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Understanding the Surfaces of Nanodiamonds Jeffrey Thomas Paci, Han Bin Man, Biswajit Saha, Dean Ho, and George C. Schatz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp404311a • Publication Date (Web): 18 Jul 2013 Downloaded from http://pubs.acs.org on July 19, 2013

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The Journal of Physical Chemistry

Understanding the Surfaces of Nanodiamonds Jeffrey T. Paci,∗,† Han B. Man,‡ Biswajit Saha,¶ Dean Ho,§ and George C. Schatz∗,¶ Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA, and Department of Chemistry, University of Victoria, P.O. Box 3065, Victoria, British Columbia, Canada V8W 3V6, Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA, Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA, and Division of Oral Biology and Medicine, Division of Advanced Prosthodontics, The Jane and Jerry Weintraub Center for Reconstructive Biotechnology, UCLA School of Dentistry, UCLA Department of Bioengineering, Jonsson Comprehensive Cancer Center, California NanoSystems Institute, Los Angeles, California, 90095, USA E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA, and Department of Chemistry, University of Victoria, P.O. Box 3065, Victoria, British Columbia, Canada V8W 3V6 ‡ Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA ¶ Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA § Division of Oral Biology and Medicine, Division of Advanced Prosthodontics, The Jane and Jerry Weintraub Center for Reconstructive Biotechnology, UCLA School of Dentistry, UCLA Department of Bioengineering, Jonsson Comprehensive Cancer Center, California NanoSystems Institute, Los Angeles, California, 90095, USA † Department

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Abstract Functional groups and their associated charges are responsible for the binding and release of molecules from the surfaces of particles in nanodiamond colloids. We describe a combined set of experimental and computational techniques that are used to characterize these functional groups quantitatively. The surfaces of the particles examined during this study are amphoteric, as one would expect for surfaces made of carbon, with high concentrations of phenols, pyrones, and sulfonic acid groups; the average 50 nm diameter nanodiamond aggregate has approximately 22000 phenols, 7000 pyrones, and 9000 sulfonic acids. The aggregates also have at least 2000 fixed positive charges, stabilized within pyrones and/or chromenes. No evidence for a significant concentration of carboxylic acid groups was found, although some are probably present. There are hydroxyl and epoxide groups on some areas of the surfaces. The surfaces are graphitized, so the presence of phenols and pyrones is not surprising because they are common on graphitic surfaces. The sulfonic acid is due to the sulfuric acid treatment used to remove amorphous carbon and graphite during particle cleaning. The fixed charges are also due to the cleaning procedure that includes the use of KMnO4 with the sulfuric acid. Based on titration and zeta potential experiments, elemental and particle size analyses, and modeling using semiempirical quantum mechanics, a model is proposed for the types and concentrations of surface groups. The modeling shows how functional groups form during the bead milling and cleaning used in the preparation of the colloid. It also shows that the pKa associated with the phenols and pyrones that are formed (pKa = 7.6 to 10.0) is consistent with that predicted using titration experiments (pKa ≥ 7.3). The positive surface potential means that the latter pKa is significantly larger than a Henderson-Hasselbalch-based estimate. The model is shown to be useful in explaining a number of recent experiments in which nanodiamonds were used to bind and release therapeutic drug and polymer molecules. key words: nanodiamond, surface chemistry, graphitization, drug delivery, colloid.


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Introduction Nanodiamonds have become a material of interest for use in a number of applications, including therapeutic drug and gene delivery. 1–6 The surfaces of the material and especially their functionalization are of fundamental importance, as they provide platforms for drug or gene binding, and are what needs to be influenced for controlled release. 1,3,7 A variety of types of nanodiamond are now available which are produced using different detonation and processing techniques. 8 The resulting surface chemistry is sensitive to the methods used for processing. 9 An outstanding challenge in the field is the development of techniques for the quantitative analysis of these chemistries. 10 The nanodiamonds are produced by the detonation of high explosives such as TNT and RDX. 11 The resulting material contains diamonds that are ∼ 4 − 5 nm in diameter, and that are attached to each other forming agglutinates (strongly-bound aggregates). The agglutinates have irregular shapes, and have diameters ∼ 100 − 300 nm. 8 In addition to the diamonds, a large amount of graphitic material and amorphous carbon is also produced by the detonation. In the case of the material prepared by NanoCarbon Research Institute Ltd. that is used in our study, as much of the graphite and amorphous carbon as possible is reacted away. 12 The processing involves reaction with potassium permanganate, and sulfuric and phosphoric acids, plus rinsing with water, HCl, and ethanol (details can be found in the Supporting Information). The method is similar to that used to make graphite oxide (GO) by the Hummers method, 13 but differences include the higher temperature (63-68 ◦ C versus 35 ◦ C), the longer reaction time (24 hrs. versus 30 min.), and the use of phosphoric acid. The agglutinates are then milled in water using zirconia beads until the individual 4 − 5 nm diamonds have been separated. 14 The individual diamonds have graphitic surfaces; they are a type of bucky diamond, 15–22 and the underlying diamond may be disordered to a depth of approximately 0.6 nm. 23 The particles form themselves into a colloidal dispersion of aggregates in solution. These aggregates are of a variety of sizes, and most of them are smaller than the agglutinates. This suggests that only a subset of the material at the surfaces of the aggregates was directly exposed to the permanganate/H2 SO4 treatment. The particles within the aggregates are not covalently bound to each other. 14 Past work 3 ACS Paragon Plus Environment


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has been undertaken to examine the details of the interactions between particles within the aggregates. The analysis in our work assumes a higher level of surface graphitization than was assumed in work such as ref 22, where aggregation was explained in terms of Coulomb interactions between diamond facets. To react away amorphous carbon and graphite, strong oxidative environments are necessary. This combined with the graphitic surfaces of the 4 − 5 nm particles suggests that holes and defects will exist in surfaces exposed to the oxidative treatment. In an acidic solution, permanganate undergoes the reduction reaction − 2+ + 4H2 O, 8H+ + MnO− 4 + 5e → Mn

(1)

and it is known to oxidize graphitic surfaces. 13 Also, the reduction of sulfuric acid,

