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Substrate-Mediated Cooperative Adsorption of Sodium Cholate on (6,5) Single-Wall Carbon Nanotubes Felix F. Bergler, Sabine Stahl, Annika Goy, Friedrich Schöppler, and Tobias Hertel Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02759 • Publication Date (Web): 30 Aug 2016 Downloaded from http://pubs.acs.org on September 3, 2016

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Substrate-Mediated Cooperative Adsorption of Sodium Cholate on (6,5) Single-Wall Carbon Nanotubes Felix F. Bergler,† Sabine Stahl,† Annika Goy,† Friedrich Schöppler,† and Tobias Hertel∗,†,‡ †Institute of Physical and Theoretical Chemistry, Julius-Maximilian University Würzburg, Germany ‡Röntgen Research Center for Complex Material Systems, Julius-Maximilian University Würzburg, Germany E-mail: [email protected] Phone: +49 931 3186300 Abstract The interaction of sodium cholate (NaC) with (6,5) single-wall carbon nanotubes (SWNTs) is investigated using photoluminescence spectroscopy. Dilution of SWNTNaC suspensions is accompanied by changes in the exciton PL quantum yield and peak emission energy. An abrupt change of the exciton emission peak-energy at NaC concentrations between 10 and 14 mM indicates strongly cooperative formation of a micellar phase on (6,5) SWNT surfaces with a Hill coefficient of nH = 65 ± 6. This is in contrast to the formation of free NaC micelles with aggregation numbers of only about 4 and suggests that the cooperativity of NaC micelle formation on nanotube surfaces is strongly substrate-enhanced. The temperature dependence of this previously

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⊖

unobserved transition is used for a determination of ∆mic G /(1+β) = −(11.4±0.2) kJ· mol−1 which, for typical Na+ counterion binding with β ≈ 0.2, yields a free SWNT-NaC ⊖

micellization enthalpy ∆mic G of −13.7 kJ · mol−1 .

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Introduction Surfactants are widely used for the dispersion and purification of single-wall carbon nanotube (SWNT) suspensions and are thus key for their spectroscopic exploration 1–13 as well as for their potential utilization in applications. 14–16 The ability of ionic surfactants to stabilize individualized SWNTs against reaggregation in aqueous environments can be attributed to the surfactants ability to negotiate favourable interactions at the interface between the hydrophobic graphitic surfaces of SWNTs and the surrounding water. 10,17,18 Refined sample preparation protocols using density gradient ultracentrifugation, 4,7 specialized surfactants or surfactant mixtures, 4,7 aqueous two-phase extraction 11 or gel permeation 9 have successfully been used to separate SWNTs by chirality and diameter, 3 length, 19,20 water loading, 8 electronic character or by handedness. 3,7,19,21 Despite considerable progress in this field, the future development of new SWNT preparation protocols should benefit tremendously from a more detailed understanding of the interaction of surfactants with SWNTs and the accompanying structure-function relationships. 22 Extensive molecular dynamics (MD) simulations have provided useful insights 10,17,18 into the structure of adsorbate layers but also rely on the availability on experimental benchmarks such as formation enthalpies, critical micelle concentrations (CMCs) or structural characteristics of SWNT-surfactant systems. Presently, thermodynamic properties of the SWNT interaction with molecular ionic surfactants have only been reported for exchange reactions of sodium dodecyl benzene sulfonate (NaDBS), sodium dodecyl sulphate (NaDS) or sodium cholate (NaC) with flavin mononucleotide (FMN) wrapped SWNTs. 23–25 The experiments suggest that FMN displacement by these ionic surfactants is cooperative, with a Hill coefficient of about 15 in the case of displacement by NaC. 23 However, micellization enthalpies and entropies of a pure SWNT-surfactant system still remain to be uncovered. Here we present a study of the thermodynamic properties of NaC interaction with (6,5) SWNTs using nanotube exciton photoluminescence as a sensitive probe of changes in the SWNT environment. The exciton emission energy strongly depends on dielectric properties 3


