ARTICLE pubs.acs.org/JPCC
Dynamic Behavior of Carbon Nanotube and Bio-/Artificial Surfactants Complexes in an Aqueous Environment Shigeaki Obata and Kazumasa Honda* Research Institute of Science for Safety and Sustainability (RISS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
bS Supporting Information ABSTRACT: We examined the characteristics and behaviors of the carbon nanotube (CNT) and surfactants complexes in an aqueous environment using computational techniques to elucidate the effects of surfactants used to disperse the CNTs in toxicity studies of CNTs. We found that the cohesive energy per one adsorbed surfactant molecule of the CNTsurfactants complex depends on the type and the amount of the adsorbed surfactant molecules on the CNT surface. The CNTdipalmitoyl phosphatidylcoline (DPPC; a primary component of human lung surfactants) complex was more energetically stable than the CNTTween 80 (an artificial surfactant often used to disperse CNTs) complex by 2060 kJ/mol. The average cohesive energy of the complexes was 330 kJ/mol. Such high cohesive energy suggests that the CNT molecule that was once covered by surfactant molecules is unlikely to return to its original bared form. Furthermore, we found that reactions of adsorption and desorption of surfactant molecules occur on the CNT surface in a time scale of milliseconds. Hence, the CNTs are thought to be coated by the “surfactant corona” composed of amphiphilic molecules, which is similar to a “protein corona” in the biological system. Moreover, CNTsurfactants complexes are believed to convert to some other more energetically stable CNTsurfactants complexes through a surfactant exchange due to the adsorption and desorption of surfactants on the CNT surface in the biological system. The specific surface area of the CNTs, which is one of the most important parameters for assessing the toxicity of a nanomaterial, is thought to change because of the surfactant exchange.
’ INTRODUCTION Nanomaterials have impacted modern scientific and engineering fields because of their novel physical, thermal, mechanical, and electronic characteristics. In particular, carbon nanotubes (CNTs)1 possess unique properties of mechanical strength, thermal conductivity, and electrical conductivity and hence have great potential for applications in electronics, energetic, and nanocomposite fields.25 Recently, the CNTs have been considered for use in biomedical application as an intercellular transporter for delivery and for enabling the functionality of extracellular agents such as medicinal compounds without causing cell membrane damages.6,7 Donaldson et al. reported that long multiwalled CNTs (MWCNTs) cause asbestos-like pathogenic behavior in mice.8 Therefore, the interactions between CNTs and biomolecules912 and the hazards and risks of the CNTs to the human health have also received an increasing amount of attention. Recently, some of our colleagues assessed the pulmonary hazards and risks of inhalation exposure to the CNTs.1316 The assessment was performed by administering individually dispersed MWCNTs or SWCNTs with artificial surfactants into respiratory organs of rats. The CNT agglomerates had been used for test samples in most of the previous CNT toxicity studies.1721 Some researchers believe that toxicity studies should include not r 2011 American Chemical Society
only the CNT agglomerates but also the dispersed CNTs to evaluate the hazards and risks of CNTs because the toxic potential of CNTs depends on their particle size.22,23 In addition, exposures to dispersed CNTs may occur because the application of CNTs often requires a homogeneous dispersion of CNTs in an aqueous solvent.24,25 However, the effects of artificial surfactants that are used to disperse the CNTs have not yet been fully elucidated in the toxicity studies of CNTs. There has recently been an increase in the recognitions that the nanoparticles are coated by biomolecules such as proteins and lipids, and the biomolecules are exchanged with a collection of free biomolecules on surfaces of the nanoparticles in the biological system.2628 Therefore, much attention has been placed on the biological behaviors and impacts of nanoparticles with the biomolecular interface organization, which is called a “corona”. (The organization composed of proteins with some lipids is called “protein corona”.2628) We believe that the CNTs are also coated by the artificial surfactants, amphipathicity biomolecules such as biosurfactants, or both, in the biological system, and the CNTs with a “surfactant corona” might produce harmful influences on the human health. Received: July 30, 2011 Revised: September 1, 2011 Published: September 02, 2011 19659
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Figure 1. Molecular structures of (a) Tween 80 and (b) DPPC.