H2 SO4 + e− → HSO− 4 + 1/2H2 ,

(2)

proceeds spontaneously in the presence of carbon nanotube bundles at room temperature 24 and for graphite in boiling H2 SO4 . 25 The curved graphitic surfaces of the 4 − 5 nm nanodiamonds suggest that this reaction could also be important for NanoCarbon nanodiamonds. The resulting HSO− 4 would be acidic. These oxidation reactions could result in fixed positive charges on the surfaces of the aggregates. For example, it has been postulated that oxonium ions (=O+ ) can exist as salts of pyrylium ions or betaines on carbon surfaces, and that carbenium ions (R3 C+ ) (referred to as carbonium in older literature) coexists as resonance forms of oxonium ions (see ref 26 and references therein, and ref 27). The functional groups involved include chromenes and pyrones, groups that are frequently present at edges and holes in graphitic surfaces. 26 The oxidants do not need to penetrate to the inner surfaces of the agglutinates to have an effect on the inner surfaces. This analysis suggests the aggregates may behave differently than a simple oxide, 28 as some of the protons supplied by the acid have become parts of H2 O or H2 molecules, and may have resulted in positive charges 4 ACS Paragon Plus Environment

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on the aggregate surfaces. GO does not have fixed charges, which may be due to the fact that its manufacture starts with graphite which is conductive whereas diamond is an insulator. Sulfonation 29 reactions may also occur, resulting in surfaces decorated with phenyl (Ph)-SO− 3 groups.

The agglutinates are milled into 4 − 5 nm particles in water and form a colloidal dispersion of aggregates. Binding between the aggregates and drug or gene molecules is presumed to be due to interactions between functional groups on the surfaces of the aggregates and the molecule of interest. These functional groups can become charged in solution. When added to the colloid, charges on the drug or gene molecules can result in attractive interactions and binding. One of the ways surfaces of both the aggregates and drug or gene molecules can become charged is by way of acid-base chemistry. The behavior of a functional group in this regard is described by its pKa , which indicates the degree to which it is associated with protons in solution at a given pH. Phenol-type functional groups (Ph-OH) often exist at edges and holes in graphitic materials exposed to permanganate and H2 SO4 . 13,30 The OH proton is acidic, and the negative charge that results on the oxygen atom can be delocalized by resonance over the ring. Phenol has a pKa of 9.89. 31 Such exposures can also lead to epoxide and hydroxyl functional groups on graphitic basal planes, including intercalation of such groups between graphitic layers, and to carboxylic acids at holes and sheet edges. 30,32 Significant intercalation between the individual particles in the agglutinates seems unlikely, as there is evidence the agglutinates are held together by covalent bonds, 16,33 although investigations of the nature of the bonding continue. 22 Measurements of the ζ potential can provide useful information about the charges associated with the surfaces of particles in a colloid. This is the potential at the slipping plane; the plane between the portion of the electric double layer that does and the portion that does not move with a particle in solution. 34 The surface potential, which includes the transiently adsorbed ions within the first ∼ 2 Å of the surface [the outer Helmholtz plane (OHP)], is different than the ζ potential because some ions on the solvent-side of the OHP also move with the particle during ζ potential measurements. 26,35 This ∼ 2 Å layer is called the Stern layer. 35 As acid or base are added to a colloidal dispersion, the ζ potential does not change very quickly because additional counter ions,



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such as Cl− or Na+ , mostly screen any new charges that are created by the formation of water. 35 Although the number of counter ions on the aggregate-side of the slipping plane will always be less than the number of surface charges, care must be exercised while interpreting ζ potential results, because a given measurement can be associated with different surface potentials, depending on solution conditions. 26 For Hummers GO, it has been shown that although the ζ potential as a function of pH depends on the size of the sheets, 36 the potential is negative over a broad range of pH values. 37 This behavior is consistent with the presence of carboxylic acid groups at sheet edges and holes. The pKa values associated with these groups can be complicated by the presence of neighboring hydroxyl groups. 38 Sulfuric acid has pKa values of ∼ −5 and 1.9 associated with the release of its first and second protons, respectively. 31 Thus, above a pH of ∼ 2, it is mostly ionized, forming two protons (H3 O+ ) 8 and SO2− 4 in aqueous solution. Some types of nanodiamond surfaces are decorated with amines,

and these functional groups can have pKa values ∼ 10. However, investigations of the agglutinates that are used as starting material for the NanoCarbon colloid indicate that there is no significant concentration of NH2 -type groups on the material. 16,39 Nitrogen atoms are often found within the lattices of diamonds. 40 Phosphoric acid may provide a certain level of protection from random hole formation in graphitic materials, by protecting vicinal diols that form during permanganate/H2 SO4 oxidation. 41 However, the cyclic structures that are hypothesized to be involved are expected to hydrolyze spontaneously during subsequent aqueous work up. This protection is most relevant for creating GO nanoribbons from multiwalled carbon nanotubes. The use of H3 PO4 also tends to be associated with a relatively high concentration of hydroxyl groups and a relatively low concentration of carboxylic acid groups compared to the use of H2 SO4 as the only acid. 41 The pKa associated with the first proton of H3 PO4 is 2.1. 31 The remainder of this paper describes a combined experimental and theoretical investigation into the surface chemistry of the nanodiamond colloid produced by NanoCarbon Research Insti-


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tute Ltd. The experiments involve standard analytical measurements of the nanodiamond structural, electrical, acid-base and spectroscopic properties, while the theory uses electronic structure calculations to study reactions that take place during the agglutinate processes, together with the development of models for the surface chemistry. The combined approach provides insight into the sources of the behavior of the surfaces of the aggregates at the level of individual functional groups. The methods used constitute a general approach, as they are also suitable for the characterization of other types of nanodiamonds.

Experimental methods and materials Elemental analysis Nanodiamond was diluted in pure water to a concentration of 20 mg/ml and underwent ultrasonication (Fisher Scientific). It was then adjusted to a concentration of 4 mg/ml. 1 ml samples were freeze dried to remove water. The samples were sent to Intertek (NJ, USA) for elemental analysis.

Dynamic light scattering and ζ potential measurements All dynamic light scattering and ζ potential measurements were performed using a Zetasizer Nano (Malvern, UK). Size measurements were performed using disposable micro cuvettes at 0.1 mg/ml (nanodiamond concentration), with a sample volume of 0.05 ml. ζ potential measurements were performed using disposable capillary cells with a sample volume of 1 ml. All values reported are averages of three or more samples. Nanodiamond was allowed to equilibrate at ambient conditions for 1 hour before measurements. pH values were adjusted by adding the appropriate amounts of NaOH and HCl to nanodiamond samples, monitored using a pH meter (Mettler Toledo).



