Dependence of ion intensity in electrospray mass spectrometry on the

Anal. Chem. 1999, 65, 3654-3668

9854

Dependence of Ion Intensity in Electrospray Mass Spectrometry on the Concentration of the Analytes in the Electrosprayed Solution Liang Tang and Paul Kebarle' Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2

The dependence of the mass-analyzedion intensity 1.4 and IB of analytes A+ and B+, whose concentration in the electrosprayed methanol solution was [A+]and [B+], was determined in a series of experiments and for a variety of concentrations. A proposed equation relating IAand IBto [A+]and [B+] (see eq 4) was found to provide useful predictions. Coefficients k for the ions Li+,Na+, K+,Cs+,and NH4+and several protonated alkaloids, (ethyl)aN+,(m-propyl)~N+, (n-butyl)dN+,m-C.IHl6NH3+,and ~ - C ~ ~ H Z ~ N were H Sobtained. +, The values of the coefficients are compared with predictions of the Iribarneionevaporationtheory. Rates of solvent loss from the droplets and the fission of the droplets due to Rayleigh instability are also included in the analysis. It is concluded that the observed coefficients k depend on the surface activities of the analytes when [A+]and [B+]are in the range 10-*-5 X lo* mol/L and on the ion evaporation rate constants and surface activities for [A+]and [B+]in the range 6 X 10-6-10-2 mol/L. The ion evaporation rates predicted by the Iribarne equation are found just barely consistent with the experimental coefficients. Alternate methods for gas-phase ion production are also considered.

INTRODUCT10N Electrospray mass spectrometry (ESMS),whose extraordinary potential was evident from ita introduction,'-' is experiencing rapid development with demonstrated applications that surpass even the most optimistic forecasts. ES has ushered a new era in the application of mass spectrometry to the analysis of compounds of biological intere~t.~?"~ The exciting applications of the techniquehave also created a great interest in the mechanism by which the gas-phase ions required for the mass spectrometric analysis are produced. On the basis of previous work@-14 it has become clear that electrospray is a method by which ions present in solution, (1) Yamashita, M.; Fenn, J. B. J.Phys. Chem. 1984,88,4451; 1984,

-- - .

RR --, &71.

(2) Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Science 1989,246,64. (3) Covey, T. R.; Bonner, R. F.; Shushan, B. I.; Henion, J. Rapid Commun. Mass Spectrom. 1988,2, 249. (4) Smith, R. D.; Olivares, J. A., Nguyen, N. T.; Udseth, H. R. Awl. Chem. 1988,60,436. ( 6 ) Mirza, A. U.; Cohen, S. L.; Chait, B. T. Anal. Chem. 1993,65, 1. (6) Winger, B. E.; Light-Wahl, K. J.; Rockwood, A. L.; Smith, R. D. J. Am. Chem. Soc. 1992,114,5897. (7) Ben, S. C.; Senko, M. W.; Quinn, J. P.; Wampler,F. M., McLafferty, F. W. J. Am. Chem. SOC.Mass Spectrom., in press. (8) Bailey, A. G. Electrostatic Spraying of Liquids; John Wiley and Sons: New York, 1988. 0003-2700/93/0365-3654$04.00/0

i.e., ions due to an electrolyte, are transferred to the gas phase. The presence of the very high electric field at the capillary tip leads to a partial separation of positive from negative ions present in the solution. For convenience in all subsequent discussions, we will assume that the capillary is of positive polarity. At this polarity, the liquid near the surface, meniscus, becomes enriched in positive ions. The effect of the field on this positive charge leads to a destabilization of the meniscus, the formation of a liquid cone, and the emission of charged dropleta whose charge is due to an excess of positive electrolyte ions over the negative counterions. The negative ions remaining in the solution are either electrolytically discharged on the wall of the capillary or electrolytically provided by positive counterions by formation of positive ions from the capillary wall. Therefore, the electrospray process can be likened to an electrolysis cell of a special kind where oxidationoccurs at the capillary anode and the positive current is carried away by the charged dr0p1eta.l~ In the present work we will examine how the analyte ion signal detected with the mass spectrometer depends on the concentration of the analyte ion in the solution and also how this signal is affected by the presence of other electrolytes. Other electrolytesare practically always present aa impurities in the solvent, as other coanalytes, and particularly aa buffers required in the reversed-phase chromatographicseparation or capillary electrophoresis. The ions in the gas phase are due to the excess charges on the dropleta. Therefore, the currentlleaving the ES capillary is a measure of the rate at which excess positive electrolyte ions leave the capillary. This current is easily measured and is found to depend on the conductivity a of the solution.15 There is a minimum (threshold) conductivity below which there is no ES. The threshold occurs a c le7Wlcm (methanol)13which corresponds to a concentration of 10-e M of electrolytes such as NaCl or NH4C1,15J6 As the conductivity is increased above this value, the current Zleaving the capillary increases and becomes stable. Z is only a very weak function of the conductivity:11J3Jb

