(XIET) from Nanomaterial Donors to Nanomaterial Acceptors

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C: Physical Processes in Nanomaterials and Nanostructures

Theoretical Study of X-ray Induced Energy Transfer (XIET) from Nanomaterial Donors to Nanomaterial Acceptors Arjun Sharmah, Jennifer Lien, Mengqi Su, and Ting Guo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01696 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 11, 2018

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The Journal of Physical Chemistry

Theoretical Study of X-ray Induced Energy Transfer (XIET) from Nanomaterial Donors to Nanomaterial Acceptors Arjun Sharmah, Jennifer Lien, Mengqi Su and Ting Guo* Department of Chemistry, University of California, Davis, CA 95616

ABSTRACT. A systematic theoretical study was carried out here to investigate a new phenomenon of X-ray Induced Energy Transfer (XIET) within the purview of X-ray nanochemistry. XIET occurs between a strongly X-ray absorbing nanomaterial such as one or more gold nanoparticles (donors) and a weakly X-ray absorbing nanomaterial such as a hollow silica nanoparticle filled with water (acceptor) and part of the energy absorbed by the former can be transferred to the latter when the two are positioned sufficiently close together and under 20100 keV X-ray irradiation. XIET was studied as a function of dimension, composition, configuration and orientation of donors and acceptors, number of donors and X-ray energy. Relative and percentage XIET efficiencies were calculated. These results provide a theoretical framework to guide future experimental XIET studies.

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1. Introduction Nanosystems can absorb hard X-rays and convert the absorbed energy into chemical and electrical energies.1,2 These energy transfer processes can impact many potential applications such as cancer therapy, imaging, and chemical production.3-7 It is important to understand detailed energy transfer mechanisms, starting with X-ray absorption, in order to realize the full potential of interactions between nanoscale systems and X-ray radiation. Hard X-rays (20-100 keV) can be highly penetrating, especially in low Z media such as water or biological tissues. Absorption events of a single photon are thus spread over a long path or a large volume in the media through Compton scattering of the X-ray photon by the low-Z media. Nanomaterials made of high density heavy elements have been used to increase the probability of absorbing X-rays at specific locations in low Z media through the photoelectric effect4,8,9, a concept that has been explored to assist cancer treatment.10-13 The added nanomaterial acts as a sensitizer or enhancer to increase absorption of X-rays, the number of electrons emitted, as well as energy deposited in the media. Using nanomaterials therefore effectively shrinks the location randomness of X-ray driven reactions because upon absorption, the distance over which the emitted electrons deposit their kinetic energy is much shorter than that of incoming X-rays. Since the process is of physical origin, the resulting energy deposition enhancement is called physical enhancement (PE), which differs from chemical or biological enhancement (CE or BE) that rely on catalytic properties of nanomaterials or their behaviors in biological systems.7,14-19 These categories of enhancement are defined in X-ray nanochemistry, a discipline that studies the use of nanomaterials and nanochemistry to enhance the effectiveness of X-ray irradiation. Each of the aforementioned enhancement categories can be further divided into different types. For


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example, there are at least two types of PE: types 1 and 2 physical enhancement, noted as T1PE and T2PE, respectively. T1PE and T2PE are caused respectively by energetic and low energy electrons released from nanomaterials as a result of X-ray irradiation. The origins of these enhancements have been discussed in the literature.1,9,15,20 A majority of the enhancement studies reported in the literature to date have measured the (linear) sum of the average T1PE and T2PE, or PE without differentiation of the two. In this framework, T1PE is constant in the whole sample and affects the whole sample volume due to the long travels by energetic electrons in the low Z media. T1PE is independent of location of probes with respect to the nanomaterials, and . The magnitude of T1PE is approximately 100% increase or one-fold increase to the detected signal per one weight percent (WP) of gold in water, or can be noted as 1.0 dose enhancement unit (DEU) WP-1 at 33 keV X-rays. T2PE depends on the location of probes with respect to the nanoparticles because it exists strongly near the surface of nanomaterials. T2PE is caused by energy deposition by low energy electrons released from X-ray irradiated nanomaterials, and has been theoretically studied by many groups.8,9,20-24 If probes are uniformly distributed in the whole sample volume, then the magnitude of the average T2PE for 100 nm gold nanoparticles is approximately 0.4 DEU WP-1 under 33 keV X-ray irradiation, even though only a small portion of the probes are affected by the enhancement. The peak T2PE value, however, can be much greater than 1 DEU. The total (average) PE, which is the sum of the T1PE and average T2PE, is 1.4 DEU WP-1, which is numerically close to T1PE.25 Unlike T1PE, if probes are placed only near the surface of nanoparticles, significantly higher enhancements can be detected. For example, a single 100-nm gold nanoparticle gives rise to 8.2 DEU T2PE in a 5-nm theoretical shell-like deposition region


