Multiplication Algorithm for Combined Physical and Chemical

Article pubs.acs.org/JPCC

Multiplication Algorithm for Combined Physical and Chemical Enhancement of X‑ray Effect by Nanomaterials R. Andrew Davidson and Ting Guo* Department of Chemistry, University of California, Davis, California 95616, United States

Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date (Web): August 10, 2015 | doi: 10.1021/acs.jpcc.5b05309

S Supporting Information *

ABSTRACT: The total enhancement obtained from mixing silica-covered 90 nm gold nanoparticles and tetrakis (hydroxymethyl) phosphonium-covered 2 nm gold nanoparticles that individually under X-ray irradiation produced average physical enhancement and chemical enhancement respectively was studied experimentally and theoretically. The total or combined enhancement was shown to be the multiplication of the two individual enhancements, and this algorithm can be derived from the original definition of physical and chemical enhancement. The maximum total enhancement was 18-fold, whereas the maximum measured average physical enhancement was 7-fold and the derived chemical enhancement was 3.9-fold; all three maxima were achieved under different experimental conditions. The results of simulation using rate equations for the combined physical and chemical enhancement were obtained and were found to agree with the measured total enhancements.

1. INTRODUCTION The work of using nanomaterials to enhance the effect of Xrays began more than a decade ago.1−3 Since then hundreds of publications from many research groups around the world have been reported in the literature. The origins of enhancement come from at least two main sources: (1) the increased absorption of X-rays that in turn causes an increased release of electrons from nanomaterials and (2) catalytic functionality of nanoparticles enabled by X-ray generated species such as superoxide or OH radicals in solution.4−8 Unless special cares are given to isolating and maximizing the origin of individual enhancements, which can be divided into several categories including physical, chemical, anti-, and possibly biological enhancement, many enhancement mechanisms coexist, interfere, and convolute in most experiments to create a total enhancement. Each category of enhancement can be further separated into many types. For instance, physical enhancement (PE) can be separated into at least two types, 1 and 2. Type 1 PE (T1PE) represents the average physical enhancement, whereas type 2 PE (T2PE) describes the local or nanoscale physical enhancement.9,10 Unlike PE, chemical enhancement (CE) is reaction dependent and does not require the nanoparticles to absorb much more X-rays than the surrounding water.7 Furthermore, CE needs the nanoparticles to be catalytically active when they interact with X-ray generated species in solution. In addition to PE and CE, many nanomaterials scavenge radicals so that these nanomaterials act as antienhancement chemical reagents.11 When these individual enhancements are arbitrarily combined, the total enhancement produced is generally lower than the highest possible enhancement a nanomaterial or several of them may potentially create. This problem can be corrected if these individual enhancements are properly identified, isolated, © 2015 American Chemical Society

optimized, and then combined to achieve a much higher total enhancement. Furthermore, the total enhancement obtained after the isolation−optimization−combination process may depend on the individual enhancements through different algorithms such as addition, subtraction, or multiplication. Recent efforts have been given to investigating individual enhancement and some of the above-mentioned enhancements have been isolated. For example, T1PE has been studied experimentally.9 CE can be isolated by using small nanoparticles that do not generate significant PE, and several CE reactions have been identified. One example of CE is polymerization of aniline enabled by OH radical oxidation of metal nanostructures.8 Another example is superoxide-caused catalytic conversion of intermediates.7 Despite these efforts, there has been no attempt to combine these individually identified enhancements to create a much higher total enhancement. Here, as a demonstration, we investigated how T1PE and CE interact with each other. When two or more enhancements are combined, the total enhancement depends on the individual enhancements in a complex way. Since antienhancement generally reduces all other enhancements, a subtraction algorithm should exist between antienhancement and any other individual enhancements. On the other hand, the enhancements may also reinforce each other. For example, T1PE and CE may interact favorably with each other. Because CE is dose rate dependent7 and because T1PE is equivalent to increasing the dose rate,9 the total enhancement should be dependent on both T1PE and CE. Demonstration and verification of these algorithms are Received: June 3, 2015 Revised: July 22, 2015 Published: July 30, 2015 19513

