Molecular Dynamics of Cyclodextrins in Water Solutions from NMR

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Article

Molecular dynamics of cyclodextrins in water solutions from NMR deuterium relaxation. Implications for cyclodextrin aggregation Artur José Monteiro Valente, Rui Albuquerque Carvalho, Dina Murtinho, and Olle Soderman Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01923 • Publication Date (Web): 27 Jul 2017 Downloaded from http://pubs.acs.org on July 29, 2017

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Molecular dynamics of cyclodextrins in water solutions from

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NMR deuterium relaxation. Implications for cyclodextrin

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aggregation.

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A.J.M. Valente 1,*, R.A. Carvalho 2, D. Murtinho 1, O. Söderman 3

5 6 7

1

8 9

2

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3

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[email protected]

CQC, Department of Chemistry, University of Coimbra, 3004-535 Coimbra, Portugal

Centre for Functional Ecology, Department of Life Sciences, University of Coimbra, 3004-535 Coimbra, Portugal Division of Physical Chemistry, Lund University, PO Box 124, S-22100 Lund, Sweden

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* Corresponding author:

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Dr. Artur J.M. Valente

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Departamento de Química

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Universidade de Coimbra

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3004-535 Coimbra, Portugal

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Phone: +351 239854459

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Fax: +351 239827703

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email: [email protected]

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1 ACS Paragon Plus Environment

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Abstract

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The aggregation of the most common natural cyclodextrins (α-, β- and γ-) in aqueous

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solutions is addressed by studying the CD-CD interactions using deuterium relaxation

30

rates for deuterium labelled CDs. Relaxation times (T1) and its corresponding relaxation

31

rates (R1=1/T1) provide information about the rotational correlation times of CDs and

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serve as a proxy for solute-solute interactions. Measured T1’s for α-, β-, and γ-CD at the

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lowest CD concentrations were in agreement with predictions of a hydrodynamic model

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for toroids, in particular with regard to the dependence of T1 on CD size. On the other

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hand, the dependence of T1’s with respect to the increase in CD concentration could not

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be explained by hydrodynamic or direct interaction between CD molecules, and it is

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suggested that there is an equilibrium between monomeric and dimeric CD to account

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for the observed concentration dependence. No evidence in favor of large aggregates of

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CD involving a non-negligible fraction was found for the investigated CDs.

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Keywords:

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Cyclodextrin; molecular dynamics; aggregation; NMR; deuterium spin-lattice

43

relaxation.

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1. INTRODUCTION

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Cyclodextrins (CD) are cyclic oligomers of glucose. They are derived from starch, and

48

the most commonly used CDs are α-, β- and γ-, containing 6, 7 and 8 glucose units,

49

respectively. CDs have the form of a truncated cone, with hydroxyl groups on the

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outside of the molecules while a carbon and ether skeleton face the cavity. These

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structural features impart amphiphilic properties to CD. This fact makes CDs amenable

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for a significant number of applications including detergency 1, pharmacy

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analytical chemistry 4. Several issues regarding the structure and dynamics of CDs are

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still not fully understood. One such issue pertains to their solubility in water, with α-

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and γ-CD being rather soluble, while β-CD are less soluble (interestingly, δ-CD with 9

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glucose units is less soluble than both α- and γ-CD 5). It is argued that the low solubility

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of β-CD is mainly due to the occurrence of intramolecular hydrogen-bonding in

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aqueous solutions 6, although some authors also argue that this is due to the relatively

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high crystal lattice energy of CDs molecules 7; the latter argument being the usual way

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to account for questions pertaining to solubility of solid substances. A different issue is

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related to the possible formation of CD aggregates in water; the formation of CD

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aggregates was initially reported by Miyajima et al. in 1983, suggesting that α- and γ-

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CD can form dimers, or larger aggregates8; subsequently other authors have reported

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similar conclusions based on different techniques (see, for example,

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Bonini et al. 12, who reported the formation of β-CD aggregates at concentrations above

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3 mM on the basis of cryo-TEM data. The topic has been reviewed in several

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publications 11,13,14.

