Dispersion of Water Proton SpinâLattice Relaxation Rates in Aqueous

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The Dispersion of Water Proton Spin-Lattice Relaxation Rates in Aqueous Solutions of MWCNTs Stabilized via Alkyloxymethylimidazolium Surfactants Maria Dobies, Justyna Izykowska, Michalina Wilkowska, Aneta WozniakBraszak, Kosma Szutkowski, Andrzej Skrzypczak, Stefan Jurga, and Maciej Kozak J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 08 May 2017 Downloaded from http://pubs.acs.org on May 13, 2017

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The Journal of Physical Chemistry

The Dispersion Of Water Proton Spin-Lattice Relaxation Rates In Aqueous Solutions Of MWCNTs Stabilized Via Alkyloxymethylimidazolium Surfactants Maria Dobies1, Justyna Iżykowska1,2, Michalina Wilkowska1, Aneta Woźniak-Braszak3, Kosma Szutkowski1,2, Andrzej Skrzypczak4, Stefan Jurga1,2, Maciej Kozak1,5* 1

Departament of Macromolecular Physics, Faculty of Physics, Adam Mickiewicz University,

Umultowska 85, 61-614 Poznań, Poland 2

NanoBioMedical Centre, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań,

Poland 3

High Pressure Physics Division, Department of Physics, Adam Mickiewicz University,

Umultowska 85, 61-614 Poznań, Poland 4

Faculty of Chemical Technology Poznan University of Technology, Berdychowo 4,

60-965 Poznań, Poland 5

Joint Laboratory for SAXS studies, Faculty of Physics, Adam Mickiewicz University,

Umultowska 85, 61–614, Poznań, Poland *corresponding author: [email protected]

ACS Paragon Plus Environment


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Abstract Carbon nanotubes and a number of other carbon nanomaterials have a tendency to aggregate, which often resulted in difficulties of dispersion of these nanomaterials in aqueous solutions. The ability of dicationic (gemini) surfactants to disperse multiwall carbon nanotubes in water and the dynamic processes taking place at the water-MWCTs interface are studied. Stable dispersions of multi-wall carbon nanotubes with selected gemini surfactants (1,1’-(1,6hexanediyl)bis(3-alkyloxymethylimidazolium) dichlorides) were prepared and characterized by nuclear magnetic relaxation dispersion (NMRD), NMR diffusometry, scanning and transmission electron microscopy, and Fourier transform infrared spectroscopy. The addition of multiwall carbon nanotubes to aqueous solutions of studied gemini surfactants leads to significant paramagnetic enhancement of the spin-lattice relaxation processes, which gets more pronounced with increasing concentration of well-dispersed MWNTs in water. The dominant role of outer sphere (OS) relaxation mechanism in total observed R1, governed by twodimensional diffusion of water on the carbon nanotube surface in the vicinity of paramagnetic centers incorporated in the MWCNTs side-walls (mainly of iron origin), was assumed to explain NMRD data. The NMR diffusion experiments confirm the existence of restricted water diffusion in the studied supernatants. The NMR diffusion results are consistent with the FTIR and NMR proton spin-lattice relaxation dispersion in which the more effective R1 dispersion noticed for the sample with IMIC6C12 was ascribed to the better accessibility of water molecules to the surface of the MWCNTs.


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Introduction Carbon nanotubes (CNTs) are the cylindrical nanostructures of low density which consist of single (single-wall carbon nanotubes – SWCNTs) or multiple (multi-wall carbon nanotubes – MWCNTs) coaxially rolled graphene layers, treated as one-dimensional nanomaterials because of the high aspect ratio. These substances reveal remarkable mechanical properties (i.e. high strength and stiffness, elastic deformability), chemical stability, high electrical and thermal conductivity. The unique features of carbon nanotubes are very promising for new applications in composite materials, electronics, optics, environmental science, biology and medicine.1–4 The high surface area of carbon nanotubes and considerable inter-tube van der Waals attractions lead to self-aggregation of CNTs into ropes consisting of several tens of individual tubes entangled in a complicated network. The unique properties of individual carbon nanotubes in aggregates are significantly impaired, while the chemical modification and physical manipulation are highly difficult. In view of the above finding an effective separation procedure of CNTs bundles into individual nanotubes is crucial in order to use their full potential.5,6 The un-bundling process is realized by dispersing carbon nanotubes in solvents. Water as a non-toxic substance is the most interesting liquid medium used in this procedure in the context of the carbon nanotubes biomedical applications. Pristine CNTs exhibit strong hydrophobic nature therefore they are practically insoluble in water and because of that the phase separation is observed immediately after addition to water. Special treatments are needed to obtain aqueous CNTs dispersion of high quality and stability. To overcome the problem of low water-solubility, the surface of carbon nanotubes is chemically modified via the attachment of polar groups (i.e. hydroxyl, carboxyl groups) to CNTs side walls. Unfortunately, the chemical functionalization leads to defects in the CNTs structure therefore does not preserve



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the original properties of nanotubes.6 Another method which effectively improves the affinity of CNTs to water is based on the non-covalent functionalization of CNTs.7,8 In this method, the physical adsorption of appropriate dispersing agents onto carbon nanotubes is needed to disperse them in water. It has been found that the most effective dispersants are surfactants9–13, block copolymers14–17, natural polymers and proteins.5,18–20 The adsorption process is driven by the hydrophobic interaction leading to the attraction of hydrophobic surface of CNTs and waterinsoluble part of dispersants to reach the minimum of total free energy of the system. Equally important in the physical adsorption of additives are the π―π stacking interactions taking place between aromatic molecules. Because of the above mentioned interactions, the adsorption of dispersants onto CNTs surface is possible, only if the energy of ultrasonication is high enough to separate the ends of particular carbon nanotubes entangled in the aggregate. The long term stabilization of aqueous suspensions of CNTs enables, in turn, the electrostatic repulsion and/or steric interactions between dispersing agents adsorbed onto neighboring nanotubes. These interactions form a repulsive barrier and effectively prevent re-aggregation processes of CNTs in a solvent, depending on the electric charge, the chain conformation, the flexibility and length of hydrophilic part of the additives.6,8 For polymers, two types of physical associations with CNTs surface have been identified and described as the wrapping or non-wrapping mechanisms, characteristic of strong and specific polymer-nanotube associations or the loose adsorption onto CNT surface of a hydrophobic parts of macromolecules, respectively.14 The dispersibility and stabilization of carbon nanotubes in water in the presence of surfactants have been widely discussed in literature.9–13 Adsorption of amphiphilic molecules of this type onto the CNTs surface leads to minimization of the interfacial energy realized mainly by van-der Waals and π-CH interactions between the surface of CNTs and the hydrophobic tails of surfactants, and also by simultaneous exposition of their hydrophilic heads into water which, in turn, enables efficient dispersibility of CNTs in water. Therefore, the