In the present study, we investigate the characteristics and behaviors of the CNTsurfactants complexes in an aqueous environment using computational techniques to elucidate the effects of surfactants used to disperse the CNTs in toxicity studies of CNTs. We examine the cohesive structures, their energies, and the interactions on complexes of CNT and polysorbate 80 (Tween 80) and complexes of CNT and dipalmitoyl phosphatidylcoline (DPPC) by molecular dynamics (MD) simulations. Adsorption and desorption properties of Tween 80/DPPC on the CNT surfaces are also examined by MD simulations. Tween 80 is an artificial surfactant that is often used to disperse CNTs (Figure 1a). DPPC is a biosurfactant (Figure 1b) and is a primary component of human lung surfactants. Furthermore, we calculate specific surface areas (SSAs) of CNTTween 80 complexes and CNTDPPC complexes, which have been shown to correlate with an inflammation activity of the nanomaterials. The SSAs of an isolated CNT and bundled CNTs are also calculated for comparison with the SSAs of CNTsurfactants complexes and for the verification of our results for the SSA.
’ COMPUTATIONAL DETAILS Simulation Models. We generated a (10, 10) singlewalled CNT (SWCNT) with a diameter of 1.36 nm by the Nanostructure Builder at Materials Studio 5.029 of Accelrys. A bond length between carbon atoms was set to 0.142 nm. The chilarity of the SWCNT was found because the diameter of the (10, 10) SWCNT was ∼1.4 nm. Journet et al. showed that high yields of SWCNT could be obtained using the electric-arc technique, and the SWCNT diameters were ∼1.4 nm.30 Furthermore, multilayered graphene sheet (MLGS) assumed as an MWCNT with a diameter of >50 nm were also generated using the crystal structure of graphite with the alpha form.31 The MLGS was composed of five graphene sheets. To generate the MWCNT model, we assumed the surface of the MWCNT to be planar and considered five walls in the MWCNT because the size of the entire MWCNT is much bigger than the accessible scale of the MD simulation. We believe that the resulting errors in the cohesive energy and interactions due to the simplification for the MWCNT model are acceptably small. The angle between the tangent and the chord at the point of contact on a circle with a diameter of 50 nm is 2.29°, and the separated distance from the curve of the circle to the tangent is only 0.08 nm when the length of the chord is 2 nm, which corresponds to the lengths of alkyl chains of Tween 80 and DPPC. Furthermore, the van der Waals (vdW) interactions mainly work between CNT and hydrophobic molecular fragments of surfactants, and the magnitude of vdW interactions decreases rapidly as r6 with increasing the distance (r) between the inner wall and the surfactants. The experimental
CNT with a length of a few micrometers is much longer than the accessible scale of the MD simulation. Therefore, we used the periodic boundary conditions to create effectively an infinitely long SWCNT along the z axis and an infinite MLGS surface parallel to the xy plane. The initial structure of the Tween 80 molecule was generated as follows. First, we generated the hydrophilic molecular fragment of the Tween 80 molecule by changing the oleyl group of the Tween 80 molecule into a methyl group and obtained a stable conformer of the hydrophilic molecular fragment through a conformational search on the molecular fragment using the CONFLEX3234 and Merck Molecular Force Field (MMFF94s).35 Next, we replaced the methyl group, which was added at the generation of the hydrophilic molecular fragment, in the stable conformer to an oleyl group using the atomic coordinates of oleyl group of cholesteryl oleate molecule in its X-ray crystal structure36 to create an entire Tween 80 molecule. Then, the oleate group of the Tween 80 molecule was rotated in the range of 0 to 360° with an incremental step of 30° around the CC bond of the oxyethylene group bonded to the oleate group, and the 12 generated conformers were optimized using the CONFLEX and MMFF94s. The most stable molecular structure among the 12 optimized structures was selected as an initial structure of the Tween 80 molecule. In this work, Tween 80 molecular model with x + y + z + w = 4 was used (Figure 1a). The initial structure of the DPPC molecule was generated by the addition of two carbons to each hydrocarbon chain of the dimyristoyl phosphatidylcholine (DMPC) molecule. The molecular coordinates of DMPC were obtained from its X-ray crystal structure.37,38 We constructed 12 simulation models in this work. The concentrations of SWCNT, MLGS, Tween 80, and DPPC and the number of molecules of Tween 80, DPPC, and water in the 12 simulation models are summarized in Table 1. The concentration values of 46 mg/mL of Tween 80 for the SW-TCexp model and of DPPC for the SW-DCexp model and of 188 mg/mL of the Tween 80 for the MG-TCexp model and of DPPC for the MG-DCexp model were determined from the CNT/surfactant molar ratio under the experimental condition of the CNT dispersion process.14 In the simulation models containing the SWCNT, the SWCNT was positioned through the center of the 12 nm 12 nm 10 nm simulation box and along the z axis, and the surfactants were arranged around the SWCNT based on the cylindrical micelle model (Figure 2a). The length of the SWCNT was 10 nm per original simulation box. In the simulation models containing the MLGS, the MLGS was placed on the xy plane in the 10 nm 10 nm 10 nm simulation box, and the surfactants were arranged on the top layer of the MLGS based on the cylindrical micelle model (Figure 2a). The dimension of the MLGS surface was 10 nm 10 nm per original simulation box. Water molecules were added to each simulation model using 19660