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of the SWNT and its environment 26–30 while PL quantum efficiencies are also believed to be controlled by diffusion-limited non-radiative decay of excitons at impurities. 9,20 Both, the PL intensity and peak emission energy of the first subband exciton can thus be used as extraordinarily sensitive probes of the formation and of structural changes in the surfactant and water shell around SWNTs. The experiments presented here suggest that the formation of a NaC surfactant shell around (6,5) SWNTs is strongly cooperative with a Hill coefficient on the order of 65. In contrast, the formation of free NaC micelles in pure water is only weakly cooperative with an aggregation number of about 4. 31,32 This suggests that cooperativity is substrate mediated, possibly due to enhanced hydophobic association of the apolar β-faces of NaC in the proximity of the likewise hydrophobic SWNT surface. This phenomenon can also be interpreted as steric stabilization of larger NaC micellar structures by the hydrophobic SWNT surface.

Experimental Section Sample Preparation Aqueous nanotube suspensions were prepared from commercial CoMoCAT SG65 material (SouthWest NanoTechnologies Inc.) using customized preparation protocols based on the work by Arnold et al. 3,4 by density-gradient ultracentrifugation (DGU) with sodium deoxycholate (NaDC) and sodium dodecyl sulphate (NaDS) mixtures as dispersing agents. 30 This process yields suspensions strongly enriched in the semiconducting (6,5) s-SWNT species. Subsequently, suspensions were dialyzed with 50 kDa mass cutoff against aqueous 1.0% wt. NaC solutions. Five dialysis cycles against 50 ml of fresh surfactant solutions were carried out with dialysis times increasing from 2 to 12 hours to ensure complete removal of iodixanol density gradient medium as well as replacement of the dispersion additives used in density gradient runs. The resulting suspensions exhibit no iodixanol absorption signature at 245 nm. 4


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Optical Setup A schematic illustration of the homebuilt epifluorescence setup is shown in Figure 1. Laser light from a 568 nm laser diode is focussed with a 10x microscope objective into the 1 cm sample cell. The cell temperature is maintained by a home built controller using a Peltier element. 1 ml of a (6,5) SWNT-enriched starting suspension with an optical density of 0.05 at the first subband exciton transition is diluted with up to 2 ml of water at a typical rate of 1 µl · s−1 . Prompt mixing with the fresh water is facilitated by a magnetic stirrer. Further dilution is allowed after removal of 2 ml of the mixed suspension. Repetition of this procedure in combination with the excellent PL signal-to-noise ratios obtained for the starting suspensions allowed dilution of the surfactant concentration by well over one order of magnitude. This procedure was repeated for several temperatures to obtain the datasets analyzed further below. Photoluminescence (PL) was collected by the same 10x microscope objective and is detected with an imaging spectrograph after passing through a dichroic mirror which separates scattered excitation light from the PL signal. Further suppression of unwanted scattered light is achieved by a 850 nm long-pass filter in the detection arm of this setup. The PL signal is focussed onto the spectrograph using a f = 75 mm lens. PL is detected by a spectrograph (Acton Advanced SP2500i, Princeton Instruments) equipped with a 300 line · mm−1 grating and a CCD-camera (Pixis 256 BR, Princeton Instruments). Changes of the first subband exciton PL peak intensity and energy, such as those seen in Figure 1c were analyzed by fitting a Gaussian intensity distribution to a roughly 5 nm wide energy window around the peak of the measured PL spectra. About 4,000 such spectra were analyzed per dilution run. Changes of peak positions were found to be most useful to this study and were determined from the fit with a variance of about 0.1 meV for a single spectrum. Changes in PL peak intensity were normalized to the added water volume to account for the decrease of the PL intensity due to sample dilution. Reabsorption is neglected in the data analysis due to relatively low optical densities in the starting suspensions and 5


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a syringe pump water ! 1 µl/s

SWNT suspen-! sion

DM

!em ! 984 nm spectrograph

stirrer !ex = 568 nm thermostat diode laser

hνmax

c

b OD IPL

Figure 1: (a) Schematic illustration of the epifluorescence setup used for the measurement of SWNT exciton PL-changes during dilution experiments. (b) Representative absorption and PL spectrum of a (6,5)-enriched SWNT suspension. (c) Illustration of changes in PL intensity and peak position during a dilution experiment.

