Interaction of Polymers with Single-Wall Carbon Nanotubes - The

Article pubs.acs.org/JPCC

Interaction of Polymers with Single-Wall Carbon Nanotubes Frank K. Brunecker,† Friedrich Schöppler,† and Tobias Hertel*,†,‡ †

Institute of Physical and Theoretical Chemistry and ‡Röntgen Research Center for Complex Material Systems, Julius-Maximilian University Würzburg, 97074 Würzburg, Germany S Supporting Information *

ABSTRACT: Polymers are widely used for postsynthesis processing, purification, and individualization of single-wall carbon nanotubes (SWNTs) in aqueous or organic solvent environments. Here, the interaction of single-stranded DNA oligomers (ssDNA) and of a polyfluorene copolymer (F8T2) with (6,5) SWNTs was investigated from desorption kinetics and in the case of ssDNA also using adsorption isotherms. Eyring analysis of desorption rate constants reveals a linear increase of activation enthalpies with ssDNA oligomer length until ΔdesH‡ saturates at (155 ± 5) kJ·mol−1 for oligomers exceeding the ssDNA Kuhn length of about 6 nm. The Gibbs energy for desorption of ΔdesG‡ = (96 ± 1) kJ·mol−1 is lengthindependent because of entropy−enthalpy compensation. The saturation of desorption energies at the high polymer coverages studied here is attributed to incomplete adsorption with typically no more than a single Kuhn segment of a polymer attached to a SWNT.

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determination of thermodynamic properties.25−28 Albertorio et al. investigated ssDNA−SWNT interactions without interference from coadsorbed surfactants by temperaturedependent kinetic studies.29 These authors obtained activation energies for d-(C)12, d-(A)12, and d-(T)12 desorption in the range from (61.9 ± 4.6) kJ·mol−1 to (102 ± 1) kJ·mol−1.29 In one study, authors used single-molecule force spectroscopy to obtain poly(G) and poly(T) binding energies to SWNTs of ≈75 J·mol−1 and ≈55 J·mol−1 and per nucleotide, respectively.30 The use of polyfluorene and other (co)-polymers for the selective dispersion of SWNTs in organic solvents has also found widespread adoption after reports showed this to be a powerful and easy approach for chirality-selective purification of SWNTs with the potential for highly efficient elimination of metallic SWNTs from processed samples.31−35 Here, we present a thermodynamic and kinetic study of ssDNA and F8T2 (poly-[(9,9-dioctylfluorenyl-2,7-diyl)-cobithiophene]) adsorption on (6,5) SWNTs. We investigate the interaction of these molecules with SWNTs at or near saturation coverage, i.e., when further polymer adsorption is believed to be sterically unfavorable. The design of the experiments presented here allows such measurements without the interference with preadsorbed surfactant molecules. We determine thermodynamic functions as well as their coverage dependence and thereby provide a more detailed microscopic perspective of polymer−SWNT interactions in both aqueous and organic solvents.

INTRODUCTION The fabrication of colloidal suspensions is key for nanoparticle utilization in thin film and other technologies as well as for fundamental studies of their electronic and optical properties. The exploration of single-wall carbon nanotubes (SWNTs) and of their potential for applications has thus largely been driven by the development of dispersion and purification techniques.1−17 Amphiphilic molecules are frequently used as dispersion agents because of their ability to negotiate favorable interactions between hydrophobic SWNT surfaces and hydrogen bonds in water.1−4,7,8,10−13,16,17 Among others, singlestranded DNA oligomers (ssDNA) have been used, not only for the dispersion of SWNTs in aqueous environments but also for chirality enrichment using tailored nucleotide sequences and oligomer lengths.10,11 However, due to a lack of suitable methodology for the experimental determination of molecule−nanoparticle interactions,18 insights into the microscopic character of molecular interactions with SWNTs are frequently based on molecular dynamics (MD) simulations.19−22 According to such simulations, selective dispersion of SWNT species by ssDNA may be attributed to sequence-specific adsorption configurations.11,20,23−25 Moreover, ssDNA is predicted to be helically adsorbed on SWNTs with binding energies in the range of 9.6 kJ·mol−1·nucleotide−1 to 13.6 kJ· mol−1·nucleotide−1.19−21 Consequently, as for the use of amphiphilic surfactant mixtures for SWNT purification,7 the optimization of ssDNA nucleotide-sequence and oligomer lengths has so far mostly been based on trial and error.11 Most investigations of ssDNA−SWNT interactions have focused on ssDNA bile-salt exchange reactions for the © XXXX American Chemical Society

Received: March 1, 2016 Revised: April 14, 2016

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DOI: 10.1021/acs.jpcc.6b02198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

