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Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Does Twinning Impact Structure/Property Relationships in Diamond Nanoparticles? Amanda S. Barnard,*,† George Opletal,† and Shery L. Y. Chang‡ †

Data61 CSIRO, Docklands, Victoria 3008, Australia Eyring Materials Center, Arizona State University, Tempe, Arizona 85281, United States

‡

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S Supporting Information *

ABSTRACT: Although the majority of computational predictions of the properties of diamond nanoparticles (nanodiamonds) are based on sets of exclusively single-crystal structures, most experimental observations contain twins. The influence of twins is difficult to characterize computationally since they are metastable and their relative stability will depend on the thermochemical conditions. The properties of entire samples of nanodiamonds will also depend on how many twins there actually are. In this study, we have used a combination of electronic structure simulations, ab initio thermodynamics, and a simple statistical method called ensemble filtering to investigate the probability of twinning in nanodiamond and their impact on charge transfer properties such as the ionization potential, the electron affinity, and the electronic band gap. We find that, provided some degree of control can be exercised over the surfaces, increasing the number of twinned particles in samples could shift the selectivity of the electron affinity and the band gap and could greatly improve the quality of samples by decreasing the bandwidth, improving the sensitivity and specificity.

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INTRODUCTION Diamond nanoparticles (nanodiamonds) are proving invaluable in the fields of biotechnology and medicine,1,2 as drug delivery vehicles,3−5 luminescent biomarkers,6−9 and radiosensitizers under X-ray or γ irradiation.10−12 Stable suspensions of colloidal nanodiamonds with a hydrostatic diameter of ∼3.0 nm have been shown to enhance chemotherapy, increase selectivity13,14 and sensitivity,15 moderate dosage,16 and sustain treatments without burst effusion.17 More extensive reviews of this field of research, the opportunities, and the remaining challenges have been recently compiled.18−22 Many of these advancements have been underpinned by a deeper understanding of how the bulk and surface structures of nanodiamonds (their size, shape, and surface chemistry) impact their reactive properties obtained via electronic structure simulations.23−27 However, the vast majority of computer simulations have focused on a single-crystal nanodiamond, regardless of the fact that twinning is often observed28−31 and the impact of twinning on the stability and charge transfer properties of nanodiamond samples is poorly understood. Twin planes are high-energy defects in single crystals (such as diamond) that provide a source of strain in the lattice and intersect with free surfaces at concave or convex edges. These edges behave differently to the regular edges of polyhedra and may result in different types of atomic reconstructions. The most common types in diamond are [111] twins, where the twin axis is perpendicular to an octahedral plane and the two halves are mirror images of each other. The twin plane has a hexagonal close-packed (lonsdalite) structure and is much lower in energy than a grain boundary typically observed in © XXXX American Chemical Society

polycrystalline diamond. The challenge associated with the simulation of these highly symmetric twins is that, depending on the method used, the lattice can undergo reconstruction and transform the lonsdalite plane to a diamond plane, thereby eliminating the twin. This is particularly prevalent in simulations of nanodiamond where significant reconstruction occurs at the surface anyway.23 At this stage, it has not been confirmed whether twinning increases or decreases the likelihood of nondiamond surface reconstructions, or whether functional properties are affected by the presence of twinned particles in nanodiamond samples. One approach to overcome this conundrum is to devise a twinning configuration where the energy barrier to reconstruction/removal is very high and/or the reconstruction pathways are effectively blocked. This is the case with decahedral twinning, characterized by five intersecting twin planes with a common twisted icosahedral axis. This type of twinning is common in metallic nanoparticles32−34 and is observed frequently in nanodiamond from different sources for many years.35−39 Figure 1 shows high-resolution transmission electron microscopy images of selected examples of nanodiamond particles with multiple twins within one particle. The twin planes occur along {111} planes and can present multiple parallel twin planes, giving a lonsdalite type of structure, as shown in the examples in Figure 1a,b. Intersecting twin planes with the intersecting angle around 70° (Figure 1c) are also Received: January 6, 2019 Revised: April 1, 2019