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Titration Nanodiamond was diluted in pure water to a concentration of 20 mg/ml and underwent ultrasonication (Fisher Scientific). The solution was adjusted to a concentration of 4 mg/ml prior to titration. A 50 ml solution was titrated with 0.01 M NaOH and 0.01 M HCl (Sigma Aldrich) added at 0.5 ml increments. The pH of the solution was recorded prior to each addition using a pH meter (Mettler Toledo).

Theoretical Methods Molecular dynamics using forces derived from self-consistent charge density functional-based tight binding (SCC-DFTB) calculations were used for the simulations, 42,43 as implemented within DFTB+. 44 SCC-DFTB is a semi-empirical method based on density functional theory (DFT), that is more than an order of magnitude faster and yet maintains much of the accuracy of DFT. SCCDFTB uses a two-centered approximation for the matrix elements of the Hamiltonian, and a minimal linear combination of atomic orbitals-type basis set that includes only valence electrons. Three-dimensional periodic boundary conditions were applied. Their use within the plane of the graphene eliminates unphysical edge effects that are caused by the other commonly-used method of capping with hydrogen atoms. The lattice vector perpendicular to the graphene plane was set to 30 Å, a distance large enough so that there were no spurious forces due to interactions with neighboring virtual unit cells in this direction. Electron spins were allowed to become polarized, and the Γ point was used to sample the Brillouin zone. Slater-Koster files from the mio set were used, because it is reactions that are analogous to those of organic chemistry that we wish to model. 45 Dispersion corrections were not included as they were not considered for the parameterization of the mio set.


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Results and Discussion Elemental analysis An elemental analysis of dried nanodiamond aggregate is presented in Table 1. Aside from the expected high concentration of carbon atoms, oxygen, nitrogen, and hydrogen are also present in significant amounts. The concentration of oxygen is suggestive of high levels of functionalization with oxygen-containing groups. Also, the analysis is consistent with the expected high concentration of hydrogen on graphitic surfaces exposed to permanganate and H2 SO4 . 30 It may not have been possible to remove all of the water upon drying the sample, 46 so the oxygen and hydrogen concentrations in the table may be unrealistically high. Infrared spectra of the agglutinates do not show evidence of nitrate ester, cyano or amide groups, suggesting that most of the nitrogen is within the diamond phase of the particles. 16 Table 1: Elemental analysis of the nanodiamond colloid after drying. Element C O N H Zr S K Mn

Amount 90.13 % 2.86 % 1.91 % 0.80 % 0.20 % 730 ppm < 1 ppm < 1 ppm

The zirconia beads are softer than diamond, so the beads erode during milling. The resulting zirconia particles are difficult to remove, and tend to be ∼ 5 nm in diameter. 14 As a result, there is a measurable amount of zirconia contamination (0.20 %) in the aggregates. The surfaces of zirconia form Zr(OH)4 in aqueous solution, and they are protonated at low pH and acidic at high pH. So zirconia will be involved in the acid-based chemistry of the colloid, but its particle size and concentration suggest that it will not play an important role. The low concentrations of K and Mn suggests that they were almost entirely removed with 9 ACS Paragon Plus Environment


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Figure 1: Average aggregate size versus pH. pH changes were induced using 0.01 M NaOH or 0.01 M HCl, with an initial nanodiamond concentration of 5 mg/ml. 2− equal parts of perhaps HSO− 4 and SO4 during the washing of the agglutinates (charge balance),

after the oxidative treatment. The significance of the presence of sulfur will be discussed in detail below.

Aggregates and charges The agglutinates are approximately 200 nm in diameter after the H2 SO4 /permanganate treatment and before bead milling. 14 The agglutinates are milled to particles ∼ 4 − 5 nm in diameter in water, and the particles then interact to form aggregates. Aggregate sizes are ∼ 50 nm and remain relatively unchanged upon titration to pH as low as ∼ 2.5 and as high as ∼ 8.5 (see Fig. 1). The aggregate diameter implies there are approximately 1000 particles in the average aggregate, assuming a particle diameter of 5 nm. The ζ potential of the nanodiamond aggregates as a function of pH is shown in Fig. 2. The as-received colloid has a potential of ∼ 60 mV, and the potential is above 30 mV over a broad pH range. Colloids tend to be stable provided the magnitudes of their associated ζ potentials are greater than ∼ 30 mV. 34 As the potential drops below 30, forces due to dispersion begin to dominate over Coulomb repulsion, as described by DVLO theory. 35 Comparison of Figures 1 and 2 suggests that this stability behavior is followed by the aggregates. 10 ACS Paragon Plus Environment

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ζ potential (mV)

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pH Figure 2: pH dependence of the ζ potential for the nanodiamond aggregates. Titrations were performed using 0.01 M NaOH and HCl, changing the colloid towards higher and lower pH values, respectively. The number of excess positive charges on the aggregate-side of the slipping plane for a typical aggregate in solution can be estimated. The as-received aggregates have a ζ potential of ∼ 60 mV (see Fig. 2). The charge necessary to create a potential is given by

ψ = q/(4πε0 z),

(3)

where ψ is the potential, q is the charge, ε0 is permittivity constant, and z is the radius of the particle. We assume a shape that is approximately spherical, and based on Fig. 1 we use a radius of 25 nm (50 nm diameter). This means there are approximately 80 net electron deficiencies per aggregate on the aggregate-side of the slipping plane, when the relative permittivity of water has been accounted for. A 50 nm aggregate will contain approximately 1.1 × 107 carbon atoms, where the density of single-crystal diamond (3.5 g/cm3 ) has been assumed. At a concentration of 730 ppm (see Table 1), this means there are approximately 9300 sulfur atoms associated with each aggregate. The sulfuric acid treatment of the agglutinates suggests that sulfonation has occurred, i.e., Ph-SO− 3 groups have been formed. 29 Their average concentration is approximately one per 84 Å2 of aggregate surface, assuming a spherical aggregate and that all sulfur atoms are present as Ph-SO− 3 groups. The pKa of benzosulfonic acid is 0.7. 31 Some of the sulfur in the elemental analysis may be from H2 SO4 that was not washed away during the washing of the agglutinates. Assuming all sulfur atoms are present as sulfonic acid, these ∼ 9300 sulfur atoms are associated



