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Oct 15, 1997 - Quantitative analysis of technical polymer mixtures by matrix assisted laser desorption/ionization time of flight mass spectrometry. We...
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Anal. Chem. 1997, 69, 4176-4183

Mass Discrimination in the Analysis of Polydisperse Polymers by MALDI Time-of-Flight Mass Spectrometry. 2. Instrumental Issues David C. Schriemer and Liang Li*

Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2

Mass discrimination is generally observed in the analysis of polydisperse polymers by matrix-assisted laser desorption/ionization (MALDI) time-of-flight (TOF) mass spectrometry. Using multicomponent blends of polystyrene of narrow polydispersity, instrumental effects on the mass analysis of polydisperse polymers were investigated in a time-lag focusing linear TOF mass spectrometer. It is shown that the lensing action provided by the source electrodes in TOF gives rise to a mass-dependent distribution of ions in the plane of the microchannel plate detector. Therefore, the size of the detector aperture must be sufficient to ensure acceptance of the full ion packet. This distribution is also affected by the choice of pushout pulse delay. For the mass range investigated, ion detection with the use of a multichannel plate detector results from a combination of primary ion to electron conversion, as well as secondary ion to electron conversion. Both processes are shown to give rise to different influences on the measured Mn values of the polystyrene blends. Detector saturation also adds to the observed mass discrimination, due mainly to the saturation caused by matrix species. The issue regarding preservation of the measured polymer distribution function in data presentation is also discussed. In addition to the sample-related concerns addressed in the preceding paper,1 there are a number of instrument-related contributions to mass discrimination in the matrix-assisted laser desorption/ionization (MALDI) analysis of polydisperse polymers. A standard linear time-of-flight (TOF) instrument is defined by how it provides ion focusing (axial and temporal), ion detection, and data recording and manipulation. A complete survey of mass discrimination in the analysis of polydisperse polymers should include an investigation of each of these parameters. Most of the literature discussing the instrumental effects on average molecular weight determination have focused on the detector issue and on the primary detection event, namely, ion-to-electron conversion in microchannel plates (MCP) or electron multipliers. Such discussions have only considered polymers of narrow polydispersity. For example, Larsen et al.2 have demonstrated a uniform instrumental response for two PMMA oligomers of 25 and 50 repeat units for high acceleration voltages. At low acceleration voltages, a discrimination against the larger oligomer was found. (1) Schriemer, D. C.; Li, L. Anal. Chem. 1997, 69, 4169-4175 (preceding paper in this issue). (2) Larsen, B. S.; Simonsick, J., W. J.; McEwen, C. N. J. Am. Soc. Mass Spectrom. 1996, 7, 287-292.

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Similar discriminatory behavior had been observed by Tang et al. for PMMA samples of narrow polydispersity, over a similar mass range.3 A recent study by McEwen et al. has suggested that detector saturation as well can introduce mass discrimination in the analysis of polydisperse polymers.4 However, while it has been acknowledged that the above-mentioned instrumental parameters could all contribute to mass discrimination,5 there has been no detailed study as to their individual contributions. The present study is concerned with the investigation of ion focusing (axial and temporal), ion detection in an MCP system (primary and secondary ion conversion events), detector saturation, and data processing considerations. A linear TOF system designed around the time-lag focusing principal was used for this work. This type of instrument provides the greatest benefits for the MALDI analysis of polymers, in terms of both resolution and accuracy of average molecular weight information, and it is likely that an increasing number of polymer applications will involve such instrumentation. As in the companion paper, this study is based upon polystyrene analysis using one sample preparation technique (all-trans-retinoic acid as matrix, with silver cationization).6 EXPERIMENTAL SECTION A description of the instrumental configuration can be found in the companion paper to this study1 and in a previous publication.7 Briefly, the mass spectrometer consists of a nitrogen laser (Model VSL 337ND, Laser Sciences, Inc., Newton MA), a 1-m flight tube, a four-plate source region designed for time-lag focusing and operation up to 30 kV, and a dual MCP detector. Further details on instrument design and operation are cited where appropriate. Spectra were collected and calibrated in the same fashion as in the foregoing work, with Mn values determined from five separate measurements. The same polystyrene samples and preparative procedures as discussed in the companion paper were used. RESULTS AND DISCUSSION The differences among the available linear time-of-flight instruments are essentially defined according to their approaches to ion source/extraction geometry and detector design. To provide an accurate assessment of all available platforms for MALDI analysis of polydisperse polymers is difficult; however, key features (3) Tang, X.; Dreifuss, P. A.; Vertes, A. Rapid Commun. Mass Spectrom. 1995, 9, 1141-1147. (4) McEwen, C. N.; Jackson, C.; Larsen, B. S. Int. J. Mass Spectrom. Ion Processes 1997, 160, 387-394. (5) Jackson, C.; Larsen, B.; McEwen, C. Anal. Chem. 1996, 68, 1303-1308. (6) Schriemer, D. C.; Li, L. Anal. Chem. 1996, 68, 2721-2725. (7) Whittal, R. M.; Li, L. Anal. Chem. 1995, 67, 1950-1954. S0003-2700(97)00779-8 CCC: $14.00