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EXPERIMENTAL SECTION Sample Preparation. SWNT−ssDNA complexes were fabricated by density gradient ultracentrifugation (DGU) using customized sonication, centrifugation, and filtration protocols based on the work of Arnold et al. and Hain et al.4,36 Fluorophore-labeled single-stranded DNA oligomers (ssDNA) of the type d(GT)n-FAM (n = 2, 4, 6, 8, 12, 16, 20; FAM, 6carboxyfluorescein) and d(TAT)4-FAM (biomers.net GmbH) were used for desorption studies. For preparation of SWNT− ssDNA complex raw suspensions, 0.3 mg of CoMoCAT type SWNT soot (SWeNT SG 65, SouthWest NanoTechnologies) were sonicated for 2 h (Branson Sonifier S-450A, gain level 3− 4, CW-mode) at room temperature in 1.8 mL of a phosphatebuffered ssDNA solution. The nucleotide concentration of the ssDNA solution was 0.5 mmol·L−1. The resulting heterogeneous mixture was then layered into a density gradient as described by Hain et al.36 Ultracentrifugation for 18 h at 41 000 rpm yielded well-separated top layers of isolated SWNT− ssDNA complexes and layers with more strongly aggregated material toward the vial bottom.4 The 150 μL aliquots from the density gradients were characterized by ultraviolet−visible− near-infraredNIR absorption spectroscopy (Cary 5000, Varian). Fractions with (6,5)-SWNT content exceeding 75%, as estimated by absorption spectroscopy, were combined to obtain 4 mL of (6,5)-SWNT−ssDNA complex-enriched suspensions with a SWNT carbon atom concentration of about 80 μM corresponding to an SWNT concentration in the 6 nM range.37 d(GT)2−FAM suspensions were benchtop centrifuged for 90 min to remove larger aggregates before the supernatant was used for further investigations. For kinetic studies, the suspensions were depleted of ssDNA by benchtop centrifuge-assisted filtration with a molecular weight cutoff at 100 kDa (Ultracel YM-100, Microcon). The filter membrane allowed free d(GT)2−FAM and d(GT)20− FAM ssDNA oligomers with a molar mass of 1.7 kDa and 13 kDa, respectively, to pass while SWNT−ssDNA complexes with a molecular weight on the order of 300 kDa were retained. Prior to redispersion and spectroscopic characterization, the SWNT−ssDNA complex residue on the filter membrane was repeatedly rinsed with phosphate-buffered saline (PBS) to ensure that the majority of free ssDNA oligomers was removed. Subsequently, the SWNT−ssDNA complexes were resuspended in 2.3 mL of PBS solution yielding a clear suspension of violet tint. The latter was promptly divided into 11 aliquots with 200 μL volume each and frozen in liquid nitrogen to provide a batch of identical samples for later use. Samples were stored at −32 °C to minimize ssDNA desorption before experimentation. Immediately before kinetic studies the aliquots were defrosted for 20 s at 100 °C and were allowed to settle at room temperature for another 40 s before being injected into a spectroscopy cell for dilution experiments. SWNT−ssDNA complexes were not noticeably aggregated as judged from the first exciton subband S1 transition which was not significantly broadened or red-shifted after the filtration and frosting− defrosting process. We also verified that frosting−defrosting cycles did not have any noticeable effect on the measured kinetics. For preparation of SWNT-F8T2 complexes, 7.5 mg of CoMoCAT type SWNT soot was mixed with 9.0 mg of F8T2 (99.9%, Sigma-Aldrich), suspended in 15 mL toluene, and sonicated for 8 h at 0 °C.34,38,39 Bench-top centrifugation at

14 000 rpm for 3 min was used to remove bundles and aggregates, and a clear yellow supernatant was obtained and characterized by absorption spectroscopy. A 4.0 mL sample of this suspension were filtered by mixed cellulose ester membranes (IsoporeTM Membrane Filters 0.1 μm VCWP, Merck Millipore) and rinsed several times with toluene to remove excess polymer. The filter was dissolved in acetone, and the residue was resuspended in 2.0 mL of toluene. This suspension was stored at 4 °C to minimize polymer desorption before kinetic studies. Photoluminescence Measurements. Dilution experiments were carried out using a home-built, temperaturecontrolled sample cell and epifluorescence microscope. For kinetic studies, 6-FAM and F8T2 fluorophores were excited at 488 nm using an argon ion laser (Stabilite 2016, SpectraPhysics). Excitation laser light was focused into the spectroscopy cell by an infinity-corrected objective, and the photoluminescence signal was collected with the same objective before being detected using a single-photon-counting setup with a Si avalanche photodiode (SPAD, Micro Photon Devices). The combination of low excitation intensity (typically 100 μW) with highly sensitive single-photon detection, a small detection volume, and its diffusive replenishment with fresh nonilluminated SWNT−ssDNA complexes from within the spectroscopy cell allowed the reduction of the rate of FAM photobleaching to below 1 ‰ per hour. We associate the changes of photoluminescence (PL) signals directly with changes in the surface concentration of adsorbed ssDNA. Configurational changes of the adsorbed ssDNA and their potential effect on PL quantum yields are assumed to be negligible for the small coverage changes of less than 5% used for determination of rate constants. For each measurement, 3.0 mL of a suitable solvent, PBS for SWNT−ssDNA samples, methylcyclohexane, toluene, orthoxylene or chlorobenzene for SWNT-F8T2 samples, was actively temperature stabilized. Aliquots of filtered SWNT−ssDNA samples (150 μL) and SWNT-F8T2 samples (10 μL) were then injected into the spectroscopy cell. The aliquots rapidly equilibrate at the temperature of the solvent because of its large heat capacity. Temperatures ranged from 15 to 55 °C, and data sets were collected at increments of 10 °C (5−45 °C for SWNT-F8T2 in chlorobenzene). Nucleotide absorption at 245 nm at low ssDNA concentrations was too strongly affected by background absorption for a determination of ssDNA concentration by absorption measurements. ssDNA concentrations were therefore determined by measuring FAM photoluminescence in the filtrate of repeatedly and heavily diluted, filtered, and resuspended SWNT−ssDNA suspensions. For SWNT-F8T2 complexes, the polymer concentration was determined using polymer absorption bands between 375 and 545 nm. The F8T2 solubility in different solvents at room temperature was determined to be (0.18 ± 0.01) g·L−1 for methylcyclohexane, (0.63 ± 0.09) g·L−1 for toluene, (0.82 ± 0.02) g·L−1 for ortho-xylene, and (3.5 ± 0.3) g·L−1 for chlorobenzene.