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Recently, we have used different NMR experiments to investigate α-, β- and γ-CDs in

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aqueous solutions 13. NMR diffusometry, relaxometry and proton peak intensities were

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measured and experimental data did not show any clear evidence in favor of 3 ACS Paragon Plus Environment

6,9–11

2,3

, and

), including

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aggregation; however, we cannot exclude the presence of more transient aggregates

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involving moderate numbers of CD. The fraction of CDs present in very large

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aggregates, not contributing to the NMR spectra on account of their slow rotational

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tumbling, was estimated to be below 1%.

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Recently two papers have been published where the formation of aggregates is

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discussed. Based on different scattering and microscopic techniques, Hernandez-

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Pascacio et al. 15 have suggested that α-CD spontaneously forms aggregates in aqueous

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solutions, driven by intermolecular H-bonding, while Saokham et al.

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permeability set-up, based on dialysis membranes (with a molecular weight-cut off

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higher or equal than 2 kDa), to measure the flux (permeation) of CDs across the

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membranes. The occurrence of two well defined steady-state permeation profiles of

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CDs through the membrane was attributed to the occurrence of CD aggregation; the

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calculated values for the critical aggregation concentration (cac) of α-, β- and γ-CDs are

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1.19, 0.69 and 0.93 % (w/v), respectively.

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In the present manuscript, we present an investigation of the CD-CD interactions in

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aqueous solutions by measuring deuterium relaxation rates for deuterium labelled CDs.

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The longitudinal (T1) relaxation time and its corresponding relaxation rate R1 (=1/T1),

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give information about the rotational correlation times of CDs which serve as a proxy

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for solute-solute interactions 18.

16,17

developed a

90 91 92

2. EXPERIMENTAL SECTION

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2.1. Materials

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β-CD (≥99% purity) and ruthenium 5% on activated charcoal were purchased from

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Aldrich (≥99% purity). α-CD and γ-CD were from Fluka both with a purity of 98%.


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The concentrations of CDs were corrected for the amount of hydration water according

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to the manufacturer. For NMR spectroscopy, samples were prepared either in deuterated

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water (isotope substitution >99.9%) from Eurisotop or in Milli-Q deionized water (for

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the case of deuterium NMR measurements).

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2.2. Calculation of volume fractions

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We will use volume fractions of CD, ΦCD, as concentration variable in the analysis of

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the relaxation data. These were obtained from mCD

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Φ CD =

ρCD

m M H 2O +  CD r  M CD ρ H O  2 mCD mH 2O +

ρCD

  

(1)

ρH O 2

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where m and M are the mass and molecular weight, respectively, ρ H 2O is the density of

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water (0.997043 g cm−3) and ρ CD the densities of CD, taken as 1.58 g cm−3 for α-CD,

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and 1.62 g cm−3 for β-CD and γ-CD

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completely fill the cavities of CDs (5.8, 8.7 and 14.2 for α-, β- and α-CD, respectively

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20

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affects the values of ΦCD marginally.

8,19

. r is the number of water molecules needed to

). It should be noted that the neglect of taking the water inside the cavity into account

111 112

2.3. Deuteration of cyclodextrins

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Deuterium-labeled compounds are frequently used in a number of applications.

114

Therefore, a variety of synthetic methods have been developed for this purpose,

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including multistep synthesis from small deuterated compounds, reduction of functional

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groups with deuterated reducing agents and exchange reactions

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catalysts are widely used to promote the H/D exchange reaction with the advantage that

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cheap sources of deuterium can be utilized. 5 ACS Paragon Plus Environment

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. Transition- metal

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Sajiki and coworkers developed a very efficient deuteration method for sugars using

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D2O as deuterium source and ruthenium on activated carbon as catalyst (Ru/C), under a

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hydrogen atmosphere

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strategy for the deuteration of α-, β- and γ-CDs 23. Using reaction conditions analogous

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to those reported by Ikeda, we also prepared deuterated α-, β- and γ-CDs (CD). Briefly,

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0.649 g of α- or β-CD or 0.324 g of γ-CD were dissolved in 16 mL of D2O and 0.808 g

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of 5% Ru-activated carbon was added. The reaction mixture was heated at 80 °C, in a

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hydrogen atmosphere (balloon), for 24h. After cooling to room temperature, the reaction

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mixture was filtered through Celite and evaporated.