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with up to 9300 protons (present as H3 O+ ) in solution per aggregate, and it is probable that these protons are the cause of the acidic character of the as-received nanodiamond colloid (see Fig. 2). The pH of a colloid containing 4 mg of nanodiamond per ml is 4.3 (∼ 2000 protons/aggregate). 9300 protons per aggregate implies a pH of 3.6. A plausible explanation for the difference in these pH values is discussed below. 9300 protons per aggregate is suggestive of a Debye length of approximately 26 nm. 34 The Fourier transform infrared spectra (FT-IR) of the material has been reported elsewhere. 1 It is consistent with the presence of significant concentrations of phenol-type hydroxylic acid groups. It is also consistent with the presence of carbonyl, and ether groups. The intensities of IR absorption peaks are often presumed to be linearly related to the concentration of the species giving rise to them. However, it is not straightforward to establish the necessary conversion factors for complex materials such as carbons. 47

Titration with NaOH The pH of the nanodiamond colloid as a function of the addition of base is shown in Fig. 3. Based on the Henderson-Hasselbalch equation and a set of four titrations, the pH at the half equivalence point suggests the pKa is 5.79 ± 0.27. 48 However, the positive surface potential of the aggregates will have a significant effect on the acid-base behavior of functional groups on their surfaces. The

ζ potential of the aggregates is ∼ 60 mV as-received, and is between ∼ 50 − 60 mV between pH ∼ 5 − 6 (see Fig. 2). Note the difference in as-received pH values in Figs. 2 and 3 is due to a difference in aggregate concentrations. The surface potential and oxygen content means that an additional term needs to be added to the Henderson-Hasselbalch equation. 28,34 This is because the high oxygen content (see Table 1) means the surface will behave like an oxide. 26 In this case, the relationship between the pH and the pKa is 34

¶ eψ0 [HA] , − 0.434 · pH = pKa − log − [A ] kB T µ


(4)

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pH

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Volume of NaOH (ml) Figure 3: pH versus volume of 0.01 M NaOH added to nanodiamond aggregates in water. where [HA] is the concentration of un-ionized acid, [A− ] is the concentration of its conjugate base, −e is the charge on the electron, ψ0 is the surface potential, kB is Boltzmann’s constant, and T is the temperature. The last term in Eq. (4) accounts for the tendency of protons to have a low concentration, relative to their concentration in the bulk liquid, adjacent to surfaces which are positively charged, and vice versa. In our case, this potential makes it more likely for a surface group to lose a proton, making the apparent pKa of a group smaller than it would be were the group to instead be isolated in solution. The surface potential is different than the ζ potential. The latter includes some ions that move with the particle during ζ potential measurements, but that are on the solvent-side of the Stern layer. 26 More counter ions than co ions are present in this solvent-side region, 35 so the surface potential is larger than the ζ potential in our case. For a surface potential of 60 mV and T = 298 K the last term in Eq. (4) is 1.0, which suggests the pKa of the functional group or groups responsible for the acid-base behavior shown in Fig. 3 is ≥ 6.8. The Gouy-Chapman equation as used in ref 38 in conjunction with the Grahame equation 35



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can be used to estimate the surface potential. The result is 90 mV, based on a 60 mV zeta potential and ions from 3 × 10−4 M H2 SO4 (upper bound on sulfur-related ions). The oxidative treatment and washing of the agglutinates means there are probably other ions in solution, so 90 mV should be viewed as a better estimate of the surface potential than 60 mV but still a rough estimate. Using 90 mV in Eq. (4) gives pKa = 7.3.

Ions and functional groups at the surfaces As discussed above, the data suggests that the as-received aggregates may have 9300 Ph-SO− 3 groups on their surfaces, on average. They will reduce the surface potential, and solvated H3 O+ will act as counter ions towards them. The local Coulomb environment experienced by individual functional groups on the surface is expected to be quite varied. Functional groups are expected to be in random locations as in GO. 30 It is unlikely that the surfaces are uniformly functionalized, as only up to approximately 1/4 of them were directly exposed to the permanganate/H2 SO4 treatment. Also, the surfaces are amphoteric, i.e., they have acidic and basic centers coexisting on their surfaces. 26 Note that it may be that more than one functional group is associated with the acid-base behavior shown in Fig. 3. The steep slope of the curve on the acidic-side of the equivalence point (pH ∼ 8) compared to that observed for simpler systems, 49 and the tendency of carbon surfaces to support a wide variety of functional groups are suggestive of this possibility, although the behavior may be due to a single functional group type in a range of local environments (e.g., different neighboring functional groups). The number of protons removed from each aggregate during the titration shown in Fig. 3 can be estimated. It was necessary to add 4.5 ml of 0.01 M NaOH to take 50 ml of colloid that contains 4 × 10−6 kg of nanodiamond/ml to its equivalence point. This means 2.7 × 1019 OH− groups were added, each of which removed a proton from solution or the aggregates. Fifty ml of colloid contains 87.5 × 1013 aggregates, which suggests that there are 31000 protons removed for each aggregate, on average. The pH changed by more than 3 units, so essentially all 2000 protons per aggregate in solution associated with the presence of sulfonic acid groups were also consumed by 14 ACS Paragon Plus Environment