© 1997 American Chemical Society

in the ion source and detector can be addressed for their effect on polymer mass spectra. As many linear TOF instruments use MCP-based detectors, and are now developed around the timelag focusing principle, this system was chosen for investigation. Ion Focusing. The MALDI process results in the generation of gas phase ions containing appreciable axial and radial velocity components.8,9 The velocity of the ions produced in this event are broadly distributed but are largely independent of mass (except perhaps below ∼5000 u10,11). The ion optics design used in the TOF system must provide focusing of this ion packet on a detector surface oriented perpendicular to the axis of the spectrometer. In a source defined by simple parallel plate elements, if one assumes a uniform electric field with no field penetration between regions in the source (a planar equipotential field), the source does not provide axial lensing of the ions produced. This would have the effect of producing a distribution of ions in a plane parallel to the detector surface that bears a mass distribution: the higher mass ions would display a greater radius of impact on the detector surface than the lower mass ions, for the case where the ions have the same initial velocity and velocity distribution. The extent to which this is true, and the effective aperture of the detector, will determine the effect this mass-dependent radial dispersion has on the collected mass spectrum. There are complicating factors, however. Coulombic repulsion could impart relatively higher velocities and wider velocity distributions to ions of lower masses and thereby change the radial distribution of masses at the detector. Collisional scattering could also affect the lower masses more. Furthermore, most ion sources impart a certain amount of lensing action, either intentionally built in (focusing repellers, Einzel lenses, xy deflectors, wire ion guides, etc.) or due to field penetration between source elements. Lensing action can alter the mass discrimination in the radial distribution of ions at the detector surface. Theoretically, the trajectories of equal-energy ions bearing different mass-to-charge ratios are the same in electrostatic fields, giving rise to a common focal point.12 The ion source and the potentials applied to the source elements should be tailored to establishing this focal point near the detector surface. In a time-lag focusing MALDI instrument, this focal point can change since the voltage applied to the source is a variable for achieving good resolution. Therefore, the “quality” of the lens with respect to axial ion focusing is variable, and a poor focus will translate into a wide distribution of ions in the plane of the detector. The extent to which the ion optics are defocused will also determine the severity of the mass discrimination in this distribution. The mass discrimination imparted to ion detection from these focusing considerations needs to be investigated when ion detection across a wide mass range is considered, such as in the MALDI analysis of polydisperse polymers. To illuminate some of the above points, an experiment designed to determine mass discrimination in the radial distribution of ions at the detector was undertaken. This experiment was conducted with a source (8) Beavis, R. C.; Chait, B. T. Chem. Phys. Lett. 1991, 181, 479-484. (9) Zhang, W.; Chait, B. T. In Proceedings of the 44th ASMS Conference on Mass Spectrometry and Allied Topics; May 12-16, Portland, OR, 1996; p 268. (10) Juhasz, P.; Vestal, M. L.; Martin, S. A. In Proceedings of the 44th ASMS Conference on Mass Spectrometry and Allied Topics; May 12-16, Portland, OR, 1996; p 730. (11) Russon, L. M.; Whittal, R. M.; Li, L. In Proceedings of the 44th ASMS Conference on Mass Spectrometry and Allied Topics; Portland, OR, May 1216, 1996; p 731. (12) Szilagyi, M. Electron and Ion Optics; Plenum Press: New York, 1988.

Figure 1. (A) Investigation of the ion focusing properties of the MALDI TOF instrument used in this work. The sample consisted of polystyrene 5050 and 28 500, 100 pmol of each loaded to the probe. Expected Mn of 16 980. The ion source was operated with 20 kV dc applied, and a 3.6 kV push-out pulse with a 0.3 µs delay, for all detector apertures. (B) As in (A), with an additional trace corresponding to a 1.0-µs delay. Error bars in (B) represent the removal of sample-to-sample error.

