Organic Depth Profiling of a Binary System: the Compositional Effect on Secondary IonYield 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 ofBiophysics 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 usecluster ion beam sputtering in conjunction with a surface analytical technique, such as SIMS, to obtain depthprofiles and three-dimensional images of the distribution of organic species in the near-surface region. ForSIMS organic depth profiling to be useful as an analytical tool, it is important that it is able to measurephysically 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 thereis a strong surface enrichment of poly(lactide), which provides a reference signal and permits the directcomparison of different samples in terms of secondary ion yield behavior. We demonstrate that it is possibleto relate secondary ion intensities to local concentrations for a binary system and that there is a directcorrespondence 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 limitedtransfer of charge between secondary ions and secondary neutrals. Application of the model to pure materialsunder the assumption that only highly fragmented secondary ions are initially produced and interact withunfragmented secondary neutrals leads to the prediction that high molecular mass quasi-molecular ions haveintensities proportional to the square of the total secondary ion yield. This relationship has been independentlyobserved in other work (Seah, M. P. Surf. Interface Anal. 2007, 39, 634.).

Introduction

The use of cluster primary ion beams with secondary ion massspectrometry (SIMS) to depth profile organic materials hasattracted considerable attention in recent years, and a numberof detailed studies on single component organic films havedeveloped an understanding of the salient features of thetechnique.1-7 These and other related studies have demonstratedthat a number of organic materials may be successfully profiled,where the measure of success is the maintenance of detectablecharacteristic secondary ion intensities throughout the profile.However, a large number of other materials are not successfullyprofiled; archetypal examples for C60 ion sputtering are poly-(styrene)7 and aluminum tris(hydroxyquinolate),4 in which casesit is suggested that radiation-induced cross-linking occurs,7

which rapidly reduces the sputtering yield causing excessivedamage accumulation. Poly(lactide), a polymer used in drugdelivery, reconstructive surgery, and tissue engineering, maybe successfully profiled by cluster ion beams.4,8,9 This isfortuitous, because there is considerable interest in determiningthe distribution of drugs within polymers for drug deliveryapplications, such as drug-eluting stents.10-12 However, evenpoly(lactide) has limitations. Cluster ion beam sputtering over

depths larger than ∼1 µm is problematic at room temperature,both for SF5 cluster ions10 and, in our own investigations, forC60 cluster ions, resulting in a loss of secondary ion intensitybeyond that depth. Mahoney et al. have demonstrated thatcooling the sample can mitigate this problem,8 although themechanism that causes this change in sputtering behavior isunknown.

There are many literature examples of organic depth profilingof mixed systems in which the components can be readilydistinguished using their characteristic secondary ions. Theserange from binary and layered systems1,4,9,12-19 to complicatedmixtures20 and biological materials.21,22 Such studies are im-portant in that they demonstrate that the location of individualcomponents may be identified using the technique. The questionas to whether the technique can be employed to quantify thelocal 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 amountof one component could be obtained if sputtering yield andsecondary ion yield were adequately described.17 The motivationbehind the work described here was to evaluate whether theconcentrations of intimately mixed blend components could beobtained in a simple manner for binary organic films. We havechosen a poly(lactide)/molecule binary blend that is known fromdifferential scanning calorimetry measurements to be miscibleand is also of relevance to drug delivery systems. While themolecule chosen (codeine) is not used in depot-based slowrelease formulations, it serves as a model low molecular weight

* Corresponding author. E-mail alex.shard@npl.co.uk.† National Physical Laboratory.‡ University of Nottingham.§ Kratos Analytical.⊥ Current address: Interdisciplinary Nanoscience Center (iNano), Uni-

versity of Aarhus, Ny Munkegade, Aarhus, Denmark.

J. Phys. Chem. B 2009, 113, 11574–1158211574

10.1021/jp904911n CCC: $40.75 2009 American Chemical SocietyPublished on Web 07/31/2009

drug. The results of this study should therefore be useful fordeveloping interpretational methods for the SIMS organic depthprofiling of similar systems.

Experimental Section

Poly(lactide) (Polysciences, Warrington, PA: number-aver-aged molecular weight, Mn ) 22000 g/mol to 39000 g/mol)films were spin-cast from chloroform solution onto piranha-solution-cleaned silicon wafers. For binary mixtures, mixedsolutions of poly(lactide) and codeine (Sigma Aldrich) ofvarying concentrations were used. XPS analysis (data notshown) of duplicate samples demonstrated that there was asignificant surface excess of poly(lactide) compared to thecomposition in solution. Compositions of the casting solutionsranged from 2.4% to 28.6% by mass of the drug in poly(lactide).