A

DOI: 10.1021/acs.jpcc.9b00142 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

simulations, ab initio thermodynamics, and simple statistical methods to investigate the impact of twinning on the charge transfer properties such as the ionization potential, the electron affinity, and the electronic band gap. We have created an ensemble of both twinned and untwinned particles of various sizes, shapes, and surface chemistries and used ensemble filtering to explore how the properties change in response to filters that reflect different design decisions. This analysis focuses on full-particle structure and properties (rather than atomic-level variations) and includes the impact of temperature, which determines the relative probabilities of observation and compares to different chemical and material reference states. We find that, provided some degree of control can be exercised over the surfaces, increasing the number of twinned particles in samples shifts the electron affinity and the band gap and could significantly improve the quality of samples by decreasing the bandwidth.

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METHODS In this study, the structures and properties of the nanodiamonds have been simulated using density functional tightbinding with self-consistent charges (SCC-DFTB), as implemented in the DFTB+ code.41−43 All structures have been fully relaxed with a conjugate gradient methodology until forces on each atom were minimized to be less than 10−4 au (i.e., ≈5 meV/Å). In all of the calculations, the “PBC” set of parameters is used to describe the contributions from diatomic interactions of carbon.44 This method has been shown to provide good and reliable results for diamond nanoparticles in the past.45 As mentioned above, twin planes are often eliminated during the structural relaxations that aggressively seek the ground state. In this study, we have included structures with decahedral twinning. Although more rarely observed in nanodiamond samples, the use of 5-fold twins effectively pins the twin planes and prevents large-scale restructuring that would converge to an untwinned crystal upon relaxation. This trick ensures that we have fully relaxed

Figure 1. Selected examples of detonation nanodiamond particles showing twinning along {111} planes (marked by blue lines). Multiple twins are observed within one nanodiamond particle and can give (a, b) lonsdalite type of structure or (c) intersecting twin planes.

shown. In the case of the smaller nanodiamond particle (∼3 nm as shown in Figure 1a), the twin planes protrude from the surfaces, bisecting the surface reconstructions into smaller segments than appear on single-crystal counterparts. These smaller segments give a structure with higher curvature, corresponding to a higher fraction of sp2+x hybridization, consistent with our previous report.40 In the case of larger particles (∼6 nm size as shown in Figure 1b,c), the twin planes have less pronounced effect on the surface reconstructions. Predicting the impact of these sorts of particles on the properties of the sample as a whole requires a suite of theoretical, computational, and statistical methods. In this study, we have used a combination of electronic structure

Figure 2. Examples of reconstructed diamond nanoparticles in the data set, including a (a) 615 atom, 5-fold twinned particle, (b) 624 atom, singlecrystal, small rhombicuboctahedron, (c) 635 atom, 5-fold twinned particle, (d) 660 atom, single-crystal cuboctahedron, (e) 665 atom, 5-fold twinned particle, and (f) 674 atom, single-crystal modified truncated octahedron (also referred to as a doubly-truncated octahedron). Blue denotes sp2 hybridization, green denotes sp2+x hybridization, and gray denotes sp3 hybridization. B


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Figure 3. Size-dependent number densities of all nanodiamonds including (a) lonsdalite-type atoms residing in the twin planes (where present), (b) diamond-type atoms residing between the twin planes, and (c) nondiamond-type atoms residing at the surfaces, either reconstructed or passivated (C−C coordination of 3).

