Anal. Chem. 1988,60,2334-2338
2334
Radial Dispersion from Commercial High-Performance Liquid Chromatography Columns Investigated with Microvoltammetric Electrodes J o h n E. B a u r , Eric
W.Kristensen, and R. Mark Wightman*
Department of Chemistry, Indiana University, Bloomington, Indiana 47405
The band shape of compounds eluting from a commercial, reverse-phase chromatographlc column has been examined as a function of radial position with a microvoltammetric electrode. The diameter of the cyllndrlcal electrode ( I O Mm) is much smaller than that of the column. Therefore, the electrode can be placed with a mkroposftioner at dtfferent locations across the column outlet. The radial dispersion measured In this way is much greater than that expected for a centrally injected compound. The observed dispersion suggests that Its primary orlgln Is the method used to Introduce the sample Into the column. Axlal dispersion Is also found to vary with radial position. When evaluated as an exponentially mod#led, Gausslan peak, the standard deviation for the peak remalns almost constant as a fundon of radlal position, but the exponential modlfler increases as the column wall Is approached. The radial profile measured with a mlcroelectrode can be used to reconstruct the band shape observed with a bulk detector. However, highest efflclencles are obtained with the microelectrode in the center of the exit frlt. At slow flow rates and for a compound with short retention tlme, a reduced plate height of 1.5 Is obtained for a centrally located microelectrode.
A variety of factors affect the shape of components eluting from chromatographic columns. Extracolumn broadening of chromatographic peaks can seriously degrade chromatographic resolution. Amperometric detectors fabricated in the form of microdisks or cylinders can minimize this effect at the end of liquid chromatographic columns because they can be directly mated with the column end. This has been demonstrated with the use of carbon fiber electrodes as detectors for microcolumns (1, 2). If the dimensions of the column greatly exceed the dimensions of the electrode, then the electrode could be used to map out the radial distribution of the concentration of species eluting from the column. This approach has been used to examine the broadening of an unretained species in columns packed with spherical beads (3, 4 ) . For a small sample injected centrally onto a chromatographic column, it has been shown that the radial dispersion can be characterized by a radial plate height, H,, defined as
HI= a,2/L where L is the column length and ur is the standard deviation of the concentration profiie in the radial direction. The radial dispersion, expressed as a reduced plate height, h, (=H,/dp, where d, is the mean diameter of the packing material), has been shown experimentally to follow the relation h, = B/u C (2)
+
where the first term in this equation is identical with the term
* Author to whom correspondence should be addressed. 0003-2700/88/0360-2334$01 S O / O
used to describe molecular diffusion in axial dispersion and values of C vary between 0.05 and 0.2 ( 3 , 4 ) . (The reduced velocity, u, is defined as ud,/Dm where u is the average linear velocity through the column and D, is the diffusion coefficient of the sample molecule.) However, as the concentration approaches the edges of the column, a significantly greater dispersion is observed because of interactions with the wall. It has been shown that for centrally injected compounds the wall effect can be avoided (3) when
(3) where d, is the column diameter and r, is the number of particle diameters that the wall effect extends from the side of the column (r, = 30). For packed columns it has been experimentally found that B = 1.4 and C ;= 0.060 ( 3 ) . For a 10 cm X 3.2 mm column packed with 3-pm particles operated at a flow rate of 1mL/min the left-hand term in eq 3 is 30.4 and the right-hand term is 1.9. Thus, the wall effect should not be important for a centrally injected compound under typical conditions used with commercial columns. For trans-annular injections (3, 4 ) it has been shown in model studies that the linear velocity increases near the column wall and peaks become more asymmetric. This phenomenon is believed to be caused by poor column packing at the wall. Despite this basic understanding of radial broadening in chromatographiccolumns, it is not clear how these effects are manifested when commercial loop injectors and columns are employed. Microelectrodes fabricated from carbon fibers are sufficiently small (5 pm radius) that they provide a way to investigate radial dispersion in conventional, high-performance liquid chromatographic apparatus. We have previously shown that these electrodes can be used to examine the radial dispersion at the outlet of a loop injector (5). In this report we show that a similar investigation can be made at the outlet of the column. Such investigations provide a method to compare the performance of chromatographicequipment with the model studies described above. In this way modes of band broadening can be delineated. EXPERIMENTAL SECTION Chromatographic System. A reciprocating piston pump (Milton Roy Co., Riviera Beach, FL) delivered the mobile phase through a damping column and coil to a pneumatically actuated loop injector with a selectable internal loop (Model3XL, Scientific Systems, Inc., State College, PA). The 10-pL loop size was used throughout this study. A 10-cm reverse-phase cartridge column of 3.2 mm internal diameter with 3-pm RP-18 particles (Brownlee Labs, Santa Clara, CA) was connected to the loop injector via approximately 4 cm of 0.01 in. i.d. stainless steel tubing. The detector was either a commercially available amperometric detector with downstream Pt auxiliary and reference electrodes (Model TL-8A with 5-mil spacer, Bioanalytical Systems, West Lafayette, IN) or a carbon-fiber microvoltammetric electrode. Figure 1shows the apparatus used with the microvoltammetric electrode. A stainless steel column end fitting was fabricated to hold the cartridge column in place and allow exposure of the column outlet frit so that spatially resolved measurements could 0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 21, NOVEMBER 1, 1988
2335
RE
0
20
40
60
80
100
Time (s) Flgure 2. Chromatograms of 5 nmol each NE, E, and DHBA whh microvoltammetric electrode near the center of the column and near the edge of the column. Flow rate was 1.0 mL min-’.