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RESULTS AND DISCUSSION Desorption Kinetics of ssDNA. The ad- and desorption of a polymer at a nanotube surface are illustrated schematically in Figure 1a. Adsorption is characterized by the rate constant kads and desorption by the rate constant kdes. The polymer− nanotube complex features polymer train segments which are B


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Figure 1. Interaction of ssDNA oligomers with SWNTs. (a) Schematic illustration of a generic adsorption geometry. The extent to which the oligomer is adsorbed in the train configuration depends on the strength of the oligomer-SWNT interaction. (b) Generic oligomer− SWNT interaction potential.

Figure 2. Determination of ssDNA desorption kinetics. (a) Typical PL time-trace after injection and dilution of a ssDNA−SWNT suspension into the spectroscopy cell. (b) Change of ssDNA coverage on the SWNT as obtained from the PL time-trace. (c) Temperature dependence of the initial rate constant of the PL decay for oligomers with different lengths. The curves serve as a guide to the eye.

adsorbed on the surface while tail and loop sections may extend into the proximal or dilute distal corona layers in the solvent.40 For ssDNA interaction with SWNTs, we can formulate the generic reaction mechanism

The temperature dependence of kdes is shown in Figure 2c for d(GT)n oligomers with n = 2, 4, 6, 8, 12, 16, and 20. Next, this data is used to determine activation enthalpy, ΔdesH‡, and activation entropy, ΔdesS‡, for desorption from an Eyring analysis according to

kads

SWNT + ssDNA XoooY SWNT−ssDNA kdes

⎛k h⎞ Δ H‡ Δ S‡ ln⎜ des ⎟ = − des + des RT R ⎝ kBT ⎠

The equilibrium constant for this reaction is given by the ratio of rate constants for adsorption and desorption, Keq = kads/kdes. Desorption of fluorophore-labeled ssDNA can be monitored by recording changes of the PL-intensity from the FAM fluorophore, which is quenched substantially when in proximity to the SWNT (see Figure 1a).37 The kinetics of ssDNA oligomer desorption were obtained from the time dependence of the FAM PL-intensity following dilution of small aliquots of SWNT−ssDNA complex suspensions that have been depleted of free ssDNA as described above. A typical dilution experiment for fluorophore-labeled d(GT)12-FAM at 35 °C in PBS solution is shown in Figure 2a. At time t = 0 the photoluminescence intensity jumps from zero to a finite value as concentrated SWNT− ssDNA suspension is introduced into the cell and is rapidly diluted about 20-fold. The change of the absolute concentration of adsorbed ssDNA and the rate of desorption was determined by comparison of the PL signal changes with PL from a pure ssDNA solution with known oligomer concentration. The initial surface coverage in the saturation regime of about 0.2 has been determined previously.36,37,41 The increase of the PLintensity can then be directly related to a decrease of the surface coverage as shown in Figure 2b for the data set of Figure 2a. The initial slope of the decrease in coverage directly corresponds to the desorption rate constant kdes. ssDNA readsorption from the solution can be neglected at early times when the concentration of free ssDNA in the solvent is negligible.

