Dec 11, 2014 - diamond surfaces have a negative electron affinity, where the vacuum level is ..... Platform for Controlled Drug Deliver. ACS Nano 2008, 2, ...
Article pubs.acs.org/JPCC
Tuning the Electron Transfer Properties of Entire Nanodiamond Ensembles L. Lai and A. S. Barnard* CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville 3052, Victoria, Australia S Supporting Information *
ABSTRACT: Many of the promising new biomedical applications of diamond nanoparticles are moderated by charge transfer reactions, occurring between different surface facets and the surrounding molecules and/or environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity, and chemical hardness can be useful indicators of the efficiency of nanodiamonds for different reactions and can help identify new application areas. However, because nanodiamond samples cannot currently be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of particles and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of ensembles where restrictions have been placed on the diversity of the structures. By predicting quality factors for a variety of cases, we find that there is a clear motivation for enriching samples with {111} facets (or suppressing the prevalence of {100} facets) to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified.
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INTRODUCTION In recent years nontoxic diamond nanoparticles (nanodiamonds) have emerged as a new tool in the fields of biotechnology and medicine,1−3 which has facilitated the next generation of drug delivery vehicles.4−7 Adding nanodiamonds to familiar treatment regimes has been shown to increase selectivity8,9 and sensitivity,10 moderate dosage,11 and sustain treatments without burst effusion.12 It is now possible to produce stable suspensions of nanodiamonds with a hydrostatic diameter of ∼3.0 nm, with a narrow size distribution,13,14 which provides an even greater specific surface area for carrying therapeutic agents, biomarkers, and ligands.15 In most cases, the controlled binding and release of these agents are moderated by a charge transfer reaction, which occurs between different surface facets and the surrounding molecules and/or environment. The direction and efficiency of charge transfer depend on whether the host nanodiamond acts as a donor or acceptor, so, in the case of electron transfer, the sign and value of the ionization potential (the donation of an electron) and the electron affinity (the accepting of an electron) are ideal indicators. Other related indicators are the electronegativity, which was described by Pauling as “the power of an atom in a molecule to attract electrons”16 and is defined as the average between the absolute values of the ionization potential and the electron affinity,17 and the chemical hardness which describes the preferred coordination of acids and bases.18 These properties have been little studied for nanodiamond, though yet another indicator, the surface electrostatic potential (SEP), has been the subject of lengthy investigations in the past. Some years ago it was shown that the charge distribution across the different surfaces19,20 is fundamental to how nanodiamonds interact with other particles and molecules,21−25 Published 2014 by the American Chemical Society
including interactions with functional moieties such as drugs,15,26−29 but is difficult to measure directly. When it comes to the intrinsic charge transfer mentioned previously, it is possible to make direct measurements,30,31 as has been done extensively in the past for diamond surfaces.32−41 It has been long established that H-terminated diamond surfaces have a negative electron affinity, where the vacuum level is equal to or below the conduction band minimum. This is a unique property not shared with any other semiconductor, but the precise value of the threshold (typically between 4.2 and 4.5 eV38−40) depends on a variety of factors. For example, the existence of a negative or positive electron affinity has been correlated with different types of metal− diamond interfaces,35,36 and adsorbates42 or atmospheric changes41 (though it is stable in air43). Although it is possible to simulate charge transfer properties such as the ionization potential, electron affinity, electronegativity, and chemical hardness, previous works on chemical systems have shown that the values are unique to a given structure and sensitive to isomeric variations.44,45 This does not pose a problem in samples that can be purified, but (like many nanoparticle systems) nanodiamond samples cannot. Structural polydispersivity is always present in as-grown samples, so it is far more useful to simulate the ensemble average of these properties, using a virtual sample that mimics diversity of real specimens.46 In this study we use the same computational methods previously used to model the SEP to explore the size and shape Received: September 15, 2014 Revised: November 24, 2014 Published: December 11, 2014 30209
dx.doi.org/10.1021/jp509355g | J. Phys. Chem. C 2014, 118, 30209−30215
The Journal of Physical Chemistry C
Article
Figure 1. Morphologies represented in the data set used in this study: (a) octahedron, (b) truncated octahedron, (c) cuboctahedron, (d) truncated cube, (e) cube, (f) doubly truncated octahedron, (g) great rhombicuboctahedron, (h) small rhombicuboctahedron, (i) rhombi-truncated octahedron, (j) rhombi-truncated hexahedron and (k) rhombic dodecahedron.
