Adsorption of Single Walled Carbon Nanotubes onto Silicon Oxide

Jun 19, 2009 - Liu , J. C. M. J. C., M., Walter , D. A., Boul , P., Lu , W., Rimberg , A. J., Smith , K. A., .... Usrey, Monica L.; Lippmann, Ethan S...
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Adsorption of Single Walled Carbon Nanotubes onto Silicon Oxide Surface Gradients of 3-Aminopropyltri(ethoxysilane) Described by Polymer Adsorption Theory Monica L. Usrey and Michael S. Strano* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received March 27, 2009. Revised Manuscript Received May 13, 2009 Integration of single-walled carbon nanotubes (SWNT) into complex sensing and electronic devices can necessitate the selective placement of individual nanotubes from solution onto custom-prepared surfaces. Existing studies indicate carbon nanotube adsorption can be controlled by creating hydrophilic and/or hydrophobic surfaces, depending on the nanotube surface chemistry and solvent. Various recipes exist for specific conditions, but no quantitative theoretical model describing experimental observations has been developed. This work examines the adsorption behavior of SWNT functionalized with aryl hydroxyl (OH-SWNT) or aryl carboxylic acid groups (COOH-SWNT) onto 3-aminopropyltri (ethoxysilane) (APTES) concentration gradients on SiO2 wafers. For the first time, self-consistent field polymer adsorption theory is utilized to quantitatively describe SWNT adsorption onto planar surfaces. Experimental results indicate SWNT adsorption strongly depends on three key factors: concentration of APTES molecules on the silicon oxide and the type and number of SWNT functional groups. In general, COOH-SWNT adsorb to the greatest extent, followed by OH-SWNT and P2-SWNT. The data show a distinct threshold phenomenon, with appreciable adsorption detected only when the APTES concentration exceeded 2.6  1014 molecules/cm2.

Introduction Advanced device applications, including nanoelectronics and chemical or biological sensors, utilizing carbon nanotubes can require control over the location and orientation of carbon nanotube patterns over large areas. Previous methods for achieving this include capillary force-driven assembly,1 aligned growth on miscut crystalline surfaces,2 electric-field induced alignment,3,4 flow cell techniques,5 and directed growth on patterned catalysts.6,7 Although success has been found with these methods, maintaining precise control over large areas has proven difficult. Directed assembly processes based on the interaction between carbon nanotubes and self-assembled monolayer (SAM) patterns *The author to whom all correspondence should be addressed. Fax: (617) 258-8224; e-mail: [email protected]. (1) Wang, Y. H.; Maspoch, D.; Zou, S. L.; Schatz, G. C.; Smalley, R. E.; Mirkin, C. A. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 2026. (2) Kocabas, C.; Hur, S. H.; Gaur, A.; Meitl, M. A.; Shim, M.; Rogers, J. A. Small 2005, 1, 1110. (3) Krupke, R.; Hennrich, F.; von Lohneysen, H.; Kappes, M. M. Science 2003, 301, 344. (4) McLean, R. S.; Huang, X. Y.; Khripin, C.; Jagota, A.; Zheng, M. Nano Lett. 2006, 6, 55. (5) Huang, Y.; Duan, X. F.; Wei, Q. Q.; Lieber, C. M. Science 2001, 291, 630. (6) Fan, S. S.; Chapline, M. G.; Franklin, N. R.; Tombler, T. W.; Cassell, A. M.; Dai, H. J. Science 1999, 283, 512. (7) Kong, J.; Soh, H. T.; Cassell, A. M.; Quate, C. F.; Dai, H. J. Nature 1998, 395, 878. (8) Choi, K. H. B. J. P. A., S.; Esteve, D.; Duesberg, G.; Roth, S.; Burghard, M. Surf. Sci. 2000, 462, 195. (9) McGill, S. A.; Rao, S. G.; Manandhar, P.; Xiong, P.; Hong, S. Appl. Phys. Lett. 2006, 89. (10) Im, J.; Kang, J.; Lee, M.; Kim, B.; Hong, S. J. Phys. Chem. B 2006, 110, 12839. (11) Krupke, R.; Malik, S.; Weber, H. B.; Hampe, O.; Kappes, M. M.; von Lohneysen, H. Nano Lett. 2002, 2, 1161. (12) Oh, S. J.; Cheng, Y.; Zhang, J.; Shimoda, H.; Zhou, O. Appl. Phys. Lett. 2003, 82, 2521. (13) Zhang, Y. G.; Chang, A. L.; Cao, J.; Wang, Q.; Kim, W.; Li, Y. M.; Morris, N.; Yenilmez, E.; Kong, J.; Dai, H. J. Appl. Phys. Lett. 2001, 79, 3155. (14) Liu, J. C. M. J. C., M.; Walter, D. A.; Boul, P.; Lu, W.; Rimberg, A. J.; Smith, K. A.; Colbert, D. T.; Smalley, R. E. Chem. Phys. Lett. 1999, 303, 125.