because the number of twin planes does not change (always 5) and the fcc wedges between the twin planes increase more rapidly in size than the twin planes themselves. Both hydrogenpassivated and clean, fully reconstructed nanodiamonds have been included, and the entire set of fully relaxed diamond nanostructures are openly provided online.46,47 As this set represents a statistically valid ensemble (where all structures are unique), we may define the ensemble average, ⟨x⟩, of any functional property x as

twinned particles (with a predetermined twin plane area) at the end of the simulations. The data set used in this study contains 70 face-centered cubic (fcc) diamond nanoparticles with a diameter between 0.97 and 2.20 nm and a 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), great rhombicuboctahedron, small rhombicuboctahedron, doublytruncated octahedron, rhombi-truncated octahedron, rhombitruncated hexahedron, and rhombic dodecahedron. In addition to this, 70 decahedral twinned diamond nanoparticles have also been simulated and included, with varying aspect ratios within the same size range. Examples of particles in this structure set are provided in Figure 2. Based on a previous work on untwinned particles, it is well-known that the trends identified for small nanodiamonds extrapolate well to larger particles. However, given the size range included herein, it is important to point that some of the effects may be more exaggerated and can be expected to be more subtle for larger particles. All of the nanodiamonds included in this study are plotted in Figure 3, wherein we can see the number densities of all nanodiamonds including lonsdalite-type atoms residing in the twin planes (Figure 3a), diamond-type atoms residing between the twin planes (Figure 3b), and C atoms residing at the surfaces, either reconstructed or passivated with a C−C coordination number of 3. We can see that, as a function of size, the fraction of fcc diamond-like atoms and surface C atoms increases and decreases, respectively, but the fraction of lonsdalite-type atoms is a constant within uncertainties. This is

n

⟨x⟩ =

∑ px i i

(1)

i=1

and the variance, σ2, as n

σ2 =

∑ pi (xi − ⟨x⟩)2 i=1

(2)

Both are calculated by summing over the individual properties xi 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 particle i. There are numerous ways to define this probability based on different statistical distributions. If the synthesis and/ or stability is thermodynamically limited, we may define the normalized probability using the thermodynamic distribution ptherm (i) =

exp−ΔGi / kBT n

∑i = 1 exp−ΔGi / kBT

(3)

where kB is the Boltzmann constant and the denominator is the canonical partition function. The change in the free energy, C


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The Journal of Physical Chemistry C ΔGi, describes the thermodynamic stability (with respect to the reference state). The energies obtained from the DFTB simulations account for only the ground-state (temperature T ≈ 0 K, pressure P = 0 Pa) electronic energies, E, which are a part of the thermodynamic internal energies or free energies at finite temperatures, whereas the free energies, ΔGi, refer to the constituent elements in their stable forms at the standard state. To extend the ground-state energy to finite temperatures, phonon vibrational frequencies can be calculated, from which various thermodynamic functions can be derived, including vibrational entropy, heat capacity, and the Helmholtz free energy.48 However, both the direct method49 and the linear response method50 are computationally demanding. Moreover, the integration tends to be difficult if there are phase transformations in the temperature range between 0 K and the temperature of interest because all of the phonon modes of both phases need to be evaluated. In addition to this, certain thermodynamic functions may diverge at the phase transformation point. To overcome this issue and extend the ground-state DFTB energies to finite temperatures and pressures, we have used the ab initio thermodynamics method,51 which combines the results calculated from electronic structure simulations at the ground state and the extensive thermochemical data measured at the standard state. Under the assumption that the change in electronic energies represents the most significant contribution to the change in free energy (i.e., other contributions cancel out), the free energy change in a reaction xA + yB → C at the standard state can be calculated as ΔG 0(T ) = Δf GC0(T ) − xΔf GA0 (T ) − yΔf G B0(T ) =[ΔEC(T0) +

ΔμC0 (T )]

− y[ΔE B(T0) +

− x[ΔEA (T0) +

Alternatively, if the synthesis and/or stability is rate limited, rather than thermodynamically limited, then a range of other distributions are possible. This includes a normal distribution over the size range prate (i) =

(4)

(5)

(6)

where T0 is 0 K, and μ0 is the chemical potential under the standard pressure (P0 = 1 atm). The chemical potential μ0(T) can be calculated using the heat capacities, Cp, and entropy, S, fitted to the Shomate equation with coefficients from the NIST WebBook,52 such that μ0 (T ) = μ0 (Ta) +

∫T

T

Cp dT − T

a

∫T

T

a

Cp T

E IP(i) = Ei+ − Ei

(10)

