Anal. Chem. l903, 55, 367-372
at constant [U02]Tto [H+]-2. These relationships are not those reflected in the data in Figures 2 and 3. Perhaps the actinyl is extracted as an ion pair-e.g., U02C104+or UOzC1+-into the membrane since the concentration of the ion pair in such a situation would be directly proportional to [An022+],, and the electrode would respond with a slope of approximately 57 mV. The selectivity to Mt, M+2,and M+3 ions is good. For example, when Sm(III);[AnOz2+]= 10, the AE term in eq 3 will be less than 6 mV for [UO?+] = 10" M and less than 1.5 mV for [UOz2+]= M. Figure 5 confirms the sensitivity to An022+ concentration even in the presence of 10-fold greater Sm(II1) concentrations. Similarly, we see that response to AnOZ2+concentrations is good in the presence of An02+ concentrations as much as 100 times that of AnOz2+. An4' species interfere more severely such that [An0,2+1:[An4+]must be 21 for useful operation of the CWE to monitor changes in [AnOZ2+]. The "effective" charge of the uranium atom in UO?+ is about +3.3 (IO). Since the DTDD membrane responds s e lectively to UOz2+compared to Sm3+and has roughly equal sensitivity to Th4+,the rnetal charge density alone does not explain the selectivity. A possible explanation lies in the structure of the actinyl cations, O=An=O. A neutral-carrier ligand functions by coordination to a metal cation. In the process, the metal is stripped of its hydration sheath and rendered soluble in the olrganic matrix of the membrane. It is plausible that the special affinity of the actinyl cations for the membrane lies in the fact that these cations have fewer water molecules in their primary coordination sphere due to the covalently bound oxygens. Hence, they are easier to dehydrate. Such an explanation is supported by construction of models of DTDD, which show that only one carbonyl and two ether oxygens can coordinate simultaneously to a metal ion. This leaves the metal axial sites relatively unobstructed. Therefore, it seems that DTDD would not remove water from the axial sites of a chelated metal, which would decrease its solubility in the membrane. However, the actinyl cations lack waters and, therefore, theiir DTDD complex is less hydrophilic.
367
Obviously, charge density also plays a role since Np02+,also an O=An=O structure, interacts poorly with the membrane while the simple tetrapositive Th4+provides the most severe interference to response to AnOzZ+.Although Th4+interferes, the electrodes show little dependence of EMF on [Th4'] (see Figure 4) so the mechanism of the interference is not related simply to Th4+incorporation in the DTDD membrane. The DTDD-CWE should be useful in redox studies of An(VI)/An(V) couples and, to a more limited extent, of An(VI)/An(IV) couples. It can also be used to study complexation of AnO?+ species since it responds to the concentration of "free" AnOzz+and not the total concentration. The range of AnOzz+concentrations to which the electrode responds satisfactorily is sufficient for many purposes. Unfortunately, the useful p H range is a limitation as it excludes the use of the electrode in acid systems used in many separations. Registry No. DTDD, 69844-41-3;Th, 7440-29-1;U, 7440-61-1; Np, 7439-99-8;Pu, 7440-07-5.
LITERATURE CITED (1) Manning, D. L.; Stokely, J. R.; Magouyrk, D. W. Anal. Chem. 1974, 46, 1116. (2) Goidberg, I.; Meyerstein, D. Anal. Chem. 1980, 52, 2105. (3) Senkyr, J.; Ammann, D.; Meier, P. C.; Mod, W. E.; Pretsch, E.; Simon, W. Anal. Chem. 1979, 5 1 , 786. (4) Frieser, H. "Ion-Selective Electrodes in Analytical Chemistry"; Freiser, H., Ed.; Plenum: New York, 1960; Vol. 2, Chapter 2. (5) Martin, C. R.; Frelser, H. J . Chem. €doc. 1980, 57, 512. (6) Caceci, M., submitted for publication in J . Chem . Educ (7) Moody, G. J.; Thomas, J. D. R. "Selective Ion Sensitive Electrodes"; Merrow: England, 1971. (8) Miyake, C.; Nurnberg, H. W. J . Inorg. Nucl. Chem. 1967, 29, 2411. (9) Baes. C. F.; Mesmer, R. E. "The Hydrolysis of Cations"; Wiiey: New York. 1976: D 181. (10) Choppln, G: A,; Unrein, P. J. "Transpiutonium Elements"; Muller, W., Lindner, R., Eds.; North-Holland: Amsterdam, 1976; p 97.
