Anal. Chem. 1980, 52, 1808-1811
1808
Determination of Molecular Weight Distributions of Polystyrene Oligomers by Field Desorption Mass Spectrometry Robert P. Lattlmer" and Dale J. Harmon The BFGoodrich Research and Development Center, 992 7 Brecksviiie Road, Brecksville, Ohio 44 14 1
Gordon E. Hansen Department of Pharmacology and Experimental Therapeutics, The Johns Hopkins University School of Medicine, 725 North Wolfe Street, Baltimore, Maryland 2 7205
Three polystyrene standards were analyzed by field desorptlon mass spectrometry (FDMS). Essentially pure molecular Ion spectra were obtained for the polystyrene oligomers. FDMS derived molecular weight averages ( Mnand R,) compared favorably to values obtained by conventional techniques (vapor pressure osmometry, Intrinsic vlscoslly, klnetlc data, and gel permeation chromatography). This agreement Indicates that the relative intensities of the FDMS oligomer molecular Ions (wlth approprlate correctlons for isotoplc abundances) can be used dlrectly to glve reasonably accurate relatlve molar concentrations of the oligomers. The oligomer molecular weights ranged up to nearly 5300 amu.
Table I. Molecular Weight Parameters for Polystyrene Standardsa batch Mnb M"C
41.30 811 t 5% 1024 t 5% 41.10 1 7 1 0 k 7% 2200k 7% 3600 k 3% G1.10 llb 3100 i 5% a From data sheets supplied by Pressure Chemical Co. Determined by vapor pressure osmometry (VPO). Determined by intrinsic viscosity (cyclohexane or benzene solvent). d Determined by kinetic considerations and comparison of GPC data (see ref 1 2 ) . 61004 12a
series of n-paraffins. Mead concluded that the relative FIMS sensitivities of the molecular ions of the n-paraffins (carbon number range 20-40) were essentially equal t o each other. In this report we evaluate the molecular weight distributions of a series of commerically available polystyrene standards by using FDMS. These polymers are prepared by an anionic, butyllithium-catalyzed system (12), and as a result they have narrow molecular weight distributions. The polymers are used primarily for calibration in gel permeation chromatography (GPC), and their general structure is as follows (mol wt = 58
Field desorption mass spectrometry (FDMS) has been shown t o be a method of choice for determining molecular weights of nonvolatile and higher molecular weight chemicals (1-3). Field desorption provides a gentle means of ionization t h a t imparts little excess energy t o t h e molecule. Consequently, molecular ions (or a t times protonated or cationadduct molecular ions) are frequently the strongest ions observed. Fragment ions and ions due to thermal decomposition products are often absent or else of relatively low intensity. Numerous reports have shown t h a t FDMS can be used to obtain good qualitative distributions of oligomers for low molecular weight polymers. Oligomeric mixtures studied in this regard include n-paraffins ( 4 ) ,polypivalolactone (5, 6 ) , poly(2,2,4-trimethyl-1,2-dihydroquinoline) (7,8),polystyrene (7-9), and poly(propy1ene glycol) (7,9). Components of several oligomeric polymer chemical mixtures have also been qualitatively characterized by FDMS (10, 11). None of the above reports attempted to determine accurate molecular weight averages (6fn and 6fw)for the polymer systems studied. I n principle i t should be possible t o determine such parameters by FDMS, since the technique directly provides t h e information needed (molecular weights and relative intensities of oligomers). Three potential difficulties with this type of analysis might be anticipated. First, t h e oligomers should give intense molecular ions and show little tendency t o give fragment or thermal decomposition ions under F D analysis. Second, the molecular weight range needed for a particular polymer has t o be accessible on the mass spectrometer. This obviously restricts the FDMS technique a t present t o relatively low molecular weight polymer systems, b u t recent developments suggest t h a t an accessible mass range of up to several thousand mass units is possible with modern instrumentation (9). Third, the relative ionization, transmission, and detection efficiencies of the various oligomers in the polymer system must be evaluated. This is a potentially difficult task. Mead ( 4 ) used comparative gas chromatography and field ionization mass spectrometry (FIMS, razor blade emitter) data to study a 0003-2700/80/0352-1808$0 1.OO/O
Mw/;t3,d
+ 104n).
