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Organic Depth Profiling of a Binary System: the Compositional Effect on Secondary Ion Yield and a Model for Charge Transfer during Secondary Ion Emission Alexander G. Shard,*,† Ali Rafati,‡ Ryosuke Ogaki,‡,⊥ Joanna L. S. Lee,† Simon Hutton,§ Gautam Mishra,§ Martyn C. Davies,‡ and Morgan R. Alexander‡ Quality of Life DiVision, National Physical Laboratory, Teddington, Middlesex TW11 0LW, U.K.; Laboratory of Biophysics and Surface Analysis, School of Pharmacy, UniVersity of Nottingham, Nottingham NG7 2RD, U.K.; and Kratos Analytical, Wharfside, Trafford Wharf Road, Manchester M17 1GP, U.K. ReceiVed: May 26, 2009; ReVised Manuscript ReceiVed: July 2, 2009
In recent years, it has been demonstrated that cluster ion beams may be used to sputter some materials, particularly organic materials, without the significant accumulation of damage. It is therefore possible to use cluster ion beam sputtering in conjunction with a surface analytical technique, such as SIMS, to obtain depth profiles and three-dimensional images of the distribution of organic species in the near-surface region. For SIMS organic depth profiling to be useful as an analytical tool, it is important that it is able to measure physically meaningful quantities, such as the local concentration of a species within a blend. In this paper, we investigate a model system of a miscible binary mixture of codeine and poly(lactide). We show that there is a strong surface enrichment of poly(lactide), which provides a reference signal and permits the direct comparison of different samples in terms of secondary ion yield behavior. We demonstrate that it is possible to relate secondary ion intensities to local concentrations for a binary system and that there is a direct correspondence between the yield enhancement of one component and the yield suppression of the other. The dependence of secondary ion yield on composition is described using a model of the kinetically limited transfer of charge between secondary ions and secondary neutrals. Application of the model to pure materials under the assumption that only highly fragmented secondary ions are initially produced and interact with unfragmented secondary neutrals leads to the prediction that high molecular mass quasi-molecular ions have intensities proportional to the square of the total secondary ion yield. This relationship has been independently observed in other work (Seah, M. P. Surf. Interface Anal. 2007, 39, 634.). Introduction The use of cluster primary ion beams with secondary ion mass spectrometry (SIMS) to depth profile organic materials has attracted considerable attention in recent years, and a number of detailed studies on single component organic films have developed an understanding of the salient features of the technique.1-7 These and other related studies have demonstrated that a number of organic materials may be successfully profiled, where the measure of success is the maintenance of detectable characteristic secondary ion intensities throughout the profile. However, a large number of other materials are not successfully profiled; archetypal examples for C60 ion sputtering are poly(styrene)7 and aluminum tris(hydroxyquinolate),4 in which cases it is suggested that radiation-induced cross-linking occurs,7 which rapidly reduces the sputtering yield causing excessive damage accumulation. Poly(lactide), a polymer used in drug delivery, reconstructive surgery, and tissue engineering, may be successfully profiled by cluster ion beams.4,8,9 This is fortuitous, because there is considerable interest in determining the distribution of drugs within polymers for drug delivery applications, such as drug-eluting stents.10-12 However, even poly(lactide) has limitations. Cluster ion beam sputtering over * Corresponding author. E-mail
[email protected]. † National Physical Laboratory. ‡ University of Nottingham. § Kratos Analytical. ⊥ Current address: Interdisciplinary Nanoscience Center (iNano), University of Aarhus, Ny Munkegade, Aarhus, Denmark.