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on surfaces provide a possible solution.2,5,8-17 Research has found that carbon nanotube surface adsorption can be controlled by covalent and/or noncovalent modification of either nanotube or surface. In general, carbon nanotubes prefer to adsorb onto hydrophilic over hydrophobic surfaces.10,16 Specifically, hydrophobic SAM patterns (methyl-terminated) have been prepared to block adsorption of double-walled carbon nanotubes (DWNT) suspended in organic solvent for back gate resistor applications. Preferential deposition of DWNT on gold, silicon dioxide, and hydrophilic SAM-treated patterns was observed when compared to hydrophobic SAM-treated surfaces.10 Most commonly, hydrophilic surfaces are used as SWNT-attractive surfaces, while hydrophobic surfaces repel SWNT. The nature of the SWNT chemistry can also be a factor. For example, multiwalled carbon nanotubes (MWNT) reacted with octadecylester displayed selective affinity for hydrogen-terminated silicon over silicon dioxide.17 In this application, the hydrophobic surface chemistry was designed to be attracted to the nonpolar hydrogen terminated surface. The majority of previous studies seek to identify a particular surface chemistry and nanotube complex that result in selective placement for one set of conditions. To date, no systematic study has taken place with the goal of quantitatively describing why carbon nanotubes adsorb onto certain functionalized surfaces on a theoretical basis. This work aims to link adsorption behavior for aryl hydroxyl and aryl carboxyl functionalized SWNT onto APTES gradients to predictions made by modified polymer adsorption theory. Separate studies consider more complex systems, such as SWNT samples with both covalent and noncovalent functionalization.18 The ability to quantitatively predict (15) Burgin, T. P.; Lewenstein, J. C.; Werho, D. Langmuir 2005, 21, 6596. (16) Valentin, E.; Auvray, S.; Goethals, J.; Lewenstein, J.; Capes, L.; Filoramo, A.; Ribayrol, A.; Tsui, R.; Bourgoin, J. P.; Patillon, J. N. Microelectron. Eng. 2002, 61-2, 491. (17) Widenkvist, E.; Li, J. X.; Jansson, U.; Grennberg, H. Carbon 2007, 45, 2732. (18) Usrey, M. L., Strano, M. S. J. Phys. Chem. C 2009, accepted.

Published on Web 06/19/2009

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the adsorption of rod-like nanoparticles based upon the chemistry of both particle and surface may enable precise control of this process and allow rational design of CNT complexes and/or functionalized surfaces.