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. Based on this work, Ikeda and coworkers used the same

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2.4. NMR measurements

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1

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MHz spectrometer using a 5-mm BBFO NMR probe. Spectra were obtained using 32 k

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data points covering a spectral width of 8.5 kHz, a radiofrequency excitation pulse of

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45°, and a scan repetition time of 4.5 s to allow for full relaxation.

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The degree of deuteration was assessed by 1H NMR spectroscopy. The NMR spectra for

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deuterated CDs (cf. Figure 1) show six different types of well-defined protons with the

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following assignments (cf. Figure 2): H1 at approx. 4.9 ppm, H3 at around 3.9 ppm, and

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H5 and H6 overlapping in the range of 3.7-3.8 ppm, H4 is characterized by an up-field

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triplet at ca. 3.5-3.6 ppm. H2, finally, is slightly less shielded than H4 and is located at

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around 3.6 ppm (overlapping with H4 in Fig. 1).

H NMR spectra for deuterated CDs were recorded at 25.0±0.1 °C on a Bruker 400

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Figure 1. 1H NMR spectra of deuterated α-CD, β-CD and γ-CD in D2O

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H OH 4

O HO

6

5 HO

1 H 3 H 2 OH

H

O n

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Figure 2. CDs structures (α-CD, n=6; β-CD, n=7 and γ-CD, n=8)

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The proton peak integrals, obtained from 1H NMR after CD deuteration, and the

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corresponding degree of deuteration are reported in Table 1.

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Table 1. Proton peak integrals (1H NMR data) and degree of deuteration of CDs CD

H1

H2

H3

H4

H5+H6

Degree of deuteration

α-

1.00

0.07

0.99

1.00

1.72

0.32

β-

1.00

0.09

0.92

1.00

1.42

0.37

γ-

1.00

0.03

1.00

1.00

1.59

0.34

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The 1H NMR peak integrals show that C1, C3 and C4 were only marginally deuterated

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(C3 shows a minor degree of deuteration for α- and β-CD) (Figure 1). The different C2

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were almost completely deuterated (93, 91 and 97 % exchange for α-, β- and γ-CD,

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respectively). According to Ikeda 23, the procedure yields a low degree of deuteration of

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C5. On the assumption that no exchange occurred on C5, C6 carries 1.3, 1.6, and 1.4

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deuterons for α-, β- and γ-CD, respectively (please note that C6 carries two protons).

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2

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concentration range 7.53 - 146 mmol kg−1), β-CD (4.42 - 16.3 mmol kg−1) and γ-CD

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(8.21 - 161 mmol kg−1) at 25.0±0.1 °C on a Bruker 500 MHz spectrometer using a 5-

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mm double resonance selective direct detection probe SEX with fluorine lock, for direct

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observation of deuterium with proton decoupling. The upper limit concentrations of

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deuterated CDs are similar to the solubility of non-deuterated cyclodextrins. Typical 2H

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acquisition parameters included a 840 Hz spectral width and 16 scans per τ increment.

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The T1-values were determined by measuring the initial intensity immediately after the

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observe 90 º pulse using an inversion recovery (IR) pulse sequence 24: [RD-180ºx-τ-90ºx-

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acq] where RD is the relaxation delay time allowing the complete (at least 5T1)

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longitudinal magnetization recovery; τ is the delay time between 180º and 90º pulses,

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and acq is the acquisition time. The IR relaxation curves (not shown) were obtained

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from τ values ranging from 1 µs to 0.2 s. T1 values were computed from experimental

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raw data by using the following equation:

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H longitudinal relaxation times (T1) were recorded for deuterated α-CD (in the

A = A0 (1 − Be−τ /T1 )

(2)

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where A is the signal integral measured at time τ, proportional to the z-magnetization at

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that time, A0 is the integral obtained after full relaxation (equilibrium magnetization)

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between the 180º and 90º pulses (very long τ values), and B is a constant (in general


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close to 2). The uncertainty in the fitting procedure to obtain T1 is typically around 1 %,

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taking only random errors into consideration 25.