DOI: 10.1021/acs.jpcc.5b05309 J. Phys. Chem. C 2015, 119, 19513−19519

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The Journal of Physical Chemistry C critical because if it is a multiplication algorithm for combining T1PE and CE, then the total enhancement can be much higher than either enhancement. For example, isolated T1PE and CE reported in the literature were 6 and 30-fold, respectively.8,9 If these two enhancements follow a multiplication algorithm then the total enhancement can be 180-fold, whereas an addition algorithm will give only 35-fold total enhancement, demonstrating the significance of uncovering the algorithm. Here we chose nanomaterials that have only T1PE and CE respectively and mixed them together to study the combined effect of T1PE and CE. To produce T1PE, one needs nanoparticles of large diameters, low surface areas and inert surface. To create high CE, on the other hand, small diameter, high surface area, and active surface nanoparticles are required. These two requirements lie at the opposite ends of the parameter space defining nanomaterials, implying that two different kinds of nanomaterials are needed. Furthermore, these two nanomaterials should not interfere with each other with respect to their solubility and stability so that they still retain their functionalities when mixed. Although it is remotely possible to use just one kind of AuNPs to accomplish both T1PE and CE, it is much more difficult for a nanoparticle to meet all the requirements. Specifically, we used a chemically inert nanomaterial AuNP@ SiO2 to generate T1PE, and a chemically active, small tetrakis (hydroxymethyl) phosphonium chloride (THPC)-coated AuNPs to create CE. In the work shown here, T1PE is of the order of several-fold at the rate of 1-fold per 1 wt % (wp) of gold in water using AuNP@SiO2, and CE is about 1 to 3-fold with 0.02 wp of gold in water using THPC-AuNPs. We demonstrated that the total enhancement depends on the two enhancements through a multiplication algorithm. The outcome shown here exemplifies the importance of categorizing these enhancements, which enables us to isolate individual enhancements so that they can be optimized and recombined to generate a much higher total enhancement.

Scheme 1. Illustration of How T1PE and CE Are Generated by AuNP@SiO2 and THPC-AuNPs, Respectivelya

a TEM images of AuNP@SiO2 and THPC-AuNPs are also shown in the insets. Lines and arrows are drawn to represent the trajectories of electrons released from large AuNPs in silica shells and these electrons are responsible for T1PE. CE is caused by the gold surface of the small THPC-AuNPs reacting with superoxide radicals.

(THPC) 80% in water were purchased from Sigma-Aldrich and used as received. Ammonium hydroxide (28 wp), sodium hydroxide pellets (NaOH), dimethyl sulfoxide (DMSO), potassium phosphate dibasic, and potassium phosphate monobasic were purchased from Fisher Scientific and used as received. Ethanol 200 proof (Koptec) was obtained from VWR International. Metal foils of 0.127 mm thick Cu (99.9%) and 0.25 mm thick Sn (99.988%) as X-ray filters were obtained from Alfa Aeser and Strem Chemicals Inc., respectively. Milli-Q (MQ) water was used exclusively. Gold Core−Silica Shell Nanoparticles (AuNP@SiO2). These particles were made according to a procedure published recently.9 Briefly, large AuNP cores were synthesized first. They were then coated with PVP ligands and the PVP-coated AuNPs were coated with a layer of silica by reacting with TEOS in the presence of NH3OH. AuNP@SiO2 was concentrated by centrifugation to about 15 wp of gold in water. THPC stabilized AuNPs (THPC-AuNPs, 2.3 nm). In a beaker, 1 mL of 6 M NaOH and 12 μL of THPC were added to 45.5 mL of MQ water with stirring. Separately, 35 μL of HAuCl4 was added to 1.97 mL of MQ water. Under vigorous stirring, the gold solution was quickly added to the beaker. The solution was allowed to stir for 5 min after which the beaker was sealed with parafilm and stored in the dark at 4 °C for 24 h. Dialysis was performed to purify the THPC-AuNPs. FisherBrand dialysis tubing [12k−14k MWCO] was used, and dialysis water was changed 3 times over a 24 h period. Once purified, the solution was concentrated approximately 17-fold using centrifugal filtration at 5k rpm for 8 min. (Amicon Ultra15 Centrifugal Filter Unit, 30k MWCO). The concentration was verified by dissolution in aqua regia and measured by atomic absorption spectroscopy (AA) and the size was 2.3 ± 0.75 nm measured with transmission electron microscopy (TEM). TEM Imaging. Samples were prepared by drop drying 15 μL of a sample on a lacey carbon grid (Ted Pella Inc.). TEM was performed with a JEOL 1230 operated at 100 kVp. 3-CCA Assay. A 20 mM 3-CCA solution dissolved in 10 mL of 80 mM pH 7.4 phosphate buffer (PB) was gently heated and stirred in a sealed flask until dissolution. The solution was then