Experimental Methods In Situ Covalent Functionalization with Diazonium Salts. P2-SWNT (Carbon Solutions, Inc.) are carbon nanotubes produced via electric arc discharge and purified by oxidation to remove catalyst without appreciable functionalization. P2-SWNT were suspended in 1,2-orthodichlorobenzene (0.267 mg/mL) via bath sonication in a sealed flask for 1 h. The in situ reaction, where the reactive diazonium salt is synthesized from an aryl aniline using isoamyl nitrite directly in the carbon nanotubes solution, was carried out according to a published protocol.19 The aniline compounds used were 4-aminobenzoic acid for reaction with the aryl carboxlic acid group (COOH-SWNT) and 4-aminophenol for the aryl hydroxyl group (OH-SWNT). The extent of reaction was controlled by the ratio of moles aniline added per mole of carbon with a constant excess of isoamyl nitrite. For the OH-SWNT reaction, 4-aminophenol (0.2246 g) and isoamyl nitrite (2.938 mmol) was used. For the COOH-SWNT reaction, 4-aminobenzoic acid (0.1571 g) and isoamyl nitrite (1.763 mmol) was used. The extent of reaction was determined using Raman spectroscopy (785 nm excitation). An established correlation allows the calculation of extent of functionalization (# of functional groups per 100 carbon atoms) based upon the normalized D/G ratio from Raman analysis.20 The OH-SWNT and COOH-SWNT contain 7.9% and 3.0%, functionalization, respectively. APTES Surface Chemistry Gradient. Silicon oxide wafers (100 A˚ SiO2/Si) were cleaned using the well-established SC1/SC2 technique. This two step cleaning process removes organic and metal contaminants and leaves the surface saturated in silanol groups (SiOH).21 The SC1 cleaning solution is prepared with a 5:1:1 volume ratio of deionized water, hydrogen peroxide (30%) and ammonium hydroxide (29%). The SC2 cleaning solution is prepared with a 4:1:1 volume ratio of deionized water, hydrogen peroxide (30%), and hydrochloric acid (10N) were used. Contact angle goniometry measurements conducted on silicon oxide wafers following a 5 min SC1/SC2 clean showed a contact angle of 15-20 indicating successful formation of a hydrophilic surface of silanol groups. Note that this procedure involves the use of strong acids and/or bases. Extreme safety precautions should be taken. The SC1 and SC2 cleaning solutions were prepared and used in separate fume hoods. For the vapor deposition, a 50:50 mixture by volume of APTES and paraffin oil is placed into a reservoir in a Petri dish. APTES (3aminopropyltri(ethoxysilane)) was purchased from Sigma Aldrich and was used as received. A clean wafer (1 cm x 5 cm) is placed with the 1 cm edge against the reservoir and is sealed for 330 min. Following deposition, the wafer is rinsed with water and dried with nitrogen. The gradient in surface concentration is controlled by diffusion of the APTES molecules. For the liquid deposition, a clean silicon wafer (1 cm x 5 cm) is immersed into an APTES/water solution at 5 step gradients (1 cm each). After deposition, the wafer is rinsed with deionized water and dried with nitrogen. The gradient in surface coverage is created by increasing soak time (5 step gradient) and varying APTES concentration (1, 10, 100 mM). Two time step gradients were prepared: 0s/15s/45s/105s/285s (step1) with all three APTES concentrations and 0s/1s/2s/5s/10s (step 2) with 1 mM APTES. Characterization of APTES Gradient. X-ray photoelectron spectroscopy (XPS) was utilized to determine the elemental composition (Si, O, N) of the APTES-treated surfaces. No (19) Bahr, J. L.; Tour, J. M. Chem. Mater. 2001, 13, 3823. (20) Usrey, M. L.; Lippmann, E. S.; Strano, M. S. J. Am. Chem. Soc. 2005, 127, 16129. (21) Aswal, D. K.; Lenfant, S.; Guerin, D.; Yakhmi, J. V.; Vuillaume, D. Anal. Chim. Acta 2006, 568, 84.

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Article nitrogen source other than APTES is present; therefore, the atomic concentration of nitrogen was assumed to represent the concentration of APTES. The N and Si peak areas were utilized to calculate an APTES surface concentration (see Supporting Information). Ellipsometry was conducted on the 10 and 100 mM liquid deposition gradients. The sample was modeled as 1 mm silicon with two layers: a 117.67 A˚ SiO2 layer (exact thickness measured via a standard) and a Cauchy layer of unknown thickness to represent the APTES layer. SWNT Deposition. Aqueous solutions of the P2-SWNT control and reactions (∼50 mg/L) were prepared via probe tip sonication (15W, 20 min) at pH 9. HiPco SWNT (Rice University) were suspended in water with sodium dodecyl sulfate (SDS) via a published protocol22 as an additional unreacted control (SDSSWNT). All samples were stable in solution for several days (data not shown). Immediately following the APTES deposition, each wafer soaked in SWNT solution (20 mL) for 60 min. Previous experiments (data not shown) indicate that deposition saturates at >45 min. Following deposition, samples were rinsed with water and dried with nitrogen. Characterization of SWNT Deposition. Atomic Force Microscopy (AFM) was collected in tapping mode on the silicon oxide wafers following SWNT deposition using a Dimension 3100 (Digital Instruments). Three images (10  10 μm) were taken per step gradient at 512  512 resolution. A custom-made Matlab program was utilized to quantify SWNT deposition.23 The program filtered noise, identified rodlike shapes, and presented an image showing the location of the nanotubes. If accurate, the number of SWNT deposited as well as the corresponding length and diameter distributions was calculated. This allowed the quantitative analysis of visual AFM data. If the surface contained sufficient debris or the program encountered an error, a manual count was conducted. Before a direct comparison between model and experiment was made, the experimental data was converted from the nanotube distribution (output from the custom Matlab program) to mass adsorbed per unit area (Γ, g/cm2) as described in Supporting Information.