Here we recall that the Eyring analysis stipulates that interaction potentials are themselves temperature-independent, an assumption which may bias the interpretation of kinetics in complex systems to some degree but which, for a lack of better alternatives, is nonetheless also prudent. As expected for endothermic reactions, the rate of desorption is found to increase with temperature for all oligomers (see Figure 2c). In addition, kdes also tends to decrease with increasing oligomer length. The results of the Eyring analysis are shown in Figure 3a along with the Gibbs energy obtained from ΔdesG‡ = ΔdesH‡ − TΔdesS‡. The black scale-bar indicates the approximate range of the Kuhn length of 5−8 nm.19,42,43 The length dependence of ΔdesH‡ is initially characterized by a pronounced linear increase at a rate of (13 ± 1)kJ·mol−1·nucleotide−1, somewhat smaller than the experimentally determined enthalpy ΔadsH(A) = −20 kJ·mol−1 for adsorption of a single adenine nucleotide on a graphite surface in water44 but in good agreement with recent predictions from MD simulations.19−21 Adenine adsorption may here be an appropriate reference point because another study found the affinity of adenine toward graphite to be between that of thymine and guanine, of which the ssDNA oligomers in this study are composed.45 At the length of the Kuhn segment with about 12 nucleotides length, the activation enthalpy and entropy are found to saturate at ΔdesH‡ = (155 ± 5) kJ·mol−1 and TΔdesS‡ = (58 ± C


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between enthalpy and entropy for transformations at constant pressure (∂H/∂S)p = T. An important question that remains is whether the apparent entropy−enthalpy compensation can indeed be attributed to intrinsic correlations and not to experimental bias. Such bias may be introduced by the need to balance data acquisition times with the requirements for suitable signal-to-noise ratios. In other words, experimentalists may unwillingly be biased to report on those experimental outcomes in which significant changes of desorption signals can be observed over the duration of a typical experiment. Using kdes = (kB T/h) exp[−ΔdesG‡/RT] in combination with the sensitivity of our setup, i.e., the smallest detectable rate constants, we calculate an upper limit of detectable Gibbs energies for desorption of 130 kJ·mol−1. The time-resolution of the experimental setup and the times taken to stabilize SWNTs in a nonequilibrium configuration on the order of a few minutes place a lower limit on detectable free enthalpies of 87 kJ·mol−1. Our experimental setup thus should allow an unambiguous determination of desorption enthalpies in the range from 87 to 130 kJ·mol−1 without being affected by experimental bias. Desorption Kinetics of a Tethered Dimer. One of the most surprising findings of the previous discussion is perhaps the saturation of desorption enthalpy and entropy for desorption once oligomers exceed the Kuhn length (see Figure 3a). This appears to contradict the fundamental paradigm that heats of adsorption should be extensive in the polymer length.49 In the following we therefore discuss two alternative interpretations for the absence of length scaling beyond the Kuhn length: (i) the temperature dependence of desorption kinetics for different oligomers does not reflect changes the heat of adsorption, and (ii) ssDNA oligomers are only partially adsorbed such that ssDNA interaction with SWNTs in these experiments is limited to a single Kuhn segment. To address the first hypothesis, that measured activation energies scale differently than heats of adsorption, we discuss the kinetics of desorption of a tethered dimer as the simplest model for desorption of the shortest possible oligomer. The monomer unit here represents a polymer Kuhn segment which can consist of several nucleotides; in the case of ssDNA, this should be 9−14. We recall that the length of the Kuhn segment is twice the persistence length and corresponds to the length of monomer units used in the description of polymer thermodynamics, as for example within the freely jointed chain (FJC) or worm-like chain (WLC) models.40,46,50 We start by calculating the thermodynamic functions obtained from an Eyring analysis of tethered dimer desorption. As we will see, this simple kinetic model may offer some intriguing insights into the kinetics of desorption of flexible molecules weakly bound to a rigid substrate. A schematic illustration of the mechanism of desorption of the tethered dimer is shown in Figure 4. Within this model we treat the kinetics of each of the dimer units independently. Desorption of the dimer from the adsorbed state A proceeds to the half-detached stage B with rate constant kf and eventually to the fully detached state C, again with kf. The forward and backward rate constants, kf and kb, respectively, for monomer motion from the adsorbed state with energy Ea across the transition state with energy Et are given by

Figure 3. (a) Dependence of activation enthalpy, entropy, and Gibbs energy on ssDNA oligomer length. Surprisingly, all thermodynamic functions are found to saturate at oligomer lengths exceeding about one Kuhn segment. (b) Nearly ideal enthalpy−entropy compensation for the same data set.

