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13C NMR relaxation time measurements of macrocyclic ether complexes. Part XII: the association constants of benzo[15]crown-5 and benzo[12]crown-4 with NaClO4 · H2O
Chemical Physics 303 (2004) 115–120 www.elsevier.com/locate/chemphys
13
C NMR relaxation time measurements of macrocyclic ether complexes. Part XII: the association constants of benzo[15]crown-5 and benzo[12]crown-4 with NaClO4 H2O q C ß akıl Erk b
a,*
, Manfred D. Zeidler
b
a Organic Chemistry Laboratoires, Department of Chemistry, Technical University of Istanbul, Maslak, TR-80626 Istanbul, Turkey Institut f€ ur Physikalische Chemie, Rheinisch-Westf€alische Technische Hochschule Aachen, Templergraben 59, D-52056 Aachen, Germany
Received 26 January 2004; accepted 5 May 2004 Available online 8 June 2004
Abstract In order to investigate the cation binding power of macrocyclic ethers the 13 C NMR relaxation times, T1 , of free benzo[15]crown5 and benzo[12]crown-4 as well as their 1/1 Naþ complexes were determined at different temperatures in acetonitrile. The dipolar contributions to NMR relaxation were separated by nuclear Overhauser enhancement measurements. The dipolar relaxation times of free and complexed crown ethers were explained on the basis of intramolecular [1 H]–13 C interactions of the molecules CH2 –O– CH2 backbone. From 13 C NMR relaxation times observed at extreme narrowing conditions the association constants, Ka , of the sodium-crown ether complexes were obtained as a function of temperature; the Naþ associations were shown to depend on the carbon–oxygen sites reducing directly the O–C–H relaxation times, T1 . Benzo[15]crown-5 displayed different T1 for different carbon segments on the ring, while benzo[12]crown-4 showed less T1 changes among the macrocyclic backbone carbons. Complexed macrocyclic ethers exhibited higher barrier energies for internal motion than the uncomplexed macrocycles because the oxygen charges of the former are attracted by the cation in a complex. Ó 2004 Elsevier B.V. All rights reserved. Keywords: NMR;
13
C dipolar relaxation; Association constants; Macrocyclic ethers; Naþ binding
1. Introduction Macrocycles that possess ion binding ability have been subject to wide investigations for numerous technological and analytical applications since their discovery. A great many of the applications have been reported including solvent extraction and membrane transport procedures, ion selective electrodes and related analytical utilities, and recently, functionality of macrocycles via NMR spectroscopy [1]. In this paper, among the several reports, we present cationic recognition studies using a dynamic NMR method. The interaction mechanism of cations with macrocycle oxygen q
Part XI, [1]. Corresponding author. Tel.: +90-212-285-3227; fax: +90-212-2856386. E-mail address: [email protected] (C ¸ . Erk). *
0301-0104/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.05.009
dipoles could be examined by this method since the cationic interactions with macrocyclic carbon–oxygen dipoles are displayed on the internal molecular motions. Current interest in cationic preferential binding by macrocyclic ethers encouraged us to study NMR relaxation times in order to estimate the binding effect of diamagnetic cations using NMR methods. We recently reported our results on Naþ /benzo[18]crown-6 association, using 13 C dipolar relaxation time measurements, and showed the selectivity of the six macrocyclic oxygens on Naþ binding [1]. Because 13 C relaxation is caused via the hydrogens bound to the carbons upon intramolecular dipolar interaction [2–8], we think that further 13 C relaxation rate measurements on macrocycles were needed in order to ascertain the effect of cationic preferential binding in more detail which leads to information on the macrocyclic backbone flexibility as well.
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C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
The cation association process may be formulated in the following way where Aþ and L stand for the cation and the macrocyclic ether, respectively, Eqs. (1)–(3) [9– 13] nAþ þ mL $ Aþ n Lm :
ð6Þ
where the mol fraction Pa refers to the bound and Pf to the free state of macrocycles, respectively.
ð1Þ
We introduce the analytical concentrations, þ þ þ ½Aþ 0 ¼ n½An Lm þ ½A and ½L0 ¼ m½An Lm þ ½L of the cation and macrocycle. The association constant of the process of Eq. (1) is written as m
n
þ Ka ¼ ½Aþ n Lm =f½L ½A g:
ð2Þ
However, we restrict our study to 1:1 association (m ¼ n ¼ 1) and introduce the mol fraction of the associated complex, Pa ¼ ½Aþ L=½L0 which yields with Eq. (2), Ka ¼ Pa =fð1 Pa Þ ð½Aþ 0 Pa ½L0 g. Finally we fix the analytical concentrations experimentally to ½Aþ 0 ¼ ½L0 and obtain Eq. (3) [9–13] 2
Ka ¼ Pa =f½L0 ð1 Pa Þ g:
ð3Þ
In the present work we use 13 C NMR relaxation time measurements of –H2 C–O– moieties of macrocyclic ethers at different temperatures to estimate 1:1 association constants, Ka , of NaClO4 with benzo-1,4,7,10,13pentaoxacyclopentadecane (benzo[15]crown-5) and with benzo-1,4,7,10-tetraoxacyclododecane (benzo[12]crown4) in CD3 CN, respectively. As the cationic interactions should influence the molecular motion via the oxygen dipoles, the cationic preferential binding is observed through the different rates of segmental motions of the complexed molecule. The correlation time, sCH , for the reorientational motion is given by Eq. (4) under extreme narrowing condition where the correlation time, sCH , is much smaller than the reciprocal resonance frequency, 1=x, of 13 C NMR resonance 6 1=T1DD ¼ ðl0 =4pÞ2 h2 c2C c2H rCH sCH :