.
RECEIVE^ for review September 13,1982. Accepted November 9, 1982. This research was supported by contracts from the Offices of Basic Energy Sciences and of Health and Environmental Research of the U.S.D.O.E. L.F.R. is on leave from the Radiochemistry Laboratory, Institute of Atomic Energy, Beijing, P.R.C.
Isotopic Patterns of Fragment Ions from Dissociation of Mass-Selected Ions James C. Tou Analytical Laboratories, Michigan Division, The Do w Chemical Company, Midland, Michigan 48640
A mathematical approach is developed for the calculatlon of the lsotoplc patterns of fragment Ions from dissoclation of mass-selected Ions contalnlng two elements, each of whlch consists of two naturally occurring Isotopes. The equatlons derlved are applied to the cases of ions contalnlng up to six chiorlne and/or bromine atoms. The calculated patterns are utlilred in the analysis of several coillsional activation mass spectra.
The unique mass spectral patterns due to naturally occurring isotopes of elements have long been utilized by mass spectroscopists for identification of the type and the number of atoms present in a molecule ( I ) . In mass spectrometry/ mass spectrometry (MS/MS) analysis ( 2 , 3 ) ,a mass-selected ion containing statistically distributed isotopes is subjected to collision with neutrals and a new isotopic pattern is expected to appear in the resiulting collisional activation (CA) 0003-2700/63/0355-0367$0 1.50/0
mass spectrum of the mass-selected ion due to a statistical loss of isotopic atom(s) contained in the fragment which is lost during the dissociation process. This has been reported recently (4, 5). The above new isotopic patterns are also expected to be shown in the mass spectra of the fragment ions arising from unimolecular ion decomposition (metastable ion transition) and photodissociation of mass-selected ions (6). In this paper, a mathematical approach is developed for the calculation of the isotopic patterns of the daughter ions from parent ions containing two elements, each of which consists of two naturally occurring isotopes. The equations derived are applied to the cases of ions containing up to six chlorine and/or bromine atoms.
MATHEMATICAL FORMULA The calculations are based on the parent ions containing two types of elements, each of which has two isotopes with 0 1963 American Chemical Society
368
ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
2 daltons difference between them. They are designated as A, A' and B, B' with natural abundances a, a' and b, b', respectively. The parent ions contain n atoms of A-type element and m atoms of B-type element, which are statistically distributed in various groups in the ion. As a representative case, the statistical loss of one and two atoms from the parent ion, [p + 6]+, is formulated, where p is the monoisotopic parent ion containing nA and mB. The four possible parent ions, [p + 6]+, due to different combinations of A and B types of elements and their associated probabilities are listed in Table
Table I possibilities [ P + 61+ AnA'Bm An.,A2'Bm.,B' A,. A B., B,' AnBm.,B,'
1 2 3 4 a
probabilitiesa nC3an-3a' 'bm ,,C, mC,an-za'zbm-lb' .C I C, an- a' bm-'b' ' c anbm-3b'3 m 3
.C,, .C,, etc. are the binomial coefficients.
I.
