A Straightforward Method For Interpreting XPS Data From Core–Shell

Article pubs.acs.org/JPCC

A Straightforward Method For Interpreting XPS Data From Core− Shell Nanoparticles Alexander G. Shard* National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom ABSTRACT: This paper describes a simple and direct method to calculate the shell thickness of spherical core−shell nanoparticles from X-ray photoelectron spectroscopy data. In contrast to existing methods, it is not iterative and involves a simple forward calculation that is accurate to a typical error of 4%. The method is applicable to any core−shell material pair, but the accuracy becomes worse when the kinetic energy of photoelectrons arising from the core and the shell are widely separated. Application of the method to two example systems from the literature is demonstrated: silicon oxide on silicon and carbon on gold. In both cases, accuracy in shell thickness that is significantly better than an atomic diameter is demonstrated. An accurate direct equation to calculate the thickness of overlayers on planar samples is also provided.

■

INTRODUCTION Engineered nanoparticles are increasingly used in innovative products, and the careful control of size, shape, and chemistry are vital to their function. Electron microscopy is routinely employed to measure the size and shape of particles, and techniques based upon the mobility of particles in fluids provide results that are affected to varying extents by the size, shape, or density of the particles. These methods are well established and have a strong theoretical underpinning, and algorithms for the interpretation of data are available. The measurement of nanoparticle chemistry, in particular the chemistry at the surface of nanoparticles, is of increasing concern.1−3 The surface chemistry of nanoparticles is important for both the application and processing of nanoparticles, since it affects the manner in which the nanoparticles interact with the surrounding environment. The dispersion and aggregation of particles critically depend upon their surface chemistry, and for a number of particles, a surface passivation layer is required to insulate the core from the environment. In both biotechnology and nanoparticle toxicology, the intentional or adventitious attachment of organic compounds to the exterior of nanoparticles is of great importance, as these mediate the manner in which the particles bind to other molecules and affect living organisms. Quantitatively measuring the amount of material at the surface of a nanoparticle is therefore of major importance for understanding the behavior of nanoparticles and ensuring consistency in manufacture. Of the many readily accessible methods by which this quantitative measurement could be achieved, X-ray photoelectron spectroscopy (XPS) is an appropriate and widely used method.4−22 The specific advantages of XPS are that it is quantitative, chemically specific, has an information depth similar to the size of nanoparticles, and, in comparison to electron beam methods, does not significantly damage the analyzed material. It is therefore no surprise that XPS has long © 2012 American Chemical Society

been a mainstay for the analysis of supported heterogeneous catalysts,23,24 which are usually in nanoparticulate form. The two major problems in XPS analysis of nanoparticles are the preparation of samples for analysis and the interpretation of data. The preparation of samples for analysis is not the topic of this paper, but should not be trivialized since it is a major barrier to the application of XPS in this regard, particularly on nanoparticles that are prepared and used in liquid suspension. The application of XPS requires that the nanoparticles be in a dry solid form without significant surface contamination and on a substrate that does not produce signals coincident with those of the nanoparticles. Within this paper, it is assumed that these issues have been overcome, and we concentrate on the issue of data interpretation. For spherical nanoparticles at submonolayer surface coverage, XPS analysis provides a single spectrum with intensities for the photoemission lines of elements present in the near surface (∼10 nm). In contrast to planar surfaces, angle-resolved XPS analysis of spherical nanoparticles provides no additional information of any significant use. Interpretation requires, as a minimum, knowledge or assumption of the core chemistry and size of the particle. For large (>10 nm) particles, it should be possible to use the shape of the energy loss background to infer which signals arise from the core, following the method of Tougaard.25 However, for small particles, the contribution of signal from the shell chemistry under the core may make distinction by this method difficult. Knowledge or assumption of which signals arise from the shell and which from the core enables the amount of material in the shell to be determined. The essential problem is the conversion of the relative XPS intensities, usually expressed as a ratio of the intensity of photoelectrons arising from the shell to the intensity of photoelectrons arising from the core, into a shell Received: May 30, 2012 Revised: July 12, 2012 Published: July 16, 2012 16806