CA
Figure 1. Column end-assembly configured for microvoltammetric electrochemical detector: AE, awiliary electrode; CA, carbldge holder; CH, column holder: CM, column; EH, electrode holder; FR, frit; MM, micromanipulator; PP, piezoelectric poshloner; RE, reference electrode; SC, screw cap; WE, working electrode.
be made at the surface of the frit. The frit in the Brownlee column is crimped into place, which facilitatesthe measurementsdescribed here. The chromatographic system was assembled so that the mobile phase flowed upward from the injector through the column. The small pool formed at the outlet of the column (volume approximately 50 pL) served as the electrochemicalcell. The eluate flowed over the sides of the cell to a waste container. The electrode could be positioned with 100-pm resolution in three dimensions with a micromanipulator (Narishige Co., Ltd., Tokyo, Japan). Vertical resolution was enhanced with a piezoelectric positioner with 0.5-pm resolution (Burleigh Instruments, Inc., Fishers, NY). This device allowed accurate placement of the electrode 5 pm from the surface of the frit. A saturated sodium calomel electrode (SSCE) was placed inside a pulled glass tube, which served as the reference compartment. A platinum wire wrapped around this compartment served as the auxiliary electrode. The tip of this assembly, approximately 1 mm in diameter, was positioned in the cell with a micromanipulator. The three-electrode potentiostat was of local design and construction and employed a low pass filter (RC = 70 ms). All chromatograms were recorded at 0.8 V vs SSCE. An IBM personal computer with a Labmaster board (Scientific Solutions, Solon, OH) was used to actuate sample injection and to collect the data at a rate of 50 points per second at 1.0 mL m i d and 30 points per second at 0.56 mL m i d . The chromatographic figures of merit were evaluated as statistical moments (6-9),which have been shown to be more accurate than traditional graphical methods for peaks that deviate from the ideal Gaussian shape (10). Locally written software was used for peak analysis using the exponentially modified Gaussian model (11). The validity of this model was confirmed by reconstructionof measured peaks with the experimentally determined parameters. Electrodes. Carbon fibers (ro = 5 gm) were sealed in pulled glass capillaries (12)and cut so that the electrode had the geometry of a cylinder with a length less than 100 pm. The electrodes were electrochemically pretreated by applying a 5 0 - H ~ triangle wave between 0 and 2 V vs SSCE for approximately 30 s. The pretreatment was repeated daily. Under quasi-steady-stateconditions in unstirred solutions, the diffusion layer (6) at a cylindrical electrode is given by b = ro In [2(D,t)1/2/ro]
(4)
where the value for D , for catecholamines in aqueous solution
is =5 X lo4 cm2s-l and t is the time scale of the experiment (13). At the flow rate employed in the majority of the studies reported here, 1.0 mL mi&, the average linear flow rate at the column exit is 200 pm s-l, and the transit time by the electrode is less than 0.5 s. Thus, the dimension of the solution sampled by the electrode is comparable to the radius of the cylindrical electrode. Reagents. All chemicals were reagent grade and used as received from commercial sources. Test compounds were norepinephrine (NE), epinephrine (E), dihydroxybenzylamine (DHBA),and uric acid (UA). 2,5-Dihydroxy-1,4-benzened~~o~~ acid, dipotassium salt, was used to mark the solvent front. The mobile phase (pH 4.4) contained 0.1 mM disodium ethylenediaminetetraacetate, 1.0 mM octyl sodium sulfate, and 10% methanol in 0.2 M monobasic sodium phosphate, and was fiitered with 0.45-pm filter paper (Gelman Sciences, Inc., Ann Arbor, MI).