2. EXPERIMENTAL AND THEORETICAL METHODS The overall experimental procedure of combining T1PE from large AuNP@SiO2 and CE from small THPC-AuNPs as well as theoretical simulation using rate equations are described in this section. Briefly, large gold nanoparticles in silica shells (AuNP@SiO2) were synthesized using a seed growth method modified from an established method.12,13 Small THPC-AuNPs were synthesized using an established method.14 A microfocus X-ray source with a tungsten target and two sets of filters (Cu filter and Cu + Sn filters) to produce three X-ray spectra (including the unfiltered X-ray spectrum) were used in the experiments. The dosimetric reaction of 3-carboxycourmarin acid (3-CCA) to 7-hydroxycoumarin-3-carboxylic acid (7-OH− CCA) was used to measure the enhancement and Fricke dosimeter was used to measure the dose rate associated with the three X-ray spectra.15 Modeling of the algorithm enhancement using rate laws was carried out using a previously established method.7 Scheme 1 shows the two nanomaterials separately achieving T1PE and CE and together the total enhancement. The following sections give the details of these experimental and theoretical procedures. Chemicals. Thirty wp gold(III) chloride solution in dilute HCl (HAuCl4), hydroquinone, trisodium citrate, polyvinylpyrrolidone (PVP, 40 kDa MW), tetraethyl orthosilicate (TEOS), 3-carboycoumarin acid (3-CCA), sodium borohydride (NaBH4), tetrakis (hydroxymethyl) phospohonium chloride 19514


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The Journal of Physical Chemistry C Scheme 2. Enhancement Definitionsa

cooled to room temperature and kept protected from light; 7.1 μL of DMSO was added to 1 mL of the 3-CCA solution to yield a 20 mM 3-CCA/100 mM DMSO solution. X-ray Source and Filters. A microfocus X-ray source with a tungsten target (PXS10-WB-10 mm, Thermo-Kevex) was used in all irradiation experiments. Operation parameters were 400 μA and 120 kVp with Cu and Sn foils as filters: the single filter set consists of 0.127 mm thick Cu and the double filter set 0.127 mm Cu and 0.25 mm Sn were used to filter the X-ray spectrum. For X-ray irradiation experiments without filters, the operational parameters were 200 μA 120 kVp. The dose rate was measured using a Fricke dosimeter according to the IRS protocol.15 X-ray Irradiation Procedure. X-ray irradiation was performed as follows. Four samples were irradiated by X-rays simultaneously. All irradiation times were 20 min. Samples were prepared to contain 5 mM 3-CCA and 25 mM DMSO in 40 μL of water. T1PE samples included 0 to 7.5 wp Au@SiO2. Samples for the purpose of combining T1PE and CE included 0.02 wp THPC-AuNPs and 0 to 7.5 wp Au@SiO2. Control samples were irradiated with X-rays and then spiked with predetermined amounts of Au nanomaterials. Once samples were irradiated, they were diluted to 300 μL with MQ water, vortexed, and centrifuged at 13k rpm for 10 min to remove Au nanomaterials. A 100 μL aliquot of supernatant was diluted to 500 μL with 80 mM pH 10 PB. Quantitative fluorometric analysis on the final sample solutions was performed with an excitation wavelength of 395 nm and emission wavelength of 442 nm (FluoroMax-P, HORIBA Jobin Yvon). Simulation Method. Rate law equations were used to model the enhanced production of 7-OH−CCA in the presence of Au nanomaterials. The rate equations were developed previously and modified with the inclusion of T1PE from adding [email protected] The rate constants used here are given in the Supporting Information. Enhancement Definition. We define the enhancement as the ratio of the measured fluorescent signal from 7-OH−CCA in the presence of nanomaterials to that without nanomaterials. Following this definition, the enhancement for pure water is 1.0. We call this the relative enhancement. It is also possible to define an absolute enhancement, which is relative enhancement minus 1 and should be zero without nanomaterials. Scheme 2 illustrates how these measured signals and various enhancements are defined. The fluorescent signal of 7-OH−CCA without nanomaterials is denoted I0. If there is only CE, then the signal is increased to ICE. We define relative CE (ϵrCE) as the ratio of ICE to I0. The net increase is ΔICE (=ICE − I0) and the absolute CE ϵaCE is the ratio of ΔICE to I0 and ϵaCE = ϵrCE − 1. Similarly, if there is only T1PE, then the measured signal is IT1PE. The net increase is ΔIT1PE. The relative T1PE ϵrT1PE is the ratio of IT1PE to I0, and the absolute T1PE ϵaT1PE is the ratio of ΔIT1PE to I0. When both CE and T1PE are present, the total signal is ITotal, and the total enhancement ϵrTotal is the ratio of ITotal to I0. If the signal is displayed in the unit of I0, then the enhancement and signal share the same numerical values, as shown in Scheme 2. We can also define the CE at a dose rate without AuNP@SiO2 as ϵrCE0, which is the net CE (denoted as CE0) without T1PE but still dose rate dependent.