H
H
Hf+-++C4Hg
+ H n
EXPERIMENTAL SECTION Three low molecular weight batches of polystyrene were analyzed by FDMS. The samples were obtained from Pressure Chemical Co. of Pittsburgh, PA. The batch numbers were 61004 (mol wt "750"), 12a (mol wt "2030"), and 1 l b (mol wt "4000"). The molecular weight parameters supplied by the manufacturer for each are given in Table I. The number average molecular weight is defined as
Mn = C N i M ; / C N i
(1)
The weight average is
Mw = CNiMi2/CNiMi
(2)
The viscosity average is defined as
Mv= [ ~ N ; M i ' + " / ~ N ; M i ] ' / "
(3)
where a is the constant from the Mark-Houwink viscosity weight relationship [?7] =
KM"
(4)
For a "most probable" distribution, it can be shown (13) that
Mn:Mv:Mw::i:[(i + a)r(i+ ~ ) l / ~ 1 : 2 r(l + a) is the r function of 1 + a. When a
(5)
where = l,_the viscosity average (A?") is identical with the weight average (Mw). Mass Spectroscopy. All three polystyrene standards were analyzed by field desorption mass spectroscopy using a Kratos
C
1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980
MS-50 mass spectrometer (The Johns Hopkins University). A combination field ionization/field desorption/electron impact (FI/FD/EI) ion source was used. Polystyrene batch 61004 was analyzed by using a standard high-temperature activated carbon emitter. The other two samples were analyzed by using silicon emitters, prepared as described previously (14) except that 10-pm wire was used. We have not evaluated the performance of carbon vs. silicon emitters for higher mass FD work. Silicon emitters were used for this work simply because they are readily available in our laboratory. The samples were deposited on the emitter by using the normal dipping technique from tetrahydrofuran solution. Spectra were recorded by oscillographic trace, and masses were determined with reference to the E1 mass spectrum of tris(perfluorohepty1)-s-triazine(mol wt 1185)or else by counting the regularly spaced polystyrene oligomers. The ion source temperature was -150 “C. Two to five FDMS runs were made with each polymer sample. Several spectra were recorded (with repetitive scanning) as the field emitter was slowly heated with up to 30 mA heating current. The high-field magnet was scanned at 10 s/decade with a bandwidth of 100 Hz. The static resolution ( M / N , 10% valley) was -3000, and the dynamic resolution was -500. The Kratos MS-50 was operated at low resolution in order to achieve maximum sensitivity for detection. It was not necessary t o operate at higher resolution, since the objective of the work was to obtain reliable relative intensity measurements of oligomers. For studies involving structural elucidation of unknown compounds, the instrument can be operated at higher resolution t o achieve separation of isotopic species for mass measurement. The ion source was tuned to the FI molecular ion of tris(perfluorohepty1)-striazine ( m / z 1185) prior to each run. The accelerating voltage was 8 kV and the ion extraction plate voltage was -2 kV for the runs with batch 61004. Corresponding values for the other samples were 6 and -4 kV (batch 12a) and 4 and -6 kV (batch Ilb), respectively. This provided a mass range of up to -5800 amu for the runs at 4 kV accelerating voltage. Ions were detected by using a Daly scintillation detector (15, 16) which provides better sensitivity for higher mass ions than the standard secondary electron multiplier. Field desorption measurements were also made on batch 61004 by using a Varian MAT 311A mass spectrometer (The BFGoodrich Co.). The measurements were made with 2 kV accelerating voltage under essentially the same conditions as described previously (8). A standard carbon emitter was used, and ions were detected with a secondary electron multiplier. Static resolution was -600, and dynamic resolution was -400. Essentially pure molecular ion spectra were obtained by FDMS (on either instrument). No fragment ions were noticeable, although doubly charged molecular ions were present to a small extent, particularly for the higher mass oligomers. Doubly charged molecular ions were ignored in determining the relative oligomer intensities. Liquid Chromatography. Polystyrene sample 61004 was also analyzed by liquid chromatography (LC) under the same conditions described previously ( 8 ) . The liquid chromatogram provided essentially complete separation of the polystyrene oligomers (8). Thus the relative abundances of the oligomers could be determined by using LC for comparison with FDMS. Computer Programs. The polystyrene oligomer peaks observed by FDMS showed little or no resolution of isotopic species above m / z 1000, due to the low dynamic resolution employed ( M / M -400 or 500). This presented no particular problem in analysis provided the isotopic distributions were accounted for. A computer program (HIMAS) was written (in FORTRAN) which provided “correction factors“ for the abundances of the naturally occurring isotopes 13C and *H. Input data for the program were instrument dynamic resolution ( M I A M = 500 for the Kratos MS-50 or 400 for the Varian MAT 311A) and elemental formulas for the various oligomers. The computer program determined the relationship between the observed height at peak maximum (which was taken as the observed “raw intensity”) and the total abundance of all the isotopic species. The program generated “correction factors” which were then applied to the observed raw intensities (see Table 11). The application of these correction factors was important in determining the accurate relative oligomer intensities for the average molecular weight calculations.