E EA (i) = Ei − Ei−

(11)

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RESULTS AND DISCUSSION Ensemble Properties. The structure of the nanodiamonds used in this study can be characterized in various ways, including the size distribution of bond lengths, bond angles, and different types of C−C hybridization. These types of characterizations are shown in the Supporting Information, wherein we can see that there is very little difference between the twinned and single-crystal nanodiamonds. The main difference between the two groups is the degree of surface

(7)

where Ta is the ambient room temperature (298.15 K) and extended to include finite pressures, P, using ij P yz μ0 (T , P) = μ0 (T ) + RT lnjjj zzz j P0 z k {

(9)

obtained via the variance), ⟨x⟩/ σ 2 (determined in this case in eV). This is a powerful way to use large data sets to provide new insights into collective behavior of entire samples.57

dT

− (T − Ta)S(Ta)

2 2πσsize

ij (D − ⟨x⟩size )2 yz zz expjjj− i zz 2 j σ 2 size k {

The band gap is obtained from the relation EBG = EIP − EEA. At this point, it is worth pointing out that although hydrogenated diamond surfaces are known to exhibit negative electron affinity,53−56 this is not the case for “clean” reconstructed nanodiamonds, and so the electron affinities reported in this study will be both positive and negative. One of the advantages of applying a statistical analysis of the structures is the ability to assess quality, as well as quantities. The quality factor (Q-factor) is a dimensionless parameter used throughout physics and engineering to describe efficiency, particularly for devices such as oscillators and resonators. In the context of nanoparticle properties, it provides a measure of specificity and can be easily determined by dividing the expectation value by the bandwidth (or standard deviation,

where ΔE(T0) are the electronic energies with respect to the DFTB reference state, Δμ0(T) are the chemical potentials of the reactants and products, and ΔfG0(T) are the Gibb’s free energies of formation for the reactants and products, which can be extracted from the thermochemical tables. In this method, the gap between the ground state and the standard state in the chemical potential is filled by the connection energy Δμ0 (T ) = μ0 (T ) − μ(T0)

1

where Z is the partition function over all of the structure i, ⟨x⟩size is the average size of the nanodiamonds in the ensemble, Di is the spherically averaged diameter of each i, and σsize is the variance of the size distribution of the ensemble. As the size of these particles is largely determined by the formation kinetics, this distribution may be tuned to match the characteristic kinetically driven size distribution exhibited postsynthesis. In cases where the synthesis is typically rate limited and the stability is thermodynamically limited, it is convenient to construct a combined distribution that reflects real observations. In this study, we have multiplied the Boltzmann and sizedependent normal distributions (p(i) = Ptherm(i) × prate(i)) to recognize that the probability of a particular particles being present in a sample will be a function of the thermodynamics stability and the formation kinetics, simultaneously. Examples for purely thermodynamically limited (Boltzmann) or ratelimited (normal) distributions will follow. This study has focused on three properties (x) related to the transfer of electrons: the ionization potential (EIP), the electron affinity (EEA), and the electronic band gap (EBG). The EIP and EEA properties are defined adiabatically with respect to the total energy of the neutral structure E, the corresponding anion E−, and cation E+, such that

ΔμA0 (T )]

ΔμB0 (T )]

1 Z

(8)

where P0 is the vacuum and R is the gas constant. D


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Figure 4. Size-dependent probability distributions for the entire nanodiamond sample showing that the different subsets of bulk and surface structures exhibit different relative populations based on their free energy of formation, at ambient pressure and T = 298.15 K with respect to a methane reference state. The normal probabilities for the reconstructed and passivated particles of the same bulk structure subset are coincident.

Figure 5. Size-dependent charge transfer properties of all nanodiamonds including (a) ionization potential, EIP, (b) electron affinity, EEA, and (c) band gap, EBG.