Results The systematic variation of experimental parameters was used to determine the effect of SWNT chemistry (none, aryl-COOH, or aryl-OH) and silicon oxide surface chemistry (APTES concentration) on SWNT adsorption behavior. Creating a reproducible APTES concentration step gradient on a SiO2 wafer allowed the simultaneous exposure of a SWNT sample to five distinct surface chemistries with a single experiment. In this work, vapor diffusion and gradual liquid immersion formation methods are compared to identify which technique provides the optimal APTES gradient. Figure 1 summarizes the APTES concentration profiles determined from XPS for the vapor and liquid deposition methods. For the 3 min vapor deposition (Figure 1a), the highest concentration (1.5  1014 molecules/cm2) occurs closest to the reservoir and stabilizes beyond 3 cm (200 CNTs). OH-SWNT deposition also follows the gradient, but decreases following saturation (above 105s). Similar qualitative trends were observed for COOH-SWNT and OH-SWNT exposed to 1 mM (step 1, step 2) and 10 mM (step 1) gradients, despite quantitative differences (see Supporting Information). In all, each reaction was tested against 20 distinct surface chemistry environments. Simple comparison of the number of SWNT deposited is not accurate due to the polydispersity of carbon nanotube samples in both length and diameter. To facilitate a suitable analysis, the SWNT count was converted to a total adsorbed mass using the length and diameter information provided by the Matlab program. Figure 4 compares all experimental mass adsorbed data (Γexp) for the COOH-SWNT and OH-SWNT samples with the corresponding APTES concentration. Both SWNT reactions show similar behavior: little to no deposition below 2.8  1014 APTES/cm2, a sudden increase to Langmuir 2009, 25(17), 9922–9930

maximum deposition near 3.0  1014 APTES/cm2, and reduced deposition above 5.0  1014 APTES/cm2. Reduced deposition at high APTES concentration suggests a decreased driving force for deposition above 3.5  1014 APTES/cm2. Overall, higher adsorption is achieved for the COOH-SWNT compared to the OHSWNT for all APTES concentrations. This agrees with qualitative AFM data presented in Figure 3. Model Development. A statistical mechanics self-consistent field model adapted for homopolymer adsorption from a two component solution onto a planar surface was utilized.27 In this theory, polymers are chains of continuously distributed segments as opposed to occupying specific lattice points. Lattice models require a monomer segment and solvent molecule to have the same molar volume. A continuous distribution includes polymer stiffness by allowing larger monomer segments for more rigid polymers. The model describes the polymer/solvent/surface system using 8 model parameters to calculate the mass of polymer absorbed per unit area (Γ, g/cm2). These parameters can be divided into three groups: experimental conditions, model parameters, and thermodynamic parameters. Experimental conditions include the system temperature (T, K), polymer molar volume (Vp, cm3/mol), solvent molar volume (VS, cm3/mol), and polymer bulk volume fraction (φbp, unitless). Model parameters are the statistical length of the polymer unit (l , cm) and number of units in the polymer chain (ZP, unitless). The thermodynamic parameters are the FloryHuggins interaction parameter (χ, unitless) and the relative surface adsorption energy (χS, unitless). The model contains three calculation steps: determination of the polymer surface coverage (φ0, unitless), calculation of the polymer volume fraction profile (φp(z), unitless), and prediction of mass of polymer absorbed (Γ, g/cm2). Complete derivation of these equations has been outlined previously.27 (27) Ploehn, H. Colloids and Surfaces a-Physicochemical and Engineering Aspects 1994, 86, 25.

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Figure 3. Representative AFM image and quantitative analysis of (a) P2-SWNT, (b) COOH-SWNT, and (c) OH-SWNT aqueous solutions exposed to 100 mM APTES/water gradient. Inset images show structure of functional groups. These images show that COOH-SWNT adsorb to a greater extent than OH-SWNT or unfunctionalized SWNT. Also, the debris level of these samples, due to lack of centrifugation is clearly shown.