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the base, so the per aggregate contribution is approximately 29000. The surface area of a 50-nm sphere is 7.85 × 105 Å2 . This suggests one proton was removed from each 30 Å2 of the aggregate surface, on average. The aggregates are not spherical and thus will have surface areas larger than what is suggested by this estimate. 22 The aggregates will also be less dense than single-crystal diamond because of voids left after particle packing, 22 and the surfaces may be composed of multiple graphitic layers. These layers, potentially produced during milling, could allow intercalation and thus provide a surface area that is larger than the estimate based on the assumption of a single layer. The solvent may also have some access to particle surfaces within in addition to on the surfaces of the aggregates. The estimate based on the 50-nm sphere is motivated by the average aggregate diameter. The most probable particle size could be smaller as in ref 14 (most probable diameter < 10 nm), and smaller aggregates have larger surface area to volume ratios. These factors suggest that this protons per area estimate is probably too high, and perhaps much too high; for example, the use of a 5-nm instead of a 50-nm sphere gives one proton per 300 Å2 . These issues warrant additional investigation. The permanganate and sulfuric acid treatment suggests phenolic OH groups as a major contributor to the behavior observed in Fig. 3. These groups are produced by such treatments, 30 and are also known to be important on some other carbon surfaces exposed to other oxidizing agents. 50 Functional groups on complex surfaces exhibit a range of pKa values, as the local environment is expected to influence these values. Reference 26 gives a range of pKa of 8 − 11 for phenols on carbon surfaces, so the presence of phenols is consistent with the behavior shown in Fig. 3. They are neutral at low pH and negatively charged at high pH, so when they are charged they will reduce the overall surface charge of the aggregates. Na+ ions associated with the addition of base as well as H3 O+ will act as counter ions towards Ph-O− , although the concentration of the latter is relatively small by the time the equivalence point is reached. Note that although Fig. 3 suggests the depletion of proton donors by pH ∼ 9 − 10, these pH values also correspond to values at which the aggregates coagulate (see Fig. 1), rendering some surfaces inaccessible to solvent. Other types of functional groups exhibit behavior that is similar to phenols. For example,



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lactones have a pKa = 7 − 9, and are frequently associated with graphitic surfaces. 26,50,51 Although they are not known to be in particularly high concentrations after graphitic materials are treated with permanganate and H2 SO4 , or seemingly particularly likely to form when graphitic materials are broken in water as occurs during milling, they are probably present in small concentrations on the colloids, where they behave as acids. Oxygen-containing groups are unlikely to form during agglutinate formation because the temperature is too high.

Modeling of surface chemistry and pKa Bead milling is thought to break covalent bonds between graphitic surfaces during the processing of the agglutinates. 16,33 The newly-formed surface radicals are exposed to liquid water during the process to allow for reactions between the radicals and water. 16,17,19 The water will also contain dissolved oxygen molecules at a concentration of ∼ 8 mg/l. To explore the resulting chemistry, we used molecular dynamics combined with SCC-DFTB to model the exposure of defects in graphene to oxygen and water molecules. A typical initial structure is shown in Fig. 4.

Figure 4: Top and side views of the initial structure for an MD simulation in which carbon radicals were exposed to water and oxygen molecules. A set of five SCC-DFTB-based molecular dynamics simulations in which O2 and H2 O molecules were initially located near vacancy defects in graphene sheets were performed. The simulations 16 ACS Paragon Plus Environment

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were run for 10 ps at 298 K, and included three oxygen and three water molecules. The experimental temperature might be higher than 298 K at times. 17 Different initial conditions were generated by moving the oxygen and water molecules by rotation around the sheet center surface normal. The initial separations between these molecules and the basal plane were between 2 and 2.5 Å. The initial separations were chosen to be larger than any likely C-O or C-H transition state distance yet small enough so that atoms have time to move sufficiently far to possibly react in less than the full simulation time. The shape of the hole was chosen to provide some edge carbon atoms which belong to hexagons with one or more missing carbon atoms. Similar reactivity is expected at sheet edges. The final structure corresponding to the initial conditions shown in Fig. 4 is shown in Fig. 5. An ether and a carbonyl group were formed. The formation of these groups was also observed in other simulations in which different hole sizes and shapes, and different numbers of and initial locations of oxygen and water molecules were used. These are the two functional groups that, when they are in reasonably close proximity to each other (∼< 10 Å), constitute pyrones. Thus, their formation in these simulations suggests the plausibility of their formation during the bead milling. Another species that we find is a six-membered non-aromatic ring containing an ether that is bonded to a benzene-type ring; this is called a chromene.

Figure 5: Top and side views of the final structure for an MD simulation in which carbon radicals were exposed to water and oxygen molecules. 17 ACS Paragon Plus Environment


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A peroxide and a hydroxyl radical were also present at the end of this and some of the other simulations. These were short simulations, so it is unclear how long one should expect such species to exist. For example, one would not expect hydroxyl radicals to remain unreacted for long, particularly in an environment rich in other radicals. Peroxides like the one shown in Fig. 5 were observed to react to form pairs of carbonyl groups in other similar simulations. Five simulations in which only water was exposed to defects were also performed. Although water took somewhat longer to react and reacted less frequently than O2 , water was observed to form phenol and C-H group pairs. These reactions took place in less than 10 ps. The dissociation energies of HO-H and H-C6 H5 are 498 +/- 4 kJ/mol and 464 +/- 8 kJ/mol, respectively. 31 Based solely on these energies, one would not expect a phenyl-type radical to remove a hydrogen atom from a water molecule. Snapshots from a simulation are shown in Figs. 6 - 9, and they indicate that the mechanism involved does not require the creation of a hydroxyl radical.

Figure 6: Top and side views of an MD simulation in which carbon radicals were exposed to water molecules. The graphene sheet and the three water molecules included in this simulation are shown in Fig. 6. As the dynamics proceeds, a water molecule bonds to a carbon radical, forming a R-OH2 radical (see Fig. 7). The R-OH2 exists for ∼ 100 fs. A second water molecule is then involved to which the R-COH2 transfers a hydrogen atom, forming an R-OH group and a transient H3 O radical (see


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Figure 7: As the dynamics proceed, a water molecule bonds to what was a carbon radical, forming a R-OH2 radical.

Figure 8: The R-OH2 radical transfers a hydrogen atom to a second water molecule, forming a hydroxyl group and a H3 O radical.