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Table 1. Constructed Simulation Models for Molecular Dynamics Simulations concn of SWCNT
concn of MLGS
concn of Tween 80
concn of DPPC
models
(mg/mL)
(mg/mL)
(mg/mL)
(mg/mL)
no. of Tween 80s
no. of DPPCs
no. of waters
SW-TClow
27.1
23
27
39, 231
SW-TCexp
27.3
46
56
38, 937
SW-TChigh
28
87
108
37, 825
MG-TClow
389
96
65
20, 618
MG-TCexp
401
188
135
19, 596
MG-TChigh
411
317
260
SW-DClow SW-DCexp
27.1 27.3
SW-DChigh
28
22 46
18, 804 22 46
39, 231 38, 937
87
89
37, 825
MG-DClow
389
96
54
20, 618
MG-DCexp
401
188
111
19, 596
MG-DChigh
411
317
214
18, 804
Figure 2. CNTsurfactants complex model39 and definitions on orientations of surfactant: (a) cylindrical micelle, left: side view, right: cross section; (b) random adsorption; and (c) left: θCNTCC, right: θCNTaxisCC. The left Figure is viewed parallel to the vCNTaxis.
the Genbox program in the GROMACS 4.0.6 MD simulation package.4043 Molecular Dynamics Simulations. All of the MD simulations were performed using the GROMACS 4.0.6.4043 The general amber force field (GAFF)44 was employed, and the TIP3P model was used for the water molecules in our MD simulations. The atomic charges for the Tween 80 and DPPC molecules were evaluated using the Antechamber program45 with the restrained electrostatic potential (RESP) fit method46,47 after optimization and fitting the electrostatic potential at selected points according to the MerzSinghKollman scheme48,49 at the HF/6-31G* level using the Gaussian 09.50 Martinek et al. calculated the membrane properties such as area per lipid and area compressibility modulus of the 1-palmitoyl 2-oleoyl phosphatidylcholine (POPC) membrane bilayers from the MD simulations using GAFF, POPC with RESP charges, and the TIP3P water model.51 They reported that these calculated values showed a good agreement with the experimental results.51 Electrostatic interactions were calculated
using particle mesh Ewald (PME) sums, and the cutoff radius for vdW interactions was set to 1 nm. The assembly of the CNT and surfactants was simulated at constant pressure (1 bar) and temperature (323 K), that is, NPT ensemble, for 4 ns. The adsorption and desorption of surfactants on the CNT surfaces in the SW-TCexp, SW-DCexp, MG-TCexp, and MG-DCexp models were simulated at constant volume and temperature (800, 1000, 1200, and 1400 K), that is, NVT ensemble, for 2 ns after the assembly MD simulations of these models. The NoseHoover thermostat and the ParrinelloRahman barostat were used for the temperature and pressure controls, respectively. The time step was set to 0.5 fs, and the system coordinates and energies were recorded every 0.1 ps during each simulation. The SWCNT was restrained in the center of the simulation box using a force constant of 1000 kJ mol1 nm2. The 12 simulation models were subjected to 2000 steps of energy optimization using the steepest decent method before starting the assembly MD simulations. 19661
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Definition of Cohesive Energy for CNTSurfactants Complex. To estimate quantitatively the difference between cohesive
forces in the each CNTsurfactants complex under different surfactant concentrations, we used the following equations to determine the cohesive energy of the complex Ecoh ¼ ECNTsurf þ Esurf surf ECNTsurf ¼
Esurfsurf
Einter CNT surf Nsurf
ð1Þ
SSA ¼
ð2Þ
Einter ¼ surf surf Nsurf
ð3Þ
where Einter CNTsurf is the sum of the intermolecular interaction energies between the CNT and the surfactant molecules in the complex, Einter surfsurf is the sum of the intermolecular interaction energies between the surfactant molecules in the complex, and Nsurf is the number of surfactant molecules in the complex. In other words, the cohesive energy is defined as the sum of the intermolecular interaction energies between the CNT and the surfactant molecules and between the surfactant molecules in the complex per one adsorbed surfactant molecule on the CNT surface. The subscript “surf” in the equations refers to a surfactant and represents Tween 80 or DPPC. The subscript “CNT” in the equations refers to a carbon nanotube and represents SWCNT or MLGS, which is assumed to be MWCNT. Characterization for Structure of CNTSurfactants Complex. To analyze the adsorption configurations of surfactants on the CNT surface and to elucidate the structures of each CNTsurfactants complex under different surfactant concentrations, we defined the orientations of the surfactant with respect to the CNT surface and with respect to the CNT axis by eqs 4 and 5, respectively (Figure 2c). vCNT 3 vCC θCNTCC ¼ 90 arccos ð4Þ jvCNT jjvCC j θCNTaxisCC ¼ arccos