RESULTS AND DISCUSSION Radial Dispersion. When a microvoltammetric electrode is placed at the center of the column axis, sharp, narrow peaks are recorded (Figure 2). However, when the electrode is placed near the column wall, the peaks recorded are broader, attenuated, and significantly tailed. In addition, the peaks have longer retention times, in contrast to what is expected for the wall effect. The radial distribution of concentration, c, for a centrally injected sample has been shown, for nonretained compounds, to follow the Gaussian distribution c / c , = exp(-r2/2u,2)
(5)
where c, is the concentration a t the central axis and r is the distance from the central axis. The standard deviation can be calculated from the expression for radial plate height (eq 1 and 2). For the conditions of this study, h, = 0.118 and b, = 0.188 mm. The calculated radial concentration distribution is superimposed on the experimentally determined distribution in Figure 3. To fiid the column center the electrode was first placed a t a visually estimated center. Next, a series of chromatograms were recorded, between which the electrode was moved in 0.3-mm increments in both the x and y directions until a minimum axial plate height was found. The measured values differ significantly from the profile for a centrally injected compound. A large portion of the solute elutes in a ring approximately 1 mm from the column center. Kirkland ( I O ) has proposed that an uneven sample band profile occurs at the head of the column with conventional injection techniques. Thus, the radial concentration distribution observed here is likely to be a result of the mode of sample introduction onto the column. Axial Dispersion as a Function of Radial Position. The reduced plate height and relative retention time determined with the microvoltammetric electrode for NE (K’ = 1.8) are shown in Figure 4A. The variation of retention time with axial position (normalized by the retention time at the center
2336
ANALYTICAL CHEMISTRY, VOL. 60, NO. 21, NOVEMBER 1, 1988
r 1.03
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1 -0.10
0.10
0.00
r
1 0.20
(4
0-0
theoretical for central Injection with uR= 0.188 mm; circles, experimental. The dashed lines are the estimated position of the column walls. Data shown for NE peak. I
(1.03
t
20 --
-R
1.01
tR.0
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-0.2-0.1
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4.01 . . . . : . 0.0
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Vertical Position (mm) Flgure 5. Normalized retention time and reduced axial plate height for
Figure 3. Normalized radial concentration distribution: solid line,
h,
tR*o
I
0.0-
4
tR -
0.99 0.0 0.1 0.2
r (cm> Flgure 4. Normalized retention time and reduced axial plate height of 5 nmol of NE as a function of radial position for (A) a new column and
(B)the same column following several weeks of experiments. Flow rate was 1.0 mL min-‘. The dashed lines are the estimated position of the column walls.
of the column) bears similarities to the flow dispersion induced by a loop injector and the connecting tubing previously reported (5). In addition to a velocity decrease near the walls, the peaks become increasingly asymmetric, evidenced by the increase in the reduced axial plate height with radial position. This experiment differs from that dwcribed by previous workers ( 3 , 4 )in that the variation of plate height with radial position was measured here for a retained compound in a real chromatographic system. Thus, stationary phase partitioning contributes to the band broadening in addition to the various flow effects. Despite this difference, the variation of reduced
5 nmol of NE as a function of vertical distance from the outlet frit surface. Liquid surface is at 1.46 mm. Flow rate was 1.0 mL min-’.