characterized by a focusing repeller and a measure of field penetration between source elements. In this experiment, a twocomponent blend was prepared consisting of polystyrene 5050 and 28 500 (expected Mn value of 16 980). MALDI spectra of this blend were collected, in which the detector’s ion acceptance window was varied in 0.5-cm intervals from a diameter of 1.0-4.0 cm. The Mn value of the blend was measured at each aperture. Figure 1 displays the results of this experiment, determined as a function of push-out pulse delay. Each point represents the average of five Mn values determined from separate sample preparations. The error bars in Figure 1A and B represent one standard deviation. In Figure 1B, however, the contribution of sample-to-sample error has been removed. This is valid since, for any given aperture, Mn values for both pulse delays were determined from the same sample preparation. Expressed in this fashion, the error bars of Figure 1B are only meaningful for the comparison between push-out pulse delays. In Figure 1A, it is found that there is mass discrimination with an aperture of ∼1.5 cm and below, for this source geometry and applied voltage. At apertures greater than 1.5 cm, there is little statistical variation in the measured Mn value for the blend. These data are consistent with the idea that each mass transmitted by the source bears a radial distribution at the detector and that the width of this distribution decreases with increasing mass. Below 1.5 cm, some of the low-mass ions are prevented from reaching the detector, giving rise to higher measured Mn values. Consequently, under the cited experimental conditions, this source Analytical Chemistry, Vol. 69, No. 20, October 15, 1997

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geometry is suitable for the analysis of polymers with a broad polydispersity, as long as the low-mass end is >3000 u, and as long as the detector aperture is greater than 1.5 cm. As demonstrated by Figure 1B, the mass discrimination in the spread of the ion packet at the detector is also affected by the push-out pulse delay. An increase in the pulse delay has the effect of allowing an increase in the axial and radial spread of ions in the source prior to extraction. Upon extraction, the increased spatial distribution in the source translates into a further defocusing of the low-mass component. This leads to an increase in the measured Mn value for the blend, as observed. Inspection of the data for the two pulse delays at a given aperture indicates the extent to which lengthening the pulse delay affects the relative defocusing of the lower mass component. The greatest difference is to be found at the 1.5-cm aperture, where this diameter begins to restrict a relatively greater amount of the low-mass ions from reaching the detector, in the long pulse delay mode. Such observations are consistent with the further widening of the radial distribution for the low-mass ions relative to the high-mass ions. One would expect the effects of defocusing to diminish with increasing aperture. This is true; however, a region of constant difference is reached at apertures greater than 2 cm. This could indicate a mass-dependent transmission loss in the source region, where a fraction of the low-mass ions are lost due to collisions with source elements. Increasing the pulse delay would increase the loss of the low-mass ions. This effect would be constant with changing aperture and manifest itself as an offset in the graph of Mn vs detector aperture. Figure 1B seems to reflect the contribution of both defocusing and transmission loss. The operator has control over the severity of the abovedescribed mass discrimination by rationally adjusting the lensing properties of the source and selecting the appropriate push-out pulse delay. In a time-lag focusing instrument, lensing properties can be altered simply by adjusting the amplitude of the push-out pulse. The required lensing properties should be determined by the mass range to be investigated. Through the analysis of blends such as described above, and the altering of the push-out pulse amplitude and delay, focusing conditions can be established to conform to reasonable detector apertures. The one drawback to this approach relates to the dependence of mass resolution on the amplitude and delay of the push-out pulse. Conceivably the optimum pulse conditions for axial focusing could place constraints upon the optimization of mass resolution. For our instrument, this study suggests that a detector with a minimum 2-cm diameter of active detection area is needed, coupled with pulse delays less than 1 µs, to fully intercept all the ions in a broad mass range. Ion Detection. Reports that MALDI fails in the direct analysis of polydisperse polymers often identify the ion detection system as one of the main areas where mass-dependent signal detection occurs. For MCP, electron multiplier, or hybrid detection systems, this is attributed to an erosion in the efficiency of ionto-electron conversion as the mass of the incident ion increases due to a decrease in impact velocity. Based on this argument, conversion efficiency for an ion of a given mass can improve with an increase in its velocity, but such an approach will not serve to remove the mass discrimination. Many designs contain a postacceleration region, where the primary ion receives an “extra” velocity component for the purpose of improving ion-to-electron conversion efficiency of the primary ions. A grounded, high optically transmissive grid (∼90%) is often used to isolate the 4178 Analytical Chemistry, Vol. 69, No. 20, October 15, 1997

Figure 2. Effect of altering the optical transmissivity of the grounded grid fronting the first MCP at a distance of 1.85 mm, on the measured Mn value. Postacceleration of -2 kV was used in all cases. Three equimolar blends were prepared: polystyrene 5050/20 000, 5050/ 28 500 and 5050/50 000. In each case, 100 pmol of each component was loaded to the probe.