177 178

3. RESULTS AND DISCUSSION

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3.1 Theoretical background

180

Deuterium is a quadrupolar nucleus and its relaxation is caused by the coupling between

181

the nuclear quadrupole moment and the fluctuating electric field gradients at the site of

182

the nucleus. Deuterium has spin I=1 and its longitudinal relaxation rate, R1 (=1/T1) is

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given by:26

184

185

R1 =

3π 2 2 χ ( 2 J (ω 0 ) + 8 J ( 2ω0 ) ) 40

(3)

186

where χ is the quadrupole coupling constant (here assigned the value 181 kHz

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J(x) is the spectral density function for the reorientation of the C-D bond vector,

188

evaluated at the given frequencies. ߱଴ is the Larmor frequency, defined by the

189

spectrometer magnetic field strength (in our case ߱଴ =481.55 106 rad s−1).

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For motions of C-D fragments in non-rigid molecules, which applies to the present case,

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Lipari and Szabo

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some rather general conditions, takes the following form:

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J (ω ) =

28

27

) and

derived an equation for the spectral density function which, under

(1 − S 2 )τ 2 2 S 2τ M + 1 + ω 2τ M2 1 + ω 2τ 2

(4)

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where S is an order parameter that quantifies the motional restrictions of the internal

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motions (S=1 for a rigid molecule), and τM and τi are the correlation times for the global

196

and for the faster, anisotropic internal motions, respectively. The correlation time τ is

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defined as follows:


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τ −1 = τ M−1 + τ i−1

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(5)

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In the derivation of Eqs. 4 and 5 it is assumed that the molecule is a spherical top and,

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consequently, its rotational diffusion is fully described by one rotational diffusion

201

coefficient Dr which is related to τM through the following equation: τM=1/(6Dr) 29.

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3.2 Experimental results

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Experimental values for longitudinal relaxation times as a function of the molality, m,

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and CD volume fraction, Φ CD, are presented in the Table 2.

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Table 2. T1 values for aqueous solutions of deuterated CDs solutions at 25 ºC. Errors in

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the values of T1 are typically around 1 %, taking only random errors in consideration. m / (mmol kg-1)

Φ

T1 (ms)

α-CD

7.530

0.0054

10.151

23.12

0.016

9.358

42.46

0.030

8.811

65.46

0.045

8.411

85.21

0.058

7.982

104.0

0.070

7.719

124.9

0.083

7.491

145.8

0.096

7.482

β-CD

4.416

0.0038

8.832

6.429

0.0055

8.800


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8.031

0.0068

8.604

9.935

0.0084

8.613

11.51

0.0098

8.576

14.20

0.0120

8.109

15.11

0.0128

7.988

16.30

0.0138

7.953

γ-CD

8.211

0.0086

7.715

29.70

0.031

7.092

48.46

0.049

6.736

63.31

0.063

6.548

87.28

0.086

6.237

108.8

0.106

6.109

135.6

0.129

5.782

161.3

0.151

5.740

209 210 211

As noted in the experimental section, the cyclic carbon 2 (C2) and the exo-cyclic carbon

212

6 (C6) are deuterated, to roughly the same extent. On account of the expected

213

differences in the internal motions for the C-D bond of carbon 2 and 6, the T1 values

214

should be different for those deuterons. In fact, the NMR deuterium spectrum is

215

expected to consist of two overlapping Lorentzian peaks. However, on account of the

216

width of the signals (around 50 Hz) and the shift difference (around 25 Hz), the

217

deconvolution is not possible and, consequently, independent relaxation rates for C2-D

218

and C6-D cannot be accurately obtained. In fact, model calculations (not shown) using


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two T1 values differing by a factor of two, yields relaxation curves practically

220

indistinguishable from a single exponential curve. Thus, the reported T1 values should

221

be considered as an average of the two (rather similar) values for C2-D and C6-D.

222

180

160

R1 / s-1

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120

100 0.00

0.04

0.08

0.12

0.16

Φ

223 224

Figure 3. Dependence of R1 (=1/T1) on the volume fraction, Φ, of cyclodextrins: (o) α-

225

CD; () β-CD; () γ-CD. Solid lines represent the predicted R1 values by using Eq.