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the short detection path within the sample cell. The reported intensity changes should thus reflect changes in the SWNTs exciton PL quantum efficiency.

Results and Discussion Dilution of SWNT-NaC samples is accompanied by a pronounced and abrupt exciton peak energy shift at concentrations between the nominal primary and secondary CMCs as seen in Figure 2. The sudden change in peak emission energy by about 5 meV near 10 mM is also accompanied by an intermittent 10% reduction of the PL intensity, which then recovers to its initial value at lower surfactant concentrations. NaC

CMC1

CMC2

Figure 2: Typical dilution run for a (6,5) SWNT-enriched sample showing changes in the PL intensity and peak emission energy of the first subband exciton. Vertical dashed lines indicate primary and secondary critical micelle concentrations CMC1 and CMC2 for pure NaC solutions.

In the following analysis we focus on the concentration and temperature-dependence of the abrupt change in PL peak emission energy for the NaC dispersed (6,5) suspension above the NaC Krafft temperature of 0◦ C. 33 The concentration-dependence of the emission energy for a NaC dilution run at 55◦ C is reproduced in Figure 3a. We have also reproduced the room temperature concentration-dependence of the I1 /I3 pyrene PL emission intensity ratio previously used for determination of CMCs in NaC solutions by Sugioka et al. 32 . This serves

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to highlight the very narrow concentration range over which the change in PL emission energy is observed for the (6,5) SWNT-NaC system. a

Hill ﬁt Langmuir ﬁt I1/I3 from ref. 32

b 287 K 293 K 299 K 305 K 310 K 316 K 322 K 328 K

Figure 3: (a) Comparison of the step in PL peak emission energy observed for NaC dispersed (6,5) SWNTs with the I1 /I3 pyrene PL intensity ratio used for the determination of CMCs of free NaC micelle formation. 32 A Hill analysis for (6,5) SWNTs yields nH = 65 (dashed line) while the free micelle formation is generally associated with the formation of tetramers. 31,32 (b) Temperature dependence of micellization and fit curves resulting from the Hill analysis at higher concentrations combined with the Langmuir analysis at lower concentrations. Free micelle formation is typically analyzed within the closed association model. It describes micellar association of a surfactant S according to the mechanism nS ⇄ Sn and for NaC association in water is characterized by aggregation numbers n of about 4. 31,32 The degree of counterion binding β also affects the equilibrium between free monomers and micelles which for NaC has been reported to be ≈ 0.20. 32,34 The small number of monomer units comprising NaC micelles in water implies that cooperativity in the bulk suspension 8


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is weak as reflected by the broad transition of the I1 /I3 intensity ratio shown in Figure 3a. A similarly broad transition from the monomer to the micellar phase is also seen in other signal types used for measuring CMCs in aqueous NaC solutions by Hao et al. 31 . The abrupt change of the PL emission energy in the SWNT-NaC system thus appears noteworthy and is investigated in further detail. For a quantitative analysis we assume that the PL spectrum can be described by a superposition of two overlapping emission features. One from the system in the reactant state A and one from the product state B such that IPL = θ · IPL,A + (1 − θ) · IPL,B . The emission wavelength is then proportional to θ, the fraction of the total SWNT-length covered with a micellar-like structure in the product state B, given that the PL quantum efficiencies in both states are similar. The abrupt change in PL intensity can then be investigated using a Hill analysis 35 which determines the Hill coefficient nH from the slope of the concentration-dependence of log(θ/(1 − θ)) vs log([NaC]/[NaC]1/2 ) in the vicinity of the inflection point [NaC]1/2 . This analysis is based on the Hill equation for cooperative chemical transformations

θ([NaC]) =

K [NaC]

n H

+1

−1

θ again refers to the fraction of the system in the cooperatively formed product state and K is the equilibrium constant. The resulting Hill coefficients for the data shown in Figure 3b yield an average nH of 65 ± 6, considerably larger than the formation of NaC micelles in pure water from 4 monomers would suggest and also larger than the Hill coefficient of 15.4 observed for the displacement of FMN bound to SWNTs by NaC. 23 In line with the closed association model for free micelle formation we thus propose an analogous mechanism for NaC micellization on SWNTs surfaces, which - if counterion