postacceleration region from the field-free drift region of the spectrometer. Recent developments in detector design indicate that the conversion of primary ions to electrons at the detector conversion surface is not the only means of signal generation. The phenomenon of secondary ion formation at surfaces has been noted13,14 and has also been incorporated into detector design for improved high-mass sensitivity.15-17 Thus aside from the consideration of mass discrimination in ion-to-electron conversion, ion transmission through the grid and secondary ion generation at the grid surface may also give rise to mass discrimination. An experiment was conducted where a number of polystyrene blends were analyzed, using a detector configuration in which grids of different transmissivity were used to define the postacceleration region. The results are displayed in Figure 2 (see inset for detector configuration). The Mn values of three twocomponent blends were measured with detector configurations incorporating a nickel grid, with either 50 or 90% optical transmissivities. As Figure 2 shows, the grid with the lower transmissivity resulted in consistently higher Mn values than the higher transmissivity grid. Based on considerations of collisional probability, this is the opposite of what is expected.18 Decreasing the optical transmissivity should have the effect of restricting passage of the high-mass ions more than the low-mass ions, resulting in a lowering of the measured Mn values. Therefore, an additional mechanism for ion detection must be operative. This can be identified as arising from secondary ions generated at the grid (13) Sullivan, P. A.; Axelsson, J.; Sundqvist, B. U. R. Rapid Commun. Mass Spectrom. 1995, 9, 377-382. (14) Westmacott, G.; Ens, W.; Standing, K. G. Nucl. Instrum. Methods Phys. Res. B 1996, 108, 282-289. (15) Weinberger, S. R.; Egan, R. W.; Hoppe, T. W.; Gassmann, E.; Schar, M. M.; Bornsen, K. O.; Tarantino, E. R. U.S. Patent 5,382,793, 1995. (16) Weinberger, S. R.; Donlon, E.; Kaplun, Y.; Kornfeld, R.; Li, L.; Whittal, R.; Russon, L. In Proceedings of the 44th ASMS Conference on Mass Spectrometry and Allied Topics; May 12-16, Portland, OR, 1996; p 269. (17) Weinberger, S. R.; Egan, R. W.; Hoppe, T. W.; Gassmann, E.; Schar, M. M.; Bornsen, K. O.; Tarantino, E. R. U.S. Patent 5,594,243, 1997. (18) Laidler, K. J.; Meiser, J. H. Physical Chemistry; The Benjamin/Cummings Publishing Co.: Don Mills, ON, Canada, 1982.

Figure 3. Effect of changing the applied postacceleration voltage from -2.0 to -4.75 kV across a fixed distance of 1.85 mm. Sample compositions and loadings as in Figure 2.

surface, in keeping with previous studies that have noticed the contribution of secondary ions in primary ion detection.2,14 These ions likely arise from the sputtering of nickel ions from the grid.19 Once formed, a certain fraction of these ions enter the postacceleration region and accelerate to the conversion surface of the detector, contributing to the ion current for the corresponding primary ions. The data presented in Figure 2 also show that the 50% transmissive grid produces a greater slope than the 90% transmissive grid. This is an indication that the high-mass components of the blends are more efficient in the ion-secondary ion conversion event than the low-mass components. For polymer analysis by MALDI, this implies that detectors with postacceleration regions can impart mass discrimination by virtue of the ground grid alone: primary ion transmission will decrease with mass, while the contribution of secondary ion generation to the measured signal will increase with mass. A polymer spanning a mass range greater than that described by the 5050/20 000 polystyrene blend would appear to be sensitive to the above-described phenomenon. Further complications arise when the potential drop across the postacceleration region is considered. Figure 3 represents measurements of Mn values for three two-component blends similar to the ones described in Figure 2, using a 90% optically transmissive Ni grid. Varying only the voltage drop across the postacceleration region results in substantial variation in the measured Mn values; that is, adjusting the applied voltage from -2 to -4.75 kV leads to an increase in the Mn of all three blends. In such an experiment, three variables are changing: the impact velocity of the primary ions on the ionto-electron conversion surface of the MCP, the velocity of the secondary ions generated at the grid after acceleration to the detector surface, and the field strength in the postacceleration region. From this experiment alone it is not possible to ascertain the relative importance of these three variables. A number of experiments were undertaken to determine the relative contribution of these variables to the measured Mn value. A single two-component blend was prepared, consisting of polystyrene 5050/28500 (expected Mn of 16 620). The Mn value (19) Whittal, R. M.; Russon, L. M.; Weinberger, S. R.; Li, L. Unpublished results, University of Alberta, 1995.