of within 0.34 nm for a simulation time of 10 ps or more was estimated to be in a state of adsorption, and a surfactant that has a moving average value of >0.34 nm for a simulation time of 10 ps or more was estimated to be in a state of desorption. Definition of Specific Surface Area for CNT and CNT Surfactants Complex. We calculated the SSAs of an isolated CNT, bundled CNTs, and the CNTsurfactants complex by
vCNTaxis 3 vCC jvCNTaxis jjvCC j
ð5Þ
where vCNT is the vertical vector with respect to the CNT axis that passes through the center of the mass of the adsorbed surfactant on the CNT surface, vcc is the vector from the carbon atom constructed methyl group at the edge of the hydrocarbon chain of the surfactant to the carbon atom at the other edge of the hydrocarbon chain, and vCNTaxis is the CNT axis vector. The subscript “CNT” in the equations refers to a carbon nanotube and represents SWCNT or MLGS, which is assumed to be MWCNT. Criteria of Adsorption and Desorption of Surfactants on Carbon Nanotube Surface. To evaluate the adsorption and desorption of surfactants on the CNT surface in the MD simulations, we calculated moving averages of 2 ps of the closest distance from the CNT to a surfactant or from an adsorbed surfactant on the CNT surface to a surfactant using MD trajectory data. The stable nonbonded distance between carbon atoms is ∼0.34 nm,31 and the periods of intermolecular vibrations are less than a few picoseconds because the vibrational spectra of intermolecular interactions such as hydrogen bonding and vdW force can be observed in the terahertz region.52,53 The time scale of 10 ps is regarded to be large enough for the model system to stabilize. Therefore, a surfactant that has a moving average value
SAS MW
ð6Þ
where MW is the molecular weight of CNT(s) (in grams), and SAS is the solvent accessible surface (in square meters) calculated by the MSMS method.54 For the calculation of SAS, the solvent probe radius was set to 0.227 nm, and the triangulation density was set to 300 vertex/nm2. The solvent prove radius was selected so that the area of circle, which appears by bisecting the sphere with a radius of 0.227 nm, is equal to the molecular occupation area of a nitrogen molecule with 0.162 nm2 because the SSA of a nanomaterial is usually determined by the Brunauer, Emmett, and Teller (BET) method55 using the adsorption of nitrogen molecule.
’ RESULTS AND DISCUSSIONS Assembly Molecular Dynamics Simulations of CNT and Surfactants. The cohesive energies (Ecoh) of each CNT
surfactants complex under different surfactant concentrations are reported as a function of time in Figure S1 of the Supporting Information. The cohesive energies of each complex show a stable energy fluctuation with an average of 2 kJ/mol standard deviation over a simulation time of 3 ns (Figure S1 of the Supporting Information). Therefore, the stable structures of each CNTsurfactants complex under those conditions are thought to have been obtained by the assembly MD simulations for 4 ns. On the basis of the results of the assembly MD simulations, we investigate the structural aspects, cohesive energies, and interactions between the CNT and the surfactant in the each CNTsurfactants complex. First, the structural aspects of the each CNTsurfactants complex are reported. The orientations of the surfactant with respect to the SWCNT surface (θSWCNTCC) are shown as a function of surfactant concentration in Figure 3a for SWCNT surfactants complexes in the SW-TC and SW-DC models. Meanwhile, the orientations of the surfactant with respect to the MLGS surface (θMLGSCC) are shown as a function of surfactant concentration in Figure 3b for MLGSsurfactants complexes in the MG-TC and MG-DC models. These values were calculated from eq 4, and the Figures contain the average of points taken every 10 ps in the trajectory in the range of 3.7 and 4.0 ns. The θSWCNTCC values of the SWCNTsurfactants complexes in the SW-TClow and SW-DClow models were 17 and 9°, respectively (Figure 3a), and the θMLGSCC values of the MLGSsurfactants complexes in the MG-TClow and MG-DClow models were 4 and 3°, respectively (Figure 3b). These values increase with an increasing concentration of surfactant (Figure 3). Therefore, the hydrocarbon chain of the surfactant is arranged parallel to the CNT surface under a low concentration of the surfactant, and the entire hydrocarbon chain is adsorbed on the CNT surface (Figures S2a,d and S3a,d of the Supporting Information). In contrast, the surfactants stand up on the CNT surface under a high concentration of the surfactant, and the tips 19662
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Figure 3. Average value of the CNTsurfactant angle as a function of surfactant concentration: (a) SWCNT and surfactant model and (b) MLGS and surfactant model.