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Figure 9: The H3 O radical transfer a hydrogen atom to a second carbon radical, forming a C-H group and reforming a water molecule. Fig. 8). After a few fs, the H3 O transfers a hydrogen atom to a second carbon radical, forming a C-H group and reforming a water molecule (see Fig. 9). The few-fs lifetime suggests the H3 O is part of a transition state in a concerted reaction mechanism. The reaction is related to the Grotthuss mechanism for proton transfer. 52 These reactions imply that it is a bond to a hydrogen atom in the R-OH2 radical not a HO-H bond that is broken. R-OH2 is an unstable species, so its O-H bonds are weaker than those of water. Also, R-OH2 reacts to form a phenyl-H and a phenol (formation energy: ∼ 400 kJ/mol), so it is not surprising that the reaction proceeds. We modeled gas phase reactions, but the complete treatment of reactions involving H3 O radicals in liquid water includes solvent-separated H3 O+ · · · e− pairs, that are accurately described at levels of theory higher than SCC-DFTB. 53 Similarly, a more complete treatment would be necessary to accurately investigate system equilibrium. One could also worry about whether SCC-DFTB is doing a sufficiently good job at predicting the size of reaction barriers, but otherwise it seems reasonable to expect this type of reaction to take place. In addition, reactions with any O2 that is in close proximity to carbon radicals created during milling will occur. These simulations suggest that reactions with water will also take place, especially after O2 has been depleted in the vicinity of such radicals, as water reaction times are too short to allow for significant O2 diffusion towards


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radical sites. Phenols were also observed to form during simulations in which oxygen in addition to water molecules were initially present near defects. The observation of the formation of pyrones in these simulations and their importance in other graphitic materials 54 was motivation for calculating the pKa associated with such groups. They are basic, and they can have a wide range of pKa values depending on their structures when they are part of small molecules. 51,55,56 We model structures like those that might be expected on the aggregate surfaces. The geometries of the structures shown in Fig. 10 were optimized using SCCDFTB. The intention was not to create the most realistic structures, but to provide a means of systematically examining how hole shape and functional group positions affect the pKa values. All but the structure shown in panel (c) have associated resonance structures that support the charge separations necessary for basicity. Of the structures shown in panels (b)-(d), the one in panel (b) is lowest in energy, the one in (d) is next lowest and the one in (c) is highest. The difference between the highest and lowest is 19 kJ/mol. (a)

(b)

(c)

(d)

Figure 10: Top views of pyrones for which PM6 was used to calculate pKa values. The pKa values of these structures were estimated using PM6 calculations. 57 PM6 is probably better than SCC-DFTB for pKa calculations, as PM6 is calibrated more closely with experiment. The calculations were performed with the carbonyls protonated, resulting in singly-charged cations 21 ACS Paragon Plus Environment


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in each case, to account for the positive charges associated with pyrones. The pKa values obtained for structures a) through d) were 8.1, 9.7, 5.7, and 7.6, respectively. The values for structures b) through d) show the trend expected based on their relative energies. Of the three, structures of the type shown in panel c) would seem least likely to form as it is relatively high in energy, its high energy presumably due to the inability to associate a viable resonance structure. The other three panels show structures with pKa values that are consistent with the behavior shown in Fig. 3. The calculations were repeated for systems containing one additional electron. In so doing, the pyrones were converted to phenols with neighboring ether groups. The associated pKa values are 10.0, 9.9, 9.0, and 8.4, values that are also consistent with the behavior shown in Fig. 3. Note that phenols with an aromatic neighboring ether that are parts of a surface such as the ones shown in Fig. 10, oxidized to a charge of +1, are equally well described as comprising a protonated pyrone. The higher the density of net-positive charge on a locally-aromatic surface, the more acidic its phenolic or protonated-pyrone protons are.

Carboxylic acid Up to ∼ 1/4 of the surfaces of the aggregates were directly exposed to the permanganate and H2 SO4 during the cleaning of the agglutinates. They are likely to be more highly functionalized with oxygen-containing groups than those in the interiors of the agglutinates, and have surfaces similar to GO. We expect there may be carboxylic acid groups present. The curvature of the 4 − 5 nm particles might make them more inclined than graphite to catalyze the production of carboxylic acid groups, as Tour et al. showed is the case for carbon nanotubes. 58 The curvature associated with the surfaces of the 4 − 5 nm particles is larger than that of the tubes used by Tour et al. (tube diameter = 40 − 80 nm). The pKa values of benzoic and acetic acids are 4.2 and 4.75, respectively, 31 so the net-positive surface potential means that most carboxylic acid groups will ionize at pH values near or just above those at which the colloids coagulate (pH approximately ≥ 2.5), if they are present. Any carboxylic acid with a hydroxyl group in an ortho position would be ionized at even lower pH values. 38 22 ACS Paragon Plus Environment

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Figure 11: pH versus volume of 0.01 M HCl added to nanodiamond aggregates in water. We titrated towards low pH to look for evidence of carboxylic acid groups (see Fig. 11). A flat region on the titration curve would have been suggestive of their presence, as these groups act as a buffer. No evidence was found, suggesting that the concentration of carboxylic groups is low compared to that of phenolic OH/protonated pyrone groups, if carboxylic groups are present at all. Note that there is a significant concentration of ionized sulfonic acid on the surfaces, so any carboxylic acid groups in an area of the surface with a locally high concentration of sulfonic acid could have an effective pKa higher than ∼ 4.5.

A comprehensive view of the surfaces All else being equal, if there were many carboxylic acid groups on the surfaces, the pH of the colloid would be lower. Similarly, if there were many pyrones, the pH would be higher. As there are potentially 9300 − 2000 ∼ 7000 protons per aggregate unaccounted for in the pH measurement of the as-received colloid, this argues for the presence of a substantial concentration of pyrones (∼ 7000 per aggregate). The fact that permanganate and H2 SO4 result in the creation of carboxylic acid groups in graphite oxide 30 means it would be somewhat surprising if some carboxylic acid 23 ACS Paragon Plus Environment


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groups were not present on the aggregate surfaces. The experiments and simulations discussed so far suggest a model of the surfaces of the aggregates. The hypothesis is: 1) Up to ∼ 1/4 of the aggregate surfaces were directly exposed to the permanganate/H2 SO4 , so they will be heavily functionalized with epoxides and hydroxyl groups, some of which are phenols. Most of these heavily oxygen-functionalized surfaces make up parts of the aggregate surfaces because they are hydrophilic. 2) 3/4 or more of the aggregate surfaces are less heavily functionalized and have groups such as phenols, pyrones, and chromenes at holes in the graphitic surface layer. Hydrogen will also be present at holes. Pyrones, evidence suggests ∼ 7000 per aggregate, are protonated by protons from sulfonic acid groups. 4 − 5 nm particles that are less oxygen-functionalized will tend to be present in the interiors of the aggregates because they are less hydrophilic than those directly exposed to permanganate/H2 SO4 . ∼ 22000 phenols per aggregate are solvent-exposed. 3) Groups, such as chromenes and pyrones, oxidized to a charge of +1, and pyrone protonated by sulfonic acid groups, are the cause of the positive ζ potential of the aggregates. There are ∼ 80 + 9300 − 7000 = 2000 chromenes or pyrones oxidized to a charge of +1 per aggregate (fixed charges). 4) A relatively small number of carboxylic acid groups and (neutral) pyrones are involved in proton transfer from Ph-COOH to pyrones. A cartoon that illustrates the structures of these various functional groups is shown in Fig. 12. How does charge balance apply for this system? There are as many as 9300 Ph-SO− 3 groups and 9300 associated protons. HSO− 4 can be produced via Reaction (2) resulting in fixed positive 2− + charges on the surface, so some sulfur may be present as HSO− 4 (i.e., H3 O + SO4 ). Perman-