a

The signals from the probe in pure water, with CE nanoparticles, T1PE nanoparticles, and both CE and T1PE nanoparticles are shown. If the signal from pure water is defined as I0, then the enhancements have the same numerical values as the signal. For instance, if CE is 1.5, then the signal of CE is 1.5 times I0. Both scales are shown.

Scheme 1 shows how these nanomaterials are used, and Scheme 2 illustrates how the enhancement signals are defined. The experimentally measured results of the total enhancement are shown in Figure 1 when THPC-AuNPs and AuNP@

Figure 1. Results of enhancement measurement using one Cu filter on the X-ray source. The total enhancements (open circle) are shown, as well as the chemical enhancement without T1PE (solid square) and T1PE without CE (open triangle). All measurements were performed with DMSO. The filtered spectrum is shown in Figure SI-1. All enhancements shown here are relative, meaning no enhancement has a value of 1.0. Selective data points were measured with multiple measurements, and the relative errors were between 5% and 10%.

SiO2 were mixed. Figure 1 shows the measured fluorescent signals. As defined in the method section, if the signal is displayed in the unit I0, which is the signal measured without any nanomaterials in water, then the signal has the same numerical values as enhancement. As a result, the vertical axis is labeled relative enhancement. The total enhancements (open circles) using X-rays with one Cu filter were higher than either of the individual enhancements, which are also shown in Figure 1. This filtration provided relatively high energy X-rays (spectrum shown in Figure SI-1) and the dose rate of X-rays

3. RESULTS The nanomaterials used here are shown in Scheme 1, which include THPC-AuNPs for CE and AuNP@SiO2 for T1PE. 19515