ð4Þ
Here l0 is the vacuum permeability, h is Planck’s constant divided by 2p, c is the magnetogyric ratio of the respective nucleus, rCH is the interatomic distance between the carbon and hydrogen nucleus, and 1=T1DD is the dipolar contribution to the 13 C relaxation rate. This rate is separated from other contributions by a measurement of the nuclear Overhauser factor, gCH (NOE) 1=T1DD ¼ gCH =1:988 T1exp ;
ð5Þ
where 1=T1exp is the experimental relaxation rate of the C nucleus in any form in a solution. Because the carbon nucleus may belong either to a free, T1fDD , or to a DD bound macrocycle, T1a , we must separate both cases. If a fast exchange between free and complexed sites is involved the following relationship, Eq. (6), is applied where T1DD is assigned to the observed relaxation time of a complex mixture [11,12] 13
DD þ Pf =T1fDD ; 1=T1DD ¼ Pa =T1a
2. Experimental Benzocrowns were purchased from Fluka, NaClO4 H2 O from Merck. Samples of the free and Naþ containing benzocrown solutions in dry CD3 CN were made up in 10 mm NMR tubes with 0.125, 0.160, 0.200 and 0.300 M/L concentrations (the latter solutions were prepared with identical amounts of sodium perchlorate and macrocyclic ether) and were used for measurements of T1exp and gCH . Before, they were degassed by several freeze-pump-thaw cycles at 106 mbar and then sealed. The 13 C relaxation times were measured at 62.5 MHz on a Bruker, model AM-250, NMR spectrometer using the inversion recovery method with (180-t-90) pulse sequence, where t is the pulse separation time [2,3]. The NOE data were obtained from measurements under broad band-decoupled and inverse gated-decoupled pulse sequences with 5–10 T1 pulse delay time. All measurements were conducted at four different temperatures with the precision of 0.1 K. Tables 2 and 3 DD present the T1exp , T1a and T1fDD values of benzocrowns þ and their Na complexes in acetonitrile-d3 with different concentrations at various temperatures, 250–318 K. We performed NOE measurements and found that the experimental gCH is very close to 1.98 (compare Eq. (5)) which showed that the interactions are almost dipolar.
3. Results and discussion 3.1. Concept of 13 C relaxation time and correlation time of internal motions Until 1980, the 13 C spin–lattice relaxation studies in liquids had little interest, although this provides even quantitative information about the rotations, pseudorotations and orientations by NMR based on dipole– dipole (or quadrupole for 14 N) coupling mechanisms [3]. Regarding the more recent reports the topic is now well understood [13]. The reorientational motions of molecules are characterised by individual correlation times, sCH [2]. The macrocyclic backbone motional correlation times of C– H bonds are much shorter than 1/x and thus we obtain sCH from T1DD data, using Eq. (4). Substituting into this equation we get 1/T DD ¼ rCH ¼ 1:085 A 1 10 4:4045 10 sCH . Correlation times markedly change upon cation binding as shown in Tables 1–3 [1]. The observed correlation time, sCH , is based on the fastest and, therefore, the lowest energy of skeletal motions.
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
117
Table 1 Dipolar relaxation and correlation times of the macrocycles in CD3 CN Macrocycles
13
T1DD (s)
18C6 18C6 18C6
s ps
Conc. (M/L)
Temp. (K)
Ref.
C/free C/Naþ C/Kþ
1.80 1.89 1.57
12.63 12.03 14.48
0.280 0.280 0.280
318 318 318
[7] [7] [7]
15C5 15C5 15C5
C/free C/Naþ C/Kþ
3.89 2.06 1.86
5.84 1.03 2.22
0.280 0.280 0.280
318 318 318
[7] [7] [7]
12C4 12C4
C/free C/Liþ
3.98 2.38
5.71 9.55
0.280 0.280
318 318
[7] [7]
Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6
C1 (T1f ) C1/Naþ C2 (T1f ) C2/Naþ C3 (T1f ) C3/Naþ C4 (T1f ) C4/Naþ C5 (T1f ) C5/Naþ
2.06 1.65 2.22 1.67 2.25 1.75 2.41 1.84 2.43 1.86
1.03 3.77 0.24 3.61 0.10 2.99 9.43 2.35 9.35 12.22
0.125
315 315 315 315 315 315 315 315 315 315
[1] [1] [1] [1] [1] [1] [1] [1] [1] [1]
Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5
C1 (T1f ) C1/Naþ C2 (T1f ) C2/Naþ C3 (T1f ) C3/Naþ C4 (T1f ) C4/Naþ
9.62 24.15 8.73 23.90 8.41 23.65 7.10 23.41
0.160
(T1a )
2.36 0.94 2.60 0.95 2.75 0.96 3.20 0.97
318 318 318 318 318 318 318 318
This This This This This This This This
work work work work work work work work
Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4
C1 (T1f ) C1/Naþ (T1a ) C2 (T1f ) C2/Naþ (T1a ) C3 (T1f ) C3/Naþ (T1a )
4.05 0.79 4.30 0.79 4.70 0.82
5.61 28.74 5.28 28.74 4.83 27.69
0.160
318 318 318 318 318 318
This This This This This This
work work work work work work
C
(T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a )
The energy barriers DEa of the correlation time sCH is derived from Eq. (4) and (7) (see Figs. 1 and 2) sCH ¼ s0CH eDE=RT :
ð7Þ
The alterations on this parameter exhibit the mechanism and power of cation–dipole interactions which are the basis for the results and conclusions in this work (see Table 1) [7]. 3.2. 13 C relaxation rates of complexed and uncomplexed benzocrowns The first step in data processing is to convert the observed relaxation times which are measured in the crown ether/sodium solution and in the sodium-free solution, at identical crown ether concentration, with the help of NOE factor using Eq. (5). Thus, we obtain the dipolar relaxation times, T1DD and T1fDD . Then we simultaneously apply Eqs. (3) and (6) and determine the DD two unknown quantities T1a and Ka from the concentration dependence (variation of ½L0 under the limitation, Pa þ Pf ¼ 1) of T1DD . The results for T1DD , T1fDD ,
