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Peak Fitting and Background Types with Example (HDPE, PEEK, Nylon)
Asymmetry
in Polymer Peaks
Curve Fitting and Polymers
The availability of data from well-characterized samples such as those offered by Beamson and Briggs [1] owe much to the popularity of XPS as a tool for understanding the chemistry of polymers. A typical C 1s envelope [2] (Figure 1) includes structure that offers chemical information about a sample, but without some initial starting point it is difficult to construct an appropriate model for the data envelope.
Figure 1: C 1s high-resolution
spectrum taken from a polymer-based sample using a VG ESCALAB 220i at
The high-resolution spectrum in Figure 1 derives from poly (acrylic acid) PAA reacted with inorganic material (or partially reacted) in an acid-base reaction. If Gaussian/Lorentzian (GL) line-shapes are added in an arbitrary way, the curve fit yields little information about the sample other than to say that it deviates from the published data for PAA and therefore demonstrates the presence of additional chemistry at the surface. Figure 2 shows a synthetic model for this data envelope where three GL peaks have been added, then fitted using a Marquardt-Levenberg [3] optimization algorithm. No constraints have been applied and the result is a reasonable fit to the experimental data but the fitting parameters are not readily open to chemical interpretation. For example, the FWHM are much bigger than would typically be expected from C 1s profiles the given instrumental resolution. The three-peak model suggests further de-convolution is required before the sample can be fully understood.
Figure 2: An initial fit to the C 1s spectra shown in Figure 1.
If it is assumed that the FWHM for a C 1s photoelectron peak is 1.1 eV (only a guess), then applying peaks with said constraint results in a peak fit shown in Figure 3. Two additional peaks appear in the model and further more three of the peaks look like they may have something to do with pure PAA. The PAA stoichiometry is still doubtful but the essential positions for a pure PAA envelope have more or less appeared. Further input is required to make sense of the new synthetic model.
To constraint a parameter so that it does not adjust during an optimization step, set the constraint interval to have the same value as the fixed value. E.g., if it is required to set the FWHM value to 1.1, the constraint interval should be entered with the value “1.1,1.1”. Actually, it is sufficient to set the parameter value outside the constraint range currently defined for the parameter.
Spectra from Beamson and Briggs (“The XPS of Polymers Database”) offer the opportunity to examine more complex polymer data in the context of known synthetic models. Figure 4 is an example of such data where a set of three line-shapes has been used to model the clean PAA C 1s data envelope. The important feature is that the stoichiometry and chemical shifts for the C 1s lines can be incorporated into the model and this information is then transferable to other polymer spectra. The peaks in Figure 4 are linked in area, but only the position of peak “C 1s b” and “C 1s a” are constrained by an offset.
Figure 3: Same C 1s envelope as Figure 2 but the synthetic peaks are all constrained to have FWHM equal to 1.1 eV.
To link a component parameter the constraints must be adjusted as follows. Each synthetic component defined on the Quantification Parameter dialog, Components Property Page, appears as a column of parameters in the scrolled list shown in Figure 3. These columns are headed “A”, “B”, “C” and so on. To constrain the area of the component in column B to be half of the area of the component in column A, the area constraint in column B should be set to “A * 0.5”. Similarly, to offset a component in column C by 0.2 from the component in column B, enter “B+0.2” in the position constraint field in column C.
Figure 4: C 1s envelope from clean PAA
acquired on a Scienta-300, RUSTI, Daresbury Laboratory
The peak shapes from a Scienta ESCA-300 may differ from a VG ESCALAB 220i (the source of the real data in Figure 1) or any other manufacturers instrument, but the essential structure should be suitable as a basis for the new model. Copying the pure PAA model into the data in Figure 3 leaves a residual that requires an adjustment for the two non-PAA peaks together with the introduction of a third peak. The new peak in Figure 5 is constrained to be the same width and position as the saturated PAA C 1s peak located at 285 eV (BE). The area of this new peak is allowed to adjust at will and accounts for carbon with the same characteristics as the PAA peak at that position. The consequence of introducing the new peak is that the PAA synthetic model can adjust without breaking the stoichiometric relationships for pure PAA, while differences in the intensity of the saturated peak from the PAA structure are allowed for by this additional constrained component (Figure 5).
Figure 5: Final form for the synthetic model. The Glass Ionomer Cement (GIC) [2] C 1s envelope containing three peaks from PAA plus three additional peaks not seen in a clean PAA spectrum.
Synthetic models such as the one in Figure 5 can be tested
using
At first glance the behavior of the GIC 2 peak at 286.54 eV is unexpected since one might think that two peaks next to one another should produce anti-correlated area distributions. The constraints have altered the concept of “next to” since the PAA sub-model spreads across the entire envelope and it becomes difficult to judge by eye what the influence of noise might be on the final result. This type of insight can only help to understand what constraints do to a fitting procedure as well as provide a rule-of-thumb estimate for error bars (multi-dimensional error distributions can seldom be described by a single number.)
Figure 6: Monte Carlo simulation results for normalized peak areas. The three peaks associated with GIC are plotted against the saturated C 1s peak area from the pure PAA model.
The exact meaning for the model in Figure 5 is left to the experimentalist and may need changing in view of other input, however such a model is only possible when peak fitting routines offer mechanisms for fixing parameters with respect to one another. The role played by the pure PAA synthetic model is that of a foundation shape from which differences in the unknown polymer can be assessed. These additional peaks may still require further interpretation, but with the aid of chemical knowledge and supporting evidence a meaningful model can emerge from seemingly intractable data.
[1] Beamson G. and Briggs D., “The XPS of Polymers Database” Surface Spectra Ltd (2000)
[2] Jones F.H., Hadley P.C., Hutton B.M., Eccles A.J.,
Steele T.A., Billington R.W.
and Pearson G.J., “Fluoride uptake by glass ionomer cements: a surface analysis
approach” ,. Submitted to Biomaterials.
[3] Press W.H. et al, “Numerical Recipes in C”, Cambridge University Press (1988)
[4] Cumpson P. J. and Seah M. P., “Random Uncertainties in AES and XPS”, Surface and Interface Analysis, 18 361 (1992)