The first step is to calculate the surface coverage (φ0), defined as the volume fraction of polymer at the surface (z=0), using 1. This equation balances the net energy gained from polymer adsorption (1st term) with the energy preserved by maintaining the polymer in solution (2nd term). φ0 χ2S -6Fðφ0 Þ ¼ 0

ð1Þ

The relative adsorption energy (χS) represents the actual driving force for polymer adsorption to a surface. It is defined as the energy change, per segment of polymer, resulting from the adsorption of a polymer segment instead of a solvent molecule, as shown in 2. This represents the enthalpic change of the system in terms of adsorption energies (U) for the solvent (A) and polymer (B). ðUA -UB Þ ð2Þ χS ¼ kT This definition does not include entropic effects, which are assumed to be negligible. In most cases, χS is not well understood 9926 DOI: 10.1021/la901078u

or capable of being determined. It can be left as an arbitrary parameter or estimated from limited experimental χS measurements.27 The function F(φ0) is determined using 3 where the free energy of mixing is calculated 1 ½ -φP ln φP þ φbP ln φbP þ φP þ φbP  ð3Þ Fðφ0 Þ ¼ VP Δa þ ZP from the Flory-Huggins equation of state (4). ! " ! φP φP VP φS VP Δa ¼ þ ln b þ φ ln b ZP VS S φP φP #   VS b b 2 ðφP -φP Þ -χððφP -φP Þ Þ þ 1VP ZP

ð4Þ

In these equations, φP represents the polymer volume fraction profile with respect to distance from the surface (z). Therefore, φ0 is substituted for φP in both equations to calculate the surface coverage (z=0). Langmuir 2009, 25(17), 9922–9930

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Supporting Information); therefore assumption of a constant 50 mg/L concentration is validated. All experiments were conducted at ambient conditions, therefore 298 K (25 C) is assumed. The polymer modeling parameters describe how the polymer chain is divided into segments for analysis. The number of segments per polymer chain (ZP) and the length of the statistical segment (l ) are not independent. The model requires the extended contour length and radii of gyration of the actual polymer and the model chain to be equal. These requirements fix the number of segments per chain (ZP) as well as the segment length (l ) with 7 and 8.

Figure 4. Experimental mass adsorbed per cm2 for surfactant-free SWNT samples: (a) COOH-SWNT (∼3.0 per 100C) and (b) OHSWNT (∼7.9 per 100C). Values were calculated based on the (10,10) nanotube. Both samples show maximum surface adsorption at 3.0-3.5 x1014 APTES molecules per cm2.

The second step in this model is to calculate the full polymer volume fraction profile, φP(z) given the surface coverage, from 5. This equation gives the polymer volume fraction as an implicit function of the distance from the surface (z).27 Z z ¼

φP φ0

dφP ½24φP FðφP Þ0:5

VP

R¥ 0

MM l ½φP ðzÞ -φbP dz

ð6Þ

The model’s output is typically presented as mass adsorbed (Γ, g/cm2) as a function of χS (relative surface adsorption energy, unitless). Determination of Model Parameters. The experimental parameters describe the actual SWNT and solvent molecules under investigation and specify other experimental conditions. The molar volume of the solvent (VS, cm3/mol) is calculated from the density and molecular weight of the solvent. For water, the value is 18 cm3/mol. The concentration of nanotubes in the bulk solution (φbP) is assumed to be 50 mg/L based on UV-vis-nIR photoabsorption spectroscopy. The SWNT volume fraction does not have a significant effect on the final modeling results (see Langmuir 2009, 25(17), 9922–9930

ð7Þ

ZP l 2 ¼ C¥ nb l 2b

ð8Þ

In these equations, l b is the average length per backbone bond and nb is the number of bonds per polymer chain. C¥ is the characteristic ratio, a measure of polymer stiffness which is dependent on the polymer/solvent pair. For a freely jointed chain, C¥ equals 1. Polystyrene and cellulose fiber exhibit C¥ values of 9.5 and ∼100, respectively. Since carbon nanotubes are not truly polymers, there is no “backbone” bond. For this work, the nanotube was considered as 1000 (nb) segments of 1 nm (l b) each. Therefore, only C¥ is required to determine both ZP and l , as shown in eqs 9 and 10. l ¼ C¥ l b

ð9Þ

nb C¥

ð10Þ

ZP ¼

The characteristic ratio is calculated from the mean-squared end-to-end distance, Ær2æ0, as shown in eq 11. 2

ð5Þ

Polymer adsorption models assume all polymer molecules that segregate near the surface will deposit. Therefore, an accurate estimate of the volume fraction profile is crucial to the final solution. The mass absorbed per unit area (Γ) is calculated from 6 where the integral represents the dimensionless absorbance; a unitless value that is used to compare data sets regardless of the individual polymers’ molecular weights and/or molar volumes. Γ ¼

ZP l ¼ n b l b

C¥ ¼

Ær2 æ0 nb l b

ð11Þ

The mean-squared end-to-end distance can also be related to the radius of gyration, Rg, as shown in eq 12. Rg ¼