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adsorption significantly modifies the surface tension, wettability and surface charge of the CNT-water interface facilitating the dispersibility of CNTs in aqueous medium. No less important factors for a good separation of nanotubes in water are the presence of aromatic compounds in the structure of surfactants and the proper concentration of surfactants Csurf in solvent. It has been shown that with increasing Csurf value, the concentration of CNTs in water increases, but this trend after reaching a plateau value reverses at higher Csurf values due to the depletion interaction effect.13,21 It is worth noticing that no correlation has been found between the effective un-bundling process of carbon nanotubes and the micellization processes, although both of them are based on hydrophobic interactions. With increasing tail length of surfactants, the critical micellar concentration decreases, which is in contrast to the value of surfactant concentration most effective to disperse CNTs in water that increases with increasing alkyl chain length.22 A few scenarios for the adsorption of single-tailed surfactants onto CNTs surface have been suggested in literature: 1) random type adsorption of surfactants by encircling the carbon nanotubes 2) adsorption of surfactants, which are vertically oriented with respect to the CNTs surface (cylindrical surfactant micelles with a carbon nanotube as a core), 3) adsorption of hemimicelles onto the CNT sidewalls.9 The work is devoted to analysis of capability of dicationic (gemini) surfactants to disperse multiwall carbon nanotubes in water and recognition of dynamical processes taking place in the water-MWCTs interface. The gemini surfactants (n-s-n) consist of two hydrocarbon chains (hydrophobic tails n) ended with ionic head groups and linked together by a spacer (s).23 These substances are the subject of the special interest because they reveal higher efficiency in unbundling and stabilizing CNTs in water than their classical single-tailed homologs (at concentrations lower than their CMC). These amphiphilic molecules reveal much stronger ability to associate with CNTs because of the existence of two hydrophobic tails, and also provide better stability CNTs in water which is a consequence of the higher packing of ionic



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head groups (due to the presence of the spacer), The complex structure of gemini surfactants entails novel properties in comparison to those of classical surfactants such as lower CMC, different phase diagram enriched by a non-spherical shape of aggregates (disk-like micelles, rod-like micelles) and the variable aggregate geometry depending on the hydrocarbon chain lengths and the spacer length (more worm-like forms are preferred with shortening n and s), and also the degree of spacer flexibility. The loose type of monolayer adsorption of gemini surfactants onto the carbon nanotube surface is suggested. It has been evidenced that with increasing length of alkyl chains the dispersibility of CNTs in water increases.13,21–25 In the frames of this work four cationic gemini surfactants of the same spacer size (hexanediyl group in s domain) and alkyl chains of different lengths (dodecyl and tetradecyl groups in n domain) were chosen to test their influence on the degree of segregation of carbon nanotubes in water. In selected aqueous MWCNTs/gemini surfactant suspensions, in which the long-term stability was noticed, the water proton nuclear spin-lattice relaxation rate dispersion was measured to study the effect of the presence of pristine MWCNTs on the water molecules dynamics in studied systems. Such studies are important in the context of the widely discussed in recent years the use of carbon nanotubes in the medicine, as novel contrast agents (CA) in magnetic resonance imaging (MRI) or as multi-functional targeting drug delivery systems.

26–29

The NMR relaxometry (or nuclear magnetic resonance dispersion - NMRD) is

the method commonly used to evaluate the efficacy of contrast agents in aqueous medium. 29– 31

Analysis of the frequency dependence of spin-lattice relaxation rates (R1=1/T1, NMRD

profile) provides the insight into the nature of observed enhancement of R1 processes. The strong paramagnetic enhancement of water proton spin-lattice relaxation rates has been noticed in the presence of various metal-ion carbon nanostructure complexes (fullerenes, nanoribbons, nanoplatelets, nanotubes, ultra-short nanotubes doped via gadolinium or manganese ions) indicating a high diagnostic potential of them.32–34 It has been found that the longitudinal


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relaxivity (r1=

𝑅1

) of these nanostructures is much higher than that of observed in

𝐶𝐶𝐴 [mM]

clinically available gadolinium-based contrast agents and that the recorded shapes of NMRD profiles differ from each other. It has been evidenced also that the incorporation or encapsulation of paramagnetic ions in graphene sheets, irrespective of the size, shape and architecture of carbon nanosystems, leads to an increase in relaxivity r1.32,35 The Solomon– Bloembergen–Morgan (SBM)36–38 theory well-established for prediction of the efficiency of low molecular metal complexes, which employs the inner sphere (IS) and outer sphere (OS) mechanisms governing the paramagnetic relaxation enhancement (PRE) of water proton R1, is not sufficient for good reproduction of experimental NMRD profiles obtained for CAs based on carbon nanostructures. Most of the research have been focused on the evaluation of paramagnetic enhancement of R1 coming from the interactions of inner-sphere water protons with paramagnetic ions (IS mechanism).32,35 Recently, the discussion has been devoted also to the importance of OS mechanism which takes into account the fact that water molecules diffuse in the magnetic field gradient generated via paramagnetic moieties.34,39,40 In this latter approach, the translational water dynamics can be analyzed similarly like in porous systems with paramagnetic impurities.41–44 It is worth noticing that the R1 dispersion can be also present in un-doped bundled and unbundled carbon nanotubes.34 It has been also illustrated for the boron nitride nanotubes (BNNT) suspended in the glycol-chitosan sole and in this system, it has been explained by the presence of residual paramagnetic cobalt impurities remaining after the synthesis in these nanostructures.40 The right description of the water proton R1 dispersion in aqueous suspensions of nanotubes doped via paramagnetic ions is still debated and need a new theoretical approach, which unfortunately does not exist yet. The proper model should include specific features of carbon nanotube structure, which frequently are consequences of applied synthesis, purification methods, and also the type of functionalization (the presence of defects, paramagnetic or superparamagnetic impurities, metallic nanoparticles).29 More experimental



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NMRD data supported by results obtained from other methods are needed in order to testify the importance of different contributions to NMRD profiles. In the frames of this work the NMR relaxometry method is applied to study R1 dispersion in water suspension of un-doped multiwall carbon nanotubes stabilized by gemini surfactants in order to identify the mechanisms responsible for enhancement of spin-lattice relaxation in the studied systems. The quality of aqueous CNTs suspensions stabilized by Gemini surfactants was monitored over a 6-month period by means of visual inspection. In order to check the degree of separation of MWCNTs and to evaluate of the content of paramagnetic metal impurities of the studied nanostructures the NMR diffusion measurements, TEM and SEM micrographs were analyzed. FTIR measurements were used for construction of a calibration curve needed for the assessment of MWCNTs concentration in the supernatants.