axial plate height with radial distance is similar to that obtained by Knox (3). Furthermore, reduced plate height variations obtained for longer retained solutes (E, k’ = 3.0, and DHBA, k’ = 4.7) were nearly identical with those obtained for NE. Following several weeks of experiments, the characteristics of the column changed. The time of solvent front changed from 17.5 to 23.4 s and the retention times of each peak increased dramatically (approximately 40%) although the volume flow rate remained constant. Subsequently, the retention times steadily increased as successive experimentswere performed. The flow profile of the “old” column is shown in Figure 4B. The retention profile is less symmetrical with a wide variation of velocities in the center portions of the column. The plate height plot, however, has not significantly changed from that of the “new” column. In fact, the reduced axial plate heights are somewhat smaller because of the increased retention time. As the column aged, it appears that channeling increased due to the deterioration of the column from the rigors of the injection process. The vertical flow profile was determined by raising the electrode from the frit surface to the top of the electrochemical cell, a distance of approximately 1.5 mm. Chromatograms of the test mixture were recorded at 0.15-mm intervals. Figure 5 shows the dependence of the reduced axial plate height and the normalized retention time with vertical position. As expected, longer retention times are observed as the detector is raised from the frit surface. The reduced axial plate height remains approximately constant for a considerable distance and severely tailing peaks are not observed until just below the liquid level (indicative of stagnation). This result suggests that a microcylinder electrode 1 mm long could be placed at the column outlet without substantial loss of efficiency. The resulting increase in surface area should enhance the sensitivity of the detector yet retain the low detection volume and spatial selectivity of the detector. Comparison of Microvoltammetric and Conventional Electrochemical Detectors. The microvoltammetric electrode can be placed at various locations across the outlet frit and sample only a small fraction of the entire outlet area. A bulk detector, on the other hand, samples the entire eluate, thus acting as an integrator of the separate concentration elements which are sampled by the microvoltammetric electrode. To evaluate this in a quantitative way, the response from a microelectrode positioned at the central axis was compared to a commercial amperometric detector. The observed efficiency is greater with the microvoltammetric electrode as shown in Table I, which compares the number of theoretical plates obtained in 1 m for the two cases. Improvements of greater than 25% are observed for each peak with greater improvement at shorter retention times. If the response of the microvoltammetric electrode at any point across the column outlet is assumed to be representative
ANALYTICAL CHEMISTRY, VOL. 60, NO. 21, NOVEMBER 1, 1988
Table I. Comparison of Number of Theoretical Plates (per Meter) between Microvoltammetric Electrode and Bulk Detector and Reconstructed Peak at 1.0 mL m i d compound"
NE E
microelectrodeb
bulk detectorbsc
peak
64 900 63 300 67 900
83 300 80 500 84 800
DHBA
reconstructed
Table 11. Comparison of U A and T between Bulk Detector and Microvoltammetric Electrode at the Center and Near the Edge of Column at 1.0 mL m i d compound' (k9
NE (1.8)
64 400 59 400 62 500
center
edgeb
amperometric
0.61 0.39
0.63 0.96
0.68 0.46
44
0.84 0.61
0.87 1.4
0.89 0.76
u(s)
0.98
4s)
1.1
1.1 2.0
1.1 1.2
u(s)
r(s)
E (3.0)
"Injection of 5 nmol. bAverage of three chromatograms. Adjusted for increased retention time due to connecting tubing.
2337
DHBA (4.7)
u(s)
"Triplicate injection of 5 nmol. 1.5 mm from center.
1 .o,
A Table 111. Comparison of Number of Theoretical Plates (per Meter) between Microvoltammetric and Bulk Electrochemical Detector at 0.56 mL min-' micro-
compound" UA 0
.
loo!80 I
I
0
4
A r
4
B
NE E DHBA
electrodeb 226 000 114000 114000 112000
bulk detectorbac 120000 86 000 92 000 93 000
%
increase 88.3 32.6 23.9 20.4
" Injection of 3.8 nmol. Average of two chromatograms (except average of three for UA). CAdjustedfor increased retention time due to connecting tubing.
3
40
2oP 0
I . . . : . : . : . : - : - : : :
128
132
136 Time (s)
140
144
Flgwe 6. Peaks for 5 nmol of DHBA: (A) microvoltammetric electrode near center and near wall at column outlet; (B) solid line, bulk detector: circles, reconstructed peak.