-

Z = Ha" n c 0.24.3 (1) H i s a constant which can be determined experimentally. A derivation of eq 1in whichH is given a functional dependence on experimental parameters such as field at the tip, radius of the capillary, surface tension of the solvent, flow rate, etc., (9) Hayati, I.,Bailey, A. I.; Tadros, T. F.J. ColloidInterface Sei. 1987, 11 7, 205, 202. (10) Smith, D. P. H. ZEEE Tram. Znd. Appl. 1986,ZA-22,527. (11) Pfeifer, R. J.; Hendricks, C. D. AZAA J. 1968, 6, 496. (12) Ikonomou, M. G.; Blades, A. T.; Kebarle, P. Anal. Chem. 1990,

62, 957. (13) Ikonomou, M. G.; Blades, A. T.; Kebarle, P. Anal. Chem. 1991, 63, 1989. (14) Blades, A. T.; Ikonomou, M. G.; Kebarle, P. Anal. Chem. 1991, 63, 2109. 116) Tang, L.; Kebarle, P. Anal. Chem. 1991,63,2709. (16) Sunner, J.; Nicol, G.; Kebarle, P. Anal. Chem. 1988, 60, 1300. 0 1993 Amerlcan Chemlcal Society

ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993

has been obtained,ll however, the validity of the derivation

9651

i n '1

I

is questionable. When strong electrolytes are used at concentrations not exceeding le2M, the conductivity u follows the relationship u = X,OC (2) where C is the concentration of the electrolyte and X, is the limiting molar conductivity of the given electrolyte. Therefore, the current I depends both on the concentration and on nature of the electr01yte.l~

I-

.OOl-I 0

"

"

I

100

"

"

t

200

.

"

'

C

300

"

'

.

I

400

mlz

I = Hun= Hko"Cn

n 0.2-0.3 (3) However, the changes of Xm from one electrolyte to the other are generally not large, and therefore, due to the small value of n in eq 1, in practice, the changes of Z with the nature of electrolyte are very small. Equation 1 is obeyed over the concentration range C = 10-5-le3 M. At higher concentrations the current levels off and even decreases slowly with concentration.13J5 When two electrolytes such as A+X-and B+Y-are present in the solution, both A+ and B+ ions w i l l be present among the excess positive ions that constitute the charges of the droplets. However, because of the very weak dependence of I on the total electrolyte concentration (see eq 3), addition of BY to AX will not materially increase the current, Le., the totalexcess charge. On the other hand, B+will compete with A+ among the excess charges on the drops. This means that the amount of gas-phase ions A+ produced from the charged droplets will decrease as BY is added to the solution. On the basis of the above consideration, we proposed15the relationship J

Z(A+ms) is the mass spectrometrically detected ion current of A+. p is a constant expressing the efficiency of the mass spectrometer for sampling the gasphase ion current, due to gas-phase ions A+ produced from the charged droplets (see eq 5), and f is the efficiency of conversion of droplet charge togas-phase ions. [A+] and lB+I are the concentrations of the ions in the electrosprayed solution. It is assumed that both p and f are (essentially) independent of the nature of the ions, A+ relative to B+. I(,+ depends on the ratio kdkB and not on the individual values of kA and kg. The ratio expresses a "fractionation" factor in the ES conversion of ions in solution to ions in the gas phase. The nature of the phenomena responsible for that ratio will be considered under Reeults and Discussion. In the previous work15 it was shown that eq 4 provided a good fit of limited,available experimentaldata. It was pointed that an examination involving a much wider variety of AX and BY partners as well as a greater change of relative concentrations of A+ and B+ would be required to establish the range over which eq 4 is applicable. The present work provides such experimental data and an examination of the validity of eq 4. Because the possible choice of concentrations is extremely wide, the comparisons were restricted to three types of experiments: (a) [AX1 was kept constant and [BY] was increased. (b) [AX1 = [BXI were increased simultaneously. (c) [AX] was increased without BY being present. Since the mass analysis was obtained with a quadrupole maas spectrometer and quadrupoles have strongly mass dependent ion transmission, all mass-analyzed ion currents Z (ma) were corrected for the mass-dependent transmission. The method used to obtain the transmission is given in the Experimental Section, which also includes other details about the apparatus and methodology of the measurements.