Table I1 daughter ions composition
probabilities
expected daughter ions
[ P + 61'
loss
1
A A'
[D t 2]+ D+
2
A A'
D+
3
A A'
[ D + 2]+ D+
4
A
[D
.C, mC3anbm-3b'3
[D
+
+
21'
2]+
Table I11 daughter ions [P + 61+
loss
1
2A AA 2A'
2
composition
probabilities n-3C2
f
n.3Cl 3C1 nC3an-3a'3bm
3C2
2A AA' 2A
nC3
1
n-2C2
2 c 2
1
n-ici
4
2A
,C, mC3a'1bm-3b'3
[P + 61'
loss
composition
1
AB
AnA'3Bm-i
n.3C, ,C,
AB
An-3A1?Bm-1
3 1'
AB AB AB' A' B'
AB' A' B'
A,.,A',B,.,B' A,.,A'B,.,B' An-3A'zBm.i A,.,ABm., A,.,A'B,.,B', An-iBm-3B12 A,.,A'B,.,B' An.lBm.,B'
AB AB'
An.iBm-4B13 A n . iBm-3B'z
n.lC,
ici
[D + 4]+ [D + 2]+ D+
[ D + 41+
,,.,C, ,C1 ,,C2 mClan-2a'Zbm-1b'
2A AA
3
expected mass of the daughter ions
.C
C2an'1a'bm-2brz
[ D + 2]+ D+ [D + 4]+ [ D t 21' [ D + 4]t
Table IV daughter ions
2
3
AB
A'B
4
probabilities mci
}
nC3an-3a'3bm
n-2C1 m - i C l 2C1
m.lC1
m2Ci
,$,
expected mass of the daughter ions [ D t 4]+ [D + 21' [D
+
4]+
[D
+
21'
C, an-2a'2bm-1 b'
IC1
D+ [ D + 4]+
ZCl IC,
.c1 , ~ , ~ n - i & b m - z b z [ D + 2l+ G'
nci
3Ci
[ D + 4]+ [ D + 21'
ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
369
Table V. The Equations for Calculating the Isotopic Abundances of the Daughter Ions from the Parent Ion Containing nA Type and mB Type of Isotopic Atomsa Loss of One A Type of Isotopic Atoms zI(D
parent ions
+ 2)’
>:ID+
P+
O(n>l,m+n>l) ( n -- 1)a‘b + mab’ (n>l,m+n>l) a’b ( n - l ) ( n - 2)a”b’ + 2m(n - 1)aa‘bb’ + m ( m - 1)a’b’‘ ( n > 1, m 2a’b[(n- 1)u‘b + mab’] eql(n> 1,tn+n>3)
[ P + 2l+ [P + 41+ [ P + GI+
+ n > 2)
Loss of Two A Type of Isotopic Atoms C I [ D + 2]+and “ [ D
parent ions
+ 21’
C ID+
C ID+
P+ ~ I F +D2 ~ + -( n - 2)a’b + mab’ (,n> 2, m C ID+ 2a’b
[ P + 21+
C I [ D + 41+ -
( n - 2)(n - 3)a“b’
2)
+ 2(n - 2)maa‘bb’ + m ( m - l)azb” %‘bZ
C IDt
eq 2 and 3 ( n b 2, m
[P + 61’
+nb
$.
( n > 2,m t n > 2)
n > 2)
Loss of One of Each of the A and B Types of Isotopic Atoms C I [ D+ 21+ and c I,+
parent ions
CIID
+ 41+
BID+
P’
+ 21’
( n - 1)a‘b i( m - ].)ab‘ (n, m > 1) a’b t ab’ zJID+ 21+ - ( n - l)a”b2 + ( n + m - 2)aa’bb’ + ( m - l)u2b‘2 (n>l,m+n>2) 2 ID+ adbb‘ z I l D+ 41+ = ( n - l ) ( n- 2 ) ~ ’ ~ bt’ 2(n - l ) ( m - 1)aa’bb’ + ( m - l ) ( m - 2)a’b’’ CI[D
[P t 21+
Z ID+
-_
-
[P + 41’
2aa’ b b’
L: ID+
1)
eq 4 and 5 ( n , m > 1, m t n > 3 )
[P + 61+ a
(n,m
a, a‘ and b, b‘ are the relative abundances of the isotopic atoms A, A’ and B, B‘ with 2 daltons difference, respectively.