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binding is accounted for in the established manner 31 - reads nC− + βnNa+ + SWNT ⇄ SWNT Naβn Cn (1−β)n−

(1)

This allows the thermodynamic analysis of SWNT-NaC micelle formation equilibrium within the same framework as that used for the association of ionic surfactants in bulk water. To do so we here use the temperature dependence of the inflection point [NaC]1/2 seen in Figure 3b as indicator of the CMC for micellization of the SWNT-NaC system. The free micellization enthalpy can then be obtained in the usual manner from ⊖

∆mic G = (1 + β)RT ln(CMC/c⊖ )

(2)

We note, that a very similar analysis can also be applied if the observed spectral changes were to be attributed to a simple phase transition. Indeed micellization is sometimes discussed in terms of a two phase separation model whose underlying premise is that micellization can be described using a two-phase equilibrium. 36 However, as discussed further below we believe that the observed spectral changes are clearly indicative of cooperative micellization and not of a phase transition. ⊖

The temperature dependence of ∆mic G /(1 + β) resulting from the analysis of the data using eq. 2 is shown in Figure 4 (grey solid circles). For the formation of NaC micelles in water the degree of counterion binding β has been reported to be near 0.20. 34 For counterion binding similar to NaC bulk suspensions one thus obtains a free micellization enthalpy for the SWNT-NaC system of −13.7 kJ · mol−1 . However, if counterion binding were more similar to NaDS association in water with β ≈ 0.80 37 and n ≈ 60, then the free micellization enthalpy would be in the range of ≈ −20 kJ · mol−1 . The micellization enthalpy and -entropy contributions can also be obtained from the ⊖

temperature dependence of ∆mic G using the Gibbs-Helmholtz relation (d(∆G/T )/dT ) = 10


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−∆H/T 2 . Here the derivative of ∆G/T is obtained from the slope of a linear regression to sets of three successive data points. Enthalpies and entropies derived in this manner are associated with somewhat larger error margins due to the sensitivity of the slope d(∆G/T )/dT to uncertainties of the sample temperature, which are here estimated to be 0.5 K. The re⊖

⊖

sulting temperature dependencies of ∆mic H /(1 + β) and T ∆mic S /(1 + β) are also included in Figure 4 along with the confidence bands indicated by the shaded backgrounds. (6,5) SWNT - NaC

T ∆mic S ∆mic H

∆mic G

⊖

⊖

⊖

⊖

NaC! from ref. 34

∆mic G , ∆mic H , T ∆mic S

⊖

NaDS! from ref. 38

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⊖

⊖

⊖

Figure 4: Temperature dependence of ∆mic G , ∆mic H and T ∆mic S for SWNT-NaC micellization normalized with (1 + β). The data is compared with recent data obtained for the formation of free NaC and NaDS micelles in pure water. 34,38 In both cases micellization is entropy driven at lower temperatures and becomes enthalpically driven at higher temperatures. The shaded light red and light blue regions indicate the σ confidence bands for enthalpic and entropic contributions to the free micellization enthalpy of SWNT-NaC. For comparison we have also included the bulk suspension data for NaC and for NaDS (sodium dodecyl sulphate) in Figure 4, as obtained by recent studies for the micellization of NaC and NaDS in pure water by Kumar et al. 34 and by Marcolongo and Mirenda 38 . The bulk data clearly show the typical crossover from micellization being entropically driven at low temperatures and becoming more enthalpically driven at higher temperatures. 34,39 This reflects the ability of free surfactant monomers in solution to increase the order of the surrounding water more strongly than in the micellar phase, a trend that diminishes in 11


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importance toward higher temperatures. The trend for the SWNT-NaC system in Figure 4 is strikingly similar to that of the pure NaDS system, again with the free micellization enthalpy being entropically driven at low temperatures and being enthalpically driven at higher temperatures. This comparison is intriguing because the thermodynamics of the SWNT-NaC system thereby more strongly resemble those of the highly cooperative formation of free NaDS micelles with aggregation numbers around 60 Shah et al. 37 than those for the formation of free NaC micelles with aggregation numbers around only 4. 31,32 We thus take the similarities of the thermodynamic behaviour of highly cooperative free NaDS micelle formation and SWNT-NaC micellization as further evidence for the closed association mechanism introduced in eq. 1.