Film thicknesses were determined prior to SIMS analysisusing an M2000 spectroscopic ellipsometer (Woollam, NE). Thethicknesses of polymer films were initially determined using awavelength range of 700-1700 nm, in which it was assumedthat the films were transparent with a refractive index followinga Cauchy dispersion. Optical constants were then calculated forthe film below wavelengths of 700 nm based on the initiallydetermined thickness and the known optical constants of silicon;a thin layer (2 nm) of silicon oxide on top of the silicon wasassumed, but exclusion of this layer made negligible differenceto the extracted data. For the blends, a series of absorbance bandsat ∼215, ∼250, and ∼285 nm were found and are consistentwith the absorption spectra of codeine.23 These bands wereabsent for pure poly(lactide), which was transparent throughoutthis region. By modeling these absorption peaks as Gaussianoscillators with fixed intensity ratios and widths, it was possibleto estimate the relative concentration of codeine within each ofthe films assuming that the extinction coefficient of these bandswas proportional to the concentration of codeine within the film.Film thicknesses were ∼60 nm (3 samples), ∼100 nm (5samples), and ∼250 nm (3 samples) for the blend films andfrom ∼10 to ∼750 nm for pure poly(lactide) films. Theestimation of blend composition by ellipsometry shows anexcellent correlation with solution compositions.24

SIMS depth profiles were acquired using a TOFSIMS IVtime-of-flight secondary ion mass spectrometer (IONTOF Gmbh,Munster, Germany) in the “interlaced” mode using 10 keV C60

+

ions rastered over a 400 µm × 400 µm area and pulsed 25 keVBi3

+ ions for analysis. The analysis beam was typically rasteredover a 100 µm × 100 µm area centrally located within the areasputtered by C60

+ ions. Ion currents were measured in a Faradaycup mounted on the sample holder and typically were 100-500pA for C60

+ and 0.1 pA for Bi3+. The C60

+ current and rasteredarea were used to calculate the areic dose in ions nm-2. Fluenceis defined25 as the number of particles passing through a surfacenormal to the beam direction and in this case may be calculatedby dividing the areic dose by cos(45°). The mass resolutionwas 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 ofbrevity and because the secondary ions selected do not havethe same nominal mass as any other intense secondary ions.Results are presented from single experiments on a range ofsamples; repeat measurements were made on three of thesamples and found to produce identical secondary ion ratioswithin the error expected from counting statistics.

The XPS spectra were acquired using an Axis Ultra DLDspectrometer (Kratos Analytical, UK) with a monochromatedAl KR source producing a 450 W energy. The data was

converted to VAMAS26 format and processed using CasaXPS,version 2.3.14. High-resolution C 1s, N 1s, O 1s, and Si 2pspectra were collected at pass energy of 80 eV and step size of0.1 eV and quantified using empirically derived relativesensitivity factors provided by Kratos Analytical. The pressurein the analysis chamber was maintained below 2 × 10-8 mbarfor data acquisition. The coronene primary ion source wasmounted at a 45° angle to the sample surface which was normalto the analyzer. The coronene beam was operated at 12 keVenergy and only C24H12

+ (singly charged polyatomic ions) wereused for depth profiling; this selection was made using a Wienmass filter. The raster size was fixed at 2.5 mm × 2.5 mm.XPS spectra were collected using a 110 µm aperture. Themajority of the XPS data has been reported previously.24

Results and Discussion

Sputtering Yields from Blend Films. Our previous inves-tigations have shown that sputtering yield may reduce duringthe course of a depth profile.4,17 It is therefore vital to have anunderstanding of the sputtering yield behavior during depthprofiling prior to any detailed analysis. One of the manifestationsof this changing yield is a decline in secondary ion intensity.However, for mixed systems it may not be possible to easilydistinguish such effects from compositional changes and, evenfor homogeneous systems, the relationship between secondaryion intensity and sputtering yield is not trivial. Therefore, wemeasure the C60

+ dose required to reached the organic/siliconinterface4,27 and calculate the film thickness assuming a constantsputtering yield in order to compare the results directly withellipsometric thicknesses.

Typical depth profiles through a blend film are shown inFigure 1 plotted as normalized secondary ion intensities versusC60

+ ion dose. Intensities are normalized to the quasi-steady-state intensity, except for the substrate ions Si+ and SiO3H-,which are normalized to their maximal intensities. The secondaryions selected to be characteristic of the substrate have a highsecondary ion yield from the oxide overlayer on silicon andare therefore suitable for determining the interface position.27

These illustrate the results obtained for all samples investigatedhere: a transient region during which poly(lactide) secondaryion intensities generally reduce and codeine secondary ionintensities rise; a quasi-steady state in which all ions intensitiesremain in a constant ratio to each other; an interfacial regionwhere secondary ions due to the substrate rise in intensity andorganic secondary ions, with the exception of CN-, decreasein intensity. The organic/silicon interface is estimated to be atthe dose when characteristic secondary ions from the siliconsubstrate first reach 50% of their maximal intensity.4,27 Withinthe quasi-steady-state region, the ratios of intensities betweencharacteristic PLA ions are constant, irrespective of the com-position and film thickness. This is true also for characteristiccodeine ions. This is evident in MCR (multivariate curveresolution)28 analysis of the data in which more than 99% ofthe variance in the data could be explained by two componentswith spectra almost identical to pure PLA and pure codeine.The MCR analysis is helpful in identifying those ions that ariseuniquely from only one of the components.