5) kJ·mol−1, respectively. These values are similar to those reported in a surfactant displacement study by Shankar et al.25 for 12−30 nucleotide long oligomers. In contrast, other values reported previously differ considerably,27,29 possibly due to the effect of ssDNA interaction with adsorbed surfactant in exchange reactions. Polymer adsorption is typically associated with a loss of conformational entropy on the order of RT, i.e., of approximately 2.5 kJ·mol−1 per Kuhn segment.46 However, this cannot account for the up to 20-fold increase of the entropy observed here, if compared to the thermal value. The large entropy increase during desorption suggest that conformational degrees of freedom of the polymer chain as well as those of individual ssDNA nucleotides are confined in the adsorbed state because of strong interactions of guanine and thymine with the SWNT surface. Strong rearrangement of nucleotides observed in MD simulations may be taken as further evidence for such interactions.19−21 This effect appears to dominate over the expected entropic reduction associated with water ordering at the hydrophobic interfaces created by ssDNA detachment. Enthalpy−Entropy Compensation. As seen in Figure 3, TΔdesS‡ increases with oligomer length at exactly the same rate as the enthalpy. This is associated with nearly ideal enthalpy− entropy compensation, as illustrated by Figure 3b. The corresponding Gibbs energy for desorption of ΔdesG‡ = (96 ± 1) kJ·mol−1 is thus length-independent. Such enthalpy− entropy compensation is typical of chemical transformations where the character of the underlying interactions is similar, i.e., if similar hydrogen bond or van der Waals interactions or a combination of these dominate the reactions.47 The phenomenon has frequently been discussed in terms of so-called isokinetic or isoequilbrium relationships48 but may also be rationalized by the fundamental thermodynamic relationship

kf = D

kBT q‡ exp[−(Et − Ea)/RT ] h qads DOI: 10.1021/acs.jpcc.6b02198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C with

1 (ν ẽ ϵa − 1 + ν 2̃ e 2ϵa + 6ν ẽ ϵa + 1 ) 2 These functions depend only on ϵa = Ea/RT and on ν̃ = qfree/ qads, which are related to the equilibrium constant of monomer adsorption Keq, m by B0 (ϵa) =

−1 Keq,m =

kf = exp( − ΔdesGm /RT ) = ν ẽ ϵa kb

Similar expressions can also be derived for the dimer desorption entropy and Gibbs energy (see the Supporting Information). Before discussing these relationships in the context of dimer desorption, we briefly review which thermodynamic parameters are experimentally accessible from desorption kinetics and which remain unknown. Hypothetical enthalpy and Gibbs energy surfaces for monomer desorption are reproduced in Figure 5a. As discussed above, desorption enthalpies, entropies,

Figure 4. Schematic illustration of the desorption of a tethered dimer from a solid substrate. (a) The interaction potential of a monomer unit is characterized by an adsorption well of depth Ea and a transition state with energy Et. (b) Desorption of the dimer across the transition state proceeds in two steps where forward and backward rate constants kf and kb, respectively, are directly related to the monomer kinetics. Only if both monomers have crossed the transition state in the forward direction is the dimer considered as desorbed.

and kBT q‡ exp( −Et /RT) h qfree

kb =

where qads, q‡, and qfree are the monomer partition functions in the adsorbed, transition, and detached state, respectively. The kinetic rate equations for the concentrations [A], [B] and [C] are then given by d[A] = −2k f [A] + k b[B] dt d[B] = 2k f [A] − (k f + k b)[B] dt d[C] = k f [B] dt

We can solve this set of coupled differential equations with the starting concentrations of the fully detached state [C(t = 0)] = 0 and of the adsorbed state [A(t = 0) ] = [A0]. Solutions of the type [A]= [A0] e−t/τ then yield the rate constant for desorption as given by kd = τ−1. It is evident that the dimer desorption rate constant, kd, also depends on temperature because of the temperature dependence of the rate constants kf and kb. This allows us to compare the resulting temperature dependence of kd for the tethered dimer with the rate constant of monomer desorption by calculating the ratios of dimer ΔH‡d to monomer ΔH‡m desorption enthalpies, as obtained from the same Eyring analysis used for analysis of experimental rate constants (see above and the Supporting Information). The subscripts d and m refer to dimer and monomer, respectively. We obtain ΔHd‡ ΔHm‡

=1−

Ea ΔHm‡

Figure 5. (a) Hypothetical enthalpy and Gibbs energy curves for monomer desorption, here for negative equilibrium desorption entropy, i.e., for ΔH < ΔG. ΔdesH‡ and ΔdesG‡ can be determined experimentally, for example, from desorption kinetics. ΔH and ΔG on the other hand represent equilibrium constants. (b) Schematic illustration of the trends to be expected for ΔH if desorption entropies are positive or negative and ΔG is held constant. (c) Comparison of predictions from the tethered dimer desorption model for the desorption enthalpy determined by an Eyring analysis of desorption kinetics.

(f − 1)

and Gibbs energies can be determined from kinetic studies. However, the equilibrium enthalpy ΔH and entropy ΔS contributions remain unknown. In Figure 5b we thus illustrate qualitative trends for three scenarios with ΔG held at a constant, say experimentally known, value. The scenarios assume that the desorption entropy is either negative, approximately zero, or positive.