depths larger than ∼1 µm is problematic at room temperature, both for SF5 cluster ions10 and, in our own investigations, for C60 cluster ions, resulting in a loss of secondary ion intensity beyond that depth. Mahoney et al. have demonstrated that cooling the sample can mitigate this problem,8 although the mechanism that causes this change in sputtering behavior is unknown. There are many literature examples of organic depth profiling of mixed systems in which the components can be readily distinguished using their characteristic secondary ions. These range from binary and layered systems1,4,9,12-19 to complicated mixtures20 and biological materials.21,22 Such studies are important in that they demonstrate that the location of individual components may be identified using the technique. The question as to whether the technique can be employed to quantify the local concentration of components has been largely unanswered. Recently, it was demonstrated that in the case of a binary, layered organic material quantitative information on the amount of one component could be obtained if sputtering yield and secondary ion yield were adequately described.17 The motivation behind the work described here was to evaluate whether the concentrations of intimately mixed blend components could be obtained in a simple manner for binary organic films. We have chosen a poly(lactide)/molecule binary blend that is known from differential scanning calorimetry measurements to be miscible and is also of relevance to drug delivery systems. While the molecule chosen (codeine) is not used in depot-based slow release formulations, it serves as a model low molecular weight
10.1021/jp904911n CCC: $40.75 2009 American Chemical Society Published on Web 07/31/2009
Organic Depth Profiling of a Binary System drug. The results of this study should therefore be useful for developing interpretational methods for the SIMS organic depth profiling of similar systems. Experimental Section Poly(lactide) (Polysciences, Warrington, PA: number-averaged molecular weight, Mn ) 22000 g/mol to 39000 g/mol) films were spin-cast from chloroform solution onto piranhasolution-cleaned silicon wafers. For binary mixtures, mixed solutions of poly(lactide) and codeine (Sigma Aldrich) of varying concentrations were used. XPS analysis (data not shown) of duplicate samples demonstrated that there was a significant surface excess of poly(lactide) compared to the composition in solution. Compositions of the casting solutions ranged from 2.4% to 28.6% by mass of the drug in poly(lactide). Film thicknesses were determined prior to SIMS analysis using an M2000 spectroscopic ellipsometer (Woollam, NE). The thicknesses of polymer films were initially determined using a wavelength range of 700-1700 nm, in which it was assumed that the films were transparent with a refractive index following a Cauchy dispersion. Optical constants were then calculated for the film below wavelengths of 700 nm based on the initially determined thickness and the known optical constants of silicon; a thin layer (2 nm) of silicon oxide on top of the silicon was assumed, but exclusion of this layer made negligible difference to the extracted data. For the blends, a series of absorbance bands at ∼215, ∼250, and ∼285 nm were found and are consistent with the absorption spectra of codeine.23 These bands were absent for pure poly(lactide), which was transparent throughout this region. By modeling these absorption peaks as Gaussian oscillators with fixed intensity ratios and widths, it was possible to estimate the relative concentration of codeine within each of the films assuming that the extinction coefficient of these bands was proportional to the concentration of codeine within the film. Film thicknesses were ∼60 nm (3 samples), ∼100 nm (5 samples), and ∼250 nm (3 samples) for the blend films and from ∼10 to ∼750 nm for pure poly(lactide) films. The estimation of blend composition by ellipsometry shows an excellent correlation with solution compositions.24 SIMS depth profiles were acquired using a TOFSIMS IV time-of-flight secondary ion mass spectrometer (IONTOF Gmbh, Mu¨nster, Germany) in the “interlaced” mode using 10 keV C60+ ions rastered over a 400 µm × 400 µm area and pulsed 25 keV Bi3+ ions for analysis. The analysis beam was typically rastered over a 100 µm × 100 µm area centrally located within the area sputtered by C60+ ions. Ion currents were measured in a Faraday cup mounted on the sample holder and typically were 100-500 pA for C60+ and 0.1 pA for Bi3+. The C60+ current and rastered area were used to calculate the areic dose in ions nm-2. Fluence is defined25 as the number of particles passing through a surface normal to the beam direction and in this case may be calculated by dividing the areic dose by cos(45°). The mass resolution was sufficient to easily distinguish, for example, C5H9O2+ (101.060 u) from C4H5O3+ (101.024 u) but nominal mass values are given throughout the remainder of the text for the sake of brevity and because the secondary ions selected do not have the same nominal mass as any other intense secondary ions. Results are presented from single experiments on a range of samples; repeat measurements were made on three of the samples and found to produce identical secondary ion ratios within the error expected from counting statistics. The XPS spectra were acquired using an Axis Ultra DLD spectrometer (Kratos Analytical, UK) with a monochromated Al KR source producing a 450 W energy. The data was
J. Phys. Chem. B, Vol. 113, No. 34, 2009 11575 converted to VAMAS26 format and processed using CasaXPS, version 2.3.14. High-resolution C 1s, N 1s, O 1s, and Si 2p spectra were collected at pass energy of 80 eV and step size of 0.1 eV and quantified using empirically derived relative sensitivity factors provided by Kratos Analytical. The pressure in the analysis chamber was maintained below 2 × 10-8 mbar for data acquisition. The coronene primary ion source was mounted at a 45° angle to the sample surface which was normal to the analyzer. The coronene beam was operated at 12 keV energy and only C24H12+ (singly charged polyatomic ions) were used for depth profiling; this selection was made using a Wien mass filter. The raster size was fixed at 2.5 mm × 2.5 mm. XPS spectra were collected using a 110 µm aperture. The majority of the XPS data has been reported previously.24 Results and Discussion Sputtering Yields from Blend Films. Our previous investigations have shown that sputtering yield may reduce during the course of a depth profile.4,17 It is therefore vital to have an understanding of the sputtering yield behavior during depth profiling prior to any detailed analysis. One of the manifestations of this changing yield is a