0.125 0.125 0.125 0.125
0.160 0.160 0.160
0.160 0.160
DD and Ka (as its logarithm) are summarized in Tables T1a 2 and 3 for different carbon atoms of the crown ethers benzo[12]crown-4 and benzo[15]crown-5 at various temperatures between 250 and 318 K. DD A plot of the relaxation times T1fDD and T1a (as their logarithms) versus the inverse absolute temperature yields the activation energy of the internal motion of the CH2 –CH2 –O– backbone, Figs. 2 and 3. The activation energies are for benzo[12]crown-4 13.0–14.0 kJ M1 for the free and 9.0–10.0 kJ M1 for the complexed species, Fig. 2, whereas for benzo[15]crown-5 they are 10.0–12.0 and 8.0 – 8.5 kJ M1 , respectively, Fig. 3. The complexed macrocycles exhibited lower barrier energies than for free macrocycles due to metal complex formation via ion–dipole interaction, although Naþ is not fully encapsulated in the macrocyclic ring. The higher barrier energies for smaller macrocyclic DD sizes are a consequence of higher ring strain, with T1a values varying even less over the segments [1]. The experimental T1fDD values of the free macrocyclic segments are large while the complexed macrocycles exhibited DD lower T1a as well as lower barrier energies, Tables 1–3,
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C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
Table 2 DD Relaxation times T1fDD and T1a and (1/1) association constants Ka of benzo[12]crown-4 O O 1
O O
3
2
T (K)
T1f a (s)
DEf b (kJ M1 )
T1a c (s)
DEa d (kJ M1 )
log Ka e
DGa f (kJ M1 )
DHa g (kJ M1 )
DSa h (J K1 M1 )
C1 C1 C1 C1
318 280 263 250
4.050 2.100 1.300 1.000
13.80
0.790 0.495 0.378 0.307
9.05
1.83 2.14 2.29 2.39
)4.80 )5.64 )6.01 )6.30
)11.81
)22.02
C2 C2 C2 C2
318 280 263 250
4.300 2.300 1.480 1.100
13.32
0.790 0.495 0.379 0.315
8.98
1.94 2.23 2.36 2.47
)5.09 )5.87 )6.22 )6.49
)11.62
)20.52
C3 C3 C3 C3
318 280 263 250
4.700 2.450 1.600 1.200
13.34
0.818 0.500 0.380 0.325
9.94
2.00 2.33 2.48 2.59
)5.27 )6.13 )6.52 )6.82
)12.52
)22.81
13
C No.
a
Relaxation time of free macrocyclic (0.160 M/L). Free energy of internal motion of free O–13 C–H site. c Relaxation time of (1/1) complexed O–13 C–H site. d Free energy of internal motion of (1/1) complexing O–13 C–H site. e Association constant of (1/1) Naþ complexing O–13 C–H site (DG ¼ DH T DS). f Free energy of (1/1) Naþ complexing O–13 C–H site at given temperature. g Free enthalpy of (1/1) Naþ complexing O–13 C–H site. h Free entropy of (1/1) Naþ complexing O–13 C–H site. b
Figs. 2 and 3. This results from the delocalisation of total bonding charges on the CH2 –CH2 –O link upon the oxygen dipole-Naþ cation interactions. However, the internal energy barriers might be controlled by the mother solvent, CD3 CN due to strong dipole–dipole interactions [1,12]. Consequently, 13 C NMR-T1 work is a valuable tool to examine the thermodynamics of macrocyclic ether–cation interactions depending on the most common properties of molecular internal motions as well as the cation–dipole interactions. 3.3. Estimation of association constants We employ the characteristics of the segmental motion of a macrocycle backbone, obtained from the selective 13 C NMR of CH2 covalently bound to oxygen for a quantitative measure. The binding power within the Naþ complexes of benzo[15]crown-5 and benzo[12]crown-4 exhibited limited selectivity of the backbone due to the strained small rings of close internal DD barrier energies. It is to note that the T1a data obtained are close to each other for the complex structures which is rather uniform and oxygen–metal distances are quite unique even for non-equivalent 13 C–O sites. Association constants, Ka , plotted on logarithmic scale versus inverse temperatures give the standard enthalpy, DH , and the standard entropy, DS, of (1:1)
complex formation, Fig. 4. The Naþ binding enthalpy is around 11.5–12.5 kJ M1 for benzo[12]crown-4 and 9.0– 10.5 kJ M1 for benzo[15]crown-5. The respective binding entropies are 22.0–23.0 and 16.0–24.0 J K1 M1 . Thus the binding enthalpy for benzo[15]crown-5 is smaller due to better encapsulation of Naþ . Conformationally oriented oxygen dipoles bind the cation, via electron delocalisation to diminish the T1 , however, if the pseudorotation rate is lowest, then the maximum binding enthalpy is achieved [16]. Furthermore, we showed that the cation association are exothermic since the macrocyclic ether separated cation complexes are formed where association constants are reduced by increasing temperatures [1,12–17]. Due to lowering of ion pairs’s Coulombic interactions with the longer distance between ions and counterions, the binding effect of macrocyclic ethers is reduced by the increasing temperature. However, the solvation of cations by the polar mother solvent, like CD3 CN in our work, is important since the strong solvation of Naþ with CD3 CN reduced the power of macrocyclic interactions which results in less selectivity of the O–CH2 –CH2 sequences [1]. 3.4. Internal motions Macrocyclic ether molecules are preorganised structures which possess specific segmental conformations.