where f is given by ϵa

f (ν ẽ ) =

2ν ẽ ϵa −

dB0 (ϵa) dϵ

2ν ẽ ϵa − B0 (ϵa) E


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saturation reached at submillimolar oligomer concentrations, evidence for high affinity adsorption characteristic of attractive polymer−surface interactions.51 Equilibrium constants, Keq, obtained for the isotherms in Figure 6 are in the range of 0.3 × 105 l·mol−1 to 1.0 × 105 l· mol−1. Accordingly, the law of mass action suggests that the standard Gibbs energies for adsorption ΔadsG for these oligomers are in the range of −26 to −29 kJ·mol−1. As mentioned before, Gibbs adsorption energies should be extensive with oligomer length, and we would thus expect ΔadsG to increase more considerably when the oligomer length is increased from 13 nm (n = 12) to about 22 nm (n = 20). The absence of a clear scaling of ΔadsG with oligomer length thus clearly suggests that adsorption may be incomplete, with only short sections of the oligomer bound to SWNTs, as illustrated schematically in Figure 7a. We next compare the total contour length of adsorbed ssDNA with the total length of SWNTs in the suspension. The total contour length of adsorbed polymer, lads, is obtained from the adsorbed polymer concentration shown in Figure 6 using

As illustrated in Figure 5b, a negative monomer desorption entropy would be associated with ΔH < ΔG while a positive monomer desorption entropy would imply that ΔH > ΔG. Negative desorption entropies may be expected if desorption of ionic surfactants leads to the formation of a highly ordered solvation shell around the free molecule. If the desorption entropy is positive, however, then the desorption would be associated with an energy barrier higher than that suggested by ΔG, see right side of Figure 5b. Somewhat surprisingly, we find that monomer and dimer desorption enthalpies, as calculated from the temperature dependence of rate constants, depend on the desorption entropy, ΔS, being positive or negative. If ΔS is negative and if the equilibrium Gibbs energy for desorption is on the order of 35 kJ·mol−1, as determined experimentally in the next section, we find that the dimer enthalpy ΔdesH‡d increases from 1.3× over 1.5× to 2.1×ΔdesH‡m when the desorption entropy changes from somewhat negative to positive (see Figure 5c). The key conclusion from this discussion is that the Eyring analysis of kinetic data does not necessarily yield heats of adsorption which are extensive in the length of the oligomer, i.e., a dimer may exhibit only a minor increase of ΔdesH‡ over the monomer desorption enthalpy. We thus need to take a closer look at experimental data to decide whether the saturation of thermodynamic functions for desorption of oligomers with a length exceeding the Kuhn segment is due to the peculiarities of Eyring analysis of desorption kinetics or if it can be attributed to incomplete oligomer adsorption. Analysis of Adsorption Isotherms. In Figure 6 we show room-temperature adsorption isotherms obtained for FAMlabeled d(GT)n adsorption by displacement of surfactant from sodium dodecyl sulfate (SDS) stabilized (6,5) SWNTs from a phosphate-buffered ssDNA solution at pH 7.4 with n = 12, 16, and 20. The isotherms show a familiar sharp onset with

Figure 7. (a) Schematic illustration of adsorbed train- and free tailsections of ssDNA oligomers. (b) Length of the adsorbed train segments for d(GT)12, d(GT)16, and d(GT)20 as obtained from adsorption isotherms. (c) Schematic representation of the corresponding adsorption conformations for these oligomers.

Figure 6. Adsorption isotherms for d(GT)12, d(GT)16, and d(GT)20. The concentrations of adsorbed oligomer are with reference to the left axis while the right axis gives the corresponding total contour length of adsorbed ssDNA. F


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where Δh‡ and Δs‡ are the coverage dependencies of desorption enthalpy and entropy, respectively. These are obtained from the fit to the temperature dependence of kinetic data in the same way as the high coverage limits of desorption enthalpy, entropy, and Gibbs energy discussed in the previous sections. We obtain Δh‡ = (880 ± 35)kJ·mol−1 and TΔs‡ = (740 ± 35)kJ·mol−1, showing no clear variation with oligomer length. To better understand the significance of Δh‡ and TΔs‡, we relate these values to the desorbed ssDNA oligomer fraction. If the amount of adsorbed DNA were to be reduced by 50%, for example, this would correspond to a change in coverage Δθ of ≈ 0.1. The remaining adsorbed ssDNA oligomers would then have twice as much SWNT length available for binding and, following the discussion in the previous section, could be adsorbed with two instead of just one Kuhn segment. The above coverage dependence thus implies that the adsorption of one additional Kuhn segment would be accompanied by an increase of desorption enthalpy from ΔdesH‡0 = 155 kJ·mol−1 to about 240 kJ·mol−1 (a 60% increase) and a change of desorption entropy from TΔdesS‡0 = 58 kJ·mol−1 to 132 kJ· mol−1. Accordingly, the Gibbs energy for desorption would increase modestly from ΔdesG‡0 = 96 kJ·mol−1 to 108 kJ·mol−1. Interestingly, the ≈60% increase of desorption enthalpy for the desorption of ssDNA that has two Kuhn segments interacting with the SWNT surface is consistent with predictions of the tethered dimer model for ΔH ≲ ΔG, equivalent to small or somewhat negative desorption entropies (see Figure 5c). We recall from the last section that the heat of adsorption is assumed to be extensive in oligomer length, i.e., it should increase by 100% when two Kuhn segments are adsorbed. The 60% increase in ΔH‡ is thus attributed to the temperature dependence of rate constants for a multistage oligomer desorption mechanism, such as the one discussed in the last section for the tethered dimer. Desorption of F8T2 from SWNTs in Different Solvents. Changing the length of an oligomer is not the only means to alter its affinity toward adsorption on a substrate. In this section we highlight the role of solvent−polymer interactions for the affinity of a polyfluorene block copolymer toward adsorption on SWNTs by studying desorption in different solvents. More specifically, we use solvents of different polarity to shift the balance of enthalpy and entropy contributions to the Gibbs energy. The affinity of F8T2 toward different solvents, as evidenced by changes in solubility, was here determined from absorbance and photoluminescence spectroscopy of polymersaturated solvents (see Figure 8a,b). The data indicate that F8T2 solubility increases from methylcyclohexane over toluene, ortho-xylene, to chlorbenzene. As expected, F8T2 has a higher affinity toward more polar solvents, presumably due to favorable interactions between the solvent dipole and the polar thiophene units of the polymer. The desorption of F8T2 was investigated in the same way as discussed above for ssDNA, by strong dilution of F8T2-SWNT aliquots in the respective solvent and by monitoring changes in F8T2 PL signals with time at different temperatures. The results of these measurements are reproduced in Table 2 and in Figure 8c. F8T2 desorption in methylcyclohexane suspension was too slow to allow determination of thermodynamic constants. As for the desorption of different ssDNA oligomers in water, we find that the Gibbs energy for F8T2 desorption in different organic solvents is similar for all systems studied here, with an