Ær2 æ0 6

ð12Þ

For a rigid rod, the radius of gyration is equal to L/12.28 Therefore, for a 1000 nm nanotube, Rg equals 83.3 nm and Ær2æ0 is 4.17  104 nm2. Substitution into 11 yields a characteristic ratio of 41.7 for carbon nanotubes. This indicates that carbon nanotubes are more rigid than polystyrene and more flexible than cellulose fibers, which is reasonable. The monomer molecular weight (MM) is determined from 13 where b is the number of bonds per monomer unit. For this case, each 1 nm unit is considered a nanotube monomer, therefore b equals 1. MM ¼

bMP ZP C¥

ð13Þ

The molar volume of the polymer (VP) is calculated on a monomer basis, as shown in 14, where mPo is the mass density of (28) Rieger, J. Polym. Bull. 1993, 30, 617.

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the polymer in the pure state. For functionalized SWNT, the additional molecular weight and volume due to the functional groups were added via group additivity theory, as outlined in the Supporting Information.29 VP ¼

MM moP

ð14Þ

The Flory-Huggins interaction parameter (χ) is defined as the energetic barrier for polymer/solvent mixing. In general, a small positive or any negative value of χ indicates a favorable enthalpic driving force for polymer and solvent mixing.30 From a surface deposition perspective, a positive value of χ indicates that enthalpic interactions favor adsorption as separation of polymer from the solvent is promoted.27 Existing models cannot predict the Flory-Huggins interaction parameters (χ) of SDS-SWNT, OH-SWNT, or COOH-SWNT in aqueous solutions. Previous experimental attempts have been limited to predicting enthalpic contributions to χ for unfunctionalized carbon nanotubes in N-methyl-pyrrolidone using static light scattering (SLS).31 To facilitate modeling of the functionalized carbon nanotube systems, χ values of 0.1, 0.2, 0.3, and 0.4 were compared. Use of the Flory-Huggins interaction parameter requires the assumption of thermodynamic equilibrium which is supported by the temporal stability of the SWNT solutions.32 The relative adsorption energy (χS), as shown in 2, is difficult to estimate via simulation or determine experimentally.27 However, for a given set of conditions the range of relevant χS values can be found.

Modeling and Discussion Determining the Sensitivity of the Model to Key Parameters. The model requires 8 parameters for a predictive solution, of which only 3 parameters are unknown for carbon nanotube systems: the characteristic ratio (C¥), the Flory-Huggins interaction parameter (χ), and the relative surface adsorption energy (χS). As mentioned above, the model provides the range of χS values relevant for each sample. Therefore, it is important to determine the sensitivity of the model output (Γ vs χS) to the characteristic ratio and Flory-Huggins interaction parameter. Figure 5 shows the predicted Γ versus χS trends for unreacted SDS-SWNT samples with C¥ values of 1.0 (freely jointed chain), 9.5 (polystyrene), and 41.7 (carbon nanotube) and χ values of 0.1, 0.2, and 0.3. Interestingly, the characteristic ratio has a greater effect on the predicted adsorption trend than the Flory-Huggins interaction parameter. As C¥ increases from 1.0 to 41.7, the initial portion of the curve flattens considerably until a critical energy is reached. This shows that as polymer stiffness increases, greater adsorption energy is required for deposition. From an entropic standpoint, surface adsorption becomes more cumbersome as flexibility decreases and additional enthalpy is required to overcome the entropic loss. The slope of the adsorption curve above critical χS also increases with characteristic ratio which reflects that more mass is deposited with each segment for a stiffer polymer. Overall, the C¥ = 41.7 trend qualitatively reflects experimental data for the deposition of carbon nanotubes from solution. (29) Ammon, H. L.; Mitchell, S. Propellants, Explosives, Pyrotechnics 1998, 23, 260. (30) Jones, R. A. L. R., R.W. Polymers at Surfaces and Interfaces; Cambridge University Press, 1999. (31) Bergin, S. D.; Nicolosi, V.; Streich, P. V.; Giordani, S.; Sun, Z. Y.; Windle, A. H.; Ryan, P.; Niraj, N. P. P.; Wang, Z. T. T.; Carpenter, L.; Blau, W. J.; Boland, J. J.; Hamilton, J. P.; Coleman, J. N. Adv. Mater. 2008, 20, 1876. (32) Usrey, M. L., Chaffee, A., Jeng, E. S., Strano, M. J. Phys. Chem. C 2009, 113, 9532-9540.