Experimental Materials Multiwall carbon nanotubes (MWCNTs) were purchased from NanoLab Inc. USA. The MWCNTs were produced with using the chemical vapor decomposition (CVD) method. The purity of the sample was declared as a 95 %. It is worth noticing that the sulfur (S) and iron (Fe) catalyst were used in the synthesis of the MWCNTs thus trace amounts of these ions can be present in all studied systems (according to the product description in the amount close to 1.08 weight %). The length of MWCNTs ranged from 5 to 20 m and the mean tube diameter was equal to 155 nm. The pristine “cotton candy” structure of studied carbon nanotubes is presented in the SEM micrograph in Figure 1. A group of quaternary bis-imidazolium chlorides was synthesized in the reaction of 1,1’(1,6-hexanediyl)bis(1H-imidazole) with the appropriate amount of chloromethylalkyl ethers (chloromethyloctyl

ether,

chloromethyldecyl

ether,

chloromethyldodecyl


ether

or

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chloromethyltetradecyl ether). Then 1,1’-(1,6-hexanediyl)bis(1H-imidazole) was synthesized in the reaction of imidazole with 1,6-dibromohexane: sodium (0.1 M) was added to 75 mL of anhydrous methanol and the imidazole (0.1 M) was dissolved. The appropriate amount (0.05 M) of 1,6-dibromohexane was added and the mixture was stirred for 6 h at 338K. Precipitated sodium bromide was filtered and the methanol was removed. The product of 1,1’-(1,6hexane)bis(1H-imidazole) was twice distilled under reduced pressure (558-560K, 1.7Pa) and the final yield was 77.0%. Chloromethylalkylethers were obtained by passing HCl - gas through a mixture of formaldehyde and appropriate alcohol according to the procedure described earlier.30 The aqueous suspensions of MWCNTs were prepared with using four cationic gemini surfactants: the 1,1’-(1,6-hexanediyl)bis(3-octyloxymethylimidazolium) dichloride, 1,1’-(1,6hexanediyl)bis(3-decyloxymethylimidazolium) (dodecyloxymethylimidazolium)

dichloride

dichloride, and

1,1’-(1,6-hexanediyl)bis 1,1’-(1,6-hexanediyl)bis

3(3-

tetradecyloxymethylimidazolium) dichloride denoted as: IMIC6C8, IMIC6C10, IMIC6C12 and IMIC6C14, respectively. These dispersing agents, differed from each other in the length of alkyl chains. The gemini surfactants besides two hydrophobic tails possess also in their structure two hydrophilic heads, in which imidazole aromatic rings, linked by the spacer of the same length are located (1,6-hexanediyl). The chemical structure of the cationic gemini surfactants used are presented in Figure 2. All dispersants were added to a proper volume of distilled and deionized water (Mili-Q, 8 mΩ) and mixed to get homogenous systems. The concentration of both gemini surfactants in water was the same and equal to 10 mg/ml. These two aqueous surfactants solutions were used as liquid media to disperse MWCNTs in water. The weighted portion of MWCNTs (0.5 mg/ml) was added to IMIC6C12 or IMIC6C14 solutions and the mixtures were sonicated for 240 min in the ultrasonic bath (60W). After this procedure all



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suspensions were stored for 3 month at room temperature in glass tubes. During this time, the visual inspection of samples was made to assess the mixtures stability.

Methods The morphology of carbon nanotubes was investigated by Scanning Electron Microscopy (SEM) (JEOL7001TTLS) and Transmission Electron Microscopy (TEM) (Jeol 1400). For SEM measurements MWCNTs suspensions were diluted in water in proportion 1:500, and drops of suspensions were placed onto glass plates, which were earlier covered by a thin layer of gold to provide better conductivity of electrons. The chemical composition of MWCNTs was evaluated by X-ray Energy Dispersive System (EDS). In the EDS experiment the samples were placed onto a silicon wafer, to minimize the number of elements in the spectrum. For TEM measurements the diluted (1:500) MWCNTs suspensions were applied onto copper grid. The fast field cycling FFC NMR relaxometry (also known as the nuclear magnetic relaxation dispersion - NMRD) was used to study nuclear relaxation processes taking place on the carbon nanotube-water interface in the system studied. This NMR technique uses variable magnetic field strengths to measure the Larmor frequency dependence of the proton spin-lattice relaxation times T1. NMRD method is suitable to probe a broad time scale of molecular motions, usually ranging from nanoseconds to milliseconds.45 The 1H NMR dispersion of spin-lattice relaxation rates R1 T 1 1 (1H NMRD) were recorded with a commercial Fast Field Cycling (FFC) Relaxometer (Stelar Spin Master 2000, Italy) in the range of proton Larmor frequencies between 10 kHz and 12 MHz. A special home-made high sensitivity RF coil with a diameter of 5 mm was used. The typical 90o RF pulse length was 5 s, and the dead time following the RF pulse was 12 s. For all Larmor frequencies the data were averaged over 8 acquisitions for 8 blocks. The values of spin-lattice relaxation times T1 were obtained by fitting the decay curve of magnetization as a function of duration time of relaxation field in each cycle by a mono-