-
1809
The HIMAS program also calculated the average molecular weight for each of the various oligomer isotope clusters (see Table 11). These values were then used with the corrected oligomer intepsitiesJo calculate the average molecular weight parameters ( M , and M,). A second computer program (MWMN) was written to perform these calculations. It should be noted that the HIMAS logic was based on the following assumptions, all of which are believed to be sufficiently valid for the purpose of the calculations. First, instrument resolution was assumed to be constant with exponential scanning. Second, triangular peak shapes were used. Third, the maximum of a particular peak envelope was assumed to occur within fl amu of the most abundant isotopic species.
RESULTS AND DISCUSSION T h e desorption of oligomer molecular ions was dependent on the FD emitter heating current applied. That is, lower mass oligomers desorbed at lower heating currents (5- 15 mA), while higher mass oligomers desorbed a t higher heating currents (15-30 mA). Relative oligomer abundances were determined from the FDMS data as follows. The height a t peak maximum for each oligomer was recorded from each mass spectral trace. The “raw” peak intensities for each oligomer were then summed over the accumulated FD mass spectra (there were 10-15 scans for each polystyrene batch). The summed peak intensity for each oligomer was then multiplied by the appropriate correction factor to obtain a “corrected” intensity. Corrected intensities were then used to determine the percent relative intensities reported in Table 11. These percent intensities were used with the average oligomer molecular weights t o obtain the molecular weight parameters (finand Ma) listed in Table
11. One polystyrene sample (batch 61004) was examined by liquid chromatography (8). T h e relative abundances and LC-derived molecular weight parameters are also listed in Table 11. T h e LC peak heights (measured after accounting for base line drift) were used to calculate the percent oligomer abundances. It was assumed that the molar LJV extinction coefficient for each oligomer was the same (8). T h e results for batch 61004 will be considered first. For this polymer the LC-derived molecular weight parameters most closely resemble the data reported from analysis by conventional techniques (Table I). The number averages (A&) determined by FDMS (with either the Kratos or Varian mass spectrometer) are apparently somewhat too high. This is most likely due to the fact that the lower mass oligomers evaporate too fast from the field emitter for accurate deterinations of their intensities to be made. (This should not be a problem with the higher molecular weight batches 12a and l l b . ) The weight averages (Ma)agree quite well regardless of the method of analysis. I t is pleasing to note the parameters determined with the two different mass spectrorneters agree quite well with each other. For batch 12a, Mn determined by FDMS (1690 m u ) agrees very well with the vapor pressure osmometry (VPO) value (1710 amu). The FDMS value for &fw/Mn(1.15) is somewhat higher than the value reported by the manufacturer (51.10). GPC measurements in our laboratory indicate t h a t the manufacturer’s value is probably too low. The M w / M , ,ratios reported by the manufacturer (Table I) are only approximations. The ratios determined by FDMS may well be more accurate. For batch l l a , the FDMS result for &fn(2890 amu) again agrees reasonably well with the VPO value (3100 amu). T h e FDMS value is lower by - 7 % , which is considered t o be within the combined experimental error of the FDMS and VPO techniques. The lower FDMS value may indicate some “mass discrimination” for the higher molecular weight species, but nevertheless the FDMS/VPO agreement is rather good. T h e molecular weight ratio determined by FDMS ( M a / M n