Figure 4. Determination of the effect of altering detector configuration on the measured Mn value over a range of total acceleration potentials, for a two-component blend consisting of polystyrene 5050 and 28 500 (100 pmol of each loaded to the probe, expected Mn of 16 620): (A) investigating the effect of changing the postacceleration potential from zero (and no grounded grid) to -4.75 kV; (B) maintaining the applied potential in the postacceleration region at -4.75 kV, but altering the length of this region to change the field strength from 1090 to 2570 V/mm.

of this blend was measured under four different detector configurations: (1) no postacceleration region, by removing the grid and operating the detector with a grounded first MCP and a positively biased anode; (2) a postacceleration region defined by -4.75 kV applied across 1.85 mm; (3) a postacceleration region defined by -2 kV applied across 1.85 mm; (4) a postacceleration region defined by -4.75 kV applied across 4.35 mm. The postacceleration field strength is therefore the same as in configuration 3. In each configuration, the voltage drops across the two MCPs were kept constant such that the gain of the detector is the same for each configuration. The detector was also operated at full 4-cm aperture, and a push-out pulse delay of 0.65 µs was used in all cases. The grid used to define the postacceleration region was constructed of stainless steel, with a 90% optical transmissivity. We have determined that this grid generates a response similar to the 90% optically transmissive Ni grid. For each configuration, the Mn value of the blend was measured over a range of source acceleration potentials. The results of these experiments are displayed in Figure 4. To provide a clear picture on the phenomena giving rise to the overall detector response, the postacceleration region was removed (detector configuration 1) and the blend measured over a range of acceleration potentials (Figure 4A, trace I). The only two variables that could change in this experiment were the initial velocity of the primary ions and possibly the ion focusing of the Analytical Chemistry, Vol. 69, No. 20, October 15, 1997

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source. Regarding this latter point, the lensing behavior of the source was maintained at all acceleration potentials by maintaining the voltage ratios on all the source elements.12 The ion packet might increase its radial spread at the detector with a decrease in acceleration potential due to the radial velocity component of the ions from the desorption event. In conjunction with the data shown in Figure 1, in all likelihood this would exacerbate the mass discrimination at the detector. Nevertheless, Figure 1B indicates that there is no noticeable mass discrimination beyond an aperture of 2 cm. At the extremes of source acceleration potential (8.3523.6 kV), the detector aperture (4 cm) is sufficient for accommodating any increased radial dispersion that might arise due to the radial component of the initial velocity. For confirmation, the push-out pulse delay was varied for select acceleration voltages, but no statistically significant changes in the measured Mn value of the blend were found. Therefore, maintaining the focusing characteristics of the source and using a wide aperture detector lead to the conclusion that ion transmission to the detector is constant over the acceleration potentials investigated. Figure 4A, trace I, reveals that the measured Mn value decreases smoothly with increasing acceleration potential. Trace I is simply an indicator of a greater percent increase in signal strength for the low-mass component than the high-mass component, with increasing acceleration potential. In a rigorous treatment of secondary ion generation in an MCP detector, Geno and Macfarlane have indicated the quasi-exponential nature of detection probability as a function of energy, for species with similar chemical compositions.20 A model was proposed and validated that expressed detection probability, P, as a function of the secondary electron coefficient, γ, in the following manner:

P ) 1 - e-γ

(1)

γ ) Am exp(BxU/m)

(2)

where

with m indicating the ion mass and U the ion energy. A and B are constants. The secondary electron coefficient, γ, is indicative of the ion-to-electron conversion efficiency at the MCP surface. Figure 5 expresses the approximate form of the detection probability equation, as a function of ion energy, for the low- and high-mass components of the blend. These equations, with the aid of Figure 5, predict what is observed in trace I of Figure 4A. For a given ion energy in the range investigated, the low-mass component is in a steeply increasing domain of its detection probability curve, whereas the high-mass component is in a very shallow domain. The mass difference is sufficiently great such that an increment in acceleration potential leads to a greater percent increase in the secondary electron generation for the lowmass component, relative to the high-mass component. The effect of this is a decrease in the measured Mn value. At the highest acceleration potentials investigated, the trace begins to flatten. This would indicate that the high-mass component is approaching the steeply rising portion of its detection probability curve. It should be stressed that it is the relation of the detection probability curves for the individual masses that determines the effect of (20) Geno, P. W.; Macfarlane, R. D. Int. J. Mass Spectrom. Ion Processes 1989, 92, 195-210.