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The Journal of Physical Chemistry C was 2.3 Gy/min measured with Fricke dosimetry without the presence of nanomaterials. The highest total enhancement is approximately 18-fold with 0.02 wt % (wp) of gold in water in the form of THPC-AuNP and 7.5 wp AuNP@SiO2. This is the highest total enhancement measured in this work. The individual enhancement results are also shown in Figure 1, which shows T1PE by AuNP@SiO2 (open triangle) alone and CE with only THPC-AuNPs (solid square at zero AuNP@ SiO2 concentration). The measured ϵrT1PE values range from 1.0-fold (no enhancement) without AuNP@SiO2 to 4.9-fold with 7.5 wp AuNP@SiO2. ϵrCE0 with only 0.02 wp THPCAuNPs and no AuNP@SiO2 is 2.1-fold at this dose rate. Because CE depends on dose rate, adding AuNP@SiO2 increases the dose rate and ϵrCE.7 The absolute T1PE (defined as relative enhancement minus 1) ranges from 0.0 to 3.9 and absolute CE is 1.1-fold. This means that adding 0.02 wp THPC-AuNPs more than doubled the 7-OH−CCA production, and adding 7.5 wp AuNP@SiO2 to the aqueous solution increased the yield of 7-OH−CCA production by 3.9-fold. CE, T1PE, and total enhancement were measured in the presence of DMSO, which is used to increase the measured CE because DMSO reduces I0 but not ΔICE. The latter depends on superoxide that is not scavenged by DMSO. On the other hand, T1PE is independent of DMSO because IT1PE and I0 are reduced proportionally by DMSO. There was no CE when only AuNP@SiO2 were added because the surface of AuNPs is covered with silica, and there was no T1PE when only THPCAuNPs are present because of the low weight percentage of the amount of THPC-AuNPs in water. Because CE is dose-rate dependent, and dose rate depends not only on the wattage of the X-ray but also the X-ray energy spectrum, CE hence depends on the X-ray energy spectrum as well. The wattage can be adjusted by the voltage or current or both for the source while the X-ray energy spectrum can be adjusted with filtration of the emitted X-ray spectrum or the voltage of the X-ray source. In addition to a single Cu filter, we also measured the enhancements without filters and with a double filter of Cu and Sn. Figures 2 and 3 show the enhancement results under these two conditions. Figure 2 shows the results without filters. The dose rate was determined

Figure 3. Results of enhancement measurements using double filter of one Cu and one Sn filter on the X-ray source. The total enhancements (open circle) are shown, as well as the chemical enhancement without T1PE (solid square) and T1PE without CE (open triangle). All measurements were performed with DMSO. The filtered spectrum is shown in Figure SI-3. All enhancements shown here are relative, meaning no enhancement has a value of 1.0. Selective data points were measured with multiple measurements and the relative errors were between 10% and 20%.

to be 16.5 Gy/min without AuNP@SiO2. The X-ray spectrum is shown in Figure SI-2. T1PE values ϵrT1PE (open triangle) are lower, ranging from 1.0 (no AuNP@SiO2) to 1.8-fold with 7.5 wp AuNP@SiO2. This is nearly 3 times lower than one filter case. With only THPC-AuNPs, the net CE ϵrCE0 (solid square) is higher, at 2.9-fold. This was the highest CE measured in this work. This is because without filters, X-ray energies are much lower, and these low energy X-rays can interact with water much more effectively, resulting in higher I0 and hence lower T1PE but higher CE0 because CE relies on superoxide generated in water by X-rays. The total enhancements for combined two nanomaterials, however, were lower than those shown in Figure 1. The highest total enhancement (open circle) for unfiltered X-rays is about 7.0-fold. Figure 3 shows the results obtained with the double filter of one Cu and one Sn. With this configuration, the X-ray dose rate at the sample was 0.82 Gy/min without AuNP@SiO2, much lower than the other two cases. ϵrCE0 (solid square) is 1.5 and relative T1PE ϵrT1PE (open triangle) ranges from 1.0 to 6.4-fold with 7.5 wp AuNP@SiO2. This was the highest T1PE measured in this work, showing that high energy X-rays favor T1PE. The X-ray spectrum is shown in Figure SI-3. When THPC-AuNPs were mixed with AuNP@SiO2, the total enhancements (open circle) are higher. The highest total enhancement is 12.5-fold. The results shown above indicate that the highest total enhancement is achieved with CE and T1PE nanoparticles using one Cu filter for a moderately high dose rate, not with either the highest CE or T1PE which were obtained with unfiltered X-rays and doubly filtered X-rays, respectively. We can use the definition of enhancement shown in Scheme 2 to derive total enhancement for the mixture of CE and T1PE nanoparticles. CE with T1PE is not the same as the net CE ϵrCE0 without T1PE. If we consider the experiment design as adding AuNP@SiO2 first and then THPC-AuNPs, we can then regard CE as the enhancement by THPC-AuNPs to T1PE by AuNP@ SiO2. The other way around of using T1PE to enhancement CE is also possible to use to derive the total enhancement algorithm, although we do not do it that way because it is conceptually less clear. When there are no THPC-AuNPs but