of the concentration ring in which it samples, the entire concentration as a function of time of a solute eluting from the column can be predicted by summing the individual responses (in real time and amplitude) weighted by the area of the particular ring. Figure 6A shows the response of the microvoltammetric electrode at the central disk and at an outer ring for DHBA (k' = 4.7). The peak reconstructed from the individual responses should be identical with the peak recorded with the bulk detector, and indeed a very good fit is obtained when two peaks are overlaid (Figure 6B). In terms of theoretical plates, corrected for the transit time from the frit through the connecting tubing to the detector, no more than a 7% error is obtained for any compound when compared with the bulk detector (Table I). Good agreement is also obtained from chromatographic figures of merit which are independent of retention time (uA,and the asymmetry factor, BIA). Insight into the causes of the axial band broadening can be gained by examining peak shapes as a function of radial position using the exponentially modified Gaussian model. With this model, the standard deviation of the parent Gaussian peak, uA, related to dispersive processes in the column, and the exponential modifier, T , can be extracted. The values of UA and T for three different compounds are compared for a centrally located micpovoltammetric electrode, a microvoltammetric electrode located near the edge of the column, and a bulk detector in Table 11. The value of uA decreases in the order DHBA > E > NE for all the measurements, which indicates that there is greater axial dispersion with increased on-column time. Interestingly, there is little variation of UA between detectors for a given peak. The
variation of T demonstrates two important points. First, the larger value of T with increased time on the column indicates that the exponential modification of the Gaussian peak occurs not because of extracolumn effects, as the value of T would remain constant. The source of the distortion must be oncolumn, perhaps poor column packing or dead volume in the column itself. Second, the large increase of T with radial position indicates that these contributions to the distortion are greatest closer to the wall. The values listed for the bulk detector can be considered to be averages for the entire column. Chromatography at Slower Flow Rates. A complete set of experiments at 0.56 mL min-l were performed and compared to the results at 1.0 mL min-'. Nearly identical flow profiies were obtained, although the peaks were more disperse because of the longer on-column time. Here greater than 100000 plates m-l were obtained with the microelectrode at the center of the column for UA, NE, E, and DHBA, and improvements of more than 19% with respect to the bulk detector were observed (Table 111). Most notable is the nearly 90% increase for uric acid (k' = 0.33), where greater than 225000 plates were realized in less than 70 s with the microvoltammetric electrode. The corresponding reduced axial plate height, 1.5, is less than the usual minimum reduced plate height of 2.0 for conventional packed columns (14). Even lower values of the reduced plate height should be attainable by further decreasing the flow rate.
CONCLUSIONS The microvoltammetric electrode has several distinct advantages over conventionalbulk electrochemical detectors for high-performance liquid chromatography. First, the small size allows placement at the region of highest efficiency directly at the column outlet while discarding the fractions of the eluate in which the solutes are more greatly dispersed. Connectingtubing that increases solute dispersion is thus not required. Second, as demonstrated here, the small size of the electrode allows a complete mapping of the radial dispersion from the columns. Third, the microelectrode is less sensitive to bakcground currents and flow variations than the bulk electrochemical detector (15). The chief disadvantage, how-
Anal. Chem. 1988, 60,2338-2346
2338
ever, is that because of its small size, only a very small fraction of the entire eluate is sampled and thus the microvoltammetric electrode is much less sensitive than conventional bulk detectors. Experiments designed to remove this disadvantage are currently being pursued.
LITERATURE CITED (1) Knecht, L. A.; Guthrle, E. J.; Jorgenson, J. W. Anal. Chem. 1984, 56,
479-482. (2) White. J. G.;Jorgenson, J. W. Anal. Chem. 1986, 58, 2992-2995. (3) Knox, J. H.; Laird, G. R.; Raven, P. A. J . Chromatog. 1976, 122, 129-145. (4)Eon, C. H. J . Chromatogr. 1978, 149, 29-42. (5) Krlstensen, E. W.; Wilson, R. L.; Wightman, R. M. Anal. Chem. 1988, 58,986-988. (6) Kucera, E. J . Chromatogr. 1965, 19, 237-248. (7) Sternberg, J. C. I n Advances ln Chromatography; GkMings. J. C., Keller, R. A., Eds.; Dekker: New York, 1966: Vol. 2, pp 205-270.
(8) Grubner, 0. I n Advances in Chromatography; Giddlngs, J. C., Keller, R. A., Eds.; Dekker: New York, 1968;Vol. 6,pp 173-209. (9) Grushka, E.; Myers, M. N.; Schemer, P. D.; W i n g s , J. C. Anal. Chem. 1969, 41, 889-892. (IO) Kirkland, J. J.; Yau, W. W.; Stoklosa, H. J.; Dilks, C. H., Jr. J . Chromatogr. Sci. 1977, 15, 303-316. (11) Foley, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730-737. (12)Dayton, M. A.; Brown, J. C.; Stutts. K. J.; Wlghtman, R. M. Anal. Chem. 1980. 5 2 , 946-950. (13) Wlghtman, R. M.;Wlpf. D. 0. I n Electroenalyticel Chemkhy; Bard, A. J., Ed.; Dekker: New York, 1988;Vol. 16. (14) Knox, J. H. J . Chromatogr. Sci. 1980, 18, 453-472. (15)Caudill, W. L.; Howell, J. 0.;Wlghtman. R. M. Anal. Chem. 1982, 5 4 ,
2532-2535.