decline in secondary ion intensity. However, for mixed systems it may not be possible to easily distinguish such effects from compositional changes and, even for homogeneous systems, the relationship between secondary ion intensity and sputtering yield is not trivial. Therefore, we measure the C60+ dose required to reached the organic/silicon interface4,27 and calculate the film thickness assuming a constant sputtering yield in order to compare the results directly with ellipsometric thicknesses. Typical depth profiles through a blend film are shown in Figure 1 plotted as normalized secondary ion intensities versus C60+ ion dose. Intensities are normalized to the quasi-steadystate intensity, except for the substrate ions Si+ and SiO3H-, which are normalized to their maximal intensities. The secondary ions selected to be characteristic of the substrate have a high secondary ion yield from the oxide overlayer on silicon and are therefore suitable for determining the interface position.27 These illustrate the results obtained for all samples investigated here: a transient region during which poly(lactide) secondary ion intensities generally reduce and codeine secondary ion intensities rise; a quasi-steady state in which all ions intensities remain in a constant ratio to each other; an interfacial region where secondary ions due to the substrate rise in intensity and organic secondary ions, with the exception of CN-, decrease in intensity. The organic/silicon interface is estimated to be at the dose when characteristic secondary ions from the silicon substrate first reach 50% of their maximal intensity.4,27 Within the quasi-steady-state region, the ratios of intensities between characteristic PLA ions are constant, irrespective of the composition and film thickness. This is true also for characteristic codeine ions. This is evident in MCR (multivariate curve resolution)28 analysis of the data in which more than 99% of the variance in the data could be explained by two components with spectra almost identical to pure PLA and pure codeine. The MCR analysis is helpful in identifying those ions that arise uniquely from only one of the components. By assuming that all the films have the same sputtering yield volume under these conditions (72 nm3 ion-1), we can estimate the film thickness from the profile and compare to the ellipsometric thickness. This comparison is shown in Figure 2 for all films investigated here, including pure poly(lactide) films. The two measurements are identical, within the uncertainty of the data, with the exception of the thickest, pure poly(lactide) film,
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Figure 3. Positive secondary ion intensities, characteristic of poly(lactide) normalized to initial intensities, as a function of depth for the first 40 nm of ∼100 nm thick films. Data are shown for four ions from pure poly(lactide) films (0), 4.8% by mass codeine (4), and 28.6% by mass codeine (]).
Figure 1. Secondary ion intensities of selected ions plotted against ion dose for a 95 nm thick blend film of poly(lactide) containing 9.1% by mass codeine. Intensities are normalized to the quasi-steady-state intensity, except for the substrate ions, which are normalized to their maximal intensities. The transient and quasi-steady-state regions are indicated.
Figure 2. Depth profile thickness (assuming a constant sputtering yield volume of 72 nm3 ion-1) plotted against ellipsometric thickness for pure poly(lactide) films (0) and blend films (×). The solid line indicates identity between the two measurements.
which is added for information only. We assume that the sputtering yield is constant, irrespective of film thickness or composition, within the ranges used in this study. A depth scale within the blend films may thus be easily established by multiplying the dose by the sputtering yield volume, noting that this depth scale is only relevant to the organic overlayer and not the silicon substrate or interface.
Poly(lactide) Secondary Ions in SIMS Depth Profiles of Pure Material and Blends. Cluster ion beam sputtering of pure poly(lactide) films has been extensively studied,4,8,9,14 and it has been shown that, for films of up to ∼1 µm in thickness, characteristic secondary ion intensities undergo an initial transient change over 10-20 nm depth and are then constant until the substrate interface. The transient change depends upon a balance between damage accumulation and precursor formation, with high mass secondary ions showing significant transient declines in intensity. The characteristic secondary ions of poly(lactide) have been reported previously and extensively discussed.29-31 Figure 3 presents the transient region for some characteristic poly(lactide) positive secondary ions normalized to initial intensity and plotted against the depth in the blend for films of different codeine concentration. The behaviors of secondary ion intensities, even from pure poly(lactide) (data shown as squares), in this region are rather complicated and cannot be described using the simple damage model of Cheng et al.,1 which was developed for, and is applicable to, quasimolecular secondary ions. They may be rationalized by using a scheme proposed previously by Gilmore and Seah32 which uses a bond-breaking model to demonstrate that secondary ions may increase as well as decrease in intensity with increasing primary ion dose. Such modeling is beyond the scope of this paper. For pure poly(lactide), C3H4O•+ exhibits a slight decline in intensity, C3H5O+ an interesting rise in intensity and C3H3O+ is almost constant throughout the transient. Higher mass secondary ions show a greater degree of decline in intensity during the transient, as described previously.4 Following the admixture of codeine, it appears that all of the characteristic poly(lactide) secondary ions have a lower quasisteady-state intensity compared to pure poly(lactide). The converse interpretation that the initial intensities are enhanced is not supported by the observation that the absolute initial intensities are very similar in comparable data sets (i.e., samples run on the same day with the same primary ion parameters). We show later that the surface of the blends are strongly
Organic Depth Profiling of a Binary System
J. Phys. Chem. B, Vol. 113, No. 34, 2009 11577 TABLE 1: Intense Characteristic Positive Secondary Ions from Codeine (Molecular Mass 299u) with Assignments 300 u 58 u 44 u 42 u 26 u
Figure 4. Negative secondary ion intensities, characteristic of poly(lactide) normalized to initial intensities, as a function of depth for the first 40 nm of ∼100 nm thick films. Data are shown for four ions from pure poly(lactide) films (0), 4.8% by mass codeine (4), and 28.6% by mass codeine (]).