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

A practical estimate29 of B can be found from (E1/E2)0.872, where Ei are the photoelectron kinetic energies. Similarly, a useful estimate of C is given by (Zb/Za)0.3, where Zj is the number-averaged atomic number of the material; this requires some knowledge of the core and shell stoichiometry. Such information may be found from a more detailed analysis of the XPS data, although materials that contain hydrogen will be problematic in this regard. For organic materials, Z = 4 is a reasonable estimate.29 These estimates of B and C provide useful support for the assumption that the fourth attenuation length of importance here can be estimated from the other three. This assumption is given in eq 4 and is used throughout this paper:

thickness. A straightforward and direct method for this has not been reported, although careful modeling and calculation has been shown to be effective. A simple method for performing this conversion would be helpful to many analysts who do not have the time or expertise to undertake detailed modeling; this method would also be helpful in demonstrating the general features of the problem, assessing the sensitivity of XPS analysis to various parameters, and providing a simple route to the evaluation of uncertainties. It is not surprising that a simple method for this conversion has not been reported, since a direct method of converting XPS data to thickness for uniform, planar overlayers has not been reported. Currently, an iterative or graphical method is required.26 This paper reports a direct and accurate empirical method for converting XPS intensities into overlayer thicknesses, with a particular emphasis on spherical nanoparticles. The variable input to the equations is the ratio of normalized XPS intensities, denoted here by the variable A, and the relative electron attenuation lengths denoted by B and C. Although the equations are relatively straightforward and easy to implement, they are not quite as simple as A, B, C, since a variable R, the radius of the particle core, is also required.

L1,a L 2,b

= BC (4)

Figure 1 schematically demonstrates the influence of the terms B and C on photoelectron intensities arising from the

■

THEORY All calculations and theory in this paper do not account for the effects of the elastic scattering of electrons in detail but assume these can be neglected or compensated.27 The “straight line” approximation is assumed with effective attenuation lengths, L, to describe the diminution of photoelectron intensity with distance through a material according to a simple exponential decay. Nanoparticles are assumed to be spherical with a uniform shell thickness. Terminology. To simplify the equations in the paper, the important inputs are combined into dimensionless terms. The XPS experimental result is denoted by A, which is a ratio of the normalized integrated intensities of a unique signal from the nanoparticle shell to that of a unique signal from the core. Thus, A=

I1I2∞ I2I1∞

Figure 1. A schematic illustration of relative XPS intensities for core− shell nanoparticles showing the regional contributions to the XPS signal. Contributions to the XPS signal are represented on a gray scale (white representing the largest contribution) and calculated using R = 1 and T = 0.5. The boundaries between phases are marked in black.

(1)

core and shell of small nanoparticles. It can be seen that the intensity from the underside of the shell is influenced by the term C, which describes the relative opacity of the core. The intensity from the core of the particle is also influenced by this term, but more strongly by B, which describes the relative penetration length of photoelectrons from the two materials. It is clear from these figures that when both B and C are large, the effect of the finite depth of the core is small and the situation is similar to that for large particles. Planar Samples. An essential step in providing a direct equation for nanoparticles is a demonstration that a similar equation can be found for the much simpler case of planar samples. The “Thickogram” equation26 for the iterative or graphical calculation of film thickness is given in eq 5 using the terminology in this paper,

Ii∞

where Ii is the measured XPS intensity and is the measured or calculated intensity for the pure material of unique photoelectrons from the shell (overlayer), i = 1, and the core (substrate), i = 2, respectively. Using the notation from a recent paper on the effects of topography on XPS analysis of overlayer thickness,28 all of the lengths are described as a ratio to the attenuation length of electrons arising from the unique overlayer signal in the overlayer material. If Li,j is the attenuation length of photoelectrons arising from material i traveling through material j, where j = a represents the shell and j = b represents the core, the following definitions are used to simplify later expressions: B=

C=

L1,a L 2,a

(2)

A=

L1,a L1,b

1 − e−Tplanar e−BTplanar

(5)

in which the photoelectron emission angle is assumed to be normal to the surface. If this is not the case, then the value of Tplanar that results from this analysis can simply be corrected through multiplication by cos θ, where θ is the electron

(3)