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
119
Table 3 DD Relaxation times, T1fDD , T1a and (1/1) association constants, Ka of benzo[15]crown-5 2 3
O
4
1
O
O O
O
T (K)
T1f a (s)
DEf b (kJ M1 )
T1a c (s)
DEa d (kJ M1 )
log Ka e
DGa f (kJ M1 )
DHa g (kJ M1 )
DSa h (J K1 M1 )
C1 C1 C1 C1
318 280 263 250
2.360 1.340 0.990 l.790
10.66
0.940 0.585 0.490 0.400
8.19
1.11 1.67 1.97 2.23
)2.79 )3.69 )4.10 )4.40
)10.30
)23.60
C2 C2 C2 C2
318 280 263 250
2.600 1.390 1.040 0.833
11.09
0.945 0.590 0.491 0.405
8.15
1.28 1.81 2.10 2.35
)3.20 )4.00 )4.36 )4.64
)9.90
)21.06
C3 C3 C3 C3
318 280 263 250
2.750 1.530 1.120 0.850
11.16
0.960 0.595 0.492 0.403
8.35
1.44 1.93 2.19 2.42
)3.61 )4.27 )4.56 )4.79
)9.11
)17.31
C4 C4 C4 C4
318 280 263 250
3.200 1.650 1.200 0.910
12.18
0.970 0.600 0.493 0.402
8.47
1.53 2.02 2.28 2.50
)3.84 )4.46 )4.74 )4.94
)9.06
)16.32
13
C No.
a
Relaxation time of free macrocyclic (0.160 M/L). Free energy of internal motion of free O–13 C–H site. c Relaxation time of (1/1) complexed O–13 C–H site. d Free energy of internal motion of (1/1) complexing O–13 C–H site. e Association constant of (1/1) Naþ complexing O–13 C–H site (DG ¼ DH T DS). f Free energy of (1/1) Naþ complexing O–13 C–H site at given temperature. g Free enthalpy of (1/1) Naþ complexing O–13 C–H site. h Free entropy of (1/1) Naþ complexing O–13 C–H site. b
2.00
c H
1
O
2
b
H
a
O
1.75
C1a
1.50
C2a
1.25
C3a C4a
1.00
ln T1
H
H
H
M
+
H
C1f
0.75
C2f
0.50
C3f
0.25
C4f
0.00 -0.25 -0.50 -0.75
Fig. 1. The projection of –O–CH2 –CH2 –O–CH2 – bonds with internal motions in a metal complex.
To bind cations they may change the conformation of each segment, thereby reducing the relaxation times, € although, C–O–C bond electrons are partially transferred via oxygen–metal interaction. Thus, the torsional barrier is less restricted due to loss of electron density throughout the H–C–C–O bonds as shown in Fig. 1 [4– 6]. It should be noted that the four oxygen free ether rings displayed higher T1 and higher DEf compared to five and six oxygen macrocyclics, Table 1 [1,10,18].
-1.00 3.00
3.20
3.40
3.60
3.80
4.00
4.20
1000 K / T
Fig. 2. Dependence of relaxation rates of free, 1/T1f , and complexed, 1/ T1a , benzo[15]crown-5 on the inverse temperature.
It should be noted that the cation–ligand dynamics of preferred ‘‘anti, gauche, anti’’ unit segments, in particular for five and four oxygen members, determine the fastest internal motion along the O–CH2 –CH2 – (motion b, Fig. 1) segments. In a ligand binding site of crown
120
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
C1a
2.0
C2a C3a
1.5
C4a
ln T1
1.0
C1f C2f
0.5
C3f C4f
0.0 -0.5 -1.0 3.00
3.20
3.40
3.60
3.80
4.00
4.20
1000 K / T
Fig. 3. Dependence of relaxation rates of free, 1/T1f , and complexed, 1/ T1a , benzo[12]crown-4 on the inverse temperature.
4,0 3,5
C112
Acknowledgements
C212
ln Ka
C312 3,0
C115
2,5
C215 C315 C415
rings do not encapsulate the cations completely, 1:1 complexation may also be accompanied by 1:2 or 2:1 cation/ligand binding ratios [15,16]. It is interesting to note that benzo[12]crown-4 displays marked correlation time changes upon complex formation and higher association constants as compared to benzo[15]crown-5 due to binding enthalpy-entropy compensations, Table 2 [16]. To compare our results with the earlier literature data we presented the Table 1 including the correlation times of macrocyclic ethers. Recently, much larger rings studied in this way have shown clearly the correlations between the NMR relaxation time and internal motions [17,18]. The theoretical fundamentals and use of such relaxation rate measurements for polymers have also been discussed [19].
One of the authors, C ß .E., acknowledges the research grants of TUBITAK and Deutsche Forschungsgemeinschaft, DFG, to work at the Institute of Physical Chemistry of RWTH.
2,0 1,5 1,0 3,00
References 3,20
3,40
3,60
3,80
4,00
4,20
1000 K / T
Fig. 4. Naþ (1/1) association constants, ln Ka , of macrocyclics versus inverse temperatures.