By assuming that all the films have the same sputtering yieldvolume under these conditions (72 nm3 ion-1), we can estimatethe film thickness from the profile and compare to the ellipso-metric thickness. This comparison is shown in Figure 2 for allfilms investigated here, including pure poly(lactide) films. Thetwo measurements are identical, within the uncertainty of thedata, with the exception of the thickest, pure poly(lactide) film,

Organic Depth Profiling of a Binary System J. Phys. Chem. B, Vol. 113, No. 34, 2009 11575

which is added for information only. We assume that thesputtering yield is constant, irrespective of film thickness orcomposition, within the ranges used in this study. A depth scalewithin the blend films may thus be easily established bymultiplying the dose by the sputtering yield volume, noting thatthis depth scale is only relevant to the organic overlayer andnot the silicon substrate or interface.

Poly(lactide) Secondary Ions in SIMS Depth Profiles ofPure Material and Blends. Cluster ion beam sputtering of purepoly(lactide) films has been extensively studied,4,8,9,14 and it hasbeen shown that, for films of up to ∼1 µm in thickness,characteristic secondary ion intensities undergo an initialtransient change over 10-20 nm depth and are then constantuntil the substrate interface. The transient change depends upona balance between damage accumulation and precursor forma-tion, with high mass secondary ions showing significant transientdeclines in intensity. The characteristic secondary ions ofpoly(lactide) have been reported previously and extensivelydiscussed.29-31 Figure 3 presents the transient region for somecharacteristic poly(lactide) positive secondary ions normalizedto initial intensity and plotted against the depth in the blend forfilms of different codeine concentration. The behaviors ofsecondary ion intensities, even from pure poly(lactide) (datashown as squares), in this region are rather complicated andcannot be described using the simple damage model of Chenget al.,1 which was developed for, and is applicable to, quasi-molecular secondary ions. They may be rationalized by usinga scheme proposed previously by Gilmore and Seah32 whichuses a bond-breaking model to demonstrate that secondary ionsmay increase as well as decrease in intensity with increasingprimary ion dose. Such modeling is beyond the scope of thispaper. For pure poly(lactide), C3H4O•+ exhibits a slight declinein intensity, C3H5O+ an interesting rise in intensity and C3H3O+

is almost constant throughout the transient. Higher masssecondary ions show a greater degree of decline in intensityduring the transient, as described previously.4

Following the admixture of codeine, it appears that all of thecharacteristic poly(lactide) secondary ions have a lower quasi-steady-state intensity compared to pure poly(lactide). Theconverse interpretation that the initial intensities are enhancedis not supported by the observation that the absolute initialintensities are very similar in comparable data sets (i.e., samplesrun on the same day with the same primary ion parameters).We show later that the surface of the blends are strongly

Figure 1. Secondary ion intensities of selected ions plotted againstion dose for a 95 nm thick blend film of poly(lactide) containing 9.1%by mass codeine. Intensities are normalized to the quasi-steady-stateintensity, except for the substrate ions, which are normalized to theirmaximal intensities. The transient and quasi-steady-state regions areindicated.

Figure 2. Depth profile thickness (assuming a constant sputtering yieldvolume of 72 nm3 ion-1) plotted against ellipsometric thickness forpure poly(lactide) films (0) and blend films (×). The solid line indicatesidentity between the two measurements.

Figure 3. Positive secondary ion intensities, characteristic of poly-(lactide) normalized to initial intensities, as a function of depth for thefirst 40 nm of ∼100 nm thick films. Data are shown for four ions frompure poly(lactide) films (0), 4.8% by mass codeine (4), and 28.6% bymass codeine (]).

11576 J. Phys. Chem. B, Vol. 113, No. 34, 2009 Shard et al.

enriched in poly(lactide); this is supported by our XPS data onthe same systems,24 and therefore the initial intensities ofpoly(lactide) ions may be used as a useful normalizing factorfor comparison between different blend films. We may expectthat the intensity of poly(lactide)-related ions will decrease asone profiles from a surface rich in poly(lactide) to a subsurfacethat has a higher fraction of codeine, and therefore a lowerfraction of poly(lactide). A simple assumption would be thatthese secondary ion intensities are proportional to the fractionalanalyzed volume of the surface occupied by poly(lactide), i.e.,the yield of poly(lactide) ions is matrix-independent. This shouldbe comparable to the mass fraction of poly(lactide). Aninspection of the data immediately demonstrates that such anapproach 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 normalizedintensity of more than 50%; in this case the codeine massfraction will be overestimated by a factor of ∼2. The overes-timation factor is actually somewhat greater for the more diluteblends.