The core radius of the particle, R, and shell thickness, T, are expressed in units of L1,a. 16807

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

Figure 2. A comparison of direct estimates for Tplanar and TR→∞ for values of B, the ratio of electron attenuation lengths, ranging from 0.5 to 2. B = 1 is shown by a bold line, and the common practical limits of B = 0.7 and B = 1.4, by dashed lines. In parts a−d, values of B larger than 1 result in Tplanar being larger than Tactual and provide the lines above the bold line. In part e, the prediction of eq 7 for Tplanar is shown, and in part f, the prediction of eq 8 for TR→∞ on spheres.

work is that this accurate direct equation suggests that a direct equation may be found to accurately convert XPS data from nanoparticles into a shell thickness. Microscopic Spherical Particles. The determination of overlayer thickness on nonplanar samples has previously been addressed in detail, and a practical approach is to calculate an equivalent planar thickness, as described above, and multiply by a geometrical correction term, or Topofactor,28 to calculate the conformal thickness. The Topofactor depends upon the topography of the sample and the values of A and B. For microscopic spherical particles, when R is much larger than 1 but not so large that X-ray shadowing effects become significant (i.e., R is less than ∼1000), under these conditions, a constant Topofactor of ∼0.67 is acceptable at 10% error. The spherical Topofactor reduces to 0.5 for infinitesimally small values of T, and a more accurate expression to 1% error is also available.28 As described later, it is important to be able to directly calculate T from A in the case R → ∞. This is possible by introducing eq 7 into the accurate spherical Topofactor expression, but results in a cumbersome equation. A simpler approach to introduce the Topofactor is by retaining the form of eq 7 and optimizing the parameters within the equation to provide the conformal thickness of the overlayer on a large sphere, TR→∞. This introduces some additional error, providing T accurately to within 0.05, as long as T < 3, but retains a form that is relatively simple. The result optimized for large spheres is given in eq 8.

emission angle with respect to the surface normal. In the limit of small thicknesses, Tplanar = A, and in the limit of large thicknesses, Tplanar = ln(A)/B. The advantage of these approximations is that at intermediate thicknesses, the former overestimates the actual thickness and the latter underestimates it, as shown in Figure 2b and c. One may envisage that, using a relatively simple weighting, these may be spliced together to provide an accurate and direct estimate of Tplanar. In fact, a simple weighting factor using A alone, as given in eq 6 and shown in Figure 2d, can approach this for values of B close to 1. Tplanar ≈

A2 ln(A) B−1 + 2A A2 + 2

(6)

However, if B = 1, eq 5 is no longer transcendental, and direct inversion using Tplanar = ln(1 + A) is better, as shown in Figure 2a. A refinement of the weighting method results in eq 7, which is plotted in Figure 2e and provides Tplanar accurately to within 0.04 (i.e., less than the diameter of an atom) over the range 0.5 < B < 2 for all practical values of Tplanar. Tplanar =

A2.2 ln(A) B−0.95 + 2AB−0.42 A2.2 + 1.9

(7)

This equation may be implemented when a direct forward calculation of thickness from XPS data is required or to provide an initial estimate for further refinement by an iterative calculation. In practice, however, further refinement is unnecessary, since the error provided by this equation is insignificant compared with other sources of uncertainty. Equation 7 is clearly in error for very small and very large values of A, and if Tplanar < 0.1, the estimate provided by Tplanar = ln(1 + A) is better. The large values of A where the error in eq 7 becomes significant are not of practical importance, since in these cases, the XPS signal from the substrate will be too weak to permit an accurate analysis. The importance within this

TR →∞ =

0.74A3.6 ln(A) B−0.9 + 4.2AB−0.41 A3.6 + 8.9

(8)

The prediction of eq 8 is shown in Figure 2f, where deviations are evident at high and low values of T. This amounts to ∼5% error as T approaches 3, and for values of T smaller than 0.1 where the average error is more than 10%, a better prediction is given by using the planar estimate and the 16808

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

Figure 3. Results of numerical calculations to find T as a function of A, B, C, and R. A selection of data are shown that represent the normal experimental range. The values of B and C are provided in the top left corner of each part of the figure with T on a linear scale plotted against R on a logarithmic scale. Numerical data are plotted as points: ◇, A = 300; ▲, A = 100; □, A = 30; ⧫, A = 10; Δ, A = 3; ■, A = 1; ○, A = 0.3. Solid lines are the TNP predictions of eq 11.