[1] [2] [3] [4] [5] [6]
ether the geminal H–C–H angles are almost fixed to move (motion c, Fig. 1), however, the motion of C–H dipoles around the vicinal –CH2 –CH2 –O involve separate rates of CH1 and CH2 vectors (motion a, Fig. 1) during fast internal motions (pseudorotations). Since the molecule is not symmetrical the H1 and H2 (no symmetry plane in between) attached portions of methylenes may display different rates (motions b and c are no longer identical), and consequently the different 13 C–T1 values are observed as depicted in Fig. 1 [1,8]. Accordingly, the aromatic groups should also withdraw the neighbouring electrons which govern the chemical shifts. From extensive potential-energy-surface calculations the cation–ligand dynamics of ‘‘anti, gauche, anti’’ unit sequences of –O–CH2 –CH2 – are shown in a fast equilibrium with the different set of free macrocycle conformations, in particular for the six or higher oxygen member ring systems [1,8,13,14]. We consider that mostly the 1:1 complex is involved for calculations in this work because four and five oxygen macrocyclic
[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
[18]
[19]
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13
C NMR relaxation time measurements of macrocyclic ether complexes. Part XII: the association constants of benzo[15]crown-5 and benzo[12]crown-4 with NaClO4 H2O q C ß akıl Erk b
a,*
, Manfred D. Zeidler
b
a Organic Chemistry Laboratoires, Department of Chemistry, Technical University of Istanbul, Maslak, TR-80626 Istanbul, Turkey Institut f€ ur Physikalische Chemie, Rheinisch-Westf€alische Technische Hochschule Aachen, Templergraben 59, D-52056 Aachen, Germany
Received 26 January 2004; accepted 5 May 2004 Available online 8 June 2004
Abstract In order to investigate the cation binding power of macrocyclic ethers the 13 C NMR relaxation times, T1 , of free benzo[15]crown5 and benzo[12]crown-4 as well as their 1/1 Naþ complexes were determined at different temperatures in acetonitrile. The dipolar contributions to NMR relaxation were separated by nuclear Overhauser enhancement measurements. The dipolar relaxation times of free and complexed crown ethers were explained on the basis of intramolecular [1 H]–13 C interactions of the molecules CH2 –O– CH2 backbone. From 13 C NMR relaxation times observed at extreme narrowing conditions the association constants, Ka , of the sodium-crown ether complexes were obtained as a function of temperature; the Naþ associations were shown to depend on the carbon–oxygen sites reducing directly the O–C–H relaxation times, T1 . Benzo[15]crown-5 displayed different T1 for different carbon segments on the ring, while benzo[12]crown-4 showed less T1 changes among the macrocyclic backbone carbons. Complexed macrocyclic ethers exhibited higher barrier energies for internal motion than the uncomplexed macrocycles because the oxygen charges of the former are attracted by the cation in a complex. Ó 2004 Elsevier B.V. All rights reserved. Keywords: NMR;
13
C dipolar relaxation; Association constants; Macrocyclic ethers; Naþ binding
1. Introduction Macrocycles that possess ion binding ability have been subject to wide investigations for numerous technological and analytical applications since their discovery. A great many of the applications have been reported including solvent extraction and membrane transport procedures, ion selective electrodes and related analytical utilities, and recently, functionality of macrocycles via NMR spectroscopy [1]. In this paper, among the several reports, we present cationic recognition studies using a dynamic NMR method. The interaction mechanism of cations with macrocycle oxygen q
Part XI, [1]. Corresponding author. Tel.: +90-212-285-3227; fax: +90-212-2856386. E-mail address: [email protected] (C ¸ . Erk). *
0301-0104/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.05.009
dipoles could be examined by this method since the cationic interactions with macrocyclic carbon–oxygen dipoles are displayed on the internal molecular motions. Current interest in cationic preferential binding by macrocyclic ethers encouraged us to study NMR relaxation times in order to estimate the binding effect of diamagnetic cations using NMR methods. We recently reported our results on Naþ /benzo[18]crown-6 association, using 13 C dipolar relaxation time measurements, and showed the selectivity of the six macrocyclic oxygens on Naþ binding [1]. Because 13 C relaxation is caused via the hydrogens bound to the carbons upon intramolecular dipolar interaction [2–8], we think that further 13 C relaxation rate measurements on macrocycles were needed in order to ascertain the effect of cationic preferential binding in more detail which leads to information on the macrocyclic backbone flexibility as well.
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C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
The cation association process may be formulated in the following way where Aþ and L stand for the cation and the macrocyclic ether, respectively, Eqs. (1)–(3) [9– 13] nAþ þ mL $ Aþ n Lm :
ð6Þ
where the mol fraction Pa refers to the bound and Pf to the free state of macrocycles, respectively.
ð1Þ
We introduce the analytical concentrations, þ þ þ ½Aþ 0 ¼ n½An Lm þ ½A and ½L0 ¼ m½An Lm þ ½L of the cation and macrocycle. The association constant of the process of Eq. (1) is written as m
n
þ Ka ¼ ½Aþ n Lm =f½L ½A g:
ð2Þ
However, we restrict our study to 1:1 association (m ¼ n ¼ 1) and introduce the mol fraction of the associated complex, Pa ¼ ½Aþ L=½L0 which yields with Eq. (2), Ka ¼ Pa =fð1 Pa Þ ð½Aþ 0 Pa ½L0 g. Finally we fix the analytical concentrations experimentally to ½Aþ 0 ¼ ½L0 and obtain Eq. (3) [9–13] 2