226

(11) – see the text for further details. Insert: data at low volume fractions for a clearer

227

display of the dependence of relaxation rate on concentration for β-CD.

228 229 230

3.3 Discussion of NMR relaxation data.

231

From the appearance of the data in Figure 3 there are two noticeable trends: the values

232

of relaxation rates, R1, increase with both the size of the CD molecules and with the

233

volume fraction of the CDs.


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In order to interpret the data, we start by estimating a value for the rotational correlation

235

time of the CDs. This also brings up the question of whether the CD molecules can be

236

regarded as a spherical top and thus described by a single rotational diffusion

237

coefficient. We will use a hydrodynamic bead-shell model

238

estimations. To the best of our knowledge, no atomistic level hydrodynamic

239

calculations based on crystal structures have been presented for CDs. However, de la

240

Torre presents a model for toroidal particles

241

rotational diffusion coefficients. The toroidal shape has the symmetry of a symmetric

242

top and thus two rotational diffusion coefficients are obtained from the model.

243

The result for the translational diffusion coefficient is given by:

244

η Dt ro k BT

30

to carry out our

30

, which predicts translational as well as

= 0.0620 − 0.00143 x + 0.0278 x 2

(6)

245

where η is the viscosity of water (0.89 10−3 kg m−1 s−1 at T=298.15 K), ro is the outer

246

radius of the toroid and x(=ri/ro) is the ratio between the inner (ri) and outer toroid radii.

247

Using previously reported data (see, for example, ref 13) for the inner and outer radii 13,

248

and adding1.5 Å to r0 to account for an adsorbed hydration layer

249

translational diffusion coefficients as obtained from NMR data extrapolated to infinite

250

dilution for CDs 13 are well described (with a deviation smaller than 5 %) by the model

251

of de la Torre (eq 6) – see Figure 4 where Di obtained from Eq 6 are compared to the

252

experimental data.

253


31

, the experimental

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Dt / (10-10 m2 s-1)

4.0 A 3.5 3.0 2.5 0.6

r B

0.5

τ / ns

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0.4 0.3 0.32

0.36

0.40

0.44

0.48

r

254 255 256

Figure 4. Effect of the ratio between the inner and outer toroid radii (r) on the: A)

257

empirical (o) and theoretical (+) translational diffusion coefficients, and B) three

258

rotational correlation times for the toroid: (■) τa, (●)τb and (▲)τc. The following radii

259

(ri, ro) were used for α, β and γ-CD: (2.85/8.35, 3.90/9.15 and 4.75/9.95 Å),

260

respectively (see text for details).

261 262

Thus, there is good agreement between the Dt obtained experimentally and those

263

computed through the de la Torre model. This fact gives some credence for the use of

264

the same model to estimate the rotational diffusion coefficients for rotation around the

265

main symmetry axis and around a perpendicular axis in the equatorial plane ( D perp and

266

Daxis , respectively) for the toroid by using the following equations 30:

267

η Daxis ro 3 k BT

268

η D perp ro 3 k BT

= 0.0529 − 0.00444 x + 0.0404 x 2

(7)

= 0.0621 + 0.0176 x + 0.0227 x 2

(8)

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Then three rotational correlation times characterizing a toroid can be calculated:

271

τa =

272

correlation times are shown in Figure 4B.

1 6Dperp

, τb =

1 1 , and τ c = . The three rotational 5Dperp + Daxis 2Dperp + 4Daxis

273 274

From Figure 4B we infer that the three rotational correlation times are similar in

275

magnitude and, consequently, a description of the toroid as a spherical top is a

276

reasonable approximation. By taking the average of the three rotational correlation

277

times, we estimate values from the model of 0.32 (±0.02), 0.40 (±0.03), and 0.50

278

(±0.0.04) ns for α, β and γ-CD, respectively, for the rotational correlation time.

279

We now return to the discussion of the relaxation rates shown in Figure 3. To predict

280

the T1 values (Eq 3) of CD, three different parameters are required: viz. the order

281

parameter S and the two correlation times (τ and τM) of Eq 4.