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directly off the surface of the nanoparticle. As such, T2PE exists around either a single nanoparticle or a large number of nanoparticles, whereas T1PE requires a large amount of nanoparticles because it is an average effect. The average T2PE assumes the units of DEU WP-1 whereas for single nanoparticles T2PE has to be expressed in the units of DEU. Despite numerous theoretical studies, T2PE was only recently observed experimentally.20,26 In the reported work, nanoscale aqueous solutions acting as media for energy deposition and the probe for T2PE were contained in hollow calcium phosphate enclosed liposomes (CaPELs). However, the process differs from T2PE because the shape of CaPELs did not conform to traditionally defined T2PE regions reported in the literature. Instead, this new energy deposition process can be regarded as energy transfer mediated by electrons released from AuNPs after absorption of X-rays. The transfer process, called X-ray Induced Energy Transfer (XIET), is illustrated in Scheme 1. The solid CaP shell around the acceptors guarantees that only PE is probed; detection is free of anti-enhancement (AE) because AuNPs are not in contact with the solution in CaPELs. Aside from this experimental work, little is known about the energy transfer process between nanomaterial donors and acceptors induced by X-rays. Historically, a lack of distinction among types of physical enhancements – T1PE, T2PE, and XIET – is caused by the lack of nanoscale acceptors capable of detecting T2PE. Most dosimetric measurements employed probes such as dye molecules distributed uniformly throughout the whole sample volume and in such cases, the average T2PE is a fraction (~15% to 40%) of T1PE for gold nanoparticle up to 100 nm in diameter. The work involving nanoscale acceptors mentioned above makes it possible to study T2PE generated from individual nanoparticles, as well as to create and develop the concept of XIET, which can be exclusively validated theoretically.


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Hence a theoretical framework is required to more accurately describe enhancement mechanisms congruent with the nanoscale probes detecting XIET. Scheme 1 illustrates a typical XIET process, which includes X-ray absorption and electron emission by a donor and the medium, transport of electrons in medium, and energy deposition by these electrons inside of an acceptor. The amount of enhancement of energy deposition in the acceptor is measured in dose enhancement units (DEU). There are two ways to express enhancement: absolute (abs) and relative (rel). 1.0 DEU (abs) enhancement is equivalent to a 100% increase to the effect of Xrays, which is the same as an enhancement of 2.0 DEU (rel). In this work, the default enhancement is absolute enhancement.

Scheme 1. Illustration of X-ray Induced Energy Transfer (XIET) between a donor (gold nanoparticle) and a nanoscale acceptor under X-ray irradiation. A) shows energy deposition by electrons emitted from X-ray absorbing water (EW) and the nanoscale acceptor (ES). B) shows energy deposition by the AuNP donor (EXIET) in addition to water and shell of the acceptor. Energy deposition by the AuNP over that by water and the shell is considered as the relative enhancement, which is used to gauge the magnitude of XIET efficiency. Relative (rel)


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enhancement = absolute (abs) enhancement+1. The enhancement units are in dose enhancement units (DEU). Donors of AuNPs and several other materials and acceptors of water nanoparticles in silica shells are studied here, and energy transfer processes are simulated using a Monte Carlo method developed recently.20 The energy transfer is investigated as a function of a set of variables including the size of donors and acceptors, distance between donor(s) and an acceptor, composition of donors and acceptors, and X-ray energy and dose. Also simulated are the percentage efficiencies of such transfer as a function of the abovementioned properties of the two nanomaterials. The outcome of these calculations will guide experimental investigations in the future when acceptors are delivered to donors located at various locations such as in the body or in various devices such as batteries. 2. Method The main portion of the code used in this work was developed several years ago and the approach and formulae were described elsewhere.9 Several new features were added recently, and the overall program is described in a flowchart shown in Figure SI-1 in Supporting Information, with an asterisk marking the new features. Briefly, the simulation program utilized a home-built Mathematica program together with two existing packages. One of them was Geant4 developed by RD44 worldwide collaboration project to simulate passage of high energy particles through matter and was previously adapted to simulate X-ray absorption by and electron emission from nanomaterials.23,27 The other was NOREC developed by Oak Ridge National Lab to calculate energy deposition in water by electrons emitted from nanomaterials under X-ray irradiation.28,29 The Mathematica program was developed to generate nanostructures of various shapes of donors and acceptors as well as to set up enhancement calculations. For