The possibilities for loss of one of the A-type elements from each of the above [p + 6]+ ions and the compositions of the resulting daughter ions and the associated probabilities are given in Table 11, where) D+ is the lowest mass daughter ion with the expected statistical composition. Therefore the relative abundance XIrD+ z ] + / c I D + , of the daughter ion [D + 2]+ to the daughter lions D+ can be computed from the probabilities of Table I1
+
= [ ( n l ) ( n- 2 ) ( n - 3)a’3b3 3(n l ) ( n- 2 ) m ~ a ’ ~ b +3(n ~ b ‘ - l ) m ( m- 1) x u2u’bb’2 + m(m - l ) ( m - 2)a3b5]/[3a’b[(n- 1) X
cI[D+2]+/cID+
-’
(n- 2 ) ~ ’ + ~ 2b ( ~n - l)maa’bb’+ m(m - l)a2b’2]] ( 1 ) Similarly, the possibilities for loss of two of the A-type elements, and the compositions of the resulting daughter ions and the associated probabilities can be derived as shown in Table 111. The relative abundances of the daughter ions, D+, [D + 2]+, and [D + 4]+are formulated from the probabilities in Table I11
+
If the [p 6]+ parent ions lost one of each type of the isotopic atoms, the compositions of the resulting daughter ions and the associated probabilities can also be derived in a similar manner (Table IV). The relative abundances of the daughter ions are
370
ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
IO11 Of
one
ci stom
P P+2 Pi4
Pi6
31s
(11 two
ci atom3
-
P Pi? Pi4 Pi6
1
2
3
4
5
1
2
3
Flgure 1. The calculated isotopic patterns of the daughter ions generated by losses of groups containing one or two chlorine atoms from the parent Ions containing CI, Br,
.
101s of one Br stom P
P*2
Pi4
Pi6
DI
of two 6r atom
loss O f two B i atoms
P
Pt2
P
Pi4
Pi1
Pi2
Pt4
Flgure 3. The calculated Isotopic patterns of the daughter ions generated by losses of groups contalning one chlorine atom and one bromlne atom from the parent ions containing CI, Br, .
Pi6
i Loss of one CI atom
Loss of on0 Br atom
I
Loss of one CI and one Br atoms
Flgure 2. The calculated isotopic patterns of the daughter ions generated by losses of groups containing one or two bromine atoms from the parent ions containing CI, Br, .
I
CI[D+4]+ -- [ ( n- l ) ( n - 2)(n- 3)a’3b3 + 3 ( n - 1) x
Ch+4
( n - 2 ) ( m- l)au’2b2b’+ 3 ( n - l)(m - l ) ( m 2)a%’bb’2 + ( m - l ) ( m- 2) x ( m - 3 ) ~ ~ b ’ ~ ] / [ 6 ~ ~ ’-blb)q~ (+ n% ( m- l ) a b q ] ( 5 )
Flgure 4. The overall isotopic patterns, of the daughter ions from the parent ions containing CI,Br, by losing a group containing one chlorine atom, one bromine atom, or one chlorine and one bromine atom.
ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
Loss of‘ One Isotopic Atom
-
[P +
2 L
C ID+
P+ [P + 21+ [ P + 41+ [P
0
ET[D + 21’ -
parent ions
3
100-
Table VI, The Equatbns for Calculating the Isotopic Abundances of the Daughter Spectrum from a Parent Ion Contains r Isotopbc Atoms with Two Naturally Occurring Isotopes with 2 Daltons Differences
-
50T
I
O ( r 2 1) r - l ( r 2 1) r- 2 2 ( r 2 2) eq 6 ( r 2 3)
L
-
GI+
160
t t Loss of Two kotopic Atoms
-
EI[D
I;I[D + 4It -~
+ 21+
~ c ID+ - -
P+
0 (r 2) r-2 -(r> 2) 2
[P
21’
[P + 41+
I 120
0 40
60
80 100
E ID+
2(r -- 2 ) ( r > 2 )
iao
200 220
- m/z+
%I+
parent ions
371
201
A
160 tao 200 220
- m/z+
0
Flgure 6. The CA mass spectra of the [M bromo-3-chloropropane.