the length of the individual d(GT)12, d(GT)16, and d(GT)20 oligomers of 13.4, 17.9, and 22.4 nm, respectively (see second column of Table 1). Here we used a phosphate−phosphate Table 1. Summary of Total Oligomer Contour Lengths, lads, Their Relationship with the Total SWNT Length, and the Resulting Contour, Train, and Tail Lengths (GT)n (n =)

lads (m·l−1)

lads (lSWNT)

lcont (nm)

ltrain (nm)

ltail (nm)

12 16 20

3.1 × 10 3.6 × 109 4.6 × 109

2.6 3.0 3.8

13.4 17.9 22.4

5.2 6.0 5.8

8.2 11.9 16.6

9

separation of 0.56 nm.19 A comparison with the measured SWNT concentration and total SWNT length of 1.2 × 109 m· l−1 yields adsorbed ssDNA to SWNT length ratios between 2.6 and 3.8 (third column of Table 1). This estimate is obtained assuming sterically favored single file adsorption of ssDNA.19 The excess length of adsorbed polymer, if compared with the length of SWNTs in the suspension, suggests that only a fraction of the ssDNA oligomer contour is actually adsorbed on the SWNT surface. The length of the adsorbed segment, ltrain, along with contour, lcont, and tail lengths, ltail, are summarized in Table 1. The adsorbed train segment length of the three oligomers is shown in Figure 7b as a function of the nucleotide number. The intercept of a linear fit to this data with the black line representing the oligomer contour length is found at 9 nucleotides, close to the reported Kuhn lengths. This strongly suggests that these ssDNA oligomers, at high coverages, interact with SWNTs only through a fraction of their length corresponding to a Kuhn segment. Figure 7c is a schematic representation of the expected conformation of adsorbed ssDNA. Coverage Dependence of ssDNA Desorption Kinetics. A closer inspection of desorption rates, such as the one shown in Figure 2b, reveals that desorption slows more significantly than expected if the kinetics were described by a simple monoexponential time dependence. Readsorption of ssDNA as a cause can be ruled out because of the extraordinarily small coverage changes and correspondingly negligible bulk ssDNA concentrations. Instead, we attribute the slower decrease of concentrations to a coverage dependence of rate constants, as expected for example if adsorbate−adsorbate interactions lead to a coverage-dependent affinity of ssDNA toward SWNTs. The fit to experimental data was thus made using a linear correction to the coverage dependence of the Gibbs energy according to ⎡ (θ − θ )Δg ‡ ⎤ ⎥ kdes = kdes,0 exp⎢ − 0 ⎢⎣ ⎥⎦ RT

where kdes,0 and θ0 are the rate constant and coverage at the beginning of the experimental run, respectively, where ∂Δ G‡

Δg ‡ ≡ ∂desθ represents the coverage dependence of the Gibbs energy. This is equivalent to rewriting the Gibbs energy of desorption as ΔdesG‡ = ΔdesG0‡ + (θ0 − θ )Δg ‡ = (ΔdesH0‡ − T ΔdesS0‡) + (θ0 − θ )(Δh‡ − T Δs‡) G


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that solvent−polymer interactions are not strong enough to induce considerable rearrangements in the solvation shell and that desorption entropy is thus small. Desorption in a good solvent on the other hand is associated with the most pronounced decrease of entropy, providing evidence that increase of conformational entropy in the free polymer does not outweigh the reduction of entropy by ordering of the solvation shell. This is in strong contrast to ssDNA desorption from SWNTs in water where the increase of conformational entropy in the free polymer appears to dominate other entropic factors.