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absorption of monochromatic or broadband X-rays by nanomaterials or water, electrons including photoelectrons, Auger and other secondary electrons and Compton electrons emitted were first calculated using Geant4 (ver. 9.4).30,31 The package did not include several updates contained in the latest Geant4 (ver. 10.3 or newer), including the full Auger process.32,33 In addition, energy loss and deposition in nanomaterials was calculated based on the modified Bethe formula.34,35 This could underestimate the amount of low energy (10 keV) electrons from a 50-nm diameter AuNP and a 500-nm water cube based on the results shown in the right panel of Figure 2B. The results agree with energy absorption difference between the two nanomaterials.

Figure 2. Energy deposition events in a water cube surrounding a 50-nm silica nanoparticle (SiO2NP) and gold nanoparticle (AuNP) and their electron spectra. A) Energy deposition events by electrons generated from silica (red dots, left panel) and water (blue dots, left panel) and silica only (red dots, middle panel). Integrated energy spectra at different electron energies are shown in the right panel. Edge length of the box is 500 nm, X-ray energy is 40 keV, Dose is 500 Gy and PB=0. B) Energy deposition events and integrate electron emission as described in A) for a 50 nm AuNP in a 500 nm water cube.


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Figure 3A shows tracks of electrons emitted from individual gold nanoparticles in water. AuNPs of diameters of 5 nm (left panel) and 50 nm (middle panel) are used, and the box sizes are kept at 10 times the diameter of the AuNPs. As the AuNP diameter increases from 5 to 50 nm, the dose causing emission of a few electrons from the AuNPs is reduced from 20,000 to 100 Gy. Figure 3A (right panel) also shows the energy deposition events by electrons emitted from 50 nm diameter AuNPs and Compton electrons from water for a box with a 500 nm edge length with the gold nanoparticle at the center. Electrons releasing from AuNPs 200 and 2000 nm boxes are shown in Figure SI-2. Figure 3B shows the energy dependency of electrons emitted from a AuNP (red color) and in the water cube (blue color). Since the ratio of energy deposition events enabled by gold to those enabled by water represents the enhancement, the two highest enhancements occur at energies just above the L (15-20 keV) and K (>81 keV) edges of gold. Background water contributes significantly more than the gold nanoparticle for X-ray energies below the L-edge (i.e., 10 keV), thereby, reducing T2PE and lowering the relative contribution from AuNPs in XIET. Figure SI-3 displays results at other five and other seven X-ray energies. When donors are covered or protected by other materials, energy carried by electrons released from donors is attenuated, depending on the composition and thickness of the coating. Figure 3C shows energy deposition events by electrons released from composite donors. Adding shells made of low Z elements such as SiO2 does not significantly increase deposition events in nearby water because these shells do not absorb X-rays strongly. Since the code employed in this work used stopping power rather than individual inelastic collisions, the possibility of producing additional electrons through electron collision events within nanomaterials such as gold nanoparticles or SiO2 shells was not considered, which could underestimate the number of low energy electrons. The results show that a 50 nm diameter AuNP coated with 50 nm thick silica


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differ only marginally from the AuNP alone, with the main difference being a reduction of energy deposition in water by electrons emitted from the AuNP. For nanomaterials covered with heavier elements, the spectra of electrons emitted from composite nanostructures are significantly modified. For example, the spectrum of a 50-nm diameter AuNP coated with a 50nm Ag layer is closer to that of a pure 150-nm diameter AuNP, as shown in Figure 3C (silver). Figure SI-4 presents results for 5 nm and 50 nm shell thicknesses.