enriched in poly(lactide); this is supported by our XPS data on the same systems,24 and therefore the initial intensities of poly(lactide) ions may be used as a useful normalizing factor for comparison between different blend films. We may expect that the intensity of poly(lactide)-related ions will decrease as one profiles from a surface rich in poly(lactide) to a subsurface that has a higher fraction of codeine, and therefore a lower fraction of poly(lactide). A simple assumption would be that these secondary ion intensities are proportional to the fractional analyzed volume of the surface occupied by poly(lactide), i.e., the yield of poly(lactide) ions is matrix-independent. This should be comparable to the mass fraction of poly(lactide). An inspection of the data immediately demonstrates that such an approach will underestimate the mass fraction of poly(lactide); for example, the data for 71.4% by mass poly(lactide) (28.6% by mass codeine) demonstrates a fractional drop in normalized intensity of more than 50%; in this case the codeine mass fraction will be overestimated by a factor of ∼2. The overestimation factor is actually somewhat greater for the more dilute blends. One possible explanation for this anomalous decrease in poly(lactide) secondary ion intensities is that the sputtered surface is enriched in codeine compared to the bulk composition. We find little support for this interpretation from the XPS analysis of analogous films sputtered with coronene ions, in which the sputtered surface in the quasi steady state displayed an elemental composition almost identical to that expected from the bulk composition.24 Due to the differences in sputtering ion source and information depth of SIMS and XPS, it is still possible that an enriched layer exists in the case of C60+ ion sputtering and SIMS analysis. If an enriched layer did exist, it would be expected that similar effects would also be evident in the negative secondary ion depth profiles. However, as demonstrated in Figure 4, the normalized intensities of any of the poly(lactide) negative secondary ions follow closely similar curves irrespective of the bulk codeine composition. If it were
C18H22NO3+ C 3 H 8N + C 2 H 6N + C 2 H 4N + CN-
not for the weak CN- ion, it would be impossible to establish whether the blend films contained any codeine at all from these data. The most likely explanation for the larger than expected transient drop in poly(lactide) positive secondary ion intensities is therefore a change in secondary ion yield. As the volume fraction of codeine increases, the yield of positive secondary ions from poly(lactide) reduces. We can also infer that the yield of negative secondary ions increases and this seems to compensate almost exactly for the reduction in the volume fraction of poly(lactide), resulting in the identical transient changes shown in Figure 4. Jones et al. demonstrated that, in mixed systems, the quasimolecular secondary ion intensity of the molecular component with a lower gas phase basicity was strongly suppressed, while the species of higher gas-phase basicity was enhanced.33 In our system, the secondary neutrals from codeine which contain a strongly basic amine group may suppress the formation of secondary ions from the more weakly basic secondary neutrals from poly(lactide). This is probably the result of a competition between the secondary neutral species for a limited supply of charge in which the more basic species have an advantage. Negative secondary ions from poly(lactide) may be enhanced by their greater acidity. Following this argument, we would therefore expect that the yield of positive secondary ions from codeine would be enhanced; we demonstrate this is the case later. Codeine Secondary Ions in SIMS Depth Profiles of Blends. As is evident in Figure 1, characteristic codeine ions (Table 1) rise rapidly in intensity during the transient. There is a subsequent decay in intensity for the quasi-molecular ion at 300 u, prior to reaching the quasi steady state. This decay may be described in terms of Cheng’s model for molecular damage for a constant sputtering rate.1 We have previously rationalized the rise in intensity as being due to an overlayer rich in poly(lactide). In Figure 5 we demonstrate that the data are consistent with an almost pure poly(lactide) overlayer for some of the films of ∼100 nm thickness, all others of the same thickness behave identically. The rise in the 44 u ion, relative to the steady state intensity, is modeled with a (1 - exp(-D/ L)) function, in which D is the mean sputtered depth and L, a characteristic length for the rise in intensity, is 2 nm. Since L is smaller than the depth resolution of C60+ sputtering at 10 keV,17 it is unclear whether the surface is pure poly(lactide), but it is certainly very strongly enriched in poly(lactide), in accord with the XPS data. It is notable that the XPS data are consistent with a ∼2 nm overlayer of pure poly(lactide).24 These data provide the main justification for our use of initial 55 u secondary ion intensities as a normalizing factor later. The transient change in the 300 u ion can be described using Cheng’s model1 multiplied by the function used to describe the 44 u transient change. The damage cross section and other parameters in Cheng’s model are not important here, merely the fact that the same parameters describe the intensity variation for all concentrations studied. This provides indirect evidence that the sputtering yields are identical for all the blends. For thicker films,
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Figure 5. Positive secondary ion intensities, characteristic of codeine normalized to steady-state intensities, as a function of depth for the first 20 nm of ∼100 nm thick films. Data are shown for the 44 and 300 u ions from 2.4% by mass codeine (0), 9.1% by mass codeine (4), and 28.6% by mass codeine (]).