One possible explanation for this anomalous decrease inpoly(lactide) secondary ion intensities is that the sputteredsurface is enriched in codeine compared to the bulk composition.We find little support for this interpretation from the XPSanalysis of analogous films sputtered with coronene ions, inwhich the sputtered surface in the quasi steady state displayedan elemental composition almost identical to that expected fromthe bulk composition.24 Due to the differences in sputtering ionsource and information depth of SIMS and XPS, it is stillpossible that an enriched layer exists in the case of C60

+ ionsputtering and SIMS analysis. If an enriched layer did exist, itwould be expected that similar effects would also be evident inthe negative secondary ion depth profiles. However, as dem-onstrated in Figure 4, the normalized intensities of any of thepoly(lactide) negative secondary ions follow closely similarcurves irrespective of the bulk codeine composition. If it were

not for the weak CN- ion, it would be impossible to establishwhether the blend films contained any codeine at all from thesedata.

The most likely explanation for the larger than expectedtransient drop in poly(lactide) positive secondary ion intensitiesis therefore a change in secondary ion yield. As the volumefraction of codeine increases, the yield of positive secondaryions from poly(lactide) reduces. We can also infer that the yieldof negative secondary ions increases and this seems to com-pensate almost exactly for the reduction in the volume fractionof poly(lactide), resulting in the identical transient changesshown in Figure 4.

Jones et al. demonstrated that, in mixed systems, the quasi-molecular secondary ion intensity of the molecular componentwith a lower gas phase basicity was strongly suppressed, whilethe species of higher gas-phase basicity was enhanced.33 In oursystem, the secondary neutrals from codeine which contain astrongly basic amine group may suppress the formation ofsecondary ions from the more weakly basic secondary neutralsfrom poly(lactide). This is probably the result of a competitionbetween the secondary neutral species for a limited supply ofcharge in which the more basic species have an advantage.Negative secondary ions from poly(lactide) may be enhancedby their greater acidity. Following this argument, we wouldtherefore expect that the yield of positive secondary ions fromcodeine would be enhanced; we demonstrate this is the caselater.

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 asubsequent decay in intensity for the quasi-molecular ion at300 u, prior to reaching the quasi steady state. This decay maybe described in terms of Cheng’s model for molecular damagefor a constant sputtering rate.1 We have previously rationalizedthe rise in intensity as being due to an overlayer rich inpoly(lactide). In Figure 5 we demonstrate that the data areconsistent with an almost pure poly(lactide) overlayer for someof the films of ∼100 nm thickness, all others of the samethickness behave identically. The rise in the 44 u ion, relativeto the steady state intensity, is modeled with a (1 - exp(-D/L)) function, in which D is the mean sputtered depth and L, acharacteristic length for the rise in intensity, is 2 nm. Since Lis smaller than the depth resolution of C60

+ sputtering at 10keV,17 it is unclear whether the surface is pure poly(lactide),but it is certainly very strongly enriched in poly(lactide), inaccord with the XPS data. It is notable that the XPS data areconsistent with a ∼2 nm overlayer of pure poly(lactide).24 Thesedata provide the main justification for our use of initial 55 usecondary ion intensities as a normalizing factor later. Thetransient change in the 300 u ion can be described using Cheng’smodel1 multiplied by the function used to describe the 44 utransient change. The damage cross section and other parametersin Cheng’s model are not important here, merely the fact thatthe same parameters describe the intensity variation for allconcentrations studied. This provides indirect evidence that thesputtering yields are identical for all the blends. For thicker films,

Figure 4. Negative secondary ion intensities, characteristic of poly-(lactide) normalized to initial intensities, as a function of depth for thefirst 40 nm of ∼100 nm thick films. Data are shown for four ions frompure poly(lactide) films (0), 4.8% by mass codeine (4), and 28.6% bymass codeine (]).

TABLE 1: Intense Characteristic Positive Secondary Ionsfrom Codeine (Molecular Mass 299u) with Assignments

300 u C18H22NO3+

58 u C3H8N+

44 u C2H6N+

42 u C2H4N+

26 u CN-

Organic Depth Profiling of a Binary System J. Phys. Chem. B, Vol. 113, No. 34, 2009 11577

the rise in codeine characteristic secondary ion intensity isprolonged, indicating a thicker layer of poly(lactide) enrichment.The CN- negative secondary ion demonstrates very similarbehavior to the 44 u positive secondary ion, but is slightlycomplicated by the inability to clearly resolve this ion from13C12CH-.

Relationship between Composition and Ion Intensities. Acommon method of demonstrating the relationship betweenSIMS ion intensities and composition is to plot the intensity ofa secondary ion characteristic of the minority component dividedby the intensity of a secondary ion characteristic of the majoritycomponent. Such ratios have the advantage of removingexperimental factors that may globally affect ion intensities, theratios 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:

in which Ii is the intensity of a secondary ion, i, characteristicof component a (in this case, when i ) a), Xa is the volumefraction of component a, and Yi is the secondary ion yield ofthe characteristic ion i. From this, we would expect reasonablelinearity between the ion intensity ratio and X1, if component 1is dilute and the yields are constant over the composition range.In Figure 6, the ratios of characteristic positive secondary ion

intensities in the quasi-steady-state regime are plotted againstblend composition. There is a remarkable linear correspondence,which is maintained even though the film thicknesses of somesamples are quite different. This linearity is maintained irrespec-tive of the choice of the two characteristic secondary ions sincecharacteristic ions from each component are closely proportionalin intensity (the result of our MCR analysis). We do not showall the possible combinations for the sake of brevity, but wehave tested this with a suitably large range of combinations andfound that the linear relationship holds.