Ka ¼ Pa =f½L0 ð1 Pa Þ g:
ð3Þ
In the present work we use 13 C NMR relaxation time measurements of –H2 C–O– moieties of macrocyclic ethers at different temperatures to estimate 1:1 association constants, Ka , of NaClO4 with benzo-1,4,7,10,13pentaoxacyclopentadecane (benzo[15]crown-5) and with benzo-1,4,7,10-tetraoxacyclododecane (benzo[12]crown4) in CD3 CN, respectively. As the cationic interactions should influence the molecular motion via the oxygen dipoles, the cationic preferential binding is observed through the different rates of segmental motions of the complexed molecule. The correlation time, sCH , for the reorientational motion is given by Eq. (4) under extreme narrowing condition where the correlation time, sCH , is much smaller than the reciprocal resonance frequency, 1=x, of 13 C NMR resonance 6 1=T1DD ¼ ðl0 =4pÞ2 h2 c2C c2H rCH sCH :
ð4Þ
Here l0 is the vacuum permeability, h is Planck’s constant divided by 2p, c is the magnetogyric ratio of the respective nucleus, rCH is the interatomic distance between the carbon and hydrogen nucleus, and 1=T1DD is the dipolar contribution to the 13 C relaxation rate. This rate is separated from other contributions by a measurement of the nuclear Overhauser factor, gCH (NOE) 1=T1DD ¼ gCH =1:988 T1exp ;
ð5Þ
where 1=T1exp is the experimental relaxation rate of the C nucleus in any form in a solution. Because the carbon nucleus may belong either to a free, T1fDD , or to a DD bound macrocycle, T1a , we must separate both cases. If a fast exchange between free and complexed sites is involved the following relationship, Eq. (6), is applied where T1DD is assigned to the observed relaxation time of a complex mixture [11,12] 13
DD þ Pf =T1fDD ; 1=T1DD ¼ Pa =T1a
2. Experimental Benzocrowns were purchased from Fluka, NaClO4 H2 O from Merck. Samples of the free and Naþ containing benzocrown solutions in dry CD3 CN were made up in 10 mm NMR tubes with 0.125, 0.160, 0.200 and 0.300 M/L concentrations (the latter solutions were prepared with identical amounts of sodium perchlorate and macrocyclic ether) and were used for measurements of T1exp and gCH . Before, they were degassed by several freeze-pump-thaw cycles at 106 mbar and then sealed. The 13 C relaxation times were measured at 62.5 MHz on a Bruker, model AM-250, NMR spectrometer using the inversion recovery method with (180-t-90) pulse sequence, where t is the pulse separation time [2,3]. The NOE data were obtained from measurements under broad band-decoupled and inverse gated-decoupled pulse sequences with 5–10 T1 pulse delay time. All measurements were conducted at four different temperatures with the precision of 0.1 K. Tables 2 and 3 DD present the T1exp , T1a and T1fDD values of benzocrowns þ and their Na complexes in acetonitrile-d3 with different concentrations at various temperatures, 250–318 K. We performed NOE measurements and found that the experimental gCH is very close to 1.98 (compare Eq. (5)) which showed that the interactions are almost dipolar.
3. Results and discussion 3.1. Concept of 13 C relaxation time and correlation time of internal motions Until 1980, the 13 C spin–lattice relaxation studies in liquids had little interest, although this provides even quantitative information about the rotations, pseudorotations and orientations by NMR based on dipole– dipole (or quadrupole for 14 N) coupling mechanisms [3]. Regarding the more recent reports the topic is now well understood [13]. The reorientational motions of molecules are characterised by individual correlation times, sCH [2]. The macrocyclic backbone motional correlation times of C– H bonds are much shorter than 1/x and thus we obtain sCH from T1DD data, using Eq. (4). Substituting into this equation we get 1/T DD ¼ rCH ¼ 1:085 A 1 10 4:4045 10 sCH . Correlation times markedly change upon cation binding as shown in Tables 1–3 [1]. The observed correlation time, sCH , is based on the fastest and, therefore, the lowest energy of skeletal motions.
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
117
Table 1 Dipolar relaxation and correlation times of the macrocycles in CD3 CN Macrocycles
13
T1DD (s)
18C6 18C6 18C6
s ps
Conc. (M/L)
Temp. (K)
Ref.
C/free C/Naþ C/Kþ
1.80 1.89 1.57
12.63 12.03 14.48
0.280 0.280 0.280
318 318 318
[7] [7] [7]
15C5 15C5 15C5
C/free C/Naþ C/Kþ
3.89 2.06 1.86
5.84 1.03 2.22
0.280 0.280 0.280
318 318 318
[7] [7] [7]
12C4 12C4
C/free C/Liþ
3.98 2.38
5.71 9.55
0.280 0.280
318 318
[7] [7]
Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6 Benzo[18]crown-6
C1 (T1f ) C1/Naþ C2 (T1f ) C2/Naþ C3 (T1f ) C3/Naþ C4 (T1f ) C4/Naþ C5 (T1f ) C5/Naþ
2.06 1.65 2.22 1.67 2.25 1.75 2.41 1.84 2.43 1.86
1.03 3.77 0.24 3.61 0.10 2.99 9.43 2.35 9.35 12.22
0.125
315 315 315 315 315 315 315 315 315 315
[1] [1] [1] [1] [1] [1] [1] [1] [1] [1]
Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5 Benzo[15]crown-5
C1 (T1f ) C1/Naþ C2 (T1f ) C2/Naþ C3 (T1f ) C3/Naþ C4 (T1f ) C4/Naþ
9.62 24.15 8.73 23.90 8.41 23.65 7.10 23.41
0.160
(T1a )
2.36 0.94 2.60 0.95 2.75 0.96 3.20 0.97
318 318 318 318 318 318 318 318
This This This This This This This This
work work work work work work work work
Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4 Benzo[12]crown-4
C1 (T1f ) C1/Naþ (T1a ) C2 (T1f ) C2/Naþ (T1a ) C3 (T1f ) C3/Naþ (T1a )
4.05 0.79 4.30 0.79 4.70 0.82
5.61 28.74 5.28 28.74 4.83 27.69
0.160
318 318 318 318 318 318
This This This This This This
work work work work work work
C
(T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a ) (T1a )
The energy barriers DEa of the correlation time sCH is derived from Eq. (4) and (7) (see Figs. 1 and 2) sCH ¼ s0CH eDE=RT :
ð7Þ