E


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The Journal of Physical Chemistry C graphitization occurring on the (clean) reconstructed particles; the single-crystal particles showing bimodal distribution of sp2 bonding, depending strongly on the overall shape of the particle and the prevalence of {111} facets. The twinned particles, which are also enclosed by {111} facets, exhibit a near constant fraction of sp2 bonds, with a slow increase in diamond-like sp3 bonds coming at the expense of sp2+x bonds. As mentioned above, the stability has been characterized via the relative population, which is a combination of the thermodynamically limited (Boltzmann) and rate-limited (normal) distribution, which can be calculated for a T, P, and with respect to any reference state. Presented in Figure 4 are the distributions for nanodiamonds in the set, treated as a single ensemble, showing that the different subsets of bulk and surface structures exhibit different relative populations based on their free energy of formation at ambient pressure and T = 298.15 K with respect to a methane reference state. For the purposes of comparison, Boltzmann probabilities and the final (relative) populations are provided for four temperatures with respect to five different reference states (bulk diamond, methane, ethane, ethene, and bulk graphene) and are provided in the Supporting Information, but the general trend that the single-crystal particles have a slightly higher probability of observation (being the lower energy alternative) and passivated particles have a much higher probability of observation (due to the energetic preference for hydrogenated surface compared to these reference states) is thermochemically consistent. In addition to the structural and energetic (probabilistic) properties of the single-crystal and twinned nanodiamonds, the distribution of the charge transfer properties calculated at T = 0 K in a vacuum is provided in Figure 5. Here, we can see that the ionization potential, EIP (Figure 5a), is noisy but relatively consistent (with the exception of a few outliers). Twinning does not significantly impact the ionization potential at low temperature and pressure. As mentioned above, the electron affinity, EEA (Figure 5b), can be either positive for clean surfaces or negative for hydrogen-passivated surfaces, giving rise to a bimodal distribution across the set. The reconstructed particle results are relatively consistent, regardless of the internal structure, but the passivated particles show a different distribution depending on whether the interior is twinned. Twinned particles exhibit a much more constant, sizeindependent electron affinity. The band gap, EBG (Figure 5c), also shows a bimodal distribution owing to its relationship to the electron affinity, being blue-shifted (with respect to bulk diamond) as passivated particles are quantum confined, or redshifted (with respect to bulk diamond) as reconstructed particles introduce low-energy graphitic states into the band structure. The electron affinity and the band gap are largely size independent in this range and determined by the type of bulk and/or surface structure. The trends at these sizes are consistent with the behavior observed in recent experiments using scanning tunneling spectroscopy and Kelvin force microscopy,58 where diamond nanoparticles from 2 to 6 nm in size were exposed to hydrogen for 20 min. The difference in absolute values between the experiments and the simulation results in the computational data set is likely due to different levels of hydrogen coverage on the surface, different sizes, and the presence (or lack) of a substrate, which is known to be a confounder.59 Multiple classes of nanodiamond electron affinity, based on their surface heterogeneity, have recently been identified using machine learning.60

Beyond these trends, we can begin to predict how the properties of the entire sample would change if twinned or single-crystal nanodiamonds were targeted, either during synthesis or postprocessing. Using the methods described above, the expectation values, ⟨x⟩, of the ensemble average for x = EIP, EEA, EBG along with the corresponding variance, σ, and quality factor, Q-factor, were determined using the combined distribution and all particles in the ensemble. These results are provided in Table 1 for T = 298.15 K and P = 101 kPa with respect to the methane reference state. In general, with this mix of bulk and surface structures, the specificity (measured by the Q-factor) is higher for the ionization potential than the electron affinity or the band gap due to the impact of surface chemistry on the latter. Similar results for other reference states and temperatures are provided in the Supporting Information, wherein we can see that the Q-factors decrease with increasing temperature, regardless of the reference state. The EIP and EEA increase with the increasing temperature, whereas EBG decreases with increasing temperature, also regardless of the reference state. Ensemble Filtering. Once the ensemble properties have been established, it is also possible to predict the effect of different synthesis or purification strategies by restricting the ensemble in ways that reflect design decisions. Ensemble filtering is a method that effectively overlays a binary probability function that leaves the ensemble unchanged if the filter is satisfied, or zero if the filter is not satisfied. By recalculating the expectation value for each of our properties after the filters have been applied, we can investigate how attempts to control the degree of twinning in nanodiamond samples, or the surface chemistry, will likely impact the selectivity possible in electron charge transfer reactions. Similarly by recalculating Q-factors under the same filters, we can see how the specificity will be affected. In the present study, we have filtered the unrestricted mixture into four ensembles with specific bulk and surface structures such that ∀n ∈ N:p(n) = (F = 1∧p(n))∨(F = 0∧0). Explicitly, these fours filters are Fpassivated = (NH > 0 ∧ 1) ∨ (NH = 0 ∧ 0) Freconstructed = (NH = 0 ∧ 1) ∨ (NH > 0 ∧ 0) Fsinglecrystal = (NLONS = 0 ∧ 1) ∨ (NLONS > 1 ∧ 0) Ftwinned = (NLONS > 1 ∧ 1) ∨ (NLONS = 0 ∧ 0)