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Figure 5. Approximate form of the detection probability equation as a function of ion energy, for both the high- and low-mass components of a 5050/28 500 blend. Only ion-to-electron conversion from the primary ions is considered.

acceleration potential on the measured Mn value. Clearly, in the analysis of polydisperse polymers that include a low-mass component, no single practical acceleration voltage exists such that a uniform detection efficiency for the whole mass range can be expected in an MCP detection system. When a postacceleration region is added to the detection system (configurations 2 and 3), the behavior of the measured Mn value as a function of acceleration potential changes. This is shown in Figure 4A (traces II and III). These traces display a decidedly bilinear nature. The Mn value decreases with increasing acceleration potential but begins to level out (and even increase) at a lower potential than was observed for trace I. Each of these bilinear traces includes the contribution of postacceleration to the total acceleration potential. The postacceleration voltages for traces II and III are -4.75 and -2.0 kV, respectively. When this contribution is subtracted, it can be seen that the onset of bilinearity appears to occur at a common source acceleration potential (∼18 kV). This suggests that an additional mechanism for signal generation is occurring, dependent on the source voltage, and is consistent with the onset of appreciable secondary ion formation at the grid. As was stated previously, such secondary ion formation will occur to a greater extent for the higher masses. With an increase in source acceleration potential, the percent increase in secondary ion formation for the high-mass component is likely greater than for the low-mass component. The extent to which this is true will dictate the magnitude of the change to the graph. Clearly, since the negative slope of the graph changes to slightly positive, the increase in secondary ion formation and detection is sufficiently great to overcome the downward trend in Mn observed in trace I, where this secondary ion formation is absent. Note that the field strength in the postacceleration region is different for detector configurations 2 and 3. To determine the effect of field strength variation on the detection of secondary ions, a fixed potential was applied to the first MCP (-4.75 kV) and the length of the postacceleration region adjusted from 1.85 to 4.35 mm (configurations 2 and 4). This corresponds to field strengths of 2570 and 1090 V/mm, respectively. As grids do not provide perfect field boundaries, a certain amount of field penetration from the postacceleration region into the field-free region will be

expected to occur.12 This field penetration could influence the amount of secondary ions drawn into the postacceleration region. Such a phenomenon would be a function of postacceleration field strength. For this detector setup and range of field strengths, there appears to be no significant difference between the two traces shown in Figure 4B. Since the field strength does not appear to play a significant role in mass discrimination, a direct comparison of traces II and III in Figure 4A provides additional insight into the phenomenon of secondary ion generation. These two traces exhibit similar features, although trace II demonstrates consistently higher Mn values. At a given total acceleration potential, corresponding points in traces II and III exhibit the same contribution to secondary electron formation from the impact of primary ions on the MCP surface. For corresponding points, trace III exhibits a source potential that is 2.75 kV higher than for trace II. Therefore, two variables that do change are the impact velocity of the primary ions on the grid surface and the impact velocity of the secondary ions on the MCP surface. Regarding the former, this might suggest that more secondary ions are being formed under the experimental conditions of trace III. However, a consideration of the slopes of all three traces in Figure 4A would suggest otherwise. Below ∼20 kV, traces II and III demonstrate equivalent slopes, implying that no appreciable change in secondary ion formation occurs in this region. The fact that trace I (no grid) exhibits much the same slope in this region provides confirmation of this point and indicates that primary ion-to-electron conversion at the MCP surface dominates the rate of change. Regarding the latter variable of secondary ion velocity, a fixed amount of secondary ions formed at the grid will be detected more efficiently for the higher postacceleration cases. This is supported by eq 2, arising from the work of Geno and Macfarlane, where the energy term (U) for the secondary ions increases with postacceleration potential, leading to an increase in detection probability.20 Therefore, since it has been established that the higher mass ions generate more secondary ions, the enhanced detection of secondary ions with a higher postacceleration voltage will result in higher Mn values, even though the total acceleration potential is the same. The conclusion to be reached from the above investigations of primary ion conversion is that each process (ion-to-electron and ion-to-secondary ion conversion) can be described by the model of Geno and Macfarlane. Both conversion processes can be rationalized by eqs 1 and 2. A different set of constants will apply for the grid surface than for the MCP surface as they are constructed from different materials,20 and it is the combination of the detection probability curves for the two processes that gives rise to the bilinear features for traces II and III in Figure 4A. The departure of traces II and III in Figure 4A from the trend exhibited by trace I simply indicates that the “threshold” for efficient secondary ion generation at the grid is reached before the “threshold” for efficiency of primary ion conversion at the detector surface (for high-mass ions). One further observation can be made from Figure 4A regarding ion transmission efficiency through the grid. Comparing trace I with trace III, it appears that the enhancement in Mn from secondary ion formation at the grid is insufficient in overcoming the lowering of Mn from a decreased transmission of the highmass primary ions relative to the low-mass ions. This is true up to ∼20 kV, whereupon the increase in secondary ion formation at the grid overcomes the transmission losses. A conclusion to

Figure 6. Spectrum of a three-component blend used to investigate the effects of detector saturation on the measured Mn values. Sample consisted of polystyrene 5050, 11 600, and 35 000 (100 pmol of each loaded to probe). The experimental configuration in Table 1 (1B) was used (see discussion in the text).