Figure 3. A) Electron emission tracks from 5 nm (50 nm box, 20,000 Gy, left panel) and 50 nm (500 nm box, 100 Gy, middle panel) diameter AuNPs irradiated by 40 keV X-rays. Electron


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events for a 50 nm AuNP in a 500 nm box irradiated with 500 Gy of 82 keV X-rays is also shown (right panel). A single AuNP in an isolated water cube was calculated (non-periodic condition or PB=0). B) X-ray Energy dependency of energy deposition events by a 50-nm diameter AuNP (red dots) and water (blue dots). Deposition by water electrons dominates at 10 keV, and progressively decreases as the X-ray energy increases. The cube edge length used in the calculations is 500 nm and non-periodic condition (PB=0). The K absorption edge of Au is 80.7 keV. C) Electron emission and energy deposition events for 50-nm diameter AuNP donors in SiO2, CaP and Ag shells. A total dose of 500 Gy of 40 keV monochromatic X-rays is used. The contribution from water is not shown in order to highlight the effect of different surface coatings. Edge length is 200 nm and non-periodic condition or PB=0 is used. The results shown above indicate that for efficient XIET, which relies on electrons released from X-ray absorbing donors, large nanoparticles made of heavy elements covered with a thin shell are preferred. The shell serves to reduce anti-enhancement (AE) and eliminate chemical enhancement (CE) of reactions by eliminating direct exposure of radicals and reactants to the AuNP surface. 3.2 Nanomaterial Acceptors in XIET Based on Scheme 1, the acceptors can assume any shapes although spheres are among the most common shapes. Acceptors usually absorb much less X-ray than donors because they are usually aqueous solutions of dye molecules entrapped in hollow shells made of light elements, whereas donors are often made of solid, high density and high Z materials. As a result, acceptors themselves exert a minimal donor influence to XIET. Figure 4 shows the self-contribution (Es as defined in Scheme 1) by acceptors. The effect of different acceptors made of silica (SiO2), calcium phosphate (CaP) and Ag shells are evaluated. Other materials such as micelles and


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liposomes may also act as acceptors, but these materials interact with X-rays essentially identically to the way water does. Relatively thin SiO2 and CaP shells evidently do not produce strong energy donation or attenuation and thus are sensible choices as materials for acceptors. In contrast, Ag shells significantly modify energy deposition in acceptors and are thus not suitable for use as acceptor materials. Figure SI-5 presents the results of 50 and 100 nm diameter acceptors.

Figure 4. Electron energy deposition events in acceptors of different materials due to X-ray absorption, including hollow SiO2, CaP, and Ag with 150 nm inner diameter and 10 nm thick shells. The MC simulation employs 500 Gy of 40 keV X-rays for irradiation of the acceptor. 3.3 X-ray Induced Energy Transfer between Donors and Acceptors (XIET) Given the information about donors and acceptors shown in Figures 1-4, XIET between the two nanomaterials can be systematically studied. In this work, a single water-filled spherical shell acceptor is considered. Relative energy transfer efficiency is expressed in terms of enhancement because enhancement is an experimentally measurable quantity. The relative transfer efficiency is investigated as a function of several parameters. Results associated with multiple donors are also presented. Finally, percentage efficiencies of XIET are calculated. 3.3.A. Enhancement as a Measure to Determine XIET Efficiency


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XIET is an energy transfer process and its absolute efficiency is low, below 1% for commonly encountered donors and acceptors, as shown in Section 3.3.D, although the absolute amount of energy is a few hundred eV per X-ray absorption, enough to cause significant chemical modifications to the content in the acceptor. Nonetheless, it is difficult and often unnecessary to measure absolute energy deposition in acceptors. Instead, relative efficiencies in the form of enhancement defined as the ratio of energy deposition in acceptors with donors to that without donors is used here. This enhancement can be simulated theoretically and measured experimentally.9,20 Scheme 1 shows how enhancement is defined and calculated. The units are DEU, as specified earlier. 3.3.B. One Donor and One Acceptor Four parameters are used to define chemical systems that support XIET. They are: 1) diameter of donors denoted by φ; 2) inner diameter of acceptors denoted by 2r; 3) distance between the surface of the donor and the surface of the shell containing the acceptor denoted by d; and 4) thickness of acceptor wall, denoted by t. Each of these four parameters (φ, 2r, d, t) is varied while the other three parameters are fixed, and XIET efficiency in terms of absolute enhancement is calculated for each combination of parameters. For fixed sizes of acceptors or donors, the magnitude of energy transferred from donors to a nearby acceptor can be simulated. Spherical shell acceptors filled with water are considered. Figure 5A shows energy transfer from a AuNP donor of different diameters to a fixed-size acceptor of 100 nm inner diameter with a 10 nm thick SiO2 shell. This parameter set can be written as (φ, 100, 0, 10). As the donor size increases, increased fluctuations are seen due to the limited number of electrons emitted from gold atoms in the simulation, which is set at 1,000 to keep the calculation cost reasonable. For donor size dependency shown in Figure 5A,