the rise in codeine characteristic secondary ion intensity is prolonged, indicating a thicker layer of poly(lactide) enrichment. The CN- negative secondary ion demonstrates very similar behavior to the 44 u positive secondary ion, but is slightly complicated by the inability to clearly resolve this ion from 13 12 C CH-. Relationship between Composition and Ion Intensities. A common method of demonstrating the relationship between SIMS ion intensities and composition is to plot the intensity of a secondary ion characteristic of the minority component divided by the intensity of a secondary ion characteristic of the majority component. Such ratios have the advantage of removing experimental factors that may globally affect ion intensities, the ratios are then an expression of the (composition dependent) secondary ion yields and the volume fraction of the components. For a two-component system we may write eq 1:
I1 Y1X1 Y1X1 ) ) I2 Y2X2 Y2(1 - X1)
(1)
in which Ii is the intensity of a secondary ion, i, characteristic of component a (in this case, when i ) a), Xa is the volume fraction of component a, and Yi is the secondary ion yield of the characteristic ion i. From this, we would expect reasonable linearity between the ion intensity ratio and X1, if component 1 is dilute and the yields are constant over the composition range. In Figure 6, the ratios of characteristic positive secondary ion
Figure 6. Ratio of quasi-steady-state characteristic positive secondary ion intensities for codeine and poly(lactide) as a function of mass fraction. Error bars are estimated from counting statistics and represent 99% confidence intervals. The error in mass fraction is difficult to establish. The dashed line is a linear fit to the data, the bold line is the expected behavior with composition-independent yields and the thin line is the result of the kinetic model of charge transfer.
intensities in the quasi-steady-state regime are plotted against blend composition. There is a remarkable linear correspondence, which is maintained even though the film thicknesses of some samples are quite different. This linearity is maintained irrespective of the choice of the two characteristic secondary ions since characteristic ions from each component are closely proportional in intensity (the result of our MCR analysis). We do not show all the possible combinations for the sake of brevity, but we have tested this with a suitably large range of combinations and found that the linear relationship holds. If we were interested in providing a calibration curve for the determination of codeine concentration in poly(lactide) after C60 sputtering, then there is little need to go further than this. However, this linear relationship does require some explanation. If the yields in eq 1 were constant, the relationship should be nonlinear; examples of the expected curves are shown in Figure 6 as bold lines, with initial slopes matching the data from dilute samples. One may change the yield ratio to provide a better fit, but the curve is still significantly different from the data. This strongly indicates that the secondary ion yields are dependent upon the composition, a fact that we had established from analysis of secondary ion intensity changes during a depth profile. The question is whether the relationship between secondary ion intensities and composition can be rationalized and described.
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Figure 7. Fraction of protonated nitrogen in blends, determined from the relative intensity of the two N 1s peaks in XPS, plotted against the mass fraction of codeine, determined by XPS. Data from unsputtered films (×) and the quasi steady state of coronene sputtered films (0) are shown. Arrows link data from the same blends. Error bars are estimated uncertainties, the smooth curve indicates the expected relationship from poly(lactide) with Mn ) 26,000 g/mol and a constant bulk ionization of codeine of 40%.
A Kinetic Model of Charge Transfer. We use the idea that secondary species are able to exchange charge within an excited volume (or “selvedge”) following a primary ion impact. This is hardly a novel concept and has been used qualitatively by others, for example, in the well-known desorption/ionization model of Cooks and Busch.34 There is some evidence that this charge exchange only occurs during the events immediately following the primary ion impact,33 and there are suggestions that hydrogen or proton transfer may redistribute charge within the surface after prolonged cluster ion beam sputtering.35 This could result in residual charged species in the sputtered surface, which are then thought to change secondary ion yields in comparison to those of the unsputtered material. This postulation has been used to explain SIMS data from frozen aqueous samples.36 It is interesting, therefore, to demonstrate that the ion yield effects described in this paper arise from a change in surface composition rather than from a change in charge distribution due to cluster ion beam sputtering; although this may not change the descriptive form of our model. XPS can verify this and provide a definitive answer. The most likely candidate for protonation in the blend films is the highly basic tertiary amine group on codeine. Protonation induces a distinct chemical shift in the binding energy of the N 1s peak of ∼2 eV. Indeed, all blend films studied exhibit protonated nitrogen, and the fraction of protonated nitrogen can be determined from the ratio of the intensity of the protonated N 1s peak to the total N 1s intensity. This is plotted in Figure 7 against the film composition determined by XPS. It is clear that there are insignificant differences in the trend between sputtered and virgin samples. The overriding factor is the composition. The data may be nicely explained by considering that a poly(lactide) molecule contains one acidic end group and codeine effectively titrates this end group, and thus all nitrogen atoms would be protonated if the number of acidic poly(lactide) end groups exceeds the number of codeine molecules. A constant fraction (40%) of the remaining codeine is protonated in the blend films (presumably due to the hydroxide salt, since no other electronegative elements apart from oxygen are detected). The smooth curve in Figure 7 is a description of this behavior. The important point is that prolonged sputtering does not change the level of proton exchange between the components in this system.