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exponential function. All NMRD measurements were realized at 303 K. The temperature was controlled to the accuracy of ±0.1 K by a conventional temperature controller using a gas flow system. The NMRD frequency range for samples with MWCNTs was extended by measurements of T1 times on the two NMR homemade pulse spectrometers46–48 operating at proton frequencies of 16.5 MHz and 30.2 MHz. using standard a saturation pulse sequence. The samples were centrifuged additionally, at 7000 rpm for 30 min, to remove the large aggregates of MWCNTs and obtain homogenous systems for the study. The degassed supernatants were placed into 5mm diameter glass tubes and tightly closed. Centrifugation dramatically reduced the concentration of carbon nanotubes in the surfactant solutions, so it was necessary to verify its final value in the samples used for NMRD study. The final concentration of MWCNTs in the supernatant after centrifugation was established from the Fourier-Transform Infrared spectra (FTIR). Five standard suspensions of known concentrations and solutions selected for NMR studies were placed on CaF2 windows (drop volume 20 μl), and then they were dried at 333K for 60min. The spectra were measured by coadding 256 scans on a TENSOR 27 spectrometer (Bruker Optics, Germany) equipped with a liquid nitrogen-cooled MCT detector, at 4 cm-1 resolution at 298 K in the spectral range of 4000-1000 cm-1. Reference transmission spectra were collected using a single CaF2 window. The OPUS 7.2 (Bruker Optics, Germany) program package was used for spectral evaluation. The position of characteristic band was obtained using the second derivatives of the spectra. The water diffusion coefficients of selected aqueous suspensions of MWCNT’s and gemini surfactants were obtained in H2O with 5% of D2O for lock. The experiments were carried out by Agilent DDR2 600 MHz NMR spectrometer and DOTY DS-1374 1H/lock probe and DBPPSTE pulse sequence (Diffusion Bipolar Pulse Pair Stimulated Echo).49 The diffusion time  was varied between 10 and 500 ms in order to obtain the dependence of the apparent diffusion coefficient Dapp(). The duration of magnetic field pulses  was set to 1 ms, temperature was



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294 K and recycle delay was set to 4 s. The gradient amplitude was varied between 9-140 Gs/cm. Diffusion coefficients were obtained directly from the VnmrJ 4.2 software using algorithm based on single exponential fitting to the Stejskal-Tanner equation.50

Results and discussion The usefulness of the imidazolium gemini surfactants for making dispersions of MWCNTs in water was assessed by means of visual tests performed over 6 months from the moment of sample preparation. The pictures collected in Figure 3a and 3b illustrate inefficiency of the IMIC6C8 and IMIC6C10 surfactants as dispersing agents for MWCNTs studied. These figures clearly show the presence of the water and MWCNTs phase separation, which did not vanished even after the application of US mixing (carbon nanotubes lay on the bottom of phials). In contrast to short tailed surfactants, their long-tailed forms: IMIC6C12 and IMIC6C14 revealed high efficiency to disperse MWCNTs in water, which is evidenced in the Figures 3c and 3d. The long-term stability, lack of large amounts of sediments in these systems, not transparent character and ink-like colour are the main features expected for aqueous MWCNTs suspensions in which carbon nanotubes are well-dispersed.5 SEM images recorded for these samples reveals the existence of individual carbon nanotubes of tens nanometer size separated from bundles (Figure 4). These observations are consistent with the results of visual tests. Nuclear relaxation at the water-MWCNTs interface can help to understand the mechanisms governing the dispersibility of carbon nanotubes in water and find factors useful for the assessment of quality of aqueous suspensions of MWCNTs. Figure 5 shows frequency dependencies of spin-lattice relaxation rates R1 of aqueous suspension of multiwall carbon nanotubes prepared in the presence of the gemini surfactants IMIC6C12 and IMIC6C14, and the reference sample - a water solution of IMIC6C12, recorded at 303 K. The T1 relaxation processes in all samples are progressively enhanced with decreasing


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magnetic field strength, but are much more effective for samples containing multiwalled carbon nanotubes, although that the concentration of IMIC6C12 surfactants in the sample with MWCNTs (supernatant) can be a little smaller than that of pure IMIC6C12 suspension. It strongly suggests that the main source of changes in R1(f) is the water-nanotube interaction. The dispersion data at the high field limit exhibit distinctly lower sensitivity to the presence of MWCNTs than those in the low field range. The pure IMIC6C12 solution reveals relatively slight frequency dependence of R1 characterized by a Lorentzian-like shape in contrast to the strong logarithmic frequency dependence of R1 observed for the MWCNTs/ IMIC6C12 suspension. The most pronounced changes in the R1 value were found in the range of low magnetic field strength, which suggest the existence of slow molecular motions modulating magnetic interactions in the system studied. It has been shown that in isotropic aqueous biopolymer systems, water molecules can be trapped or adsorbed onto the solute surface which affects their dynamics in comparison to the behaviour in the bulk.45,51–56 Because of that a distribution of correlation times is usually detected and the most of NMRD data obtained for complex systems show the dispersion profiles of R1 which are extended over a frequency range wider than that for the Lorentzian dispersion form. The Lorentzian-like shape of the frequency dependence of R1 has been detected mainly in a case of diluted aqueous protein solutions.51,52 Under the assumption that the water proton spin-lattice relaxation process observed in pure aqueous solution of gemini surfactant IMIC6C12 (without MWCNTs) is dominated by homonuclear dipole–dipole interactions, the Lorentzian-like shape of the R1(f) profile with a non-dispersive tail observed in high frequency range can be explained by the existence of slow and fast molecular motions modulating spinspin interactions in the system studied. Therefore, the frequency dependence of R1 in the reference sample may be estimated from the following equation:



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R1 = R1bulk +R1slow= R1bulk+ A[0.2J(ω)+0.8J(2ω)],

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(1)

where: R1bulk (frequency independent) equal to 0.3 s-1 and R1slow describing the spin-lattice relaxation process of bulk water protons and water protons in restricted environment, respectively. The A parameter is a constant and J(ω) is the Lorentzian spectral density function 

given by 𝑱(𝝎) = 𝟏+(𝝎𝝉)𝟐 , ω = 2πf (f - Larmor frequency), τ is the correlation time. The result of the fitting procedure (equation1) is presented as the solid line in Figure 6. The mobility of water close to surfactants can be restricted and modulated by motion of micelles in the solvent. The surfactant concentration (10 mg/ml) in the reference sample is above CMC (critical micelle concentration), thus in this system, micellar aggregates are present. It has been evidenced in an atomistic molecular dynamics simulation and various experimental studies that the mobility of water molecules near an aqueous micellar interface is significantly restricted which can be attributed to the water molecules quasi-bound to the micelle surface.57 The correlation times describing this slow component of water dynamics range from hundreds to thousands of picoseconds and depend on both the mobility of water near the micelle and vibrational dynamics of the micellar atoms. The calculated correlation time equal to 5.9 10-8 s which describes the reorientation dynamics of long-lived water molecules in the studied system is a little longer in comparison to this time scale range but may be the reflection of the complex reorientational dynamics of water associated with micelles as well as larger forms of IMIC6C12 aggregates. Therefore, it is reasonable to assume that the main origin of the low-field R1 dispersion obtained for the pure aqueous solution of IMIC6C12 surfactant is the water proton fraction located near the surface micelle and their aggregates. The tumbling motion of micelles in solution modulates the dipole-dipole interaction and leads to frequency dependence of spinlattice relaxation rates similarly like in a case of aqueous solutions of proteins.51–54