The alterations on this parameter exhibit the mechanism and power of cation–dipole interactions which are the basis for the results and conclusions in this work (see Table 1) [7]. 3.2. 13 C relaxation rates of complexed and uncomplexed benzocrowns The first step in data processing is to convert the observed relaxation times which are measured in the crown ether/sodium solution and in the sodium-free solution, at identical crown ether concentration, with the help of NOE factor using Eq. (5). Thus, we obtain the dipolar relaxation times, T1DD and T1fDD . Then we simultaneously apply Eqs. (3) and (6) and determine the DD two unknown quantities T1a and Ka from the concentration dependence (variation of ½L0 under the limitation, Pa þ Pf ¼ 1) of T1DD . The results for T1DD , T1fDD ,
0.125 0.125 0.125 0.125
0.160 0.160 0.160
0.160 0.160
DD and Ka (as its logarithm) are summarized in Tables T1a 2 and 3 for different carbon atoms of the crown ethers benzo[12]crown-4 and benzo[15]crown-5 at various temperatures between 250 and 318 K. DD A plot of the relaxation times T1fDD and T1a (as their logarithms) versus the inverse absolute temperature yields the activation energy of the internal motion of the CH2 –CH2 –O– backbone, Figs. 2 and 3. The activation energies are for benzo[12]crown-4 13.0–14.0 kJ M1 for the free and 9.0–10.0 kJ M1 for the complexed species, Fig. 2, whereas for benzo[15]crown-5 they are 10.0–12.0 and 8.0 – 8.5 kJ M1 , respectively, Fig. 3. The complexed macrocycles exhibited lower barrier energies than for free macrocycles due to metal complex formation via ion–dipole interaction, although Naþ is not fully encapsulated in the macrocyclic ring. The higher barrier energies for smaller macrocyclic DD sizes are a consequence of higher ring strain, with T1a values varying even less over the segments [1]. The experimental T1fDD values of the free macrocyclic segments are large while the complexed macrocycles exhibited DD lower T1a as well as lower barrier energies, Tables 1–3,
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C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
Table 2 DD Relaxation times T1fDD and T1a and (1/1) association constants Ka of benzo[12]crown-4 O O 1
O O
3
2
T (K)
T1f a (s)
DEf b (kJ M1 )
T1a c (s)
DEa d (kJ M1 )
log Ka e
DGa f (kJ M1 )
DHa g (kJ M1 )
DSa h (J K1 M1 )
C1 C1 C1 C1
318 280 263 250
4.050 2.100 1.300 1.000
13.80
0.790 0.495 0.378 0.307
9.05
1.83 2.14 2.29 2.39
)4.80 )5.64 )6.01 )6.30
)11.81
)22.02
C2 C2 C2 C2
318 280 263 250
4.300 2.300 1.480 1.100
13.32
0.790 0.495 0.379 0.315
8.98
1.94 2.23 2.36 2.47
)5.09 )5.87 )6.22 )6.49
)11.62
)20.52
C3 C3 C3 C3
318 280 263 250
4.700 2.450 1.600 1.200
13.34
0.818 0.500 0.380 0.325
9.94
2.00 2.33 2.48 2.59
)5.27 )6.13 )6.52 )6.82
)12.52
)22.81
13
C No.
a
Relaxation time of free macrocyclic (0.160 M/L). Free energy of internal motion of free O–13 C–H site. c Relaxation time of (1/1) complexed O–13 C–H site. d Free energy of internal motion of (1/1) complexing O–13 C–H site. e Association constant of (1/1) Naþ complexing O–13 C–H site (DG ¼ DH T DS). f Free energy of (1/1) Naþ complexing O–13 C–H site at given temperature. g Free enthalpy of (1/1) Naþ complexing O–13 C–H site. h Free entropy of (1/1) Naþ complexing O–13 C–H site. b
Figs. 2 and 3. This results from the delocalisation of total bonding charges on the CH2 –CH2 –O link upon the oxygen dipole-Naþ cation interactions. However, the internal energy barriers might be controlled by the mother solvent, CD3 CN due to strong dipole–dipole interactions [1,12]. Consequently, 13 C NMR-T1 work is a valuable tool to examine the thermodynamics of macrocyclic ether–cation interactions depending on the most common properties of molecular internal motions as well as the cation–dipole interactions. 3.3. Estimation of association constants We employ the characteristics of the segmental motion of a macrocycle backbone, obtained from the selective 13 C NMR of CH2 covalently bound to oxygen for a quantitative measure. The binding power within the Naþ complexes of benzo[15]crown-5 and benzo[12]crown-4 exhibited limited selectivity of the backbone due to the strained small rings of close internal DD barrier energies. It is to note that the T1a data obtained are close to each other for the complex structures which is rather uniform and oxygen–metal distances are quite unique even for non-equivalent 13 C–O sites. Association constants, Ka , plotted on logarithmic scale versus inverse temperatures give the standard enthalpy, DH , and the standard entropy, DS, of (1:1)
complex formation, Fig. 4. The Naþ binding enthalpy is around 11.5–12.5 kJ M1 for benzo[12]crown-4 and 9.0– 10.5 kJ M1 for benzo[15]crown-5. The respective binding entropies are 22.0–23.0 and 16.0–24.0 J K1 M1 . Thus the binding enthalpy for benzo[15]crown-5 is smaller due to better encapsulation of Naþ . Conformationally oriented oxygen dipoles bind the cation, via electron delocalisation to diminish the T1 , however, if the pseudorotation rate is lowest, then the maximum binding enthalpy is achieved [16]. Furthermore, we showed that the cation association are exothermic since the macrocyclic ether separated cation complexes are formed where association constants are reduced by increasing temperatures [1,12–17]. Due to lowering of ion pairs’s Coulombic interactions with the longer distance between ions and counterions, the binding effect of macrocyclic ethers is reduced by the increasing temperature. However, the solvation of cations by the polar mother solvent, like CD3 CN in our work, is important since the strong solvation of Naþ with CD3 CN reduced the power of macrocyclic interactions which results in less selectivity of the O–CH2 –CH2 sequences [1]. 3.4. Internal motions Macrocyclic ether molecules are preorganised structures which possess specific segmental conformations.