1810
ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980
Table 11. Relative Oligomer Intensities and Molecular Weight Averages for Polystyrene
n 1
2 3 4 5 6 7
formula C12H18 ‘20H26 C28H34 C36H42 C44H50 C5?.H58 C60H66
8
9 10 11
12 13 14 15 16 17 18
-
C76H82 C84H90 ‘9ZH98 C100H106 C108Hl
‘1
14
16H122
C124H1
30
‘1
38
3ZH1
‘140H146 C148H1
54
19 20 21 22 23 24 25 26 27 28 29 30
C244H250
31
‘2
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
‘15eH162 C1b4H170 ‘17ZH178 C180Hl
86
C188H194 C196H202 2 ‘
c,
04H2 10 1 2 H 2 18
‘220H226 c 2 2 8H 2 34 ‘2
36H242
52 HZ
58
C260H266 ‘2
6BH2 7 4
2‘
7 ,HZ
82
‘28aH290 ‘29ZH2
98
‘300H306 C308H314 C316H322 C324H330 C332H338 340 H 3 4 6 C348H354 356H362 C364H370 c372H378 C380H386 C388H394 C396H102 C40,H41
0
nominal massa
av massb
162 266 370 474 578 682 7 86 890 9 94 1098 1202 1306 1410 1514 1618 1722 1826 1930 2034 2138 2242 2346 24 50 25 54 2658 2762 28GG 2970 3074 3178 3282 3386 3490 3594 3698 3802 3906 4010 4114 4218 4 3 22 44 26 4530 4634 4738 4842 4946 5050 5154 5258
162.3 266.4 370.6 47 4.7 578.9 683.0 787.2 891.3 995.5 1099.6 1203.8 1307.9 1412.1 1516.2 1620.4 1724.5 1828.7 1932.8 2037.0 2141.1 2245.3 2349.4 2453.6 2557.7 2661.9 2766.0 2870.2 2974.3 3078.5 3182.6 3286.8 3390.9 3495.1 3599.2 3703.4 3807.5 3911.7 4015.8 4120.0 4224.1 4328.3 4432.4 4536.6 4640.7 4744.9 4845.0 4953.2 5057.3 5161.4 5265.6
(res. (res. 500) 400) correc- correction tion factorC factord 1.14 1.24 1.36 1.48 1.62 1.76 1.84 1.85 1.87 1.79 1.70 1.65 1.62 1.60 1.57 1.56 1.56 1.55 1.56 1.54 1.51 1.48 1.46 1.45 1.44 1.43 1.43 1.42 1.42 1.41 1.41 1.39 1.38 1.37 1.36 1.35 1.35 1.34 1.34 1.34 1.34 1.34 1.33 1.32 1.31 1.30 1.30 1.30 1.29 1.29
1.14 1.24 1.36 1.48 1.62 1.76 1.93 2.10 2.14 2.15 1.98 1.88 1.82 1.78 1.76 1.75 1.75 1.74 1.74 1.74 1.70 1.66 1.63 1.61 1.59 1.58 1.57 1.56 1.56 1.56 1.56 1.54 1.52 1.50 1.49 1.48 1.47 1.46 1.46 1.4 5 1.45 1.45 1.44 1.43 1.42 1.41 1.40 1.39 1.39 1.39
batch 61004 LC 0.71 4.76 7.33 8.86 9.81 9.67 9.29 9.43 9.33 8.48 7.19 5.57 4.00 2.62 1.57 0.86 0.38 0.14
batch 61004 311A 0.12 0.95 4.10 6.84 10.1
14.7 16.6 13.8 12.2 9.26 5.24 2.02 1.94 1.09 0.50 0.26 0.10 0.09
batch 61004 MS-50
batch 12a. MS-50
0.04 0.19 2.31 4.36 6.86 10.9 14.0 15.8 14.7 10.9 7.32 5.45 4.00 1.34 1.09 0.48 0.13 0.07 0.03
0.88 2.51 4.46 4.58 5.18 6.02 5.92 6.52 6.49 6.11 5.52 4.74 4.74 4.89 4.47 4.23 3.82 3.19 3.07 2.56 2.41 1.68 1.32 1.12 1.04 0.90 0.85 0.52 0.25
batch llb m5-50
0.46 1.29 1.42 2.35 2.66 2.90 2.77 2.36 2.70 3.02 3.66 3.80 3.13 3.39 3.00 3.32 3.36 2.80 3.22 2.56 2.55 2.86 3.86 3.75 3.93 3.09 3.00 3.16 3.26 2.85 2.57 2.35 2.07 1.37 1.37
0.82 0.72 0.53 0.64 0.51 0.44 0.11
941 928 1690 2890 1011 1940 3230 1018 1.09 1.15 1.12 1.18 1.08 MwlMn a Nominal mass spectrometric molecular weight ( C = 12, H = 1). Number average accurate molecular weight for an oligomer isotopic cluster (determined by HIM AS computer program). Correction factor determined by HIMAS computer program ( M I A M = 4 0 0 for Varian MAT 311A). Correction factor ( M I A M = 500 for Kratos MS-50).