Flgure 1. Measuredtransmission cwve which provkles correction for -transmiadonofquabupdeused. Themlrwllhhlghest transmission T,, Is ghren the value T,, = 1. Points shown are obtained from ion intensity measurements obtained with atmpherlc pressure ionization wlng a technique described prevlously.lE

The experimental results obtained have significance for the practicing ES mass spectrometrist. For example, they show that the suppression of a desired analyte ion by a buffer does not depent only on the concentration but also on the nature of the buffer. Buffer cations with high coefficients k lead to strong suppression of the analyte and should be avoided. In trying to correlate the observed relative values of the coefficients k with properties of the ionic species, such as surface activity and ion solvation, one has to consider not only models for the escape of gas-phase ions from the charged droplets but also the fission processes through which the very small droplets are formed which lead to ions. The solvent evaporation rates from the droplets are also of great importance. In the treatment presented in the discussion,we have tried to combine all these elements to present a relatively complete account.

EXPERIMENTAL SECTION The instrument used was the SCIEX TAGA 6000E triplequadrupoleatmosphericpressure mass spectrometerfitted with an electrospray interface as described previously.1214 The stainlesssteel electrospraycapillarytip was 0.1-mmi.d. and 0.26m m 0.d. The capillarytip was -4cm from the oppoeing electrode (the interface plate) and at +4.35 kV relative to the interface plate. The solution flow rate was 20 pL/min. Reagent grade methanol from the same bottle was used in all experiments. This methanol has a conductivity of 10-6 W c m , which corresponds to an impurity level of NaCl or NIJICl of -1.3 X 106 M. In previous work, attempts were made to work with completely electrolyte free methanol solvent. It was found that the conductivity of such methanol increased rapidly on storage after purification. In order to obtain reproducible experiments, we chose to work with the reagent grade methanol, which had a constant electrolyte impurity level. Determinations of the mass-dependent transmission were obtained with use of the electric discharge atmosphericpressure ionization (API)mode of the TAGA. The method with which a transmission calibration can be obtained is described in earlier work.I8 More details concerning the present calibration can be obtained from the Ph.D. thesis of L. T.17 The transmission factors, in function of mass to charge ratio m/z are shown in Figure 1. The highest transmissionwas assigned as T m = 1. To correct the observed ion intensities, Im, for maasdependent transmission, one has to divide Iob by Tm for the given mass. Since T, changes by more than a fador of 10 over the mass range that was used, errors in the relative ion intensities are expected to increase with the mass difference of the two ions that are compared. For larger mass differences, errors as large as a factor of 2 cannot be excluded. For the subsequent interpretation of the data, it is desirable to know the values of p and f , which appear in eq 4. The product p f is easily determined. In general the two maas-analyzed ion (17) Tang,L. Ph.D. Thesis Studies of the Mechanism of Electroepray Ionization Mass Spectrometry. Chemistry Department, University of Alberta, 1993.


3858

Table I. Experimentally Determined Ratios of Coefficients k.

ion

mlz

CS+

133

Li+ Na+ K+ NH4+ MorH+ CodH+ HerH+ CocH+ Ni2+(Tpy)2 BUN+ Et4N+

Pr4N+ PemN+ C?NH3+ Cii"3+

e 23 39 18 286 300 370 304 262 242 130 186 298 115 171

kC

T,b 0.6

1

e

0.75 0.90 0.72 0.08 0.065 0.019 0.06 0.72 0.17 0.72 0.38 0.064 0.83 0.46

1.1 2.1 3.8 5.5 8.3 4.9 9.1 (3)8 (5)8

kd 1 1.6 1.6 1.0 1.3 (2.l)f (3.8)f

(8.3)f

10' 7

1

8.0 (16)f

(W 8 8

The coefficients are defiied in eq 4. All coefficients relative to kCs+ = 1. These coefficients are valid only at concentrations above 1 P M. Tm,maw-dependention transmission;see Figure 1. From plots using eq 6, where B+ = "I+; see Figures 2-4. Coefficients k obtained with [A+] = [B+]experiments. Numbers without parentheses measured for B+ = Cs+. For numbers in parentheses,