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
119
Table 3 DD Relaxation times, T1fDD , T1a and (1/1) association constants, Ka of benzo[15]crown-5 2 3
O
4
1
O
O O
O
T (K)
T1f a (s)
DEf b (kJ M1 )
T1a c (s)
DEa d (kJ M1 )
log Ka e
DGa f (kJ M1 )
DHa g (kJ M1 )
DSa h (J K1 M1 )
C1 C1 C1 C1
318 280 263 250
2.360 1.340 0.990 l.790
10.66
0.940 0.585 0.490 0.400
8.19
1.11 1.67 1.97 2.23
)2.79 )3.69 )4.10 )4.40
)10.30
)23.60
C2 C2 C2 C2
318 280 263 250
2.600 1.390 1.040 0.833
11.09
0.945 0.590 0.491 0.405
8.15
1.28 1.81 2.10 2.35
)3.20 )4.00 )4.36 )4.64
)9.90
)21.06
C3 C3 C3 C3
318 280 263 250
2.750 1.530 1.120 0.850
11.16
0.960 0.595 0.492 0.403
8.35
1.44 1.93 2.19 2.42
)3.61 )4.27 )4.56 )4.79
)9.11
)17.31
C4 C4 C4 C4
318 280 263 250
3.200 1.650 1.200 0.910
12.18
0.970 0.600 0.493 0.402
8.47
1.53 2.02 2.28 2.50
)3.84 )4.46 )4.74 )4.94
)9.06
)16.32
13
C No.
a
Relaxation time of free macrocyclic (0.160 M/L). Free energy of internal motion of free O–13 C–H site. c Relaxation time of (1/1) complexed O–13 C–H site. d Free energy of internal motion of (1/1) complexing O–13 C–H site. e Association constant of (1/1) Naþ complexing O–13 C–H site (DG ¼ DH T DS). f Free energy of (1/1) Naþ complexing O–13 C–H site at given temperature. g Free enthalpy of (1/1) Naþ complexing O–13 C–H site. h Free entropy of (1/1) Naþ complexing O–13 C–H site. b
2.00
c H
1
O
2
b
H
a
O
1.75
C1a
1.50
C2a
1.25
C3a C4a
1.00
ln T1
H
H
H
M
+
H
C1f
0.75
C2f
0.50
C3f
0.25
C4f
0.00 -0.25 -0.50 -0.75
Fig. 1. The projection of –O–CH2 –CH2 –O–CH2 – bonds with internal motions in a metal complex.
To bind cations they may change the conformation of each segment, thereby reducing the relaxation times, € although, C–O–C bond electrons are partially transferred via oxygen–metal interaction. Thus, the torsional barrier is less restricted due to loss of electron density throughout the H–C–C–O bonds as shown in Fig. 1 [4– 6]. It should be noted that the four oxygen free ether rings displayed higher T1 and higher DEf compared to five and six oxygen macrocyclics, Table 1 [1,10,18].
-1.00 3.00
3.20
3.40
3.60
3.80
4.00
4.20
1000 K / T
Fig. 2. Dependence of relaxation rates of free, 1/T1f , and complexed, 1/ T1a , benzo[15]crown-5 on the inverse temperature.
It should be noted that the cation–ligand dynamics of preferred ‘‘anti, gauche, anti’’ unit segments, in particular for five and four oxygen members, determine the fastest internal motion along the O–CH2 –CH2 – (motion b, Fig. 1) segments. In a ligand binding site of crown
120
C ß . Erk, M.D. Zeidler / Chemical Physics 303 (2004) 115–120
C1a
2.0
C2a C3a
1.5
C4a
ln T1
1.0
C1f C2f
0.5
C3f C4f
0.0 -0.5 -1.0 3.00
3.20
3.40
3.60
3.80
4.00
4.20
1000 K / T
Fig. 3. Dependence of relaxation rates of free, 1/T1f , and complexed, 1/ T1a , benzo[12]crown-4 on the inverse temperature.
4,0 3,5
C112
Acknowledgements
C212
ln Ka
C312 3,0
C115
2,5
C215 C315 C415
rings do not encapsulate the cations completely, 1:1 complexation may also be accompanied by 1:2 or 2:1 cation/ligand binding ratios [15,16]. It is interesting to note that benzo[12]crown-4 displays marked correlation time changes upon complex formation and higher association constants as compared to benzo[15]crown-5 due to binding enthalpy-entropy compensations, Table 2 [16]. To compare our results with the earlier literature data we presented the Table 1 including the correlation times of macrocyclic ethers. Recently, much larger rings studied in this way have shown clearly the correlations between the NMR relaxation time and internal motions [17,18]. The theoretical fundamentals and use of such relaxation rate measurements for polymers have also been discussed [19].
One of the authors, C ß .E., acknowledges the research grants of TUBITAK and Deutsche Forschungsgemeinschaft, DFG, to work at the Institute of Physical Chemistry of RWTH.
2,0 1,5 1,0 3,00
References 3,20
3,40
3,60
3,80
4,00
4,20
1000 K / T
Fig. 4. Naþ (1/1) association constants, ln Ka , of macrocyclics versus inverse temperatures.
[1] [2] [3] [4] [5] [6]
ether the geminal H–C–H angles are almost fixed to move (motion c, Fig. 1), however, the motion of C–H dipoles around the vicinal –CH2 –CH2 –O involve separate rates of CH1 and CH2 vectors (motion a, Fig. 1) during fast internal motions (pseudorotations). Since the molecule is not symmetrical the H1 and H2 (no symmetry plane in between) attached portions of methylenes may display different rates (motions b and c are no longer identical), and consequently the different 13 C–T1 values are observed as depicted in Fig. 1 [1,8]. Accordingly, the aromatic groups should also withdraw the neighbouring electrons which govern the chemical shifts. From extensive potential-energy-surface calculations the cation–ligand dynamics of ‘‘anti, gauche, anti’’ unit sequences of –O–CH2 –CH2 – are shown in a fast equilibrium with the different set of free macrocycle conformations, in particular for the six or higher oxygen member ring systems [1,8,13,14]. We consider that mostly the 1:1 complex is involved for calculations in this work because four and five oxygen macrocyclic
[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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[19]
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