RECEIVED for review June 14,1988. Accepted August 1,1988. This research was supported by the National Institutes of Health (R01-NS-15841).
Factors Affecting the Quantitation of Organic Compounds in Laser Mass Spectrometry Zbigniew A. Wilk, Somayajula Kasi Viswanadham, Andrew G . Sharkey, and David M. Hercules* Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Factors aff ectlng the reproduclbilHy of organic laser mass spectrometry have been studied. Laser focus, laser power denslty, sample preparatlon method, and Chemical effects contrlbute significantly to the variabtlity of the mass spectra. Defocuslngthe laser enhances production of structurally slgniflcant organlc ions. The yield of organic molecular Ions Is a nonflnear function of power density. The use of a polymer matrlx (5 % nitrocellulose) for dissolving an analyte(s) was determlned to be the optimum method of sample preparatlon. Using such a polymer matrlx, along wlth Internal standards, permitted relatlve standard deviations of f15% to be obtained.
Mass spectrometry of solid materials has, in recent years, been performed by using ion and atom beams as sputtering/ionization sources, providing an alternative approach for the analysis of solid samples (1). The two major advantages of a laser as a source for mass spectrometry are that it can volatilize/ionize solid samples directly and the beam can be focused to a micrometer-size spot permitting the analysis of microvolumes. Early work with the laser as an ionization source for mass spectrometry dealt with the analysis of inorganics, metals, and semiconductors. These early experiments were performed by using varied instrumental designs (e.g., different laser types and mass analyzers). An excellent review on the progress of laser mass spectrometry to 1979 is given by Conzemius et al. (2). In 1982 the laser was reviewed as an ionization source for the mass spectrometric analysis of involatile and thermally unstable organic molecules ( 3 , 4 ) .Additionally, laser ionization has seen application in diverse areas ranging from mycobacteria fingerprinting (5) to the biogenesis of coal macerals (6). Laser mass spectrometry (LMS) has been used primarily as a qualitative technique. Quantitative analysis is not a trivial problem but has been demonstrated. Schroeder deposited
standard materials on samples via a mask so that a regular pattern of coated and uncoated areas was formed on the surface. This was done to introduce internal standards (7). He also demonstrated that isotopic labeling can be an effective method for element quantitation. The local thermodynamic equilibrium (LTE) model has been used to rationalize relative peak intensities for various elements observed in the LMS of NBS glass fiber standards (8). It was suggested that the LTE model can be used as a good first approximation for the quantitative analysis of particles. Verbueken et al. studied ion exchange resins doped with successively increasing concentrations of metal complexes (9). A linear relationship between the concentrationof the metal and the metal ion peak intensity was observed, clearly demonstrating that laser mass spectrometry is capable of quantifying elements. Quantificationof a benzalkonium chloride mixture by LMS was performed; the results compared favorably with those obtained by high-performance liquid chromatography (10). Mattern et al. have applied LMS to quantify oligomer distributions for polytethyleneglycol) and poly(propy1ene glycol) (11);results compared favorably with those from other techniques. Similarly, it was possible to measure the percentage of backward addition in poly(viny1idine) fluoride; results correlated well with NMR measurements (12). The present paper addresses some factors that affect the quantitation of organics obtained by using a laser microprobe mass spectrometer (such as the LAMMA-lOOO),which operates in the reflection mode. In this mode the laser beam is focused onto the sample surface at an angle of 45" from the normal. Ions are extracted normal to the sample surface. Use of the reflection mode permits routine analysis of bulk samples; microvolume analysis is possible (13). The factors to be discussed are sample preparation, laser energy, laser focus, and chemical effects. Other factors that are important for quantitation but are not considered here include the stability of the laser, nature of the laser-solid interaction, the rate of analog-to-digital (A/D) conversion of the signal, and detector efficiency. These latter factors were
0003-2700/86/0360-2338$01.50/00 1986 American Chemical Society