0
k21(r - 3)
- GI]
ions from 1,2-di-
For loss of one isotopic atom, eq 1 can be reduced to
2
cI[D+Z]+- -r - 3 --
CID+
3
(6)
For loss of two isotopic atoms, both eq 2 and 3 and eq 4 and 5 can be simplified to
CI[D+Z]’ --r-3 CID+
C I I D +-~ I(r+- 3)(r - 4) -CID+
6
(7)
(8)
respectively. The equations derived in similar manner for p+, [p + 2]+, [p 4]+ etc. are summarized in Table V and the simplified forms for the cases of the parent ions containing r isotopic atoms of one type are summarized in Table VI.
+
RESULTS AND DISCUSSION
-d2+
Flgure 5. The CA mass spectrum of the molecular ion, [p 2,5,2’-trlchloroblphenyl.
+ 2]+,of
When the A and B type;s of elements are identical, Le., a = b and a’ = b’, the parent ions therefore contain r isotopic atoms of one type, where r = m n.
+
The above derived equations are applied to the parent ions, p+, [p + 2]+, [P + 4]+,and [p + 6]+, containing chlorine and bromine atoms up to n + m = 6. Shown in Figures 1-3 are the calculated isotopic patterns of the daughter ions formed from the parent ions by losing a group consisting of up to two chlorine or bromine atoms or one chlorine atom and one bromine atom. Since the parent ions also exhibit their own isotopic pattern, the true isotopic abundances of the daughter ions from different parent ions, p+, [p + 2]+, etc. can be computed by convoluting the above calculated isotopic abundances over the parent ions’ isotopic abundances. This is accomplished by normalizing the probability intensity of the daughter ion obtained previously against the probabilty intensity of the parent ion, p+, which is anbm. Shown in Figure 4 are the overall isotopic abundances of the daughter ions from the parent ions containing C13Br2by losing a group containing one chlorine atom, one bromine
Anal. Chem. 1983, 55,372-373
372
atom, or one chlorine and one bromine atom. It is noted that the most abundant parent ion is [p 4]+ whereas the most abundant daughter ions are the daughter ions from the parent ion, [ p + 21') in the cases of one chlorine atom and one bromine atom loss. Shown in Figure 5 is the CA spectrum of the molecular ion, [p 2]+, of 2,5,2'-trichlorobiphenyl,which exhibits loss of one and two chlorine atoms in the generation of the two doublets a t m / z 223, 221, 187, and 186. The isotopic abundances of the daughter ions are similar to the calculated ones shown in Figure 1, where n = 3, m = 0. The isobutane chemical ionization mass spectrum of 1,2dibromo-3-chloropropane shows that the [M - C1]+ ions are the highest mass ions and the CA spectra of the [M - C1]+ ions are shown in Figure 6. The CA mass spectrum of the monoisotopic parent ion, p+, a t m / z 199 shows three singlet daughter ions at m / z 119,93, and 39 which are generated by the losses of HBr, C9H2Br,and 2HBr from the parent ion, respectively. The similar daughter ions from the parent ion,
+
+
[p + 2]+, are expected to show two doublets and one singlet from Figure 2 where n = 0, m = 2. This expectation is confirmed experimentally as shown in Figure 6. Registry No. 2,5,2'-Trichlorobiphenyl,37680-65-2; 1,2-dibromo-3-chloropropane, 96-12-8.
LITERATURE CITED (1) Beynon, J. H. "Mass Spectrometry and Its Applications to Organic
Chemistry"; Eisvier: New York, 1960.