T were performed with R varying from 0.05 to 10 000; A, from 0.03 to 300; and B and C, from 0.5 to 2. The method used was to begin with a trial value of T and to calculate A given B, C, and R; the value of T was then iteratively refined until A matched the desired value. Some (∼10%) of the calculated values are shown in Figure 3 as data points. The relationship between T and R for moderate values of R and fixed values of A, B, and C is described very well by the simple empirical relationship shown in eq 10,

appropriate Topofactor for thin overlayers, which approaches 0.5 for very thin films. The expression TR→∞ = (0.5 + 0.1AB−2) ln(1 + A) provides an accuracy of better than 10% in this region. Infinitesimally Small Particles. For very small values of R and T, where attenuation of photoelectron intensities can be neglected, a limiting relationship among A, B, C, T, and R is straightforwardly obtained.28 This is arranged to provide T0 in eq 9, which is valid when the product ABCR approaches zero. T0 = R[(ABC + 1)1/3 − 1]

(9)

TR ∼ 1 =

In most practical situations, this limit is not reached; however, the expression provides better than 5% error for particles smaller than ∼1 nm diameter. Nanoscopic Spherical Particles. When the size of the nanoparticle is of the same order of magnitude as the attenuation lengths, eqs 8 and 9 are not appropriate, and another approach is required. An important relationship to investigate is the behavior of T as a function of R for fixed values of A, B, and C. This describes the sensitivity of the desired result (T) on the size of the core (R), given a particular experimental result, and is important in establishing, for example, the uncertainty of the result on the basis of that of the core size measurement and the effect of size dispersity. To address this problem, more than 6000 numerical calculations of

TR →∞R R+α

(10)

where α can be found by fitting the numerical data and is a function of A, B, and C. It is straightforward to see that α relates to the value of R at which T is half that of TR→∞. In the limit of R ≪ α, the form of eq 10 is not inconsistent with eq 9. However, the value of α cannot be found by making this consistency an identity, and the description becomes poor at low values of R. The accurate value for infinitesimally small particles given in eq 9 can be combined with eq 10 to provide a better estimate of shell thickness over a greater range of R, TNP = 16809

TR ∼ 1 + βT0 1+β

(11)

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

where β is a weight that is a function of A, B, C, and R and increases as these become small. Simple expressions for α and β in terms of A, B, C, and R can be found and optimized by minimizing the error in predicting the numerically calculated values. These expressions are given in eqs 12 and 13. 1.8 α = 0.1 0.5 0.4 (12) A B C

0.13α 2.5 (13) R1.5 The solid lines in Figure 3 demonstrate that, using these expressions, the TNP of eq 11 is capable of providing an excellent estimate of T for core−shell nanoparticles. More than 95% of the numerical values of T are predicted to within either 10% or 0.1. Figure 4 plots a greater range of calculations in the β=

Figure 5. Mean relative error in the TNP prediction for subsets of the numerical data plotted against the input parameter values A, B, C, and R. Note that A, B, C, and R are plotted on logarithmic scales, and the mean error is plotted on a linear scale.

absolute error in this regime is lower than 0.01, which is about one tenth of the diameter of an atom. Interestingly, the predictive quality of eq 11 improves as the core size of the particle, R, decreases. This is a remarkable result and implies that an important limiting factor is the ability to predict TR→∞ through eq 8. The mean relative error of eq 11 is largely unconnected to the value C, since this becomes important only at small R, where the prediction is, in most cases, excellent. Figure 6 provides an overview of where the equations provided in this paper may be used: TNP from eq 11 is best in all cases when accuracy of better than 10% is required. For microparticles, X-ray shadowing must be accounted for, and Figure 4. Comparison of TNP with T from numerical calculations for four different values of R. Each graph plots 441 individual calculations, shown as points, and a line describing the relationship TNP = T.