be made from an observation such as this is that whenever such grids are inserted in the path of the ions, one can expect a massdependent loss of ion intensity. To remove these detection constraints from the analysis of polydisperse polymers by MALDI, it would seem a different detection approach is required. An ideal detector for this application would be one based on charge detection, rather than secondary electron or ion generation. Such a detector exists, and it has been noted that this detector would not be sensitive to acceleration potential differences in its response to different masses.21 This detector is not sufficiently developed for application to time-lag focusing MALDI analysis of polymers, however, as the detector response time does not appear to allow for highresolution analysis. Detector Saturation. Detectors based on MCP technology are more prone to loss of gain with an increase in signal strength (saturation) than those based on electron multiplier technology. When saturated, the individual channels in an MCP require a finite time for “recovery” before the benefits of their maximum gain can be reestablished.22 A MALDI experiment is particularly sensitive to the effects of saturation, as a typical experiment generates a large number of matrix ions as the first species detected. A three-component blend of polystyrene was analyzed to determine the possible effects of detector saturation on the determination of Mn for polydisperse polymers. Figure 6 shows a spectrum of the blend of polystyrene 5050, 11 600, and 35 000. A number of analyses were done on this blend, with the goal of determining the effect of the matrix and the MCP voltages on the Mn of the blend. The results of this study are summarized in Table 1. In the first experiment (1A and 1B of Table 1), the blend was run under identical conditions with one exception: a deflection pulse applied immediately postsource for removal of matrix ions was used in 1B but not in 1A. Two Mn values were calculated for each set of spectra: one for the first and second components, and the other for the second and third components. The data obtained from each set of spectra indicate that deflecting the matrix leads to lower Mn values than if the matrix is retained. With retention of the matrix, the detector is at least partially (21) Park, M. A.; Callahan, J. H. Rapid Commun. Mass Spectrom. 1994, 8, 317322. (22) Galileo Electro-Optics Corp., Galileo Park, Sturbridge, MA.

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Table 1. Experiments and Their Corresponding Mn Values for Examining the Mass Discrimination Arising from MCP Saturation Mn/sa experiment

PS 5050 and 11600

PS 11600 and 35000

1A (matrix retained) 1B (matrix deflected) 2A (1 kV/1 kV) 2B (0.33 kV/1 kV)

8408/103 7982/94 8381/47 7946/118

18686/371 17900/64 18967/280

a

s, standard deviation.

saturated and begins slow recovery after all the transmitted matrix ions have reached the detector. This recovery is obviously occurring during the time frame of the experiment (∼100 µs), as the lower masses are suppressed more than the higher masses, leading to the observed effect on the Mn values. Appreciable matrix signal is still detected even when the matrix ions are deflected, suggesting the possibility that the full influence of detector saturation by matrix ions might not be removed with deflection. In the first experiment, the detector was operated in the standard configuration, where the voltage drop across the first MCP is two-thirds of that dropped across the second MCP (∼1 kV across second MCP). With the voltage drop across the second MCP fixed at ∼1 kV, a second experiment was performed in which the voltage drop across the first MCP was changed from 100 to 33% of the drop across the second MCP (Table 1, 2A and 2B, respectively). The matrix was deflected in both cases, as in 1B. Two Mn values were measured, as in experiments 1A and 1B. Clearly, operating this detector with matched voltage drops across the MCPs implies operation under saturating conditions, as the Mn values obtained in 2A are significantly higher than those obtained in 1B. With a 33% voltage drop across the first MCP, there is a considerable weakening of signal intensity, including that of the matrix. In this configuration, the detector is not operating under saturating conditions. In fact, the sensitivity is too poor for reliable detection of the polystyrene 33 000 component. Calculation of Mn for the first two components results in a value very similar to that obtained from 1B, implying that the detector configuration of 1B is also nonsaturating. Therefore, the amount of matrix making its way to the detector in configuration 1B does not appear to be sufficient in saturating the detector. Clearly, the extent of detector saturation can affect the Mn determination for polydisperse polymers. MCP detector designs can be different for different MALDI systems; therefore, it is suggested that tests for saturation be performed for each unique design in order to determine the conditions under which saturation occurs. As electron multiplier-based detector designs or hybrid MCP/electron multiplier detectors are less prone to saturation, this suggests that the above considerations are not as important. Data Processing and Resolution. Studies have stressed that a MALDI analysis of polymers, based on a time-of-flight analysis, generates data indicative of number of ions as a function of time and, therefore, mass.5,23,24 In the course of developing appropriate (23) Lehrle, R. S.; Sarson, D. S. Rapid Commun. Mass Spectrom. 1995, 91-92. (24) Guttman, C. M. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1996, 37, 837-838.

