n t a l r e s u l t s a r e now displayed on Fi9.3 f o r
Li ÷ complexin9 with 12.Crown.4 in CH~OD.
~5
3~)-
2~.
(llrnole) 1.0 I
2.0 I
1/[Co] 3.0 i
Fi9.3. The dependence o f mole T r a c t i o n o f Li ÷ complexed 12.crown.4 t o the inverse cation concentration, [I/A= +] o b t a i n e d from t h e r e l a x a t i o n time o$ complexed ligand, T~=b. accordin.9 t o EHu.IS in CH~OD
at
RESULTS
3~=C.
AND
D I S C U S S I O N S
The s t u d i e s on t h e d e t e r m i n a t i o n o f ~=C d i p o l e - d i p o l e r e l a x a t i o n time o f m a c r o c y l i c ligands e s t a b l i s h e d r e a l l y i n t e r e s t i n 9 r e s u l t s due
113 t o the f a c t
t h a t t h e e f f e c t i v e c o r r e l a t i o n times o f r e l a x i n g n u c l e i
i s d i r e c t l y governed by t h e m o l e c u l a r motions. T h e r e f o r e any kind o f i n t e r a c t i o n with the demonstrated nuclei e f f e c t e d the dipole-dipole rela~,'ation time o f for
t h e spin systems.The d i p o l e - d i p o l e r e l a x a t i o n time
an i n t r a m o l e c u l a r i n t e r a c t i o n o f
t h e methylene group o f a c y c l i c
backbone could be e x p r e s s e d w i t h t h e f o l l o w i n g e q u a t i o n where T , d ~ i s given f o r
t h e d i p o l a r r e l a x a t i o n time o$ t h e *=C n u c l e i o f
m a c r o c y c l i c ligand which i s e x p e c t e d t o r o t a t e
the
a n i s o t r o p i c a l l y in t h e
e x t r e m e narrowing conditions,Equ.19.
19
I l T ~ , ~ =2/3 h=~%r~t=~Ir~w
U s u a l l y t o p r e d i c t a s p e c i f i c chemical e q u i l i b r i a amon9 t h e i o n s and t h e s o l v a t i n 9 d i p o l e s i s d i f f i c u l t
due t o t h e random s t r u c t u r e
of
s o l v a t i o n o r c o o r d i n a t i o n medium. However, m a c r o c y c l i c c a v i t i e s complexin9 by c h e l a t i o n o r w i t h c a v i t y e f f e c t caused u s u a l l y ratheruniform s t r u c t u r e s which s t r i c t l y
reduced the c a t i o n exchange r a t e
and t h e s k e l e t a l - m o l e c u l a r motions o f a m a c r o c y c l i c ligand which i s in f a c t q u a n t i t a t i v e l y dedected in o u r study.(1~-12>
C o n t r a r i l y the
p o l a r b u t small molecules have no such a s p e c i f i c i n f l u e n c e even in t h e i o n i c - e l e c t r o l y t e - s o l u t i o n s due t o
t h e domination o f
the
t r a n s l a t i o n a l motions on t h e e f f e c t i v e c o r r e l a t i o n times. (5,7-9) R e c e n t l y , we t r i e d some f o r m u l a t o o b t a i n t h e e q u i l i b r i u m c o n s t a n t s , K= in s i m i l a r ways a l t h o u g h t h e y were somewhat c o n c e n t r a t i o n dependent which i s a c t u a l l y common t o a l l a n a l y t i c a l methods. However, t h e p r e s e n t e d f o r m u l a i s capable t o s u r v e y q u i t e a l a r g e c o n c e n t r a t i o n range by computing the mole f r a c t i o n , P o f t h e complexed species,Equ.14-18.(14,15>
This i s even remarked a t
Table.l.