Figure 2. Results of enhancement measurements using no filters on the X-ray source. The total enhancements (open circle) are shown, as well as the chemical enhancement without T1PE (solid square) and T1PE without CE (open triangle). All measurements were performed with DMSO. Filtered spectrum is shown in Figure SI-2. All enhancements shown here are relative, meaning no enhancement has a value of 1.0. No data points were measured with multiple measurements. 19516


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The Journal of Physical Chemistry C only AuNP@SiO2, there is only T1PE and the enhancement is defined as r ϵ T1PE =

IT1PE I0

(1)

If we choose I0 as the unit for the measured signal, then numerically ϵrT1PE = IT1PE. Adding THPC-AuNPs into the AuNP@SiO2 solution creates CE in addition to T1PE, and we can arrive at the following equation according to the definition of CE shown in Scheme 2:


r ϵCE =

ITotal IT1PE

(2)

for the total signal and the signal without CE, which is the T1PE signal. Although 3-CCA dosimetric reaction itself or many other reactions are neither dose nor dose-rate dependent, when 3CCA assay is used with THPC-AuNPs there is CE even without AuNP@SiO2. By definition, the combined enhancement generates the total enhancement signal: r ITotal = I0 ϵ Total

Figure 4. Measured net CE (solid symbols) ϵrCE0 and calculated CE ϵrCE (open symbols) as a function of dose rate in all three cases shown in Figure 1 to 3. The dose rates were cross calibrated with Fricke dosimetry. The dashed line is for visual guidance using a (a*x/b + x) + 1 formula, where a = 3, b = 5, and x is the effective dose rate. The relative errors associated with the data points obtained with filters were between 10% and 25%.

(3)

from the ones without T1PE. A special case is given below in which one may predict the total enhancement using T1PE and the net CE values, that is, CE without T1PE. When CE is under a nonsaturation condition, eq 6 can be further developed conceptually. As it is shown in this work, dose rate D can be adjusted by changing the X-ray source such as adding filters or by adding AuNP@SiO2. For a specific source setting without AuNP@SiO2, we define the dose rate as D0. Adding a low wp of THPC-AuNPs does not change D0 because its influence on T1PE is negligible. Adding AuNP@ SiO2 causes T1PE to increase, which effectively increases dose rate. The results shown in Figures 1 to 3 and previously published results both indicate that adding AuNP@SiO2 to water can increase the effective dose rate by many-fold.9 The dose rate with AuNP@SiO2 added can be expressed, assuming a linear relationship, as

Using eqs 1 and 2, the total enhancement signal can be expressed as r r ITotal = ϵCE IT1PE = ϵCE ϵrT1PEI0

(4)

Combining eq 3 and 4, we have r r r ϵCE ϵ T1PE I0 = I0 ϵ Total

(5)

Eliminating I0 on both sides of the equation, we have r r r ϵ Total = ϵ T1PE ϵCE

(6)

This equation explains how the total enhancement is related to the individual physical and chemical enhancements. Equation 6 can be used to (i) predict the total enhancement if T1PE and CE are known experimentally, (ii) derive T1PE or CE if the total enhancement and one of the two individual enhancements are known, and (iii) verify the validity of the algorithm when all three are known. All three functions can be demonstrated here. Using eq 2, the corresponding ϵrCE embedded in Figures 1 to 3 can be calculated, and the values are displayed in Figure 4 (open symbols). Also shown in Figure 4 are the measured net CE ϵrCE0 (solid symbols) at three absolute dose rates calibrated with Fricke dosimetry. The three measured ϵrCE0 values shown in Figure 4 follow the general trend of the rest of CE, confirming the validity of the algorithm. ϵrCE shown in Figure 4 increases linearly at low dose rates (3 Gy/min), for example, in the unfiltered case. This value is lower than the value of 20 Gy/min given in an early report in which it was found that CE using poly(ethylene glycol) (PEG) covered AuNPs and 3-CCA as the probe may increase (not linearly though) up to a dose rate of 20 Gy/min and saturate between 20 and 40 Gy/min using PEG-AuNPs.7 It should be noted that all the T1PE values without CE and the CE values without T1PE shown above are obtained experimentally, whether CE saturates or T1PE follows the same profile as a function of concentration of AuNP@SiO2. We do not believe T1PE will change when CE is present due to the physical nature of T1PE. However, because CE is dose rate dependent, CE values in the presence of T1PE will be different

r D = ϵ T1PE D0

(7)