Figure 8. Schematic of the kinetic model of charge transfer, the expressions involving Ni given here relate to t ) 0.
We introduce a kinetic model that describes the transfer of charge from poly(lactide) secondary ions to codeine secondary neutrals. The model is shown schematically in Figure 8. We consider that the initial number, Ni(t)0), of a secondary species, i, is proportional to the volume fraction, Xa, of the component a that gives rise to it and the constant of proportionality is the secondary yield, Yi. This secondary yield is the same as the observed yield for the pure component, a. A proportion of the secondary species, Ri, is able to interact with other emitted species in a small and dense volume, V, for a short residence time, tR. The main reaction considered here is shown in Figure 8, a charge transfer reaction that presumably involves the transfer of a proton, for which we can write the second order rate law given in eq 2.
-dnPLA+ dncod+ k ) ) nPLA+ncod0 dt dt V
(2)
In eq 2, k is the rate constant, ni(t)0) is given by RiNi(t)0) and the concentration of species i given by (ni/V). We assume that, even for samples dilute in codeine, ncod0 . nPLA+ and therefore ncod0 is constant to obtain a pseudo-first-order rate law. To check this assumption, we have used the integrated form of the second-order rate equation and found that no good fit to our data could be found with Rcod0Ycod0 < ∼50YPLA+. For Rcod0Ycod0 > ∼50YPLA+, reasonable fits could be found in all cases and Rcod0Ycod0 is found to be inversely proportional to (ktR/V). This justifies our assumption, in which (ktRRcod0Ycod0/V) is combined into a single parameter. We should, in any case, expect the yield of secondary neutrals to be orders of magnitude larger than that of secondary ions. The integrated form (between t ) 0 and t ) tR) of the pseudofirst-order rate law is provided in eq 3, where we have introduced the dimensionless parameter P ) (ktRRcod0Ycod0/V). The derivation is shown in the Appendix.
∆N ) RPLA+YPLA+(1 - Xcod)(1 - exp(-PXcod))
(3)
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Figure 9. Normalized steady-state intensities of the poly(lactide) secondary ion at 55 u as a function of codeine mass fraction (Xcod). Error bars are estimated from counting statistics and represent 99% confidence intervals. The thick solid line is a fit to the data using eq 5. The dashed bold construction line shows the expected behavior with no charge transfer and the other construction line (+ + +) shows the limiting behavior with maximum possible charge transfer.
We may now write a complete expression for the number of detectable positive secondary ions from poly(lactide), NPLA+; this is given in eq 4. NPLA+(t > tR) ) YPLA+(1 - Xcod)(1 - RPLA+(1 - exp(-PXcod)))
(4)
This expression has been derived for a single poly(lactide) ion species interacting with a single codeine neutral species. We may expect it to be valid for a single poly(lactide) ion species interacting with all codeine neutral species if some average value of P and RPLA+ could be found to describe the sum of the interactions. To test this against experimental data, it is necessary to find a means of removing experimental factors that globally affect the detection of ions. We do this by normalizing the steady-state ion intensities, IPLA+(ss), to the initial intensity, IPLA+(ref), of a characteristic poly(lactide) ion within each data set. Because the surface of the blends is highly enriched in poly(lactide), IPLA+(ref) serves as a reference intensity for pure, unsputtered poly(lactide). The complete expression is given in eq 5. IPLA+(ss) IPLA+(ref)
)
YPLA+(ss) (1 - Xcod)(1 - RPLA+(1 - exp(-PXcod))) YPLA+(ref)
Figure 10. Normalized steady-state intensities of codeine secondary ions as a function of codeine mass fraction (Xcod). Error bars are estimated from counting statistics and represent 99% confidence intervals. The curves are fits to the data using eq 6. (]) cod+ ) 44 u, Ycod+(ss)/Y55(ref) ) 0.83, fcod+ ) 0.99. (4) cod+ ) 300 u, Ycod+(ss)/ Y55(ref) ) 0.78, fcod+ ) 0.49.
competition with, poly(lactide) secondary ions; see Figure 8. To maintain the stoichiometry of the chemical reactions, the total number of codeine secondary ions produced from charge transfer must equal the total number of poly(lactide) secondary ions lost in the process. However, the distribution of the exchanged charge between the various codeine secondary neutrals is unknown and we introduce a factor, fcod+, which describes the proportion of the total number of secondary ions created during charge transfer that contribute to the intensity of a particular secondary ion. Thus, the number of secondary ions of a particular type, cod+, which are detectable, is given by Ycod+Xcod + fcod+∆N, where, because we have formulated ∆N in terms of a single, intense secondary ion of poly(lactide), we expect fcod+ to be close to unity for a single, intense secondary ion of codeine. By normalizing to a reference intensity, we choose the initial intensity of a poly(lactide) secondary ion as before, we may write eq 6.