Mn
M w -
= 1.12) is in good agreement with the value reported by the manufacturer (11.10). In summary we have shown t h a t field desorption mass spectroscopy can be used to determine molecular weight averages for polystyrene t h a t agree reasonably well with data obtained by conventional techniques. It should be noted in this regard t h a t the molecular weight averages reported by the manufacturer (Table I) seem to be internally inconsistent in some respects. T h a t is, if one makes the approximation t h a t MV MW, the calculated M v / M nratio is too large compared to the M w / M nratio estimated by kinetic/GPC considerations (Table I). For example, in batch 12a (&fv = 2200
855
1010
and A,, = 1710) the M v / M nratio is 1.29, while the reported Mw/Mnratio is 11.10. From theoretical considerations (13), however, Mw cannot be less than Mv. We do not know how to resolve this inconsistency, but we have chosen in our discussion to compare the FDMS molecular weight parameters to the A?, and M w / M nvalues reported by the manufacturer.
CONCLUSION It is clear that good molecular weight averages (Mnand Mw) were obtained by FDMS for the polystyrene standards. This indicates that the relative intensities of the FDMS oligomer molecular ions (with appropriate corrections for isotopic
Anal. Chem. 1980, 52, 1811-1814
abundances) can be used directly to obtain reasonably accurate relative molar concentrations of the oligomers. T h e FDMS method is particularly appealing since it provides a means for direct determination of Mnand Mw It is to be expected t h a t other "good desorbing" polymer systems can also be characterized in this manner. Polymers containing highly polar groups would likely yield less accurate results (due to poor desorption characteristics). T h e results for polystyrene are quite encouraging and serve to demonstrate the potential of higher mass field desorption analysis of polymers.
ACKNOWLEDGMENT T h e support a n d encouragement of J. B. Pausch (The BFGoodrich Co.) and C. C. Fenselau and R. J. Cotter (The J o h n s Hopkins University) are greatly appreciated. J. D. Wenrick (The BFGoodrich Co.) gave helpful suggestions regarding t h e computer programs. R. E. Harris ( T h e BFGoodrich Co.) assisted with the mass spectroscopy (Varian M A T 311A).
LITERATURE CITED (1) Beckey, H. D. "Principles of Field Ionization and Field Desorption Mass Spectrometry"; Pergamon Press: New York. 1977. (2) Schulten. H.-R. Adv. Mass Spectrom. 1977, 7 , 83-96.