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Figure 5 shows the 1H NMRD data obtained for two supernatants - aqueous suspensions of carbon nanotubes stabilized by gemini surfactants differing in the alkyl chain lengths (IMIC6C12 and IMIC6C14) and the reference sample-the aqueous solution of spin-IMIC6C12. The spin-lattice relaxation processes in the presence of carbon nanotubes are much more efficient in comparison to that of observed in the pure surfactant solution and reveal also a different character of the spin-lattice relaxation rate dispersion. The R1(f) data in supernatants samples vary logarithmically with frequency and show the loss of R1 dispersion at very low frequencies. NMRD profiles present shapes unlike than those of obtained for Gd-doped and undoped Boron Nitride Nanotubes, in which the low field strength plateau of R1 does not exist.40 Experimentally obtained NMRD profiles also look much different than the bell-shaped NMRD curves found in small gadolinium and manganese complexes, 33,58 and reveal other frequency dependence of R1 than in that of Mn2+-containing graphene nanoplatelets and oxidized graphite.32 However,

NMRD data recorded for the studied systems in the presence of

MWCNTs are slightly similar to the R1 dispersion profiles obtained for Gd-SWCNTs,33 graphene Nanoribbon doped via manganese32 and un-doped bundled and unbundled ultra-short (US) carbon nanotubes.34 The logarithmic dependence of the proton spin-lattice relaxation rates on the magnetic field strength noticed in studied systems suggest the existence of the twodimensional (2D) diffusion of water in the vicinity of paramagnetic species like it was observed for liquids in porous media.41–43 This similarity in the shape of NMRD profiles found for the studied aqueous MWCNTs suspensions and for the liquids confined in porous structures seems to be justified. The large surface area of well-dispersed in water carbon nanotubes should promote dynamical processes taking place at the solid-liquid interface in the studied systems. Moreover, transition metals (typically Fe, Co or Ni) usually used as catalyst in CVD method 59 in the production of carbon nanotubes can remain after the synthesis of CNTs as paramagnetic impurities being active in an acceleration of nuclear relaxation processes. The presence of



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paramagnetic enhancement of R1 coming from the catalyst in pristine CNTs has been reported proving their efficiency.34,40 To describe NMRD data in studied the supernatants it is important to discuss the potential sources of spin-lattice relaxation times shortening in the systems of this type, which can results from both the influence of spatial constraints imposed by carbon nanotubes on water molecules in the MWCNTs suspensions and the presence of paramagnetic impurities of carbon nanotubes. The confinement effect of water molecules inside nanotubes seems important because the mobility of water molecules in such one-dimensional nanostructures is significantly different and their dynamics is limited in comparison to that in the bulk.60 However, as has been evidenced for water protons in Imogolite Nanotubes,61 for the dynamical processes dominated via one-dimensional diffusion, the water proton spin-lattice relaxation rate shows power-law dependence on magnetic field strengths and thus presents distinctly different shape of NMRD profiles than those observed in studied systems. A similar power-low NMRD characteristics has been shown for water suspended in microporous media containing Fe3+ paramagnetic impurities (with a pore diameter 75Å). In this case the R1 relaxation dispersion at the pore surface has been governed by means of the one dimensional-diffusion. The lack of the low-field plateau of R1(f) dependence and significant increase in water proton spin-lattice relaxation have been explained as a result of I-S correlations (I - proton spin, S - Fe3+ electronic spins) that persist much longer at the surface layer than in the bulk.62 Taking to account these results the effect of water confinement inside carbon nanotubes, even if it exists, in minor way affects observed relaxation dispersion profiles. It is worth noticing that in MWCNTs suspensions, water can be also entrapped between the not perfectly separated ropes of carbon nanotubes which can enhance the spin-lattice relaxation. The presence of a small fraction of that kind of water can significantly affect the shape of the profile in the low magnetic fields.34,40 In the protein solutions it has been shown that the existence of trapped water molecules can


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lead to strong R1 dispersion profiles stretched towards low frequencies.63 The enormous frequency dependence of T1 has been reported for polar liquids displaying strong adsorption onto the internal surface of porous systems without paramagnetic impurities. To explain the T1 relaxation dispersions obtained in these systems the bulk-mediated surface diffusion model (BMSD) has been introduced.45,64 According to the BMSD model, in the strong adsorption limit, the residence time of polar liquid molecules near the surface, called the retention time, significantly exceeds the desorption time. Thus, during the retention time, before escaping to the bulk phase, water experiences numerous cycles of desorption and adsorption and between them undergoes diffusion in a bulk-like layer close to the surface. It results in anomalous displacement of water molecules onto the surface known as the Lévy dynamics. In the BMSD model the resulting strong dispersion of spin-lattice relaxation time for the temperatures above the freezing point of bulk liquid (for water it is 273 K) is described via the power low 𝑇1 ~𝑓𝛽 , with an exponent β equal to 0.540.04.45 The T1(f) in the studied systems reveal smaller values of β and the strong adsorption condition seems impossible to be fulfilled due to the hydrophobic nature of nanotubes. That is why the Lévy dynamics was excluded as responsible for observed R1 dispersions. The EDS analysis carried out on MWCNTs studied in the frames of this work disclosed the presence of paramagnetic impurities of iron origin, in the amount of about 1.88 % w/w (Table 1), therefore further considerations were based on the relaxation mechanisms governed by water-paramagnetic species interactions. Table 1. Results of EDS analysis of studied MWCNT. Element