where NH is the number of hydrogen atoms and NLONS is the number of atoms in the lonsdalite configuration, providing eight possible filtered and unfiltered combinations (in addition to the mixed bulk and mixed surface combination described in the previous section), i.e., both twinned and reconstructed, or mixed and passivated, etc. The results under these filters are provided in Table 1 for T = 298.15 K and P = 101 kPa with respect to the methane reference state, along with results for other reference states and temperatures in the Supporting Information. By comparing different filters, we can see how twinning can be used to tune the charge transfer properties and improve the response of the samples. The top of Table 1 provides the mixed, unrestricted ensemble for comparison, and the next two sections show the impact of controlling the surface chemistry, regardless of the bulk structure. In each case, the energy of the properties has shifted, indicating the opportunity to tune the F


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controlled. The filters that restrict the bulk structure but allow a mixture of surface structures provide similar results that do not deviate from the unrestricted sample significantly. If the surface chemistry can be simultaneously controlled, then the impact of twinning is profound. In the case of the ionization potential, clean surfaces produce properties that are slightly blue-shifted with respect to the unrestricted sample, but twinned particles have a higher Qfactor (greater specificity). Passivated surfaces produce properties that will be blue-shifted with respect to the unrestricted sample if the particles are single crystals (with significantly less specificity), or slightly red-shifted if the particles are twinned (with significantly greater specificity). The difference between twinned and untwinned passivated nanodiamonds is more than 1.8 eV. In the case of the electron affinity, clean surfaces produce properties that are significantly blue-shifted with respect to the unrestricted sample and with substantially higher Q-factors (particularly for the twinned particles), whereas passivated surfaces produce negative electron affinities with the twinned particles exhibiting a Q-factor almost 27 times that of the unrestricted ensemble. In the case of the band gap, where we can see that the impact of twinning is typically on the order of 0.1 eV if reconstructed or ∼1.2 eV if passivated, the impact on the Q-factor can be almost seven times that of the unrestricted ensemble when exclusively hydrogen-passivated twinned nanodiamonds are included. In light of these results, the role of stacking faults and dislocations is also worthy of further work, provided the issue of stacking faults/dislocations disappearing from the particles during relaxation can be overcome. Moreover, as it is known that twins in nanodiamond can act as sinks for chemical impurities, it would be interesting to dope the twinned structures here with different distributions of known impurities and color centers61 to see if the combination has an important impact on charge transfer. More generally, the impact of different types of surface passivation such as oxidation, hydroxylation, amination, and fluorination on the charge transfer of nanodiamonds (whether twinned or not) remains an unexplored area of research.