(2) Kondrat R. W.; Cooks R. G. Anal. Chem. 1978, 50,81A-92A, and
references therein. (3) McLafferty F. W. Acc. Chem. Res. 1980, 13, 33-39, and references therein. (4) Todd P. J.; Barbaias M. P.; McLafferty F. W. Org. Mass Specfrom. 1982, 17, 70-80. (5) Tou J. C.; Zakett D.; Caldecourt V. I n "The MS/MS Applications to Chemical Problems In Tandem Mass spectrometry"; McLafferty F. W., Ed.; Wiiey: New York, in press. (6) Mukhtar E. S.;Griffiths I . W.; Harris F. W.; Beynon J. H. Int. J . Mass Spectrom. Ion Phys. 1981, 3 7 , 159-166.
RECEIVEDfor review July 9,1982. Accepted November 1,1982.
CORRESPONDENCE Exchange of Comments on the Measurement of Aerosol Transport Efficiencies in Atomic Spectrometry Sir: Recently, Smith and Browner (1)have reported on the measurement of aerosol transport efficiences in some nebulizer-chamber assemblies. Of the three direct methods used with ICP systems the cascade impactor and the membrane filter technique gave mutually consistent results (1.4%), but the silica gel technique yielded a much higher value (5.3%). On this basis Smith and Browner rejected the silica gel data and analyzed possible causes for systematic errors with this technique. Since the silica gel technique was taken from one or our earlier publications ( 2 ) )we feel compelled to comment on Smith and Browner's conclusions, the more so, since the efficiences we measured with the silica gel technique for a similar nebulizer-chamber system ( 2 )were in the range expected for ICP systems (1-1.4%) and agree with the lower data of Smith and Browner. In adapting the silica gel technique to their systems, Smith and Browner made a major change to our design. Instead of measuring in the normal operation practice of the ICP (Le., with an argon flow of 1 L/min) an additional air flow of 2 L/min is pumped through the silica gel adsorption tube, probably to improve the resemblance between the silica gel technique and the other two techniques. However, the silica gel collects solvent, whereas the cascade impactor and the membrane filter collect solute. Obviously, the auxiliary air flow influences the two collection processes in a different way and, indeed, Smith and Browner argue that 60% humidity of the air (15 mg/L) might explain a major part of the observed deviation (30 mg/min out of 39 mg/min). This could have been verified with a blank run, but although a "high" blank is reported, this observation is not quantified. Experiments in our laboratory indicated a substantially lower value for laboratory air, 10 mg/L air, but this can easily be explained by a climatical difference between Smith and Browner's laboratory and our laboratory. Whatever the value, it is clear that this systematic error occurs only when addi-
tional air is pumped through and, hence, could not have faulted our results. This conclusion does not apply for the second source of systematic error advanced by Smith and Browner. A possible saturation of carrier gas argon with water might invalidate all silica gel data if the water arose from the wet walls rather than from the sample spray. At a room temperature of 20 OC the contribution would be 20 mg/L argon. The first question to answer is whether an argon flow of 1L/min can become saturated with water by a single passage through a wet Scott chamber. The general expression of mass transfer inside a tube with a constant wall concentration is $ = kA (c,~I - E)
(1)
where q5 is the mass flow (g/s), k the coefficient of mass transfer (m/s), A the wall surface (m2),c,d the constant water concentration at the wall (20 mg/L at 20 "C), and the mean concentration in the tube. For the coefficient k handbooks on technology (3) yield the following expression for laminar flow in relatively wide tubes, which reflects the present situation
k = 1.62(~D~/clL)~/~
(2)
where u is the gas velocity (m/s), D is the diffusion coefficient (m2/s),and d and L are the tube diameter and length (m), respectively. If we consider the Scott chamber as a system of two tubes with a length of 10 cm and a width of 1 cm and 4 cm, respectively, we find for an argon flow of 1L/min and a diffusion coefficient of 0.2 cm2/s that k is equal to 0.18 cm/s for the wide tube and 0.70 cm/s for the narrow tube. Substitution of these data in eq 1shows that after passage through the chamber the water content of argon could be raised from 0 to 19 mg/L. In agreement with this estimate, measurement of the water concentration of dry argon passed through a wet Scott chamber yielded a value of 15 mg/L with the silica gel
0003-2700/63/0355-0372$0 1.50/0 0 1983 American Chemical Society