Weight%

Atomic%

C

95.84

97.91

O

2.10

1.61

S

0.18

0.07

Fe

1.88

0.41



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TEM microscopy confirms the presence of iron species in the studied supernatants. It is clearly visible in Figure 7a that the iron nanoparticles can be encapsulated inside MWCNTs, as well as incorporated in the form of Fe clusters, located in the side walls of carbon nanotubes. TEM micrograph presented in the Figure 7b reveals the existence of numerous defects in the outer walls of MWCNTs, associated with the size of Fe clusters. In aqueous systems in which the PRE is observed due to the presence of contrast agents (CA), a few types of water are distinguished: i) inner-sphere water (IS) - water molecules directly coordinated to the paramagnetic center, ii) second sphere water which is not directly coordinated to CAs but is associated with other molecules (like ligands or chelates), iii) outersphere water (OS) - non-bound water, which diffuses in the proximity of the local magnetic field gradients generated by the paramagnetic ion. According to SBM theory36–38 the paramagnetic relaxation enhancement may come from either or both contributions: from the inner sphere (IS) and outer sphere (OS) mechanisms involving appropriate water molecules mentioned above.32,58 In the fast exchange limit the water proton spin -lattice relaxation rate in the studied supernatants can be expressed as a sum of the diamagnetic and paramagnetic contributions, as follows: IS

R1  R1bulk  R1sol  R1  R1

OS

(2)

where: R1bulk describes the spin-lattice relaxation rate of the bulk water, R1sol is the diamagnetic relaxation rate of water protons R1diam affecting the dipole-dipole coupling or chemical exchanges with diamagnetic dispersant molecules, R1IS is inner sphere relaxation contribution, R1OS is outer sphere relaxation contribution.


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The PRE governed by IS mechanisms depends on the number of coordinated water molecules and their mean residence time, the relaxation of the electronic spin associated with the paramagnetic ion and the correlation time describing the rotational motion of the object in which the paramagnetic center is located. In the OS mechanism the dipolar interaction between proton spins and the magnetic moment of paramagnetic species is considered. This interaction is modulated by relative translational motion of water molecules and the paramagnetic center described by a correlation time that takes into account their relative diffusion coefficient and also distance of closest approach. The shape of NMRD profiles strongly depends on the relevance of the particular contribution mentioned above to R1. It has been shown in NMRD studies of aqueous suspension of pristine BNNTs and Gd@BNNTs that the OS relaxation mechanism dominates the observed R1 dispersion.40 The authors has explained the major importance of this mechanism (OS) in total observed R1 relaxation process by the fact that the fraction of water located at the surface layer of nanotubes can mix by exchange processes with a total population observed water and that the close interactions of water molecules with paramagnetic species (the dipolar electron-dipole interaction) decays very quickly with the distance. The NMRD profiles obtained by Calucci et al. have been linear in the logarithm of the Larmor frequency, which has been ascribed to the relaxation caused by two-dimensional diffusion of proton spins (I) in the vicinity of paramagnetic species (spins S) located in the surface, according to the Korb model.62 The minor inner sphere contribution, to R1 due to the lack of exact information governing this mechanism has not been analyzed in details, but the obtained relaxivities for Gd@BNNT correspond well to those of obtained for other gadolinium based CAs.40 It is worth noticing, that the discussion concerning which mechanism, the OS or IS dominate in the observed spin-lattice NMRD relaxation dispersions is still the subject of debate.32,34,40



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The shapes of NMRD profiles obtained for MWCNTs/gemini surfactant suspensions (Figure 5) are similar to those obtained for BNNT and Gd@BNNT40 suspensions in the range of the middle and high magnetic fields, which suggests the existence of the same origin of the OS relaxation mechanism. The one important difference between NMRD profiles appears in the lowest Larmor frequencies range, in which for the studied supernatants the R1 dispersion terminates. The same R1 relaxation behavior in the function of the frequency has been found in the water suspensions of macroporous systems containing paramagnetic impurities.42,43,62 In this case the spin-lattice relaxation coming from outer sphere PRE mechanism was approximated by the following equation:

R1

OS

  1   I2 m2 ,  K m ln  2   m  s   I2 m2 





(3)

where:

K

N s  s  I  S  2 S (S  1) , 4 N 20 

(4)

where  s is the surface density of paramagnetic centers (for an iron ions Fe3+, the S is equal to 5/2), the ratio N s / N indicates the fraction of the surface protons calculated with respect to the total amounts of protons,  describes the minimal approach distance between water protons I and paramagnetic species S equal to 0.3 nm, which corresponds to the radius of water molecule. The model (3) assumes that the residence time of molecules at the surface denoted as s is limited by desorption, while the translational correlation time is given as m. The ratio of

s m

indicates the number of molecular jumps before the act of the desorption. This index is considered also as the coefficient of affinity of water to the solid surface which in the redefined conditions means the carbon nanotube surface. The presence of low-frequency plateau of R1 in


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NMRD profiles obtained for both studied supernatants evidenced the exchange of water protons from the diffusionally-restricted environment to the bulk water in which the dynamics is isotropic.34 For frequencies lower than the cut-off frequency the dipolar correlations between I and S spins are lost due to molecular surface desorption. It is a very probable scenario for the aqueous MWCNTs suspensions, in which different classes of more or less entrapped water are able to exchange with bulk water. Taking into account the literature findings mentioned above and the fact that the EDS and TEM methods confirm the presence of iron (Fe) in the structure of studied MWCNTs (Table 1), the experimental NMRD profiles were analyzed according to the approach proposed by Calucci et al.40 To the description of frequency dependencies of spinrelaxation rate equations 2 and 3 were combined into the following form:

R1  R1bulk  sol  IS

 1   2 2  I m ,  K m ln  2 2 2   m  s   I  m 





(5)

IS

where R1bulk  sol  IS  R1bulk  R1sol  R1 . Due to relatively small contribution of R1sol to the total R1 and unknown exact the nature of inner sphere relaxation mechanism (predominant above 10 MHz) in the studied systems, the sum of these terms including the relaxation rate of bulk water, were fitted as a one parameter assigned as the R1bulk+sol+IS (to avoid the overestimation). The solid lines shown in Figure 5 describe the best fits of R1 dispersion data with equation 5. The results of the fitting procedure obtained for two studied aqueous suspensions of MWCNTs stabilized by gemini surfactants: IMIC6C12 and IMIC6C14 are collected in Table 2. The relation between diffusion coefficients D⊥ (defining as a translational diffusion coefficient in direction perpendicular to the axes normal to the carbon nanotubes surface)40 and the diffusion correlation time τm in the form  m 

2 expected for the two-dimensional 4 D

diffusion was used to evaluate the values of D⊥ constants describing the restricted translational motion of water molecules on carbon nanotube’s surfaces in the system studied.