If we were interested in providing a calibration curve for thedetermination 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 benonlinear; examples of the expected curves are shown in Figure6 as bold lines, with initial slopes matching the data from dilutesamples. One may change the yield ratio to provide a better fit,but the curve is still significantly different from the data. Thisstrongly indicates that the secondary ion yields are dependentupon the composition, a fact that we had established fromanalysis of secondary ion intensity changes during a depthprofile. The question is whether the relationship betweensecondary ion intensities and composition can be rationalizedand described.

Figure 5. Positive secondary ion intensities, characteristic of codeinenormalized to steady-state intensities, as a function of depth for thefirst 20 nm of ∼100 nm thick films. Data are shown for the 44 and300 u ions from 2.4% by mass codeine (0), 9.1% by mass codeine(4), and 28.6% by mass codeine (]).

I1

I2)

Y1X1

Y2X2)

Y1X1

Y2(1 - X1)(1)

Figure 6. Ratio of quasi-steady-state characteristic positive secondaryion intensities for codeine and poly(lactide) as a function of massfraction. Error bars are estimated from counting statistics and represent99% confidence intervals. The error in mass fraction is difficult toestablish. The dashed line is a linear fit to the data, the bold line is theexpected behavior with composition-independent yields and the thinline is the result of the kinetic model of charge transfer.

11578 J. Phys. Chem. B, Vol. 113, No. 34, 2009 Shard et al.

A Kinetic Model of Charge Transfer. We use the idea thatsecondary species are able to exchange charge within an excitedvolume (or “selvedge”) following a primary ion impact. Thisis hardly a novel concept and has been used qualitatively byothers, for example, in the well-known desorption/ionizationmodel of Cooks and Busch.34 There is some evidence that thischarge exchange only occurs during the events immediatelyfollowing the primary ion impact,33 and there are suggestionsthat hydrogen or proton transfer may redistribute charge withinthe surface after prolonged cluster ion beam sputtering.35 Thiscould result in residual charged species in the sputtered surface,which are then thought to change secondary ion yields incomparison to those of the unsputtered material. This postulationhas been used to explain SIMS data from frozen aqueoussamples.36 It is interesting, therefore, to demonstrate that theion yield effects described in this paper arise from a change insurface composition rather than from a change in chargedistribution due to cluster ion beam sputtering; although thismay not change the descriptive form of our model. XPS canverify this and provide a definitive answer. The most likelycandidate for protonation in the blend films is the highly basictertiary amine group on codeine. Protonation induces a distinctchemical shift in the binding energy of the N 1s peak of ∼2eV. Indeed, all blend films studied exhibit protonated nitrogen,and the fraction of protonated nitrogen can be determined fromthe ratio of the intensity of the protonated N 1s peak to thetotal N 1s intensity. This is plotted in Figure 7 against the filmcomposition determined by XPS. It is clear that there areinsignificant differences in the trend between sputtered andvirgin samples. The overriding factor is the composition. Thedata may be nicely explained by considering that a poly(lactide)molecule contains one acidic end group and codeine effectivelytitrates this end group, and thus all nitrogen atoms would beprotonated if the number of acidic poly(lactide) end groupsexceeds 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 electro-negative elements apart from oxygen are detected). The smoothcurve in Figure 7 is a description of this behavior. The importantpoint is that prolonged sputtering does not change the level ofproton exchange between the components in this system.

We introduce a kinetic model that describes the transfer ofcharge from poly(lactide) secondary ions to codeine secondaryneutrals. The model is shown schematically in Figure 8. Weconsider that the initial number, Ni(t)0), of a secondary species,i, is proportional to the volume fraction, Xa, of the componenta that gives rise to it and the constant of proportionality isthe secondary yield, Yi. This secondary yield is the same as theobserved yield for the pure component, a. A proportion of thesecondary species, Ri, is able to interact with other emittedspecies in a small and dense volume, V, for a short residencetime, tR. The main reaction considered here is shown in Figure8, a charge transfer reaction that presumably involves the transferof a proton, for which we can write the second order rate lawgiven in eq 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 assumethat, even for samples dilute in codeine, ncod0 . nPLA+ andtherefore ncod0 is constant to obtain a pseudo-first-order rate law.To check this assumption, we have used the integrated form ofthe second-order rate equation and found that no good fit toour data could be found with Rcod0Ycod0 < ∼50YPLA+. ForRcod0Ycod0 > ∼50YPLA+, reasonable fits could be found in all casesand Rcod0Ycod0 is found to be inversely proportional to (ktR/V).This justifies our assumption, in which (ktRRcod0Ycod0/V) iscombined into a single parameter. We should, in any case,expect the yield of secondary neutrals to be orders of magnitudelarger than that of secondary ions.