same format as Figure 2 for four subsets of data defined by individual values of R ranging from R = 0.5 to R = 32 (∼2.5 nm to ∼160 nm diameter cores). These illustrate the degree of bias and scatter in TNP, which can be seen to be small. For larger particles, the value of C becomes unimportant, and the 441 points in the subset converge into 63 points defined only by the parameters A and B. For very large particles, the graph is identical to that shown in Figure 2f for eq 8. The global mean relative error for TNP over the range used here is approximately 4%, which, when compared to the ∼10% error in estimating attenuation lengths, demonstrates that use of these equations will usually not be the most significant source of error in finding the shell thickness of nanoparticles from XPS data. However, there are certain regimes in which the prediction is poor. Figure 5 plots the mean error over subsets of the numerical data set grouped by input variable. This illustrates that the prediction is worse at extreme values of B. The usual range of B is between 0.7 and 1.4; in this regime, the mean error is ∼3%. The prediction also appears poor at small values of A, which relates to very small T; however, the mean

Figure 6. Schematic representation of the regions in which the equations in this paper are valid for a given accuracy and particle diameter. Tplanar is given in eq 7; TR→∞, in eq 8; T0, in eq 9; TR∼1, in eq 10; and TNP, in eq 11. The Topofactor of 0.72 for particles that are significantly larger than the X-ray attenuation length is taken from reference 28. A dashed line provides the accuracy of attenuation lengths for comparison. 16810

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

methods to do this are described elsewhere.28 For comparison, the accuracy of attenuation lengths of ∼10% are provided, but the accuracy of the experimental intensities and normalization factors encapsulated in A must also be considered. For analyses in which a precision in the value of T of better than 5% is required, numerical methods are necessary. The Effect of Dispersity in Core Radius on XPS Thickness. Equation 10 demonstrates that at large R, the value of TNP is independent of R; therefore, dispersity in core size does not affect the average value of TNP determined for a population of nanoparticles. For smaller nanoparticles, the dependence in the value of TNP upon R is approximately linear. Detailed investigations of the forward prediction of intensities28 and the backward calculation of T in this work for simulated populations of nanoparticles show that, for monomodal and bimodal distributions in R, the value of TNP obtained by this method is robust, provided that the value of R used is the rootmean-square radius rather than the mean radius. This compensates for the greater contribution of large particles to the XPS signal, and its use is critically important only for bimodal populations.

conservation relationship and iteratively to change the core radius until the two thickness values match. Table 1 shows a comparison of the core radii and shell thicknesses found in the original paper and using the method described in this paper. The values match to within the error of extracting the input values and results from their Figures 5 and 8. This nice concordance of the approaches used here and the one used in their paper is encouraging, but it is not a general validation of either method. The match is a result of the optimization of both methods to essentially identical numerical calculations and therefore confirms only that the numerical calculations are consistent. Within the regimes in which the approximate methods have been validated, they should be expected to perform well and identically. A more detailed examination of the method used,4 which is described in detail in another paper30 reveals that their approach should be applied only when both B and C are close to 1 and when R is less than ∼10. The first restriction results from a rather ad hoc treatment of attenuation lengths for the sake of some mathematical simplicity. The second restriction results from an error in the treatment of the effect of large-scale topography on effective overlayer thicknesses. Their essential equation for A tends to eq 5 at large R, which underestimates the true value by a factor of ∼2, as explained elsewhere.28 However, within the constraints provided here, their iterative method is excellent, predicting the numerical values of A generated for this paper to within a few percent. Thiol Self-Assembled Monolayers on Gold Nanoparticles. A detailed XPS study of gold nanoparticles with carboxylic acid-terminated thiol self-assembled monolayers (SAMs), HS(CH2)n−1COOH (where n is the number of carbon atoms in the thiol), has recently been published.18 This work presents sufficient data to permit analysis using the method described in this paper. To exemplify the method, the ratio of the C1s signal, which arises from the thiol shell, to the Au4f signal, representative of the core, is used. The data were presented both in terms of elemental compositions, from which the “homogeneous” elemental ratios ([C]/[Au]) can be found and also as an equivalent (or “apparent”) overlayer thickness, from which the values A can be extracted. From these data, the average conversion factor A = 0.73 ([C]/[Au]) can also be found. Using the values given in their paper: L1,a = 3 nm, B = 0.909, and C = 2, the thickness of the carbon shell on the gold cores was then calculated using both the quick method described in this paper and using accurate numerical calculations. The input data and results of these analyses are provided in Table 2 and show that the estimate provided by the method in this paper is within 0.1 nm of the numerical method. Subsequently, one of the samples was reanalyzed in greater detail,16 along with a detailed analysis of XPS intensities. In this analysis, slightly different atomic ratios were used ([C]/[Au] = 3.00 compared with 3.66 in the first analysis18). This is possibly a result of using an instrument different from that in the original paper. A similar conversion to find A has been performed and is shown in Table 2. The importance of this last result is that it can be compared with an extensive simulation that provided,16 among other details, a total shell thickness of 1.85 nm. This includes the minor contribution of oxygen and sulfur atoms to the thickness of the SAM layer and therefore compares very well with the values obtained in this work. From the data shown in Table 2, it is possible to establish a relationship between the thickness determined from the XPS carbon/gold intensity ratio and the number of carbon atoms in