and σ2 is the variance:
dependence of the ionization potential, electron affinity, electronegativity, and chemical hardness of ensembles of hydrogen passivated nanodiamonds. We find that there are likely to be definite advantages to attempts to separate nanodiamond into more monodispersed samples. By predicting quality factors for a variety of cases, we find that there is a clear motivation for enriching samples with {111} facets (or suppressing the prevalence of {100} facets) to increase the selectivity and efficiency of charge transfer reactions. This suggests that the development of classes of nanodiamond products may be possible. The data set used in this study contains 183 fully hydrogenated nanodiamonds with a hydrostatic diameter between 2 and 4.5 nm and a large range of different morphologies defined by zonohedrons enclosed by {111}, {110}, and {100}. These include the octahedron, truncated octahedron, cuboctahedron, truncated cube, cube (or regular hexahedron), doubly truncated octahedron, great rhombicuboctahedron, small rhombicuboctahedron, rhombi-truncated octahedron, rhombi-truncated hexahedron, and the rhombic dodecahedron. A smaller set of particles with these shapes has been used in previous studies,20 and the entire set is represented schematically in Figure 1. Although previous works focused on “clean” reconstructed, bucky-diamonds, the present work is focused on hydrogenated structures that have been suitably processed.48 At this point it should be pointed out that it is difficult to preserve the exact geometric shape in each structure due to the constraints of the diamond lattice, and for our purposes it is important to preserve the right combinations of {100}/{110}/{111} facets than a particular size. It is not possible to make a structure of each shape with equivalent numbers of atoms, so we have included a range of sizes with each shape and discuss the resulting shape-dependent trends in the predicted properties. Since we are also concerned with the properties of a diverse ensemble of possible structures, we have analyzed the charge transfer property relationships statistically, using a Gaussian probability density function: ⎧ (x − μ)2 ⎫ ⎬ exp⎨− 2σ 2 ⎭ ⎩ 2πσ 2
n 2
σ =
i=1
(3)
calculated by summing over the individual properties x of all structures i. The total number of structures for each set is n, and in each case pi is the probability of observation of i: pi =
(1/qi′)e−ΔGi / kBT n
∑i = 1 (1/qi′)e−ΔGi / kBT
(4)
where kB is Boltzmann’s constant and the denominator is the canonical partition function. The change in the free energy ΔGi = ∑j (NjEj − Ei(j)) describes the thermodynamic stability, as a function of the total energy, Ei(j), of particle i, containing j elements; Nj are the number of atoms of species j, and Ej is the energy of j in the reservoir. This can be defined with respect to any chemical reservoir (temperature and/or supersaturation) that is required, but in this case we use carbon in bulk diamond and hydrogen in a gas of H2. Larger structures and lower energy shapes have a higher probability of observation and therefore contribute more to the properties of the ensemble. In addition to this, since diamond is a powerful abrasive (and the only thing that will abrade a diamond is another diamond), it is likely that nanodiamond powders will suffer from selfabrasion, which will remove the acute edges and corners. This effect can be included by applying a penalty for sharp corners, and we have done so here by weighting the probabilities by the inverse of the effective surface to volume ratio, q′i (defined as the surface-to-volume ratio of i divided by the surface-tovolume ratio of a sphere of equivalent volume). This has the effect of slightly increasing the probability of more “spherical” particles and reducing the probability that particles retain sharp edges and corners following processing. As mentioned earlier, this study has focused on four properties (x) related to the transfer of electrons: the ionization potential (IP), the electron affinity (EA), the electronegativity (χ), and the chemical hardness (η). These properties are defined adiabatically with respect to the total energy of the neutral structure E and the corresponding anion E− and cation E+, such that
1
X=
∑ pi (xi − μ)2
(1)
where X represents either the ionization potential, electron affinity, electronegativity, or chemical hardness. As usual, μ is the expectation value (or ensemble average, which should not be confused with the term used to denote the atomic or molecular chemical potential in other publications), defined as
IPi = Ei+ − Ei
(5)
EA i = Ei − Ei−
(6)
n
μ=
∑ px i i i=1
χi =
(2) 30210
1 + (Ei − Ei−) 2
(7)
dx.doi.org/10.1021/jp509355g | J. Phys. Chem. C 2014, 118, 30209−30215
The Journal of Physical Chemistry C
Article
Figure 2. Comparison of the impact on (a) the ionization potential (IP), (b) electron affinity (EA), (c) electronegativity (χ), and (d) chemical hardness (η), for 2−4.5 nm ensembles when the prevalence of specific surface facets is enriched.
ηi =
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1 + (Ei + Ei− − 2Ei) 2
the values predicted for diamondoids but is perfectly aligned with the size-dependent trend based on a power-law fit to the total-ion-yield spectroscopy results of Lenzke et al.54 The expectation value of the Mulliken electronegativity was found to be 3.808 eV, with a variance of 0.509 eV, and the chemical hardness was found to have an expectation value of 0.667 eV, with a variance of 0.427 eV. These values are consistent with other hydrocarbon molecules and carbon clusters.55 In the case of the electron affinity we find an expectation value of −3.140 eV (which is negative and is often reported as a negative electron affinity, NEA, of 3.140), with a variance of 1.695 eV. This is greater than the experimental value for the bulk diamond (111) surface measured by Brandis and Pate (