The integrated form (between t ) 0 and t ) tR) of the pseudo-first-order rate law is provided in eq 3, where we have introducedthe dimensionless parameter P ) (ktRRcod0Ycod0/V). The deriva-tion is shown in the Appendix.

Figure 7. Fraction of protonated nitrogen in blends, determined fromthe relative intensity of the two N 1s peaks in XPS, plotted against themass fraction of codeine, determined by XPS. Data from unsputteredfilms (×) and the quasi steady state of coronene sputtered films (0)are shown. Arrows link data from the same blends. Error bars areestimated uncertainties, the smooth curve indicates the expectedrelationship from poly(lactide) with Mn ) 26,000 g/mol and a constantbulk ionization of codeine of 40%.

Figure 8. Schematic of the kinetic model of charge transfer, theexpressions involving Ni given here relate to t ) 0.

-dnPLA+

dt)

dncod+

dt) k

VnPLA+ncod0 (2)

∆N ) RPLA+YPLA+(1 - Xcod)(1 - exp(-PXcod)) (3)

Organic Depth Profiling of a Binary System J. Phys. Chem. B, Vol. 113, No. 34, 2009 11579

We may now write a complete expression for the number ofdetectable positive secondary ions from poly(lactide), NPLA+;this is given in eq 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) ionspecies interacting with all codeine neutral species if someaverage value of P and RPLA+ could be found to describe thesum of the interactions. To test this against experimental data,it is necessary to find a means of removing experimental factorsthat globally affect the detection of ions. We do this bynormalizing the steady-state ion intensities, IPLA+(ss), to theinitial intensity, IPLA+(ref), of a characteristic poly(lactide) ionwithin each data set. Because the surface of the blends is highlyenriched in poly(lactide), IPLA+(ref) serves as a referenceintensity for pure, unsputtered poly(lactide). The completeexpression is given in eq 5.

In Figure 9, the experimental data for the characteristicpoly(lactide) ion at 55 u from films of different compositionare 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 linesshow the expected behavior if there is no charge transfer (i.e.,RPLA+ ) 0) and the limiting behavior when all possible chargetransfer has occurred (i.e., exp(-PXcod) ) 0). The data aredescribed nicely within the range of compositions investigated.Similar results (with a different yield ratio) can be found forany of the characteristic poly(lactide) ions, this is obvious fromthe fact that these characteristic ion intensities are almostproportional to each other within the quasi steady state.

To explain the behavior of characteristic codeine ions, weneed to consider that some are produced directly from thecodeine fraction, given by Ycod+Xcod, and some are produced asa result of the charge transfer from, or as a result of successful

competition with, poly(lactide) secondary ions; see Figure 8.To maintain the stoichiometry of the chemical reactions, thetotal number of codeine secondary ions produced from chargetransfer must equal the total number of poly(lactide) secondaryions lost in the process. However, the distribution of theexchanged charge between the various codeine secondaryneutrals is unknown and we introduce a factor, fcod+, whichdescribes the proportion of the total number of secondary ionscreated during charge transfer that contribute to the intensityof a particular secondary ion. Thus, the number of secondaryions of a particular type, cod+, which are detectable, is givenby 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, intensesecondary ion of codeine. By normalizing to a referenceintensity, we choose the initial intensity of a poly(lactide)secondary ion as before, we may write eq 6.

All the parameters except Ycod+(ss)/YPLA+(ref) and fcod+ havebeen determined previously, and these are used to fit the datafor the 44 u and 300 u secondary ions, as shown in Figure 10.The curves describe the data excellently and demonstrate theintimate link between the intensities of the two components,which is captured by the kinetic model. The ratios of steady-state intensities between codeine and poly(lactide) ions areplotted in Figure 6, and show the expected near-linearity. Thisis no surprise as we have excellent fits to the normalized absoluteintensities, as shown in Figures 9 and 10, and therefore thisnear-linearity is in no way a validation of the model, it merelyshows that such behavior can arise from the model.

We note here that exactly the same arguments can be appliedto the negative secondary ions, where we also observe a linearrelationship between the ratio of the 26 u (CN-) steady-stateintensity to poly(lactide) secondary ion intensities and thecodeine composition. In the compositional range we areexamining here, the charge transfer from codeine negative

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 withno charge transfer and the other construction line (+ + +) shows thelimiting behavior with maximum possible charge transfer.

NPLA+(t > tR) ) YPLA+(1 - Xcod)(1 - RPLA+(1 - exp(-PXcod))) (4)

IPLA+(ss)

IPLA+(ref))

YPLA+(ss)

YPLA+(ref)(1 - Xcod)(1 - RPLA+(1 - exp(-PXcod))) (5)

Figure 10. Normalized steady-state intensities of codeine secondaryions as a function of codeine mass fraction (Xcod). Error bars areestimated from counting statistics and represent 99% confidenceintervals. 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.