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methods for the comparison of MALDI and GPC data, it has been established that when displayed as a function of mass, the molecular weight distribution functions are not equivalent. Two reasons for this have been identified.6,24 One concerns the fact that intensity data from MALDI reflects the number of molecules, whereas in GPC it reflects the weight of molecules. The other relates to the way in which the data are displayed as a function of mass. Since the collected data in GPC represents weight fraction as a function of elution time, the calibration procedure will distort the weight-average molecular weight distribution. This is because, in a GPC experiment, elution time is typically a logarithmic function of mass. The approach polymer chemists have taken in recovering the measured molecular weight distribution function is to apply a correction to the intensity data of the calibrated chromatogram.24,25 This takes the following form:

p(m) ∝ D(t)/m where D(t) is the detector response as a function of time, t, and p(m) is the corrected weight molecular weight distribution as a function of mass, m. In time-of-flight, mass is proportional to t2. Therefore, calibrating the collected data and displaying it according to a mass scale also distorts the molecular weight distribution function, as determined by MALDI. While it has been recognized that the calculation of average molecular weights should not be attempted in such a distorted mass domain, there is no indication that the calibrated mass spectra displayed in the literature are corrected for this distortion. The necessary correction factor has been determined,24 and can be expressed as follows:

q(m) ∝ D(t)/(dm/dt) where D(t) is the MALDI detector response as a function of time, t, and q(m) is the corrected number molecular weight distribution as a function of mass, m. The dm/dt term is simply the derivative of the calibration equation. Correction of the data in this fashion allows one to determine the average molecular weight values directly from the mass domain and preserves the molecular weight distribution function as determined by MALDI. The effects of such a correction are most readily noticeable at the lower masses, as shown in Figure 7. These figures represent the molecular weight distribution of a two-component blend. (A) represents the spectrum without the above correction, while (B) represents the same spectrum with the correction applied. The difference between the two is marked, even over this relatively small mass range. The preservation of this distribution as determined by MALDI does not imply that it is an accurate reflection of the true molecular weight distribution, even in the absence of the previously discussed mass discrimination. MALDI spectra of polymeric species typically display a mass-dependent resolution. Figure 6, for example, provides a good illustration of the effects of massdependent resolution on the molecular weight distribution. In a figure such as this, the spectrum contains both high- and lowresolution components. Determination of the molecular weight distribution function directly from the intensity data, without (25) Determination of Molecular Weight; Cooper, A. R., Ed.; John Wiley and Sons: New York, 1989; Vol. 103.

variables can affect the measured Mn value for polydisperse polymers. In particular, ion focusing elements in the MALDI TOF instrument can induce mass discrimination, as can the detector design and operating conditions. The contribution of these instrumental factors to the overall mass discrimination can be reduced by optimizing the source and detector configurations, for example, operating under nonsaturating conditions. However, it is clear that a detection system based on ion impact with an ionto-electron or ion-to-ion conversion surface provides inherent mass biasing. The nature of this mass biasing is affected by the introduction of grids anywhere in the flight path of the primary ions. Although not studied in this work, a reflectron TOF system could give rise to further mass biasing, depending on its design and operation. Conceivably, the instrumental contributions to mass discrimination can be accounted for by developing a detection response curve. Using a number of different blends of well-characterized homopolymers with molecular weights covering a broad mass range, an overall instrumental response curve could be determined. However, the utility of such a response curve for polydisperse polymer analysis is still dependent on overcoming sample and desorption/ionization factors that contribute to mass discrimination, as indicated in the companion paper.1

Figure 7. Spectrum of a two-component blend consisting of polystyrene 5050 and 11 600 (100 pmol each) (A) with no intensitycorrection applied and (B) with the intensity correction applied.

considering the resolution differences, will weight the low-mass portion too greatly. CONCLUSIONS The analysis of polymeric species by MALDI TOF mass spectrometry imposes the requirement of uniformity of response over the mass range to be analyzed. This requirement is not met on a number of levels, as this study shows. Several instrumental

ACKNOWLEDGMENT This work was supported by the Natural Sciences and Engineering Research Council of Canada through its Industrially Oriented Research Grant Program and by the Polymer Structure and Property Research Program of the Environmental Science and Technology Alliance Canada. D. C. S. thanks the Killam Trust for a predoctoral scholarship. The authors thank Dr. Scot Weinberger of Hewlett-Packard Co. for his valuable comments on the manuscript. Received for review July 10, 1997. Accepted July 17, 1997.X AC9707794 X

Abstract published in Advance ACS Abstracts, September 1, 1997.

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