of hydrocarbon chains of surfactants are adsorbed on the CNT surface (Figure S3c,f of the Supporting Information). Therefore, the arrangement of the adsorbed surfactants on the CNT surface depends on a concentration of the surfactant, and the CNT surfactants complex is thought to form a cylindrical micelle model (Figure 2a) under a high concentration of the surfactant. These results are almost consistent with that of Sansom et al. obtained from the study on the self-assembly of DPPC with a (18, 0) SWCNT with a diameter of 1.41 nm using the coarse-grained MD simulation technique.56 However, our results showed an aligned structure of the adsorbed DPPC on the SWCNT surface under a low concentration of the surfactant (Figure S2d,e of the Supporting Information), whereas the results of Sansom et al. showed a random adsorption of the surfactant. The θSWCNTCC values in the SW-TChigh and SW-DChigh models were 23 and 28°, respectively (Figure 3a), and are smaller than the θMLGSCC values in the MG-TChigh and MG-DChigh models. Therefore, the concentrations of the surfactant in the SW-TChigh and SWDChigh models are too low to form a complete cylindrical micelle model of the (10, 10) SWCNT and the surfactants. Furthermore, to analyze the structural aspects of the CNT surfactants complex under a low concentration of the surfactant, we calculated orientations with respect to the CNT axis (θSWCNTaxisCC) of the adsorbed surfactant in the CNT surfactants complexes in the SW-TClow and SW-DClow models from eq 5, yielding average values of 40 and 20° in the range of 3.7 and 4.0 ns with a time step of 10 ps, respectively. Tween 80 tends to adsorb the SWCNT by wrapping itself around the tube. The DPPC tends to adsorb the SWCNT parallel to the CNT axis. Tween 80 is thought to be able to wrap around the SWCNT because a single hydrocarbon chain of Tween 80 is more flexible than double hydrocarbon chains of DPPC. Second, the cohesive energies and interactions between the CNT and the surfactant in each CNTsurfactants complex are reported. The cohesive energy (Ecoh), the sum of the intermolecular interaction energies between the SWCNT/MLGS and the surfactants (ESWCNTTween80, ESWCNTDPPC, EMLGSTween80, or EMLGSDPPC), and the sum of the intermolecular interaction energies between surfactants (ETween80Tween80 or EDPPCDPPC) per one surfactant molecule for CNTsurfactants complexes in the SW-TC, SW-DC, MG-TC, and MG-DC models are summarized in Figure 4a (SWCNT and Tween 80 model), 4b (SWCNT and DPPC model), 4c (MLGS and Tween 80 model), and 4d (MLGS and DPPC model). These values were calculated from eqs 13, and the Figures contain the average
of points taken every 10 ps in the trajectory in the range of 3.7 and 4.0 ns. As shown in Figure 4, the interaction strengths between the CNT and the surfactants become weaker, and the interaction strengths between surfactants become stronger with an increasing concentration of the surfactant. These changes that appear between the CNT and the surfactant and between the surfactants in the CNTsurfactants complex are evidenced by the structural changes of the complex with an increasing concentration of the surfactant; that is, the adsorption area between the CNT and the surfactant decreases and the adsorption area between the surfactants increases as the surfactants rise on the CNT surface. Therefore, the dominant strength in the cohesive strength of the CNTsurfactants complex is believed to shift from adsorption strengths between the CNT and the surfactants to adsorption strengths between the surfactants with an increasing concentration of the surfactant. Furthermore, the cohesive strength of the CNTsurfactants complex under a low concentration of surfactant is higher than that under a high concentration of surfactant because of the strong hydrophobic interaction strengths between the CNT and the surfactant. The cohesive energies tend to converge to a constant value with an increasing concentration of the surfactant (Figures 4ac). However, unlike the cohesive energetic changes of the other complexes, the cohesive energy of the MLGS-DPPC complex shows a peak of 188 mg/mL under the DPPC