ganate reduction reactions [see Reaction (1)] consume protons, so it is not entirely clear how many protons are present as, e.g., protonated pyrones (upper bound: ∼ 7000 per aggregate). Some protons and SO2− 4 may be present because they were not washed away during processing. Table 2 provides a summary of the approximate concentrations of various functional groups. Their charges at various pH values are also indicated, where low and high pH values correspond to those adjacent to the respective pH values at which the aggregates coagulate. There are uncertainties associated with the various values in the table. The titrations with NaOH suggest an


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Figure 12: Functional groups on the aggregate surfaces. Two perspectives of the same graphene sheet are shown for clarity. Carbon, oxygen, hydrogen, and sulfur atoms are shaded yellow, red, white, and gold, respectively. Hydroxyl (bottom, left), pyrone (left hole, left side), sulfonic acid (left hole, right side), phenol (left hole, bottom), epoxide (middle, top), carboxylic acid (right hole, bottom), and chromene (right hole, top) groups are shown. Hydrogen atoms are also shown at hole edges. uncertainty in the pKa estimate. This has implications for the number of protons removed during these titrations, and implies an uncertainty of approximately 5 %. As mentioned, some of the sulfur in the elemental analysis may be due to H2 SO4 and/or HSO− 4 . Further characterization of the surfaces would be beneficial, to provide additional details about the surface chemistry. 26,50 As the arguments presented indicate, all of the values in the table are affected by the sulfur uncertainty, with the exception of the carboxylic acid concentration. The size of this uncertainty is yet to be quantified, and it may be larger than 5 %. Coagulation of the aggregates begins to take place as pH is reduced below 3 or raised above 9 (see Fig. 1). As pH is decreased using HCl, Cl− ions are introduced to the colloid. They increase in concentration as acid is added, and become increasingly effective at screening the net-positive surface charge of the aggregates, causing a decrease in ζ potential and subsequent



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Table 2: Summary of the species that contribute to surface charge on the surfaces of a typical aggregate, and their charge states in the limits of low and high pH. The concentration, C, of each group assuming accessible surface areas associated with 50 and 5 nm aggregate diameters, d, are also shown. Species Number C (Å−2 ) [d = 50 nm] C (Å−2 ) [d = 5 nm] phenols 22000 0.03 0.003 sulfonic acid 9000 0.01 0.001 protonated pyrones 7000 0.009 0.0009 fixed charges 2000 0.003 0.0003 carboxylic acid trace -

Low pH neutral negative positive positive neutral

High pH negative negative neutral positive negative

collapse of the colloidal dispersion. As pH is raised using NaOH, protons are removed and Na+ − acts as counter ions to the Ph-SO− 3 and Ph-O groups. This occurs until the last solvent-accessible

protonated pyrone or Ph-OH groups has been deprotonated, at which point excess OH− ions cause a sufficiently large decrease in ζ potential for the colloid to collapse. The aggregates can not be redispersed after they have been caused to coagulate using acid or base or after they have been dried. During drying, the Ph-SO− 3 groups will be protonated by the protons in solution, but there are an insufficient number of protons in solution to neutralize all of the Ph-SO− 3 groups. Pyrones will remain protonated. As water is removed, and aggregates approach one another, positive charges on an aggregate (protonated pyrones or fixed positive charges) are attracted to negative charges on adjacent aggregates (Ph-SO− 3 ) and vice versa, resulting in an ionically-bound material. The fact that coagulation is irreversible is important, as, for example, the ζ potential at a given pH might be very different if the colloid has or has not previously been treated in such a way as to cause aggregation to take place, even if the same ions are in both solutions. 9 These coagulations involve charge regulation, and correspond to entry into the primary DLVO minimum associated with the colloid, from which the aggregates can not escape. 35

Implications for drug delivery Reference 1 describes experiments that use NanoCarbon nanodiamonds for the delivery of the drug doxorubicin hydrochloride (DOX). DOX molecules have a positive charge in a solution with 26 ACS Paragon Plus Environment

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a pH lower than ∼ 8. 59 The authors provide an explanation for the reason for binding between the nanodiamonds and DOX based on the presumed presence of carboxylic acid groups on the nanodiamonds. They use FT-IR evidence to support their claim. However, as discussed above, although the FT-IR is consistent with the presence of carbonyl and hydroxyl groups, these need not be associated with carboxylic acid groups. As the above analysis suggests, a more likely − explanation for the binding is via Ph-SO− 3 or Ph-O groups; these groups are negative and DOX is

positive so the DOX binds to the nanodiamonds by way of these groups. We also suspect that there may be a significant concentration of COO− groups on the aggregates, and they would provide sites for DOX binding. Note that the use of nitric acid instead of permanganate and H2 SO4 in the preparation of some of the older NanoCarbon agglutinates 14,19 may have meant that it was only COO− on the nanodiamonds discussed in ref 1 that allowed binding, although significant concentrations of Ph-O− are expected to be present in that case as well. The authors of ref 1 found it necessary to add salt (e.g., NaCl) to the colloid to promote binding, which is consistent with our model. The salt serves to make the electric double layer more compact, 35 to reduce the repulsive effects of the overall-positive potential of the surface, and allow for the approach of positively-charged DOX molecules. The release of DOX upon desalination described in ref 1 is also consistent with our model. Motivated by the work in ref 1, ref 4 describes molecular dynamics simulations of the interactions between nanodiamond and DOX. The pKa for the nanodiamond the authors used was 10.75. References 7 and 9 and the authors work were cited as sources of that pKa estimate. Reference 9 involves an examination of a number of different types of nanodiamond, none of which are NanoCarbon nanodiamond. Also, there is no evidence presented in ref 7 that NanoCarbon nanodiamond has a pKa of 10.75. This suggests that this value is a new result being reported in ref 4. It is not too far from our estimate. As the pH is increased from 7, DOX loses two protons. It loses one from a phenol-like OH group (pKa = 8.15 ± 0.07) and one from its amine (pKa = 10.16 ± 0.09). 59 So, over this pH = 7 − 11 range, DOX changes from having a positive charge to having a negative charge. The aggregates