Icod+(ss) Ycod+(ss) ) X + IPLA+(ref) YPLA+(ref) cod YPLA+(ss) fcod+RPLA+ (1 - Xcod)(1 - exp(-PXcod)) (6) YPLA+(ref)
(5)
In Figure 9, the experimental data for the characteristic poly(lactide) ion at 55 u from films of different composition are presented along with a fit to the data using eq 5 with Y55(ss)/ Y55(ref) ) 0.87, RPLA+ ) 0.38 and P ) 12.2. Construction lines show the expected behavior if there is no charge transfer (i.e., RPLA+ ) 0) and the limiting behavior when all possible charge transfer has occurred (i.e., exp(-PXcod) ) 0). The data are described nicely within the range of compositions investigated. Similar results (with a different yield ratio) can be found for any of the characteristic poly(lactide) ions, this is obvious from the fact that these characteristic ion intensities are almost proportional to each other within the quasi steady state. To explain the behavior of characteristic codeine ions, we need to consider that some are produced directly from the codeine fraction, given by Ycod+Xcod, and some are produced as a result of the charge transfer from, or as a result of successful
All the parameters except Ycod+(ss)/YPLA+(ref) and fcod+ have been determined previously, and these are used to fit the data for the 44 u and 300 u secondary ions, as shown in Figure 10. The curves describe the data excellently and demonstrate the intimate link between the intensities of the two components, which is captured by the kinetic model. The ratios of steadystate intensities between codeine and poly(lactide) ions are plotted in Figure 6, and show the expected near-linearity. This is no surprise as we have excellent fits to the normalized absolute intensities, as shown in Figures 9 and 10, and therefore this near-linearity is in no way a validation of the model, it merely shows that such behavior can arise from the model. We note here that exactly the same arguments can be applied to the negative secondary ions, where we also observe a linear relationship between the ratio of the 26 u (CN-) steady-state intensity to poly(lactide) secondary ion intensities and the codeine composition. In the compositional range we are examining here, the charge transfer from codeine negative
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secondary ions to poly(lactide) secondary neutrals is essentially complete (i.e., not kinetically limited, this arises because of the large number of poly(lactide) secondary neutrals) and the resulting linear relationships are not convincing demonstrations of the model. It is worth pointing out that the compositionindependent profiles shown in Figure 4 cannot be explained without some sort of matrix effect whereby the yield of negative secondary ions from poly(lactide) is increased as the fraction of codeine increases. The kinetic model of charge transfer model seems to capture many of the important features of the matrix effect observed in this system. It is also consistent with previous suggestions for ion formation mechanisms in SIMS34 and provides a mathematical framework for such ideas that may be applied to other systems. Implications of the Charge Transfer Model. There is at least one interesting implication of the model. We may consider that charge transfer should not be restricted to secondary species from different components, but should also occur between different secondary species from a single component. This would explain why delicate quasi-molecular ions can be observed intact, sometimes with high yields, when the thermal energies required for ionization should also cause major fragmentation. The scheme suggests that only highly fragmented secondary ions are initially produced, including H+, some of these exchange charge with, or attach to, less fragmented secondary neutrals to produce “characteristic” secondary ions, the intensities of which are a reflection of the number of conjugate neutral species produced and their relative stability as ions. In the blend films we have studied here, the distribution in relative intensities of secondary ions from a single component is not a function of composition, which could be expected if the internal distribution of secondary neutrals from each component is unchanged with composition. However, we may expect from the kinetic model that there is a direct implication for secondary ion intensities if the total yield changes. For a pure material, we can adapt eq 2 to provide a description of all possible ion-neutral pairwise interactions that would lead to an enhancement or diminution in a given secondary ion intensity. This is shown in eq 7, which would need to be solved for all secondary ion and neutral species simultaneously.
dni+ ) dt
∑ j
kji+ n n V j+ i0
∑ j
kij+ n n V i+ j0
(7)
In eq 7, the first term represents the production of this type of ion from charge transfer reactions between the conjugate neutral and other charged species and the final term represents the loss of this type of ion during charge transfer reactions. The rate constants kij+ are related to kji+ by the equilibrium constant for the appropriate reversible reaction, which indicates how thermodynamic quantities, for example, gas-phase basicities, may influence the relative proportions of secondary ions. For a large molecular species, we may consider that the prompt yield of quasi-molecular secondary ions is zero (NM+(t)0) ) nM+(t)0) ) 0) and therefore only the first term survives for the initial rate of change. We can then write eq 8 in which Y′ represents the prompt yield of species; previously we used Y, which represents the yield from a pure component after internal charge exchange between secondary ions and neutrals from that component has been accounted for but before charge exchange between, or in competition with, secondary species from different components had been considered.