282

From multi-field 13C NMR relaxation data, Kowalevski and Widmalm quote values of S

283

around 0.8, albeit for CD in a solvent mixture of 70/30 mol% D2O/DMSO and at 303

284

K32. One would expect a (slightly) higher S for the ring carbon deuteron than for the

285

exo-cyclic carbon deuterons on account of the latter being able to carry out local

286

motions with a higher amplitude. We take the value of S=0.8 and consider it as an

287

average for the two positions. For the internal motion τi, we assume a value of 40 ps,

288

also based on results of ref. 32. With these assumptions the only unknown in Eqs 3-5 is

289

the global correlation time τM, which can then be calculated from the relaxation data.

290

For the values at the lowest volume fraction we obtain: 0.33, 0.39 and 0.47 ns for α, β

291

and γ-CD, respectively. These values correspond closely to the case of infinite dilution

292

and can be compared to the values from predictions of the hydrodynamic calculations

293

presented above. The agreement is reasonable, indicating that the rotational dynamics of


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294

CD is well described in terms of rotational diffusion of single, unassociated CD

295

molecules at these low concentrations. We note that the contribution (given by S and τ i )

296

from the fast internal motions are comparatively small, of the order of 5 % of the values

297

of R1, and thus the results are not critically dependent on the choice of values of τ i and

298

S.

299

We now turn to the observed dependence of R1 on the volume fractions of the CDs. As

300

shown in Figure 3, there is a significant dependence of R1 on Φ. One source of this

301

dependence is the hydrodynamic coupling between CD-molecules. The magnitude of

302

this effect can be estimated for a suspension of hard spheres with stick boundary

303

conditions from continuum mechanics, by using the following equation 33:

304

(

τ M ( Φ ) = τ M ( 0 ) 1 + 0.67Φ + O ( Φ 2 )

)

(9)

305

where τM(0) is the infinite dilution correlation time of an isolated sphere and O(Φ2)

306

indicates that the next term is proportional to Φ2. In the present case, this effect would

307

predict an increase in τ M of around 10 % for the case of γ-CD, and consequently

308

roughly the same increase in R1, which is less than the observed effect, while for α-CD

309

the effect is somewhat smaller. For β-CD the effect is negligible.

310

Another cause of concentration dependence in the CD rotational dynamics is constituted

311

by direct mechanical interactions between molecules. In this context it is instructive to

312

estimate the average separation L between two CD molecules in solutions at the largest

313

values of Φ used. This can be obtained from

314

  Φ0 1/3  L = σ  − 1   Φ    

(10)

315

where Φ0=0.7405 is volume fraction of cubic close packing, and σ is the diameter of

316

the CD molecule, taken to be the outer diameter. The following results are obtained: L= 16 ACS Paragon Plus Environment

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317

13, 42 and 12 Å for α-, β- and γ-CD, respectively. Therefore, it can be concluded that

318

direct interactions should be less significant at the highest values of Φ used here, and of

319

course even less so at lower values of Φ.

320

In conclusion, neither hydrodynamic nor direct mechanical interactions between non-

321

aggregating CD molecules can explain the experimental concentration dependence of R1

322

on Φ.

323

Another possible hypothesis for the interpretation of such dependence is the formation

324

of dimers in CD solutions.34,35 Dimer formation would slow down the rotational

325

diffusion of CD. It is worth noting that the slope of the R1 vs. Φ data, in Figure 3,

326

follows a somewhat concave relationship; i.e. the R1-Φ dependence slightly decreases at

327

higher Φ values. Effects due to hydrodynamic coupling would curve in the opposite

328

manner. We consider the formation of dimers and write the process as an equilibrium:

329

2CD

330

monomeric and dimeric CD is rapid on the NMR timescale we can write for the

331

observed relaxation rate R1:

332

CD2 , characterized by an equilibrium constant K. If the exchange between

R1 = Pm R1,m + (1 − Pm ) R1,d

(11)

333

where Pm is the fraction of CD present as monomers and R1,m and R1,d are the

334

relaxation rates for monomeric and dimeric CD, respectively.