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Table 2. Best fit parameters describing experimental NMRD profiles obtained for aqueous suspensions of MWCNTs stabilized by dicationic surfactants IMIC6C12

IMIC6C14

R1bulk+sol+IS [s-1]

0.610.1

0.410.1

K 107 [s-2]

7.21.1

1.70.4

τm 10-8 [s]

0.7460.015

1.240.36

τs 10-6 [s]

3.10.5

2.90.4

τs /τm

416

237

D 10-12 [m2/s]

3.01

1.82

As shown in Table 2, the K parameter takes a much higher value for the system with the gemini surfactant of the shorter length of alkyl chains (IMIC6C12). It experimentally corresponds to the stronger frequency dependence of R1 detected for this sample in comparison to that in the sample prepared with IMIC6C14 surfactant. The K constant proportionally depends on the fraction of water protons close to the MWCNTs surface and the surface density of paramagnetic centers.40 To confirm the assumption that the main source of the increase in water proton spin-lattice relaxation in the system studied are paramagnetic impurities it is necessary to assess the final concentration of MWCNTs (CMWCNT) in supernatant solutions. The CMWCNT values after the centrifugation procedure can no longer correspond to their initial values chosen 0.5 mg/ml for both systems studied. The Fourier-Transform Infrared spectroscopy (FTIR) was used for verification of the final concentration of carbon nanotubes in supernatant solutions. For this purpose, the FTIR spectra of carbon nanotubes, pure IMIC6C12 and IMIC6C14 surfactants and suspensions of the surfactants with MWCNTs were measured (Figure 8). The characteristic spectra of MWCNTs


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and surfactants were compared to find a specific band that could be assigned only to nanotubes and not to the surfactant. From this comparison, the band at 3000 cm-1 corresponding to C-Hx stretching vibration was chosen for further analysis, because it does not exist in the solution of pure surfactant, but it has been noticed in pure MWCNTs.65 Five suspensions of known concentrations were measured, and the calibration curve was obtained as the maximum intensities of the peak at 3000 cm-1 as a function of CNTs concentration (Figure 9). For unknown concentration of the sample used for NMR experiments also the same peak was analyzed, and its value was compared with the calibration curve. The MWCNTs concentrations of studied samples were: 0.34 mg/ml for IMIC6C12/MWCNT suspension and 0.26 mg/ml for IMIC6C14/MWCNT system. Higher intensity of peak translates into a higher number of dispersed carbon nanotubes in the solution. The highest concentration of MWCNTs evidenced by FTIR measurements in the aqueous suspension of IMIC6C12/MWCNT confirms that the more effective paramagnetic enhancement of the spin-lattice relaxation noticed in this sample results from the greater accessibility of water protons to the MWNCTs surface, which contains paramagnetic impurities. These observations suggest that the efficiency of IMIC6C12 gemini surfactant to disperse MWCNTs in water is better than that of the surfactant with the longer tails (IMIC6C14). It is surprising if one considers that with increasing the length of alkyl chain, the adsorption of surfactants onto the CNT surface is better, but is not so astonishing when one considers that the value of the concentration of surfactants required to achieve the best dispersion of nanotubes in water decreases with decreasing tail length. In addition, the quality of the dispersion largely determines also the packing of heads on the surface of the nanotubes. Electrostatic repulsion between CNTs stabilizes the dispersion and prevents re-aggregation.13 Both test samples were prepared with the same starting concentration of surfactants.



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The results obtained by NMR and FTIR indicate that the chosen, initial surfactant concentration (10 mg/ml) was more suitable for IMIC6C12 than IMIC6C14, because after centrifugation the higher final MWCNTs concentration in the supernatant was found for the former.

Results of visual tests are consistent with these observations because the

IMIC6C12/MWCNT suspension is more stable in time and more homogenous (devoid of MCNTs aggregates) The evaluated values of diffusion correlation times τm are longer for the aqueous suspensions of MWCNTs stabilizing via the IMIC6C14 than IMIC6C12. The values of residence time τs of water molecules in the surface layer are, comparable in both samples. It results in a higher number of molecular jumps before the act of desorption to the bulk for aqueous suspensions of MWCNTs containing IMIC6C12 surfactant. The higher ratio of

s , equal to m

416, evidenced that in this system the affinity of water to the MWCNTs surface was better than that found in the IMIC6C14/MWCNT suspension in which the

twice smaller (

s value was approximately m

s  237 ). The calculated values of diffusion coefficients D⊥ for both samples m

are by three orders lower than the diffusion constant expected for pure water and testify to the fact that the 2D translational motion of water molecules along the surface of MWCNTs is strongly limited.43 These results can be explained by the difference in the gemini surfactants adsorption ability onto carbon nanotube surfaces depending on the length of alkyl chains. As mentioned above, with increasing tail lengths the hydrophobic character gets stronger, therefore the adsorption of the IMIC6C14 surfactant onto MWCNT surface is more favorable than for IMIC6C12. For the gemini surfactants, the loose type of adsorption was suggested, accordingly it is reasonable to assume that longer tails of IMIC6C14 enable them to cover larger area of MWCNTs.13,21 Because of the presence of the coating layer, the approaching of water


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molecules to MWCNTs surface is more difficult. It leads to less effective nuclear relaxation in the range of low magnetic field strengths. More hindered molecular diffusion of water at MWCNTs surface in the presence of IMIC6C14 than IMIC6C12 (Table 2) may suggest in the former the existence of non-perfectively resolved MWCNTs bundles with water molecules trapped inside. This population of water should have more restricted dynamics and be responsible for the observed slowing down of the surface diffusion process in the sample with IMIC6C14. The lower value of ratio

surfactant (

s  237 obtained for IMIC6C14 than for IMIC6C12 m

s  416 ) means the reduction in the water affinity to MWCNT surface. It is worth m

noting that similar values of τm,, τs and the

s ratios have been found in aqueous solutions of m

boron nitride nanotubes (BNNT) doped with Gd3+ ions (stabilized in water by chitosan) and the pristine BNNT.40 The stronger water proton dispersion of R1 detected for aqueous suspensions of MWCNTs stabilized by IMIC6C12 reflects the better ability of this surfactant to disperse and stabilize carbon nanotubes in water. This last statement is confirmed in recent research which have been done in aqueous suspensions of un-doped ultra-short (US) carbon nanotubes stabilized via Pluronics in which in bundled form of US-tubes the less pronounced spin-lattice relaxation dispersion was noticed than that of in debundled US-tubes.34 In order to confirm the NMRD findings, the NMR diffusion measurements were performed to assess the time-dependent apparent diffusion coefficients Dapp and Surface to Volume ratio (S/V), which can be obtained by performing the time-dependent NMR diffusion experiment.66 The short-time dependence of the apparent diffusion coefficient is well described by Mitra model for restricted diffusion.66,67 While the short-time dependence is controlled by Surface-to-Volume ratio S/V, the long-time diffusion limit is related to the system tortuosity 1/Deff, where Deff is the effective diffusion coefficient. An overall dependence of the Dapp() is