concentration. Therefore, we believe that the DPPC concentration is not sufficient to form the cylindrical micelle model of the MLGSDPPC complex, and the destabilizations between the MLGS and the DPPC are greater than the stabilization between the DPPCs in the structural change of the complex with an increasing concentration of the DPPC. The cohesive energies of the SWCNTTween 80 complex and the SWCNTDPPC complex were 260 to 300 kJ/mol (Figure 4a) and 280 to 350 kJ/mol (Figure 4b), respectively, whereas the cohesive energies of the MLGSTween 80 complex and the MLGSDPPC complex were 320 to 350 kJ/mol (Figure 4c) and 340 to 410 kJ/mol (Figure 4d), respectively. The SWCNT/MLGS-DPPC complex is more energetically stable than the SWCNT/MLGS-Tween 80 complex by 20 60 kJ/mol. The average cohesive energy of the complexes was 330 kJ/mol. CNTs are thought to be bundled with a strong vdW interaction energy of ∼50 000 kJ mol1 μm1 of tubetube contact.57 This value corresponds to 500 kJ mol1 per CNT length of 10 nm. The covalent bond energy between sp3-carbon atoms is 19663
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Figure 4. Intermolecular interaction energy per one surfactant molecule adsorbed on the CNT surfaces: (a) SWCNT and Tween 80 model, (b) SWCNT and DPPC model, (c) MLGS and Tween 80 model, and (d) MLGS and DPPC model.
known to be ∼350 kJ/mol. Hence, the complexes are thought to be aggregated with a similar strength for binding CNTs and bonding sp3-carbon atoms. The adsorbed surfactants do not seem to be able to desorb easily from the CNT surface, and such high cohesive energy suggests that once the CNT molecule is covered by the surfactant molecules it is unlikely to return to the original bared form. Therefore, we believe that CNT molecules exist as a CNT and adsorbed molecules complex in the biological system. Analyses of potential biological impacts of the complexes on human health are very important for toxicity studies of CNTs. Molecular Dynamics Simulations for Adsorption and Desorption of Surfactants on CNT Surface. To elucidate the adsorption and desorption properties of Tween 80 and DPPC on the CNT surfaces, we carried out MD simulations on the NVT ensemble at temperatures of 800, 1000, 1200, and 1400 K after the assembly MD simulations of the SW-TCexp, SW-DCexp, MGTCexp, and MG-DCexp models. The Arrhenius plots for the reactions of adsorption and desorption in these models are shown in Figure 5. The straight lines in Figure 5 were determined by the least-squares method using a linear equation, and the squares of the correlation coefficients, R2, were >0.9. The activation energies for the reactions were determined from the slopes of the plots and are summarized in Table 2. As shown in Table 2, the activation energies in the reactions of Tween 80 and DPPC on the CNT surfaces are similar. The activation energies in the reactions on the SWCNT surface are 1020 kJ/mol greater than the activation energies in the
reactions on the surface of the MLGS. Therefore, the adsorption and desorption of Tween 80 and DPPC on the CNT surfaces are thought to arise at a similar frequency regardless of the size of the diameter of the CNT when a concentration of Tween 80 is equal to that of DPPC. The adsorption and desorption of the surfactants are also believed to occur more easily on the surface of a CNT with a larger diameter than with a smaller diameter. Next, the reaction rates of adsorption and desorption of Tween 80 and DPPC on the CNT surfaces at 323 K, which is similar to the human body temperature, were estimated using the results in Figure 5 to extrapolate the behaviors of the CNT surfactants complexes in the aqueous environment at the temperature. Consequently, the reaction rates of the adsorption and desorption of Tween 80 and DPPC on the surfaces of the SWCNT and MLGS were 1010 and 108 ps1, respectively. Hence, Tween 80 and DPPC are expected to adsorb and desorb on the surfaces of an SWCNT and an MWCNT with a diameter of >50 nm with a time scale of about 10 and 101 ms, respectively. Regev et al. reported that the bovine serum albumin (BSA) protein adsorbs and desorbs on the CNT surfaces with a time scale of