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CONCLUSIONS We have studied the desorption of ssDNA and F8T2 from (6,5) SWNTs using photoluminescence spectroscopy. Adsorption isotherms and desorption kinetics of ssDNA of varying length from fully covered SWNTs revealed that oligomers are bound to the surface only with a fraction of their length of ≈6 nm, corresponding to a single ssDNA Kuhn segment. Desorption enthalpies and entropies are thus found to be length-independent for oligomers exceeding about 11 nucleotides in length. Gibbs energies were found to be nearly identical for all ssDNA oligomers studied here with ΔdesG‡0 = 96 kJ· mol−1. At lower surface coverages the activation enthalpy for ssDNA desorption is found to increase, consistent with a roughly 60% rise in desorption enthalpy accompanying the binding of a single additional Kuhn segment. This weak scaling of desorption enthalpy with the length of the adsorbed oligomer is attributed to the multistage nature of oligomer desorption and the associated temperature dependence of rate constants. This is supported by calculations using a simple tethered dimer model for the desorption of molecules with subunits, i.e., Kuhn segments, moving more or less independently. We also found that desorption of ssDNA from SWNTs in water is associated with a decrease of order in the system, presumably due to the dominant role of increased conformational freedom in desorbed ssDNA for the overall entropy budget. The situation is different for F8T2 desorption from SWNTs in solvents of small and higher polarity. Here, the entropy decreases during desorption and presents a significant barrier for desorption in the case of more favorable solvent−polymer interactions. Here it appears that entropy changes are dominated by formation of an ordered solvent shell around the free polymer and not by the increase of conformational freedom in the desorbed polymer. The combination of results from desorption kinetics and adsorption isotherms giving ΔadsG ≈ − 27 kJ·mol−1 suggests that the potential energy surface of ssDNA interaction with SWNTs is characterized by a potential energy barrier to adsorption with a height roughly twice the depth of the adsorption well. A graphical summary of the findings for ssDNA interaction with (6,5) SWNTs is shown in Figure 9. The considerable barrier to ssDNA adsorption is consistent with predictions for adsorption of small amphiphilic molecules on SWNTs and can be attributed to strong repulsive Coulomb interactions between adsorbing and adsorbed species.22,52 The results for F8T2 desorption from SWNTs have highlighted the role of favorable solvent−polymer interactions in facilitating efficient SWNT dispersion in organic solvents. The comparison of different solvents shows that the thermodynamic stability of the SWNT−-polymer complex is not adversely affected by good polymer solubility because of

Figure 8. (a) Absorbance and photoluminescence spectra of F8T2 in saturated chlorobenzene (green), ortho-xylene (orange), toluene (blue), and methylcyclohexane solutions for the determination of F8T2 solubility. (b) Graphical summary of the results with the same color code as in panel a. (c) Bar graph of enthalpic and entropic contributions to the Gibbs energy.

Table 2. Summary of Thermodynamic Functions for F8T2 Desorption (in Kilojoules per Mole) solvent

ΔdesH‡

TΔdesS‡

ΔdesG‡

chlorobenzene ortho-xylene toluene

67 ± 4 93 ± 5 95 ± 8

−29 ± 4 −8 ± 5 −8 ± 8

96 ± 8 101 ± 10 103 ± 15

average ΔdesG‡ = (100 ± 11)kJ·mol−1. Enthalpy and entropy contributions on the other hand show clear trends with the largest entropy decrease found for chlorobenzene, the best solvent, which also exhibits the smallest enthalpy increase. Both trends can be interpreted in terms of differences of the polymer affinity toward the different solvents. The poor solubility of F8T2 in toluene provides strong energetic incentives favoring F8T2 interactions with the SWNT surface instead of with the solvent. Poor solubility also implies H


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Figure 9. Graphical summary of the findings for ssDNA interaction with (6,5) SWNTs. (a) Transition from the adsorbed state to the transition state and finally to the desorbed ssDNA. (b) Energetics of the three states drawn to scale. The vertical scale bar corresponds to 50 kJ·mol−1. Enthalpy and Gibbs energy traces are arbitrarily alligned in the adsorbed state for better comparison. Thermodynamic functions in brackets are subject to speculation; all others were obtained from experiments.

enthalpy−entropy compensation and a more pronounced decrease of entropy if polymers are desorbed in a good solvent. The results presented in this work should help guide future developments of new SWNT dispersion protocols in aqueous and organic solvents.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b02198. Description of the tethered dimer model and its kinetic analysis (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 931 3186300. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the DFG through GRK 1221 as well as through an instrumentation grant (INST 93/756-1 FUGG). F.K.B. acknowledges financial support through a scholarship by the Fonds der Chemischen Industrie (FCI).

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Interaction of Polymers with Single-Wall Carbon Nanotubes - The

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