From Figure 4, if CE is linearly proportional to dose rate, then at a certain dose rate D, CE becomes D r a ϵCE = 1 + ϵCE0 D0 D r = 1 + (ϵCE0 − 1) D0 r r = 1 + (ϵCE0 − 1)ϵ T1PE

(8)

ϵaCE0

This is because only the absolute CE part is enhanced further by the increased dose rate after adding AuNP@SiO2, and eq 6 becomes r r r r r r ϵ Total = ϵ T1PE ϵCE = ϵ T1PE (1 + (ϵCE0 − 1)ϵ T1PE )

(9)

The benefit of using this equation is that it is possible to calculate, ahead of time, the total enhancement using the experimentally measured ϵrCE0 and ϵrT1PE if there is no dose rate saturation for CE. In practice, as shown in Figure 4, CE saturates at about 3 Gy/min. As a result, one can use eq 9 to predict total enhancement. The experimentally obtained total enhancement begins to deviate from eq 9 above 3.0 Gy/min, and eq 6 has to be used to retrieve CE values. 19517


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only 0.02 wp THPC-AuNPs, the total enhancement with 7.0 wp AuNP@SiO2 can generate 18-fold total enhancement. The third advantage is that much less nanomaterials are needed for the combined individual enhancements than individual enhancements. For example, if a 10-fold enhancement is desired, then it is possible to use 4 wp AuNP@SiO2 and 0.02 wp THPC-AuNPs to generate such a total enhancement. On the other hand, one would need nearly 12 wp AuNP@SiO2 to obtain a 10-fold T1PE if we linearly extrapolate based on Figure 3. T1PE is an average enhancement and is not confined to the surface region of nanomaterials that cause the enhancement. As a result, it is possible to generate T1PE micrometers away from the T1PE providing nanomaterials. This allows the multiplication of T1PE and CE to occur at a remote location from T1PE nanomaterials. Because CE requires the use of the surface of nanomaterials, CE nanoparticles have to be delivered to the target. For example, it is possible for a cell to take up a large quantity of large nanoparticles in the cytoplasm to create a relatively high T1PE in the nearby nucleus. Then it is possible to deliver a small quantity of small nanoparticles into the nucleus to cause CE, which could occur as shown in an earlier report.6 The combination creates a much higher total enhancement of damage to the cell under irradiation, and the overall enhancement in the target volume, say the nucleus, can be much higher than either enhancement. Another possibility to maximize the total enhancement is to use different X-ray energy spectra to generate T1PE and CE. For example, if low energy X-rays in the range of 10−30 keV are used to cause high CE and high energy X-rays in the region of 40−100 keV are used to cause high T1PE, then it is possible to maximize CE and T1PE and therefore obtain a much higher total enhancement. It is also worth noting that for much higher energy photons such as γ rays, the combined enhancement will be very similar to individual ones due to the unknown CE and low PE generated from nanomaterials. The results shown here therefore indicate the importance of using keV X-rays for enhancement purposes. It is important to point out that as long as the two nanomaterials do not interfere destructively with each other when the two nanoparticles are mixed together, which is the case here, then T1PE and CE can coexist and the overall enhancement follows the multiplicity algorithm described here. However, if the two types of NPs cause each other to precipitate or aggregate when 3-CCA or DMSO is added, then the combined enhancement may be lower. It is possible to experimentally determine the CE values in the whole dose rate range if a much more powerful X-ray is available. Currently the dose rate accomplished by adding AuNP@SiO2 using filtered X-rays cannot be reproduced using the X-ray source alone. For example, in the one filter case the highest dose rate was achieved with the largest amount of 7.0 wp of AuNP@SiO2. This dose rate with the same X-ray spectrum cannot be obtained with the current X-ray source alone, so CE at this dose rate cannot be measured without using AuNP@SiO2. Only three data points in Figure 4 are experimentally measured without AuNP@SiO2, and the rest are derived using eq 6. Equation 9 may be simplified if both ϵrCE0 and ϵrT1PE are low. In this case, which may happen to samples irradiated by MeV γ rays, there is little CE and the total enhancement is the same as T1PE. For the simulated results shown in Figure 5, the fitted data show the least degree of saturation for the lowest dose rate