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described by Pade approximant. The S/V can be easily obtained by fitting diffusion coefficients in the short-time limit by using equation: 𝐷𝑎𝑝𝑝 (∆) = 𝐷0

𝑆 𝑉

1−4 √𝐷0 ∆ 9√𝜋

+ 𝐷0 ∆,

(6)

where  is diffusion time, D0 bulk water diffusion coefficient, and S/V is the Surface-to-Volume ratio. The experimental values of apparent diffusion coefficients Dapp() are shown in Figure 10. For both samples, at relatively short diffusion times (  50 ms) the apparent diffusion coefficients are time-dependent due to obstruction effects characterized by S/V ratio. For the shortest diffusion times the values of diffusion coefficients are close to the value of bulk water (ca. 2.3×10-9 m2/s at 294 K). For the longest diffusion times so called effective diffusion coefficient Deff is obtained (dotted lines in Figure 10). The solid line in Figure 10 shows the best fits of the data to the model described by the equation 6 for IMIC6C12/MWCNT sample. Although we were unable to fit Mitra model to the IMIC6C14/MWCNT, we believe that the S/V is larger for the sample stabilized with the IMIC6C12 (S/V ca 72715 m-1). All in all, the S/V can be a measure of the number of water molecules at the layer near surface of carbon nanotubes, thus the larger the S/V value the more pronounced R1 frequency dependence (K values in the Tab.2). The S/V ratio is proportional to the porosity of the system and higher values confirm FTiR and NMRD findings that the supernatant stabilized via IMIC6C12 gemini surfactant has in fact higher concentration of MWCNTs and the higher degree of dispersion of nanotubes in the suspension. Clearly IMIC6C14 surfactant is not as efficient with that matter.

Conclusions The aim of this work was to evaluate the efficacy of four cationic gemini surfactants of different length alkyl chains in stabilizing dispersion of carbon nanotubes in water. The results


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of visual tests and analysis performed by scanning electron microscopy reveal that only two studied surfactants (IMIC6C12, IMIC6C14) can disperse carbon nanotube via the mechanism of non-covalent adsorption onto the surface of carbon nanotubes. Because the long-term stabilization of carbon nanotubes in solutions require understanding of the nature of interactions taking place at the solid–liquid interface, the water proton spin-lattice relaxation dispersion method (NMRD) and NMR diffusion measurements were used to evaluate the influence of carbon nanotubes on the dynamics of water molecules in studied systems. NMR experimental data supported by FTIR results, EDS and TEM analysis reveal that the addition of multiwall carbon nanotubes to aqueous solutions of gemini surfactants leads to significant enhancement of the spin-lattice relaxation processes, which gets more pronounced with increasing concentration of well-dispersed MWNTs in water. The existence of paramagnetic relaxation enhancement with a dominant role of outer sphere (OS) mechanism was assumed to explain NMRD results.

The OS relaxation mechanism is determined by the restricted (two-

dimensional) diffusion of water on the carbon nanotube in the vicinity of paramagnetic centers, mainly of iron origin, incorporated in the MWCNT side-walls. The NMR diffusion experiments confirm the existence of restricted water diffusion in the studied supernatants. The NMR diffusion results are consistent with the NMR proton spin-lattice relaxation dispersion in which the more effective R1 dispersion noticed for the sample with IMIC6C12 was ascribed to the better accessibility of water molecules to the surface of the MWCNTs. The study shows that the NMRD method is very helpful to monitor changes in water molecular dynamics induced by the presence of carbon nanostructures, which is very important to recognize their application potential as a new contrast agents or modern drug carriers.

Acknowledgments



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Authors thanks to Dr. Barbara Peplińska from NanoBioMedical Centre and Dr. Marek Kempka for technical support. This work was supported by Ministry of Science and Higher Education in Poland (“Najlepsi z Najlepszych” - decision DIR.5210.35.2016/1).

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FIGURE CAPTIONS

Figure 1. The SEM micrograph of the pristine “cotton candy” structure of the MWCNTs studied.

Figure 2. The chemical structure of the cationic gemini surfactants: a) n=8 IMIC6C8, b) n=10 IMIC6C10, c) n=12 IMIC6C12 and d) n=14 IMIC6C14.

Figure 3. Results of visual tests of MWCNTs water solutions prepared in the presence of the IMIC6C8 (a), IMIC6C10 (b), IMIC6C12 (c) and IMIC6C14 (d) gemini surfactants. Figure 4. The SEM images of MWCNTs water solutions prepared in the presence of the IMIC6C12 (a) and IMIC6C14 (b) surfactants. Figure 5. NMRD profiles of aqueous suspension of MWCNTs prepared in the presence of the gemini surfactant IMIC6C12 (full circles) and IMIC6C14 (solid triangles) and the reference solution of IMIC6C12 in water, recorded at 303 K (open circles).

Figure 6. NMRD profiles of the aqueous suspension of 1% aqueous solution of gemini surfactant IMIC6C12, recorded at 303 K. Solid line represents the best fits of the R1 dispersion data with the Lorentian model of the spectral density function.

Figure 7. The TEM micrograph of MWCNTs water solution prepared in the presence of IMIC6C12, a) the catalyst residue inside the CNT are marked with an arrow and in yellow circles the Fe clusters are identified, b) the circles mark the defects.


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Figure 8. FTIR spectra collected for IMIC6C12/MWCNT and IMIC6C14/MWCNT suspensions.

Figure 9. Calibration curve of MWCMT concentration in studied systems. The surfactant/MWCMT standards (black) were prepared on the basis of FTIR data and suspensions of

known

concentration

of

MWCMT.

The

studied

IMIC6C12/MWCNT

IMIC6C14/MWCNT suspensions are marked in grey.

Figure 10. The time-dependent apparent diffusion coefficient Dapp(t).


and


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TOC FIGURE


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s domain

n domain

n domain ACS Paragon Plus Environment

a)

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b)

c)

d)


a)


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b)


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a)

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b)



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Dispersion of Water Proton SpinâLattice Relaxation Rates in Aqueous

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