Figure 5: van’t Hoff plot of the temperature dependence of the equilibrium constant K obtained from a Langmuir analysis of the low concentration regime in Figure 3b). Lastly, we return to the temperature dependence of the peak emission energy at NaC concentrations below the SWNT-NaC micellization transition. The slow increase of peak emission energies toward higher NaC concentrations can be well described by a Langmuirtype behaviour, again with the emission energy being taken as a direct measure of the dilute concentration of NaC on the SWNT surface. The corresponding Langmuir fit describes both, the concentration as well as the temperature dependences reasonably well, as seen for the sample dataset of Figure 3a and from the combination of Hill and Langmuir fits shown as solid black lines in Figure 3b.

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The extrapolation of emission energies to zero surfactant concentrations gave best agreement with experimental data using a room temperature exciton transition energy hν(H2 O) = 1.245 eV corresponding to 996 nm in pure water, in very good agreement with earlier studies of gel-imbedded and water rinsed SWNTs. 30 This analysis also accounts for a temperature dependent intrinsic shift of (6,5) emission energies of +0.04 meV · K−1 as suggested by PL studies of vacuum suspended SWNTs. 40,41 The temperature dependence of equilibrium constants obtained from the Langmuir fit can next be used to estimate the equilibrium enthalpy for the adsorption of NaC monomers on the SWNT surface from a van’t Hoff plot (see Figure 5). The data yields a NaC adsorption enthalpy on (6,5) SWNTs of −(30 ± 5) kJ · mol−1 . This is significantly larger than previous experimental work by Sasaki et al. 42 for NaC adsorption on graphite surfaces with ∆ads H = −(17 ± 3) kJ · mol−1 . Interestingly, large scale MD simulations of NaC adsorption on SWNTs appear to suggest the opposite trend with adsorption of the warped hydrophobic NaC β-surface on more strongly curved SWNTs surfaces being associated with a decrease of adsorption enthalpies and not an increase, specifically in the low NaC concentration regime. 17,18 The reason for this apparent discrepancy is not entirely clear and will be the subject of future investigations.

Conclusions We have investigated the formation of SWNT-NaC micellar structures on (6,5) SWNTs using photoluminescence from nanotube excitons as a sensitive probe of surface coverage and structural changes in the surfactant shell. The formation of NaC micellar structures around (6,5) SWNTs at NaC concentrations in the 10-14 mM range appears to be strongly cooperative with a Hill coefficient of nH = 65 ± 6, in contrast to the formation of NaC micelles at small surfactant concentrations in water with only 4 monomers. 31,32 The associated thermodynamic behaviour of micellization in the SWNT-NaC system is found to be strikingly

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In the SWNT-NaC system such stabilization is offered by the SWNT substrate. This concept of substrate-mediated cooperativity is illustrated schematically in Figure 6 along with the anticipated adsorption behaviour at lower and higher NaC concentrations. At low concentrations NaC adsorption leads to the formation of a dilute phase 18 while higher concentrations are associated with the formation of the micellar SWNT-NaC phase. The estimated spatial extent of the cooperatively formed micellar structures of about 8-15 nm is drawn to scale in Figure 6c. The temperature dependence of critical NaC concentrations at which micellization occurs ⊖

was used for determining ∆mic G /(1 + β) yielding a room temperature free micellization enthalpy of −13.7 kJ · mol−1 , if pure bulk suspension NaC counterion binding constants on the order of β ≈ 0.2 are used. These results may provide additional guidance for simulations of microscopic structure and energetics which previously appear not to have encountered similarly pronounced cooperative behaviour. Future studies should also cast more light onto the behaviour in polychiral SWNT samples and mixed surfactant systems and may thereby help clarifying the role of surfactant mixtures for chirality selective SWNT preparation and purification protocols.

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Langmuir

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