Table 1. Results of the Expectation Value (Ensemble Average) of the Ionization Potential, Electron Affinity, and Electronic Band Gap for the Restricted and Unrestricted Mixtures of Twinned and Untwinned (Single-Crystal) Nanodiamonds, with Hydrogen-Passivated and/or Reconstructed Surfacesa Bulk structure|Surface structure

EIP

EEA

EBG

Mixed|Mixed expectation value, ⟨x⟩ variance, σ Q-factor

5.008 0.120 14.472

−2.764 6.186 1.111

7.771 5.902 3.199

Mixed|Reconstructed expectation value, ⟨x⟩ variance, σ Q-factor

5.894 0.245 11.918

4.072 0.136 11.061

1.822 0.198 4.099

Mixed|Passivated expectation value, ⟨x⟩ variance, σ Q-factor

4.966 0.100 15.714

−3.402 1.815 2.526

8.369 2.114 5.755

Single Crystal|Mixed expectation value, ⟨x⟩ variance, σ Q-factor

5.032 0.176 11.982

−1.985 5.909 0.817

7.018 6.009 2.863

Twinned|Mixed expectation value, ⟨x⟩ variance, σ Q-factor

4.986 0.066 19.337

−3.355 6.535 1.313

8.341 5.759 3.476

Single Crystal|Reconstructed expectation value, ⟨x⟩ variance, σ Q-factor

5.564 0.166 13.640

4.462 0.223 9.457

1.102 0.113 3.275

Twinned|Reconstructed expectation value, ⟨x⟩ variance, σ Q-factor

5.466 0.040 27.474

4.175 0.051 18.481

1.291 0.060 5.293

Single Crystal|Passivated expectation value, ⟨x⟩ variance, σ Q-factor

6.766 3.978 3.392

−3.517 3.842 1.794

10.282 12.074 2.959

4.931 0.040 24.670

−4.219 0.024 27.425

9.150 0.054 39.287

Twinned|Passivated expectation value, ⟨x⟩ variance, σ Q-factor

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CONCLUSIONS Presented here are results obtained using a combination of electronic structure simulations, ab initio thermodynamics, and a statistical technique referred to as ensemble filtering showing how the presence of twinned diamond nanoparticles may be expected to influence a range of charge transfer properties. We find that the relative population of twinned versus untwinned nanodiamonds depends on the thermochemical conditions, both the temperature and the chemical reference state that are important during synthesis, storage, and in their applications. We find that the charge transfer properties are highly dependent on the surface structure, whether passivated or reconstructed (graphitized), but if this can be controlled, the role of twinning in determining structure/property relationships can be characterized. A high proportion of twinned particles is expected to shift the charge transfer energies and to significantly improve the quality factors, decreasing the bandwidth and improving the sensitivity and specificity of samples. Through the ability to shift or improve the resolutions of the charge transfer properties, one could facilitate better targeting of reactions important in drug delivery applications. Filtering samples to have more or less twinned particles could

Results are shown for the combined Boltzmann × normal distribution, for samples that are both thermodynamically and kinetically influenced, over the entire size range at T = 298.15 K and P = 101 kPa with respect to the methane reference state. a

property, and the Q-factor has changed, indicting there will be consequences for this tuning (some advantageous, some not). The remainder of the table (and the tables in the Supporting Information) contains ensembles filtered by their bulk structure. Here, we can see that, in general, the impact of twinning is only strong if the surface chemistry is also G


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also lead to advances in drug-specific platforms, including only the fraction of twinned particles needed for one drug, but not another. In general, whether it is possible to control the formation of twins or not, or whether they can be selectively filtered during postprocessing, it is clear that the presence of twins in nanodiamond samples does influence their charge transfer properties and hence their performance in applications such as drug delivery.62 Although stochastic, rather than deterministic, these results provide insights into the correlation between the defective structures and charge transfer properties, guiding the direction of the future work exploring the causal relationship with traditional computational methods.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b00142. Statistical characterization of the bonding and C−C hybridization of all of the particles in the data set, along with the thermodynamic probabilities, relative populations, and filtered and unfiltered charge transfer properties for ensembles at temperatures of 298.15, 500, 700, and 900 K, with respect to bulk diamond, methane, ethane, ethene, and graphene reference states (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Amanda S. Barnard: 0000-0002-4784-2382 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computational resources for this project were supplied by the National Computing Infrastructure, a national facility, under grant q27.

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REFERENCES

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