As mentioned above, we modeled the experimental results shown in Figures 1 through 4 using rate equations in a report published earlier.7 In order to fit all three sets of data, we adjusted the rate constant responsible for chemical enhancement. In the fitting, experimentally obtained T1PE were used to modify the Fricke calibrated dose rates. The fitting results are shown in Figure 5, which shows a generally good agreement

Figure 5. Simulated enhancement (relative) using rate equations to model chemical enhancement described previously.7 All rate constants were kept the same as before except the constant responsible for chemical enhancement was changed for each X-ray spectral case. General agreements exist between experimental and simulation results. Saturation is observed for higher dose rate cases including both unfiltered and one Cu filter case. The simulation shows a slight quadratic trend for the lowest dose rate range associated with the double Cu/Sn filter case (open square).

between the simulated and experimental results. Because T1PE is approximately linearly proportional to concentration, the data shown in Figure 5 can also be viewed as how the total enhancement depends on T1PE. The match between the experimental and fitted results demonstrates the validity of using CE and T1PE to account for the total enhancement, which is expressed as the multiplication of the two individual enhancements.

4. DISCUSSION The results presented here reveal the multiplication algorithm for combined chemical and type 1 physical enhancement. There are several advantages to using this combined enhancement methodology. First, a much higher overall enhancement may be achieved and the algorithm may apply to many other reactions. For instance, aniline polymerization occurring on the surface of silver core−gold shell nanostructures has a chemical enhancement of 30-fold.8 We do not know if the polymerization reaction obeys exactly the same saturation process as the 3-CCA reaction. But, if that reaction is mixed with other types of physical enhancements such as the type 2 physical enhancement that can be as high as 200-fold, then it is possible to obtain a very high total enhancement value if the multiplication algorithm holds. Another benefit is that it is possible to reach an enhancement that is otherwise difficult for either enhancement mechanism. For example, the highest Au concentration used here is about 7.5 wp using AuNP@SiO2 and the highest T1PE is about 5.0fold. Although up to 15 wp AuNP@SiO2 solution can be prepared, it is nearly impossible to reach 15-fold enhancement with this nanomaterial alone. With the assistance of CE from 19518


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The Journal of Physical Chemistry C


case (double filter) and strongest saturation at the highest dose rate case (no filters). The simulation results confirm that the combined total enhancement can be satisfactorily explained by the interplay between physical and chemical enhancement, which fit in a multiplication algorithm to give rise to the total enhancement.

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5. CONCLUSIONS The experimentally obtained total enhancement ϵrTotal was shown to follow a multiplication algorithm ϵrTotal = ϵrT1PEϵrCE of the two noninterfering individual enhancements of type 1 physical enhancement ϵrT1PE and chemical enhancement ϵrCE. All enhancements were relative enhancements, meaning that the enhancement values are 1.0 when there is no enhancement. The multiplication algorithm can be directly derived from the definition of these enhancements. Chemical enhancement was found to begin to saturate at 3.0 Gy/min. No clear saturation was observed with type 1 physical enhancement at up to 30 Gy/min as a function of AuNP@SiO2 concentration. Simulation results obtained using rate equations for predicting chemical enhancement agreed with the experimentally observed total enhancements and hence confirm the validity of the algorithm that governs the total enhancement, type 1 physical enhancement, and chemical enhancement.

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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.5b05309. Rate constants and X-ray spectra. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Science Foundation (CHE-1307529).

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REFERENCES

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Multiplication Algorithm for Combined Physical and Chemical

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