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have a positive ζ potential, so the profound change in the absorption of DOX at pH ∼ 10 − 11, shown in Fig. 6 of ref 4, is due to this DOX proton loss; at low pH, both the aggregates and DOX are positively charged, so there is not much binding in the absence of salt, and at high pH the aggregates are positive and DOX is negative, so they are attracted to one another. Adsorption is not due to a change in the surface charge of the diamond as was suggested in ref 4. The aggregate surfaces have undergone substantial changes by pH ∼ 10 (see Fig. 3) but none leads to more positive surface charges. It is also possible to understand the binding between the nanodiamond aggregates and polyethelene imine (PEI) using our model. 2,3,48 PEI has a pKa ∼ 10. Mixing excess amounts of PEI with nanodiamond colloid as was done in ref 48 will result in a colloid with a pH close to 10, as the PEI will remove protons from solution as it protonates. PEI will also remove protons from the aggregate surfaces (protonated pyrones and Ph-OH) as suggested by Fig. 3. The result will be aggregate surfaces with a significant number of Ph-O− and Ph-SO− 3 sites with which positivelycharged PEI can bind. The removal of protons from protonated pyrones as PEI protonates, reduces PEI-aggregate Coulomb repulsion below what would otherwise be the case. The use of sufficient amounts of PEI is necessary to remove enough protons from the aggregate surfaces to allow for efficient binding, as suggested by Fig. 2G of ref 48. This picture is quite different from the model used in ref 48 that assumed fixed rather than ionizable surface charges on the nanodiamond (169 negative charges on a 4.1 nm particle) and PEI (20% protonated). Finally, the binding between the aggregates and insulin 7 can also be understood using our model. At neutral pH, the aggregates have a net positive charge and insulin has a net negative charge, so insulin binds to the aggregates. It was reported in ref 7 that the addition of NaOH from pH = 8.9 to pH = 11.5 caused the release of increasing amounts of insulin from the aggregates. As discussed above, the addition of base will remove thousands of phenol- and pyrone-type protons from the average aggregate surface over this pH range, making the aggregate surfaces more negative than at pH = 7. Regardless of how efficient Na+ ions are at screening the charges of the ionized phenols, insulin will interact with aggregates that are more negative than those present at


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neutral pH. As a result, the release of insulin becomes more probable with an increase in pH.

Conclusions We have developed a combined experimental and computational approach for investigating the functional groups on the surfaces of particles within nanodiamond colloids. The surfaces of the material we examined are graphitized. Consideration of the H2 SO4 /KMnO4 chemical treatment used in the preparation of the agglutinates (diameter ∼ 200 nm) suggests approximately one quarter of the surfaces of the nanodiamond aggregates have surfaces that are similar to those of graphite oxide produced using Hummers method. These surfaces are expected to be heavily functionalized with epoxide and hydroxyl groups, some of which are phenols, and probably some carboxylic acid groups. Evidence suggests that the concentration of carboxylic acid groups is relatively low. The chemical treatment also produces sulfonic acid groups on the surfaces of the agglutinates. Bead milling is used to disintegrate the agglutinate into particles that are ∼ 4 − 5 nm in diameter. The process is harsh and results in graphitization of the surfaces of the 4 − 5 nm particles. The particles form themselves into aggregates that are approximately 50 nm in diameter. We showed how various functional groups might form on surfaces during bead milling, using molecular dynamics simulations based on forces from semiempirical quantum mechanical calculations (SCC-DFTB). The formation of phenols and pyrones was observed, groups that are often found on graphitic surfaces. Titration with base suggests that approximately 31000 protons per aggregate were consumed to bring the colloid to its equivalence point. Sulfonic acid groups are acidic and are the probable cause of the acidic character of the colloids. There are approximately 9000 on the surface of each 50 nm aggregate. Sulfonic acid provides approximately 2000 protons per aggregate in solution, effectively all of which are removed by the base. Phenols are also acidic, and approximately 22000 phenols per aggregate are deprotonated by the time the equivalence point is reached. Approximately 7000 pyrones per aggregate, initially protonated by the sulfonic acid groups, are also



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deprotonated by the addition of the base. The H2 SO4 /KMnO4 treatment also produces fixed positive charges on the surfaces. The functional groups involved are (unprotonated) pyrones and/or chromenes, and there are at least 2000 per aggregate. These charges and protonated pyrones are the cause of the positive ζ potential of the aggregates. The pKa of the functional group or groups responsible for the acid-base behavior of the colloid was investigated. The positive surface potential of the aggregates means that the HendersonHasselbalch equation applied to titration data significantly underestimates the pKa because the potential tends to repel protons from the surface, increasing the apparent pKa of a functional group. Such considerations lead to an estimate of pKa ≥ 7.3 for the group or groups responsible for the acid-base behavior. Semiempirical quantum mechanical-based calculations using PM6 suggest that phenols and pyrones of the types expected to exist on the aggregate surfaces have pKa values between 7.6 and 10.0, consistent with the results based on the titration experiments. Recent experiments have been performed to investigate the suitability of nanodiamonds for use in therapeutic drug delivery. The model implied by the present work is consistent with the results of those experiments.

Supporting Information Agglutinate cleaning details. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments ¯ JTP thanks Amanda S. Barnard, Eiji Osawa, and Fraser Hof for valuable discussions. This work was supported by a grant from the National Science Foundation (CMMI-0856492).

References ¯ (1) Huang, H.; Pierstorff, E.; Osawa, E.; Ho, D. Active Nanodiamond Hydrogels for Chemotherapeutic Delivery. Nano Lett. 2007, 7, 3305–3314.


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