Namely,the t h e r m a l dependence o f energy b a r r i e r determinations,EHu.!3 has e x h i b i t e d somewhat d i f f e r e n t r e s u l t s as compare t o
the r e s u l t s
o b t a i n e d from c o n c e n t r a t i o n dependent mole f r a c t i o n d e t e r m i n a t l o n s , Equ.18, e x h i b i t i n g t h e r o l e o f c o n c e n t r a t i o n l i m i t a t l o n s on t h e well known a n a l y t i c a l methods. (14.a-c) Regarding t h e e v a l u a t i o n o f t h e e x p e r i m e n t a l r e s u l t s as t h e thermodynamic p a r a m e t e r s Table.1 e a s i l y e x h i b i t e d t h e r o l e o f t h e s o l v e n t p o l a r i t y as w e l l as t h e o t h e r medium eTfects.(lO,12,14,15) The K . v a l u e f o r
t h e complexing o f 12.crown.4
w i t h L i ÷ o b t a i n e d in
CH=OD according t o p r e s e n t e d methods i s q u i t e a g r e e a b l e with o u r e a r l i e r results,Equ.18.(1{),14) I t
is i n t e r e s t i n g to note t h a t
the
114 complexin9 o f
L i ÷ i o n w i t h 12.Crown.4
expected since
the ionic r a d i u s o f
t h e 0.12 nm t i n 9 s i z e o f
is
n o t so f a v o u r a b l e as i t
was
0.&0 A= might be e x p e c t e d t o
t e t r a o x a t i n 9. S i m i l a r r e s u l t s
fit
h a v e been
r e p o r t e d w i t h c a l o r i m e t r i c complexin 9 e n e r 9 y measurements.(11.b) t h e o t h e r hand i t studies partly
is
now p r o v e d t h a t
t o d e t e r m i n e t h e c a t i o n bindin9 p r o p e r t i e s o f d i s c r i b e d in
In
the dipolar r e l a x a t i o n r a t e
t h i s work seem r e a l l y
cyclic ethers
i n f o r m a t i v e . Accordin91y ,
t h e l a r 9 e r atomic number o f a l k a l i n e and a l k a l i n e e a r t h c a t i o n s were much more a t t r a c t e d
by t h e c y c l i c e t h e r dependin9 on t h e s o l v e n t
polarity.(10b,c,14a,b) The o b s e r v e d r e s u l t s t h e c a t i o n exchan9e r a t e electrostatic
reflected
the p a r t i c u l a r
contributions of
and i n t e r n a l m o t i o n s as w e l l as
the involved
and c o n f i 9 u r a t i o n a l i n t e r a c t i o n s . They a r e , h o w e v e r , a l l
computin 9 t o each o t h e r in t h e c a s e o f 12.Crown.4
of smallest size o f
crown e t h e r . More d e t a i l e d d i s c u s s i o n s a r e , h o w e v e r , g i v e n i n o u r r e c e n t work.(14c)
E X P E R I M E N T A L
The 1 , 4 , 7 , 1 0 - t e t r a o x a c y c l o d o d e c a n e o b t a i n e d a c c o r d i n 9 t o o u r earlier
method was r e p u r i f i e d by d i s t i l a t i o n
at
low p r e s s u r e .
(10a,15a) The s o l v e n t DOH was p r e p a r e d from D=O and CH=OD o f
the
Merck p r o d u c t . The 10 mm p y r e x NMR c a p i l l a r i e s were loaded w i t h t h e complex s o l u t i o n o f
t h e m a c r o c y c l i c e t h e r and c a t i o n o f a p p r o p r i a t e
molar c o n c e n t r a t i o n s t h e n de9assed by c o o l i n 9 in l i q u i d n i t r o g e n under
10- =
tort
and t h e n s e a l e d .
~=C d i p o l e - d i p o l e r e l a x a t i o n time measurements were t r i e d pulse s p e c t r o m e t e r o f
method s u p p l i e d as a s t a c k i n 9 program w i t h a l e a s t calculation of
squares f i t
field frequency at
in
t h e ran9e o f
0,05 -
6,00 sec p u l s e
times.
The NOE measurements were t r i e d
at
c o m p l e t e l y decoupled and p u l s e
modulated decoupled c o n d i t i o n s w i t h 10.0 sec o f and t h e below 9 i v e n f o r m u l a was used f o r c a l c u l a t i o n s , Equ.20.(16,17)
20
2000 Hz
a c o n s t a n t p r o b e t e m p e r a t u r e and 180= and
90 ~ p u l s e sequences were t r i e d interval
for-
TI values.(10c,12,14a-c)
The e x p e r i m e n t s were c o n d u c t e d on t h e s p e c t r o m e t e r - a t of
on a
JEOL, model FX-60Q, w i t h t h e i n v e r s i o n r e c o v e r y
Tidlp = T i = b .
1.99/rich
pulse i n t e r v a l
time
t h e d i p o l a r r e l a x a t i o n time
115
ACKNOWLEDGEMENT
Prof.H.G.Hertz (Karlsruhe-Germany) i s acknowled9ed due t o his kind discussions a t t h e i n i t i a t i o n o f t h i s work and Prof.W.M.-Warmuth (Munster-Germany) i s acknowled9ed due t o the experience o f the a u t h o r in his l a b o r a t o r y a t Munster.
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