181 1
(3) Schulten, Methods Biochem. Anal. 1977, 2 4 , 313-448. (4) Mead, W. L. Anal. Chem. 1968, 40, 743-747. (5) Wiley, R. H.; Cook, J. C., Jr. J . Macrornol. Sci., Chem. 1976, A10, 8 11-814. (6) Wiley, R. H . Macromol. Rev. 1979, 14, 379-417. (7) Lattimer, R. P.; Welch, K. R.; Pausch, J. 13.; Rapp, U. Varian MAT 31 1A Application Note No. 27; Varian MAT Mass Spectrometry, Florham Park, NJ, 1978. (8) Lattimer, R. P.; Harmon, D. J.; Welch, K. R. Anal. Chem. 1979, 51, 1293-1296. (9) Matsuo, T.; Matsuda, H.; Katakuse, 1. Anal. Chem. 1979, 57, 1329- 133 1, (10) Lattimer, R. P.; Welch. K. R. Rubber Chem. Technol. 1978. 51, 925-939. (11) Lattimer, R. P.; Welch, K. R. Rubber Chem. Technol. 1980, 53. 151-159. (12) Altares, T., Jr.; Wymon, D. P.; Alien, V. R . J . Polym. Sci., PartA 1964, 2 . 4533-4544. (13) Flory, P J. "Principles of Polymer Chemistry"; Cornell University Press: Ithaca. NY: ChaDter 7. (14) Matsuo, T.; Matsuda, H.: Katakuse, I. A17al. Chem. 1979, 51, 69-72. (15) Daly. N. R.; McCormick, A,; Powell, R. E. Rev. Sci. Instrum. 1966, 39, 1163-1167. (16) Daly, N. R.; McCormick, A.; Powell, R. E.; Hayes, R. Int. J . Mass Spectrom. Ion Phys. 1973, 11, 255-276.
RECEIVED for review April 8, 1980. Accepted July 7 , 1980. Appreciation is expressed to The BFGoodrich Co. and t o the National Science Foundation for support of this work.
Isotope Ratio Measurements of Urinary Calcium with a Thermal Ionization Probe in a Quadrupole Mass Spectrometer Alfred L. Yergey,' Nancy E. Vieira, and James W. Hansen Intramural Research Program and Neonatal and Pediatric Medicine Branch, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20205
A thermal ionization mass spectrometric technique using standard quadrupole instrwnentation and a special solids probe has been developed for the measurement of calcium isotope ratios in biological samples. Calcium is coated onto disposable rhenium filaments from an acidic solution after being isolated from urine by precipitation with basic oxalate. Isotope ratios of natural abundance standards were measured with an average accuracy of about 1 % ; urinary calcium concentrations were determined using an isotope dilution technique which gave results that differed by less than 10 % from values determined by two independent methods; overall reproducibility of isotope ratio measurements was about 1 % standard deviation. The method uses standard quadrupole instrumentation.
T h e rates of calcium flux across gastrointestinal and renal barriers along with interchange between soft tissue and skeletal compartments axe of great importance in the study of calcium homeostasis and skeletal development. Such rates can be readily determined in vivo by measuring the time dependent changes in the specific activity of radioactive tracers ( I , 2 ) . When newborns and children are the subjects of such investigations, however, it is both desirable and necessary to use nonradioactive tracers. Recent work with stable calcium tracers in newborns has shown ( 3 )that, measuring the atom percent enrichment of two isotopes increases the precision of determining kinetic parameters compared to the use of a single tracer. These determinations of specific activity have been
made by measuring isotope ratios using thermal ionization mass spectrometry. The thermal ionization technique has been used to measure calcium isotope ratios with relative accuracies of better than 0.05% with relative precisions of less than 0.01% standard deviation ( 4 , 5 ) . T h e mass spectrometers for such measurements are specially designed for the task. Typical measurements involve elapsed times of several hours per sample and generally require breaking vacuum between samples to change filaments. Isotope ratio measurements of the high quality provided by such thermal ionization mass spectrometry tend to be more accurate than necessary for biological samples. In this paper we report t h e development of a satisfactorily accurate, rapid method of measuring calcium isotope ratios using a thermal ionization method in a standard quadrupole mass spectrometer with a specially designed solids probe. We report very reproducible measurements t h a t are of acceptable accuracy for t h e systems studied, but which require less time per sample and use more generally available instrumentation t h a n do typical thermal ionization methods.
EXPERIMENTAL Mass Spectrometer. A Finnigan Mdel4OOO quadrupole was used as supplied by the manufacturer with one exception. For convenience the multiple-turn diaphragm type solids inlet valve was replaced with a CON-VAC quarter-turn butterfly type valve manufactured by Consolidated Instruments, 7541 Belair Road, Baltimore, Md. 21236. Solids Probe and Disposable Filaments. The solids probe designed for this work is shown schematically in Figure 1. The
This article not subject to U.S. Copyright. Published 1980 by the American Chemical Society