■

APPLICATION TO LITERATURE DATA Two examples of the application of the method are provided below. These use data in the open literature that provide sufficient detail for the method to be applied. For comparison, numerical calculations were also performed to demonstrate the accuracy of the expressions given above. Importantly, the application of the equations in this paper could be performed on all data in a few minutes using standard spreadsheet software. Silicon−Silicon Oxide Nanoparticles. A detailed XPS study of the oxidation of silicon nanoparticles has been presented,4 from which the input variables and experimental results shown in Table 1 can be extracted. For this analysis, a Table 1. Data and Variables from Reference for Core−Shell Nanoparticles of Silicon−Silicon Oxidea input variables B

C

1

1.17

L1,a 3.5 nm data and results

∞ I∞ 1 /I2

ref 4 time (days)

X(SiO)

I1/I2

0.3 1 8 21 42

0.24 0.58 0.80 0.97 0.99

0.32 1.4 4.0 32 99

0.53 eq 11

A

RL1,a (nm)

TL1,a (nm)

RL1,a (nm)

TNPL1,a (nm)

0.59 2.6 7.5 61 185

2.3 2.0 1.6 0.85 0.53

0.35 0.95 1.6 2.4 2.7

2.33 1.97 1.56 0.85 0.60

0.35 0.96 1.53 2.37 2.64

a X(SiO) is the concentration of oxidized Si deduced from the amount of elemental Si in a peak fit of the Si 2p region of the XPS spectra. Results of analyses using the method described in this paper are shown for comparison.

conservation relationship for silicon needs to be established on the basis of the assumed densities of silicon and silicon oxide because in the oxidation process, the core reduces in size and the shell increases, but the total amount of silicon is assumed to be constant. The relationship outlined in their paper is followed, beginning with a trial value of the core radius, to predict the shell thickness both through eq 11 and through the 16811

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

carbon atoms, indicating that complete exchange has not occurred and that after 61 days, ∼80% of the C2 thiol has been replaced by C11 thiol.

Table 2. Data from Reference for Core-Shell Nanoparticles of Gold-Carboxylic Acid SAM and Results of Analysis by the Method Described in This Paper and Accurate Numerical Calculations RL1,a (nm)

n

A

TNPL1,a (nm), eq 11

7 7 7 7 12.5 20

6 8 11 16 16 16

0.77 1.14 1.59 2.68 2.24 2.04

7

16

2.19

■

CONCLUSIONS This paper provides simple, direct, and accurate equations to calculate overlayer, or shell, thickness from XPS data for flat films, microparticles and nanoparticles. The direct method for nanoparticles is compared with accurate numerical calculations with example data taken from the literature and found to provide thicknesses with an error typically better than 4%, which is smaller than the expected error in attenuation lengths. The important advantage of the method given in this paper is that it is fast and simple to use, which is of great advantage to nonspecialists and general analysts. For highly accurate work and in cases when more detail is required (such as core−shell particles with an outer contaminant layer), numerical simulations are still to be preferred.