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Figure 5. Predicted surface adsorption trend (Γ vs χS) for ControlSDS assuming l b = 1.0 nm and nb = 1000. Three characteristic ratios are considered: (a) 1 - freely jointed chain, (b) 9.5 polystyrene, and (c) 41.7 - rigid rod CNT. For each, three χ values are examined: 0.1, 0.2, and 0.3.

Carbon nanotubes will not deposit onto SiO2 surfaces without any surface functionalization or at lower APTES concentrations, as shown in Figure 2. This behavior mirrors the initial trend in Figure 5c of no deposition at low χS values. The effect of the Flory-Huggins interaction parameter is less prominent. Increasing χ from 0.1 to 0.3 does not change the overall mass adsorption trend or shift the critical χS value. However, it increases the slope of the mass adsorption curve above the critical energy. χ is a direct measure of polymer solution stability and lower values indicate a more thermodynamically stable solution. Therefore, for the same relative adsorption energy, more polymer will deposit for solutions with greater χ values (i.e., more thermodynamically unstable). The sensitivity study concludes that the predicted Γ vs χS trend is highly dependent on polymer stiffness (C¥) and slightly dependent on the thermodynamic stability of the solution (χ). For all SWNT samples examined with this model, a characteristic ratio of 41.7 is utilized and the Flory-Huggins parameter is varied between 0.1 and 0.4. Comparing Model and Experiment. The model provides predictions for mass adsorbed (Γ) as a function of relative adsorption energy (χS) given an estimate for the Flory-Huggins interaction parameter (χ). Experiments produce calculated mass Langmuir 2009, 25(17), 9922–9930

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Figure 6. Predicted Γ vs χS trend for COOH-SWNT (a,b) and OH-SWNT (c,d) as a function of Flory-Huggins interaction parameter: χ = 0.1 (red squares), χ = 0.2 (blue circles), χ = 0.3 (brown diamonds), χ = 0.4 (green triangles). Maximum, average, and minimum experimental mass adsorption data include to define experimentally relevant χS region. (a,c) Full predicted range and (b,d) Zoom region near critical χS.

adsorbed (Γexp) values as a function of APTES concentration. The model is limited by the inability to predict specific χS values for experimental APTES concentrations. Instead, the relevant χS range is identified using the maximum and minimum Γexp for each reaction and the model predicts the χS vs APTES concentration relationship. In summary, the model/experiment comparison consists of 6 steps: 1 Model parameters estimated for a given SWNT sample. 2 Mass adsorbed (Γ) versus relative adsorption energy (χS) predicted. 3 Maximum and minimum experimental Γ values used to identify relevant χS range. 4 Trendline(s) fitted to model curve (Γ vs χS). 5 Predicted χS values calculated for experimental Γ data. 6 Predicted χS values compared to experimental APTES concentration. For comparison to the model, all data for each SWNT sample are displayed together to represent the overall trend, as shown in Figure 4. Figure 6 shows the predicted model curves (Γ vs χS) for the COOH-SWNT (a,b) and OH-SWNT (c,d) samples. Minimum, average, and maximum Γexp values are included to identify the region of the model trend relevant to the experimental conditions. Similar to the unreacted SDS-SWNT relationship (Figure 5c), no significant adsorption is expected until a critical surface adsorption energy is reached. Once the critical point (χS ∼ 1.6) is reached, predicted mass adsorption increases rapidly, as shown in Figure 6b and 6d. As expected, the slope increases with the Flory-Huggins interaction parameter (χ = 0.1-0.4) as a less stable solution (higher χ) promotes surface adsorption. Comparison of model and experimental data requires the calculation of predicted χS values for each experimental Γ data point. Each predicted mass adsorption trend (Γ vs χS) is divided into 4 regions and fit with an appropriate trend line (see Supporting Information). Figure 7 compares experimental SWNT mass adsorbed data with predicted χS values as a function of χ. The Γexp vs χS trend mirrors the model curves shown in Figure 6. From the range of experimental data (COOHSWNT∼4.0  10-8 g/cm2, OH SWNT∼1.0  10-8 g/cm2), an Langmuir 2009, 25(17), 9922–9930

Figure 7. Comparison of model predictions with experimental data. Experimental mass adsorbed values versus χS predictions for (a) COOH-SWNT and (b) OH-SWNT as a function of FloryHuggins interaction parameter (χ = 0.1, 0.2, 0.3, and 0.4).