335

To test this assumption we shall use eq 11 and predict values of R1. Values of Pm are

336

obtained from the definition of the equilibrium constant K in terms of its defining

337

concentrations (see, for instance,

338

concentration of the CD and we estimate R1,d by doubling the value of τ M (based on the

339

fact that τ M is proportional to the hydrodynamic volume of the molecule and a dimer

340

would to first approximation have twice the volume of a monomer). The value of K is

36

). R1, m values are taken from the value at lowest


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

341

varied so as to get agreement with the experimental data. The results are shown as solid

342

lines in Figure 3.

343

The assumption of an equilibrium between monomeric and dimeric CD molecules is

344

capable of predicting the correct trends with regard to the concentration dependence of

345

the relaxation time. We note that we have used the same value of the equilibrium

346

constant for all three CDs. This is an assumption. A priori, the constant should be

347

different, although presumably not too different. An equilibrium constant of 8 means

348

that at a volume fraction of 0.1, roughly 50 % of the CD are in dimeric form. At a

349

volume fraction of around 0.01, around 10 % are in the form of dimers. As a

350

consequence, the values of the global rotational correlation times τM given above are

351

somewhat overestimated, as they were calculated assuming that no association of CD

352

takes place.

353

Before summarizing the main conclusions of this work, we note that the transverse

354

deuterium relaxation rates, R2, (as obtained from the deuterium NMR linewidths in the

355

spectra) can also be analyzed in a manner parallel to the analysis of R1 carried out

356

above. However, the fact that the deuterium NMR spectra consist of two overlapping

357

peaks with slightly different shifts, renders a qualitative analysis difficult. Nevertheless,

358

it is possible to conclude that the deuterium linewidths are not in contradiction to the

359

analysis of the longitudinal relaxation rates given above (see SI for details).

360 361

4. CONCLUSIONS

362

The structure of aqueous solutions of CDs has been studied by measuring NMR

363

longitudinal relaxation times of deuterated labelled α-, β- and γ-cyclodextrins. The

364

deuteration was carried out in a hydrogen atmosphere, in the presence of D2O and using

365

Ru/C as catalyst. The degree of deuteration were around 34 % for all cyclodextrins,


Page 18 of 25

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366

being H6 and H2 the most deuterated protons. 2H T1 values were then measured in a

367

cyclodextrin concentration range where the upper limit coincides with the cyclodextrin

368

solubility, suggesting that the deuteration has no significant effect on the cyclodextrins’

369

solubility and thus on the structure in aqueous solutions. From T1 measurements, we can

370

conclude that:

371

•

The values of the deuterium T1 values for CD at the lowest concentrations

372

measured is in agreement with predictions of a hydrodynamic model for

373

torroids, in particular with regard to the dependence of T1 on CD size.

374

•

hydrodynamic or direct mechanical interaction between CD molecules.

375 376

The dependence of the T1 values of concentration of CD cannot be explained by

•

A model of an equilibrium between monomeric and dimeric CD reproduces the

377

observed concentration dependence of T1. The equilibrium constant is small,

378

indicating that the aggregation at low concentrations is low.

379

•

Although we cannot exclude the presence of trimers or perhaps even tetramers,

380

no evidence in favor of large aggregates of CD involving a non-negligible

381

fraction of the CD is found.

382 383

AUTHOR INFORMATION

384

Corresponding Author

385

* E-mail: [email protected]

386

Notes

387

The authors declare no competing financial interests.

388 389

ACKNOWLEDGEMENTS


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390

This work was partially funded by the Swedish Research Council and the Coimbra Chemistry

391

Centre which is supported by the Fundação para a Ciência e a Tecnologia (FCT) through the

392

programmes UID/QUI/UI0313/2013 and COMPETE. NMR data was collected at the UC-NMR

393

facility which is supported in part by FEDER – European Regional Development Fund through

394

the COMPETE Programme and by National Funds through FCT through grants

395

REEQ/481/QUI/2006, RECI/QEQ-QFI/0168/2012, CENTRO-07-CT62-FEDER-002012, and

396

RNRMN.

397 398 399

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Dependence of longitudinal relaxation rate on the concentration of deutered α-cyclodextrin. Dimerization occurs at cyclodextrin concentrations just below the solubility limit 287x201mm (300 x 300 DPI)

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