TL1,a (nm), numerical

Ref 18 0.80 1.10 1.40 1.99 2.03 2.05 Ref 16 1.74

0.81 1.10 1.40 1.98 2.01 2.01 1.74

the SAM. This is close to linear both for the approximate method described here (TNPL1,a = 0.120n + 0.100, expressed in nanometers) and for the numerical simulations (TL1,a = 0.117n + 0.128, expressed in nanometers). The constant term in the linear fits potentially arises from hydrocarbon contamination, which was previously estimated to be 0.15 nm for one of the samples.16 A study of gold nanoparticles (RL1,a = 12.1 nm) coated with amine thiol SAMs was recently published by the same group.17 In that later study, the initial SAM consisted of n = 2 thiols, and the time-dependent exchange with n = 11 thiols was investigated. Table 3 presents the results using the method

■

*Phone: +44 (0)20 8943 6193. Fax:: +44 (0)20 8943 6453. Email: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work forms part of the Chemical and Biological Programme of the National Measurement System of the UK Department of Business, Innovation and Skills (BIS). The author thanks Martin Seah and Ian Gilmore from the National Physical Laboratory and David Castner from the University of Washington for helpful discussions and suggestions.

Table 3. Data from Reference 17 for Core−Shell Nanoparticles of Gold−Amine SAM and Results of Analysis by the Method Described in This Paper and Accurate Numerical Calculations eq 11

numerical

time (days)

[C] [Au]

A

TNPL1,a (nm)

n

TL1,a (nm)

n

0.021 0.125 0.5 1 2 4 7 14 21 31 61

0.37 0.37 0.42 0.48 0.69 0.96 1.12 1.39 1.42 1.37 1.47

0.27 0.27 0.31 0.35 0.50 0.70 0.82 1.01 1.04 1.00 1.08

0.36 0.36 0.40 0.45 0.62 0.84 0.96 1.14 1.16 1.13 1.20

2.1 2.1 2.5 2.9 4.4 6.2 7.2 8.6 8.9 8.6 9.2

0.35 0.35 0.40 0.45 0.62 0.82 0.95 1.12 1.14 1.11 1.18

2.0 2.0 2.4 2.8 4.3 5.9 7.1 8.6 8.7 8.5 9.0

AUTHOR INFORMATION

Corresponding Author

■

REFERENCES

(1) Baer, D. R.; Amonette, J. E.; Engelhard, M. H.; Gaspar, D. J.; Karakoti, A. S.; Kuchibhatla, S.; Nachimuthu, P.; Nurmi, J. T.; Qiang, Y.; Sarathy, V.; Seal, S.; Sharma, A.; Tratnyek, P. G.; Wang, C. M. Surf. Interface Anal. 2008, 40, 529−537. (2) Baer, D. R.; Engelhard, M. H. J. Electron Spectrosc. Relat. Phenom. 2010, 178, 415−432. (3) Baer, D. R.; Gaspar, D. J.; Nachimuthu, P.; Techane, S. D.; Castner, D. G. Anal. Bioanal. Chem. 2010, 396, 983−1002. (4) Yang, D. Q.; Gillet, J. N.; Meunier, M.; Sacher, E. J. Appl. Phys. 2005, 97, 024303. (5) Tunc, I.; Suzer, S.; Correa-Duarte, M. A.; Liz-Marzan, L. M. J. Phys. Chem. B 2005, 109, 7597−7600. (6) Huang, K.; Demadrille, R.; Silly, M. G.; Sirotti, F.; Reiss, P.; Renault, O. ACS Nano 2010, 4, 4799−4805. (7) Zorn, G.; Dave, S. R.; Gao, X.; Castner, D. G. Anal. Chem. 2011, 83, 866−873. (8) Abel, K. A.; FitzGerald, P. A.; Wang, T.-Y.; Regier, T. Z.; Raudsepp, M.; Ringer, S. P.; Warr, G. G.; van Veggel, F. C. J. M. J. Phys. Chem. C 2012, 116, 3968−3978. (9) Wu, W.; Njoki, P. N.; Han, H.; Zhao, H.; Schiff, E. A.; Lutz, P. S.; Solomon, L.; Matthews, S.; Maye, M. M. J. Phys. Chem. C 2011, 115, 9933−9942. (10) Jang, S. G.; Khan, A.; Dimitriou, M. D.; Kim, B. J.; Lynd, N. A.; Kramer, E. J.; Hawker, C. J. Soft Matter 2011, 7, 6255−6263. (11) Guzel, R.; Ustundag, Z.; Eksi, H.; Keskin, S.; Taner, B.; Durgun, Z. G.; Turan, A. A. I.; Solak, A. O. J. Colloid Interface Sci. 2010, 351, 35−42. (12) Banerjee, R.; Katsenovich, Y.; Lagos, L.; McIintosh, M.; Zhang, X.; Li, C. Z. Curr. Med. Chem. 2010, 17, 3120−3141.