Icod+(ss)

IPLA+(ref))

Ycod+(ss)

YPLA+(ref)Xcod +

fcod+RPLA+

YPLA+(ss)

YPLA+(ref)(1 - Xcod)(1 - exp(-PXcod)) (6)

11580 J. Phys. Chem. B, Vol. 113, No. 34, 2009 Shard et al.

secondary ions to poly(lactide) secondary neutrals is essentiallycomplete (i.e., not kinetically limited, this arises because of thelarge number of poly(lactide) secondary neutrals) and theresulting linear relationships are not convincing demonstrationsof the model. It is worth pointing out that the composition-independent profiles shown in Figure 4 cannot be explainedwithout some sort of matrix effect whereby the yield of negativesecondary ions from poly(lactide) is increased as the fractionof codeine increases.

The kinetic model of charge transfer model seems to capturemany of the important features of the matrix effect observed inthis system. It is also consistent with previous suggestions forion formation mechanisms in SIMS34 and provides a mathemati-cal framework for such ideas that may be applied to othersystems.

Implications of the Charge Transfer Model. There is atleast one interesting implication of the model. We may considerthat charge transfer should not be restricted to secondary speciesfrom different components, but should also occur betweendifferent secondary species from a single component. This wouldexplain why delicate quasi-molecular ions can be observedintact, sometimes with high yields, when the thermal energiesrequired for ionization should also cause major fragmentation.The scheme suggests that only highly fragmented secondaryions are initially produced, including H+, some of theseexchange charge with, or attach to, less fragmented secondaryneutrals to produce “characteristic” secondary ions, the intensi-ties of which are a reflection of the number of conjugate neutralspecies produced and their relative stability as ions. In the blendfilms we have studied here, the distribution in relative intensitiesof secondary ions from a single component is not a function ofcomposition, which could be expected if the internal distributionof secondary neutrals from each component is unchanged withcomposition. However, we may expect from the kinetic modelthat there is a direct implication for secondary ion intensities ifthe total yield changes.

For a pure material, we can adapt eq 2 to provide a descriptionof all possible ion-neutral pairwise interactions that would leadto an enhancement or diminution in a given secondary ionintensity. This is shown in eq 7, which would need to be solvedfor all secondary ion and neutral species simultaneously.

In eq 7, the first term represents the production of this typeof ion from charge transfer reactions between the conjugateneutral and other charged species and the final term representsthe loss of this type of ion during charge transfer reactions. Therate constants kij+ are related to kji+ by the equilibrium constantfor the appropriate reversible reaction, which indicates howthermodynamic quantities, for example, gas-phase basicities,may influence the relative proportions of secondary ions.

For a large molecular species, we may consider that theprompt yield of quasi-molecular secondary ions is zero(NM+(t)0) ) nM+(t)0) ) 0) and therefore only the first termsurvives for the initial rate of change. We can then write eq 8in which Y′ represents the prompt yield of species; previouslywe used Y, which represents the yield from a pure componentafter internal charge exchange between secondary ions andneutrals from that component has been accounted for but beforecharge exchange between, or in competition with, secondaryspecies from different components had been considered.

If the molecule is sufficiently large, the prompt yield ofsecondary molecular neutrals will also be small such that theinitial rate is valid for all tR. If the combined parameter shownin square brackets is a weak function of total sputtering yield(S) and the prompt yields of all relevant secondary species areproportional 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 forthe high molecular weight quasi-molecular secondary ionintensity upon the total secondary ion intensity has beendescribed previously and the limiting case given in eq 8 hasalso been considered as one possible cause of this observation.37,38

Therefore, it is possible that the kinetic model of charge transferfor SIMS has a wider applicability than in the analysis of binarymixtures.

Conclusions

We have demonstrated that C60+ ion sputtering with SIMS

analysis of binary organic thin films may be used to determinethe concentrations of the components, providing a suitablecalibration method exists. Within this poly(lactide) and codeinesystem, at least, secondary ion yields are shown to be a strongfunction of composition. This matrix effect is consistent with atransfer of charge from poly(lactide)-derived secondary ions tocodeine-derived secondary neutrals. There is a direct andunderstandable relationship between the reduction in poly(lac-tide)-derived secondary ion yield and the enhancement incodeine-derived secondary ion yield. We have demonstrated thatsuch changes are related to the composition of the sample, ratherthan the result of proton transfer between components in thesputtered surface induced by prolonged cluster ion beamsputtering. Therefore, the charge exchange is likely to occurbetween sputtered species during events immediately followingprimary ion impact.

We have developed a pseudo-first-order kinetic model todescribe the charge transfer behavior and found that the transferof charge within a kinetic limit can account for the changes inion intensity. Further analysis of the kinetic model predicts asquare law dependence between high molecular weight second-ary ion intensities and total secondary ion intensities, whichmatches experimental observations, and suggests that the transferof charge during the emission process may be a generalphenomenon.