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enhancement is quadratically dependent on AuNP diameter for diameters smaller than 75 nm, in the form of 7⨯10-5 ϕ2.16 (R2=0.99). For AuNP diameters greater than 75 nm, the dependency is linear and is expressed using the fitted equation of 0.023φ – 1.1 (R2=0.86). Figure 5B shows the relative energy transfer in terms of absolute enhancement from a fixed size donor to acceptors of different sizes. The donor (AuNP) size is fixed at 100 nm and acceptor sizes range from 10 to 500 nm in inner diameter. The separation distance, d, is zero. The set of parameters is expressed as (100, 2r, 0, 10). Simulation results are obtained using 1,000 electron emission events as well. When the acceptor size is 20 nm (ID) in diameter, the enhancement is 3.2 DEU. Table 1 gives the formula and fitting parameters for the curve shown in Figure 5B. In this case, the acceptor size dependency follows an exponential decay as a function of acceptor size, 2r. The fitted function is .

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(R2=0.90) and the decay constant is 82.6 nm.

Figure 5. A) Energy transfer from donors of different sizes (φ) to a fixed-size acceptor with an inner diameter of 100 nm and a SiO2 shell thickness of 10 nm. Parameters for the fitted lines are given in Table 1. B) Energy transfer from a 100-nm AuNP donor to SiO2 acceptors of different inner diameters, each with a 10 nm thick shell. Parameters for the fitted lines are given in Table 1 as well.


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The scattered data shown in Figure 5 is caused by the stochastic nature of XIET, which is evident in Figure 3A. Since XIET relies on electrons to conduct energy transfer, a large number of X-ray absorption events are needed to obtain converged results when the solid angle subtended by the acceptor is small. In the results shown in Figure 5, 1,000 electron emitting events are inadequate to produce converged XIET results, especially when the acceptor is much smaller than the donor, which is the case for large diameter donors with a small acceptor shown at the right end of the horizontal axis in Figure 5A and small acceptors with fixed size donors shown at the left end of the horizontal axis in Figure 5B. Figure 6A shows an exponential dependence of enhancement on the separation distance between the 100-nm diameter AuNP donor and the acceptor. In this case, the parameter set is (100, 100, d, 0). The amount of energy transferred from donor to acceptor is approximately 100% more than the energy deposited in the acceptor without the donor, resulting in an enhancement of 1.0 DEU. Table 1 shows the formula and fitting parameters. The decay constant is 32.3 nm, which is one-third of the acceptor size decay constant (R2=0.94). Figure SI-6A shows the distance dependence of XIET between AuNP donors of different sizes and a 100-nm inner diameter acceptor with a 10-nm thick silica shell irradiated by 40 keV X-rays. The set of parameters in this case is expressed as (φ, 100, d, 10). Another parameter that can be varied is the thickness of the acceptor. The parameter set is expressed as (100, 100, 0, t). Figure 6B shows the dependency on the shell thickness for a 100nm diameter donor. Figure SI-6B shows several sizes of AuNP donors. It should be noted that changing thickness, t, also changes the distance between the donor and the acceptor. Enhancement decay with respect to the thickness change is steeper than the distance dependency between donor and acceptor. This is confirmed by the decay constants listed in Table 1. The


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thickness exponential decay constant is 21.7 nm (R2=0.92), almost half of the separation decay constant. For 100 nm inner diameter acceptors, the maximum enhancement is 1.8 DEU.

Figure 6. A) shows the decay function for a 100 nm AuNP and a 100 nm diameter acceptor with a 10-nm thick silica shell. The fitted curve is given in Table 1. B) shows the dependence of XIET on the shell thickness for a 100 nm AuNP donor. Table 1. Fitted expressions of XIET as a function of acceptor and donor size, distance between acceptor and donor, and thickness of acceptors. Decay constants are the reciprocal of the coefficients of the power raised to the exponential.

XIET Variable

Functions

Expression

Decay Constant (nm)

7⨯10-5 ϕ2.16

-

Donor Size (ϕ)

Quadratic (ϕ

(XIET) from Nanomaterial Donors to Nanomaterial Acceptors

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