described in this paper and using an accurate numerical approach, making use of the conversion factor found for the carboxylic acid SAMs to obtain A. The concordance between the accurate numerical approach and the approximate method described here is once again within 0.1 nm, indicating that the method is widely applicable. The thicknesses given here may be used to estimate the average number of carbon atoms in the SAM shell. Interestingly, the accurate numerical method provides exactly the expected number of carbon atoms in the initial sample, which is encouraging and well within the ∼10% relative standard deviation implied by the original data. The direct method developed in this paper provides the number of carbon atoms with a maximum error of 0.3 atoms compared with the numerical approach. The final thickness is equivalent to ∼9 16812

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813

The Journal of Physical Chemistry C

Article

(13) Haverkamp, R. G.; Marshall, A. T.; Cowie, B. C. C. Surf. Interface Anal. 2011, 43, 847−855. (14) Garcia-Torres, J.; Valles, E.; Gomez, E. J. Nanopart. Res. 2010, 12, 2189−2199. (15) Cirtiu, C. M.; Raychoudhury, T.; Ghoshal, S.; Moores, A. Colloids Surf., A 2011, 390, 95−104. (16) Techane, S.; Baer, D. R.; Castner, D. G. Anal. Chem. 2011, 83, 6704−6712. (17) Techane, S. D.; Gamble, L. J.; Castner, D. G. Biointerphases 2011, 6, 98−104. (18) Techane, S. D.; Gamble, L. J.; Castner, D. G. J. Phys. Chem. C 2011, 115, 9432−9441. (19) D’Addato, S.; Grillo, V.; Altieri, S.; Tondi, R.; Valeri, S.; Frabboni, S. J. Phys.: Condens. Matter 2011, 23, 175003. (20) Sarathy, V.; Tratnyek, P. G.; Nurmi, J. T.; Baer, D. R.; Amonette, J. E.; Chun, C. L.; Penn, R. L.; Reardon, E. J. J. Phys. Chem. C 2008, 112, 2286−2293. (21) Cochell, T.; Manthiram, A. Langmuir 2012, 28, 1579−1587. (22) Tao, F.; Grass, M. E.; Zhang, Y.; Butcher, D. R.; Aksoy, F.; Aloni, S.; Altoe, V.; Alayoglu, S.; Renzas, J. R.; Tsung, C.-K.; Zhu, Z.; Liu, Z.; Salmeron, M.; Somorjai, G. A. J. Am. Chem. Soc. 2010, 132, 8697−8703. (23) Wertheim, G. K.; DiCenzo, S. B. Phys. Rev. B 1988, 37, 844− 847. (24) Frydman, A.; Castner, D. G.; Schmal, M.; Campbell, C. T. J. Catal. 1995, 157, 133−144. (25) Tougaard, S. Surf. Interface Anal. 1988, 11, 453−472. (26) Cumpson, P. J. Surf. Interface Anal. 2000, 29, 403−406. (27) Seah, M. P.; Gilmore, I. S. Surf. Interface Anal. 2001, 31, 835− 846. (28) Shard, A. G.; Wang, J.; Spencer, S. J. Surf. Interface Anal. 2009, 41, 541−548. (29) Seah, M. P. Surf. Interface Anal.; In Press; DOI: 10.1002/ sia.5033. (30) Gillet, J. N.; Meunier, M. J. Phys. Chem. B 2005, 109, 8733− 8737.

16813

dx.doi.org/10.1021/jp305267d | J. Phys. Chem. C 2012, 116, 16806−16813