Acknowledgment. This work was supported by the NationalMeasurement System of the UK Department of Innovation,Universities and Skills through the Chemical and BiologicalMetrology Programme. We thank Sian Westall (University ofNottingham) for preparing some of the samples used in thisinvestigation and Felicia Green (NPL) for helpful comments.

Appendix

Derivation of eq 3:The integrated form of eq 2 in the pseudo-first-order ap-

proximation is

which provides

dni+

dt) ∑

j

kji+

Vnj+ni0 - ∑

j

kij+

Vni+nj0 (7)

dnM+

dt(t ) 0) ) ∑

j

kjM+

Vnj+nM0 ) ∑

j[kjM+Rj+RM0

V ]Y'j+Y'M0 (8)

∫nPLA+(t)0)

nPLA+(t)tR) dnPLA+

nPLA+) ∫

0

tR -kncod0(t ) 0)dt

V

Organic Depth Profiling of a Binary System J. Phys. Chem. B, Vol. 113, No. 34, 2009 11581

Substituting ni(t)0) ) RiYiXa and P ) (ktRRcod0Ycod0/V)

This may be simply rearranged to give eq 3, with the assumptionthat 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.

(14) Mahoney, C. M.; Roberson, S. V.; Gillen, G. Anal. Chem. 2004,76, 3199–3207.

(15) Gillen, G.; Fahey, A.; Wagner, M.; Mahoney, C. Appl. Surf. Sci.2006, 252, 6537–6541.

(16) Mahoney, C. M.; Yu, J. X.; Fahey, A.; Gardella, J. A. Appl. Surf.Sci. 2006, 252, 6609–6614.

(17) Shard, A. G.; Green, F. M.; Brewer, P. J.; Seah, M. P.; Gilmore,I. S. J. Phys. Chem. B 2008, 112, 2596–2605.

(18) Wagner, M. S. Anal. Chem. 2005, 77, 911–922.(19) Cheng, J.; Winograd, N. Appl. Surf. Sci. 2006, 252, 6498–6501.(20) Hinder, S. J.; Lowe, C.; Watts, J. F. Surf. Interface Anal. 2007,

39, 467–475.(21) Fletcher, J. S.; Lockyer, N. P.; Vaidyanathan, S.; Vickerman, J. C.

Anal. Chem. 2007, 79, 2199–2206.(22) Kozole, J.; Szakal, C.; Kurczy, M.; Winograd, N. Appl. Surf. Sci.

2006, 252, 6789–6792.(23) Hsu, H. C.; Chen, L. C.; Ho, K. C. Anal. Chim. Acta 2004, 504,

141–147.(24) Rafati, A.; Davies, M. C.; Shard, A. G.; Hutton, S.; Mishra, G.;

Alexander, M. R. J. Controlled Release In press.(25) ISO 18115: Surface Chemical Analysis, Vocabulary.(26) Seah, M. P. Surf. Interface Anal. 1999, 27, 693–694.(27) Green, F. M.; Shard, A. G.; Gilmore, I. S.; Seah, M. P. Anal. Chem.

2009, 81, 75–79.(28) Lee, J. L. S.; Gilmore, I. S.; Seah, M. P. Surf. Interface Anal. 2008,

40, 1–14.(29) Shard, A. G.; Volland, C.; Davies, M. C.; Kissel, T. Macromolecules

1996, 29, 748–754.(30) Ogaki, R.; Green, F. M.; Gilmore, I. S.; Shard, A. G.; Luk, S.;

Alexander, M. R.; Davies, M. C. Surf. Interface Anal. 2007, 39, 852–859.(31) Shard, A. G.; Gilmore, I. S. Int. J. Mass Spectrom. 2008, 269, 85–

94.(32) Gilmore, I. S.; Seah, M. P. Surf. Interface Anal. 1996, 24, 746–

762.(33) Jones, E. A.; Lockyer, N. P.; Kordys, J.; Vickerman, J. C. J. Am.

Soc. Mass Spectrom. 2007, 18, 1559–1567.(34) Cooks, R. G.; Busch, K. L. Int. J. Mass Spectrom. Ion Phys. 1983,

53, 111–124.(35) Garrison, B. J.; Postawa, Z.; Ryan, K. E.; Vickerman, J. C.; Webb,

R. P.; Winograd, N. Anal. Chem. 2009, 81, 2260–2267.(36) Conlan, X. A.; Lockyer, N. P.; Vickerman, J. C. Rapid Commun.

Mass Spectrom. 2006, 20, 1327–1334.(37) Seah, M. P. Surf. Interface Anal. 2007, 39, 890–897.(38) Seah, M. P. Surf. Interface Anal. 2007, 39, 634–643.

JP904911N

ln(nPLA+(t ) tR)

nPLA+(t ) 0) ) ) ln(nPLA+(t ) 0) - ∆N

nPLA+(t ) 0) ))

-kncod0(t ) 0)tR

V

RPLA+YPLA+XPLA - ∆N

RPLA+YPLA+XPLA) exp(-PXcod)

11582 J. Phys. Chem. B, Vol. 113, No. 34, 2009 Shard et al.