dnM+ dt
(t ) 0) )
∑ j
kjM+ n n ) V j+ M0
∑[ j
]
kjM+Rj+RM0 Y'j+Y'M0 V
(8)
If the molecule is sufficiently large, the prompt yield of secondary molecular neutrals will also be small such that the initial rate is valid for all tR. If the combined parameter shown in square brackets is a weak function of total sputtering yield (S) and the prompt yields of all relevant secondary species are proportional to the total sputtering yield we find that NM+ ∝ S2, even though the total secondary ion yield is proportional to S. The experimental observation of a square law dependence for the high molecular weight quasi-molecular secondary ion intensity upon the total secondary ion intensity has been described previously and the limiting case given in eq 8 has also been considered as one possible cause of this observation.37,38 Therefore, it is possible that the kinetic model of charge transfer for SIMS has a wider applicability than in the analysis of binary mixtures. Conclusions We have demonstrated that C60+ ion sputtering with SIMS analysis of binary organic thin films may be used to determine the concentrations of the components, providing a suitable calibration method exists. Within this poly(lactide) and codeine system, at least, secondary ion yields are shown to be a strong function of composition. This matrix effect is consistent with a transfer of charge from poly(lactide)-derived secondary ions to codeine-derived secondary neutrals. There is a direct and understandable relationship between the reduction in poly(lactide)-derived secondary ion yield and the enhancement in codeine-derived secondary ion yield. We have demonstrated that such changes are related to the composition of the sample, rather than the result of proton transfer between components in the sputtered surface induced by prolonged cluster ion beam sputtering. Therefore, the charge exchange is likely to occur between sputtered species during events immediately following primary ion impact. We have developed a pseudo-first-order kinetic model to describe the charge transfer behavior and found that the transfer of charge within a kinetic limit can account for the changes in ion intensity. Further analysis of the kinetic model predicts a square law dependence between high molecular weight secondary ion intensities and total secondary ion intensities, which matches experimental observations, and suggests that the transfer of charge during the emission process may be a general phenomenon. Acknowledgment. This work was supported by the National Measurement System of the UK Department of Innovation, Universities and Skills through the Chemical and Biological Metrology Programme. We thank Sian Westall (University of Nottingham) for preparing some of the samples used in this investigation and Felicia Green (NPL) for helpful comments. Appendix Derivation of eq 3: The integrated form of eq 2 in the pseudo-first-order approximation is
∫
nPLA+(t)tR)
nPLA+(t)0)
which provides
dnPLA+ ) nPLA+
∫
tR
0
-kncod0(t ) 0)dt V
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(
ln
) (
nPLA+(t ) tR) nPLA+(t ) 0) - ∆N ) ln nPLA+(t ) 0) nPLA+(t ) 0) )
Shard et al.
)
-kncod0(t ) 0)tR V
Substituting ni(t)0) ) RiYiXa and P ) (ktRRcod0Ycod0/V)
RPLA+YPLA+XPLA - ∆N ) exp(-PXcod) RPLA+YPLA+XPLA This may be simply rearranged to give eq 3, with the assumption that XPLA + Xcod ) 1. References and Notes (1) Cheng, J.; Wucher, A.; Winograd, N. J. Phys. Chem. B 2006, 110, 8329–8336. (2) Bolotin, I. L.; Tetzler, S. H.; Hanley, L. J. Phys. Chem. C 2007, 111, 9953–9960. (3) Cheng, J.; Kozole, J.; Hengstebeck, R.; Winograd, N. J. Am. Soc. Mass Spectrom. 2007, 18, 406–412. (4) Shard, A. G.; Brewer, P. J.; Green, F. M.; Gilmore, I. S. Surf. Interface Anal. 2007, 39, 294–298. (5) Szakal, C.; Sun, S.; Wucher, A.; Winograd, N. Appl. Surf. Sci. 2004, 231-2, 183–185. (6) Wagner, M. S. Anal. Chem. 2004, 76, 1264–1272. (7) Mollers, R.; Tuccitto, N.; Torrisi, V.; Niehuis, E.; Licciardello, A. Appl. Surf. Sci. 2006, 252, 6509–6512. (8) Mahoney, C. M.; Fahey, A. J.; Gillen, G.; Xu, C.; Batteas, J. D. Appl. Surf. Sci. 2006, 252, 6502–6505. (9) Mahoney, C. M. Anal. Chem. 2005, 77, 3570–3578. (10) Mahoney, C. M.; Fahey, A. J. Anal. Chem. 2008, 80, 624–632. (11) Mahoney, C. M.; Patwardhan, D. V.; McDermott, M. K. Appl. Surf. Sci. 2006, 252, 6554–6557. (12) Braun, R. M.; Cheng, J.; Parsonage, E. E.; Moeller, J.; Winograd, N. Anal. Chem. 2006, 78, 8347–8353. (13) Sostarecz, A. G.; McQuaw, C. M.; Wucher, A.; Winograd, N. Anal. Chem. 2004, 76, 6651–6658.
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