estimate of the Flory-Huggins interaction parameter can be made. No previous literature has shown appreciable polymer deposition at adsorption energies greater than 2.0.27 Therefore, χ = 0.3 or χ = 0.4 is an acceptable approximation for both COOHSWNT and OH-SWNT samples. To facilitate comparison, the COOH-SWNT and OH-SWNT data for χ = 0.3 and χ = 0.4 are summarized in Figure 8. Comparing the experimental Γ vs APTES concentration trends (Figure 4) to the experimental Γ vs χS predictions (Figure 8) clearly shows dissimilar behavior. Both curves show that there is DOI: 10.1021/la901078u

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Figure 8. Experimental mass adsorbed values versus χS predictions for COOH-SWNT and OH-SWNT for (a) χ = 0.3 and (b) χ = 0.4. Predicted χS values versus APTES concentrations for COOH-SWNT andOH-SWNT for (c) χ = 0.3 and (d) χ = 0.4.

no surface adsorption at low APTES concentration (low χS), but catastrophic adsorption occurs suddenly above a critical value. This critical value is independent of nanotube chemistry. This similarity supports the theory that the inherent stiffness of the nanotubes increases the energetic driving force required for deposition. χS describes the energy, with respect to kT, required to offset the entropic penalty that accompanies the adsorption process. The curves do not behave similarly after crossing above the critical value into the adsorption region. While the experimental data shows maximum adsorption near 3.0  1014 APTES/cm2 followed by either saturation or a slight decrease above 5.0  1014 APTES/cm2, the predicted χS relationship shows an abrupt increase that does not decline. Therefore, the relationship between χS and APTES concentration is not simply monotonic. Increasing the number of APTES groups on the SiO2 surface does not necessarily result in increasing SWNT deposition as it does not automatically increase the energy gained per adsorption event. Figure 8 also shows the relationship between predicted χS values and APTES surface concentrations for the COOH-SWNT and OH-SWNT samples. For clarity, data taken from step gradients with the same APTES concentration have been averaged for both χ = 0.3 and χ = 0.4. As predicted by the model, an initial region exists where low APTES concentration results in low χS and there is no significant adsorption. Then, at a critical APTES concentration (∼1.0  1014 per cm2), χS predictions increase sharply and saturate at surface concentrations above 2.5  1014 APTES/cm2. Both the OH-SWNT and COOH-SWNT exhibit similar behavior; the major difference between the samples is the range of the χS values accessible to each chemistry. Recall that the extents of functionalization are 7.9% and 3.0% for the OH-SWNT and COOH-SWNT, respectively. Despite having over 2x the number of functional groups, the OH-SWNT adsorption process does not provide as much energy as the COOHSWNT adsorption process. The greater deposition of COOHSWNT above critical adsorption clearly demonstrates how slight increases in χS can dramatically affect surface deposition. 9930 DOI: 10.1021/la901078u

Conclusion APTES (3-aminopropyltriethoxysilane) concentration gradients were created on SiO2 surfaces using a controlled liquid immersion technique. Exposure of these gradients to aqueous solutions of unreacted P2-SNWT, COOH-SWNT and OH-SWNT demonstrates the control of SWNT deposition with both SWNT and SiO2 functionalization. SWNT deposition increased with increasing APTES concentration and overall levels were greater for nanotubes with aryl carboxylic acid groups than aryl hydroxyl groups. Experimental mass adsorption data, collected using AFM, were compared to predicted behavior from a self-consistent field theory model for polymer adsorption. The model’s output is mass adsorbed per unit area (Γ) as a function of surface adsorption energy (χS). Adsorption behavior is primarily controlled by polymer stiffness (C¥) and the thermodynamic solution stability (χ). Neither of these variables changes significantly with SWNT functionalization; therefore, different SWNT surface groups do not dramatically affect this trend. Instead, the functional group controls the adsorption energy region occupied by a particular sample. Thus, covalent SWNT functionalization affects surface adsorption behavior by changing the χS vs APTES concentration relationship. Future studies will focus on increasing the model’s accuracy by developing robust predictions for χ and χS. Predicting χS will require a greater understanding of the specific surface composition and/or structure using angle-resolved techniques such as Auger spectroscopy or XPS. Estimating the Flory-Huggins interaction parameter for SWNT complexes using static light scattering (SLS) and/or zeta potential measurements will be investigated. Also, more complex SWNT systems with both covalent and noncovalent functionalization will be examined using the APTES gradient experimental protocol. Supporting Information Available: Quantitative Analysis of XPS Data, Preparation of Experimental Data for Model Comparison, Sensitivity of the Model to Nanotube Solution Concentration. This material is available free of charge via the Internet at http://pubs.acs.org.

Langmuir 2009, 25(17), 9922–9930