c 0

A+ and B+ are identified in footnotes. e For Li+,clusters Li(H20)+,

Li(H20)2+,LiCH30H+,LiCH3OH.H20, and Li+(CHsOH)2were also observed. k given refers to total intensity of all Li+ ions corrected for respective transmission. f Coefficient-based k values for MorH+, CodH+,and CocH+as in left column. Ratios from plots in Figure 7, on BuN+/CocH+= 2, BmN+/CodH+= 5, and BQN+/MorH+= 10, lead to a high value for BQN+ = 16 when combined with the above coefficients. 8 Coefficients based on ratios from Figure 8 and BUN+ = 8. These coefficients could be twice as high, assumingthat BQN = 16; see footnote f. intensities IAand IBdominate the mass spectrum. The total mass-analyzed ion current corrected for transmission is thus IA +IB.Th%capillaryES current I is also measured, and one obtains + IB)/I. Generally for a typical I of 0.3 PA, the product pf = (IA was found to be pf = 1 X 1V. The value of pf was found to be close to constant, i.e., independent of the nature of the analyte, for the range of analytes shown in Table I. A determination off, the fraction of droplet charge that is converted to gas-phase ions, is much more difficult and would require specialized apparatus. A rough estimate, f = 0.3, was obtained by measuring the total current, ICB,reaching the first electrode, CB, located in the vacuum of the mass analysissection. The electrode CB was closed off by spot welding a bit of metal was obtained for an API electric discharge foil to it. First, ICB operated at a total current in the atmospheric chamber, I = 0.3 PA. Then, Ice was determined with an ES capillary placed in the same position aa the API needle and electrospray current I = 0.3 PA. The ratios IcB/I = 2.1V (API) and 0.7 X 1V (ES) were determined.'* Since API produces gas-phase ions while ES produces initially charged droplets and then gas-phase ions, the ratio ES/API = 0.35 may be taken to give the yield of gas-phase ions from the droplet charge in ES,if it is assumed that space charge effecte, geometry, and other conditions for the API and ES were the same. This assumption is probably not warranted, and therefore, the estimate of the yield is very uncertain. However, it may be taken to indicate that f is in the range 0.50.1.

Taking f = 0.3, a value of p = 3 X 1V is obtained for the sampling efficiency of the interface used. This value is for the SCIEX TAGA6000E used in our laboratory, which is a somewhat obsolete instrument. We expect values higher by a factor of 10 or more have been achieved in more modern commercial instruments.

RESULTS AND DISCUSSION I. Behavior When Electrolytes Are at Higher (10-510-3 M) Concentrations. (a) Experiments Where the (18) Ikonomou, M. G.; Kebarle, P., unpublished work.

1.5

f

A

1.0j X

0

10

20

30

40

[BmI Flgure 2. Resutts from ES where [A+]= [CodH'] = 10" M and [B+] = [NH4+]is increased as shown: (a) Measured capillary current I. (b) Ion intensltles of NH4+and Codti+, corrected for transmlssbn. Cwves shown as sdtd lines are a calculated fit using eq 4. (c)Predicted linear plot based on eq 6 leads to ratio kAlke = 3.4.

Analyte Ion Concentration Is Constant and a Second Electrolyte, B+,Is Present in Increasing Concentrations. A series of experimental measurements were made in which the concentration of one of the compounds in solution was constant, [A+] = 10-5M, and a second electrolyte B+ = NH4+, was increased stepwise from 10-5to le3M. Used as A+ were Cs+, MorH+, CodH+, CocH+, HerH+, Ni2+(Tpy)z,(Bu)dN+, where Mor, Cod, COC,and Her, stand for the alkaloids morphine, codeine, cocaine, and heroin, Tpy stands for tripyridine, and Bu stands for n-butyl, respectively. A typical result is shown in Figure 2 for A+ = CodH+. The top plot (a) in the figure gives the capillary current I. As pointed out in the Introduction, this current changes very slowly with electrolyte concentration; see eq 1. Thus, an increase of concentration by a fador of 50 increasesthe current by only a factor of 2. The relationship given in eq 1predicts a straight line for the current I where a log plot is used, and this is in agreement with the experimental result in Figure 2a.

The plot in Figure 2b gives the experimentally observed mass-analyzed ion currents corrected for transmission. Addition of NH4+ decreases the ion intensity of CodH+ as predicted by eq 4. The lines drawn through the experimental


5857

3

0 7

X

, *I 1

0 0

30

20

10

["4+

40

NH4CI or KCI

]/[A+]

(M)

106

Flgure 5. Linear plots based on eq 6 (see Figure 2c) but for ions A+

as shown.

r

l

. -

105

Cs+(K+)

u

*s

+In

-

0

\Cs+(NH4+)

lo4

lo3 10-6

1 ,044 1o

.~

'

' " ' " ' ~

1o

.~

'

" " " '

NH4CI

1b . 3

1o

- ~

1o

- ~

1o

- ~

10.2

NH4CI or KCI (M)

,+cs+

10.2

(M)

intensities of [A+] = M and [B+] = [NH,'] at increasing concentrations. Solid line curves are Intensities of A+ calculated with eq 4 and coefficients k from Table I. Flgure 4. Ion

points are predicted changes calculated with eq 4. To obtain the parameter pf and kBlkA required for the fit, a rearranged form of eq 4 was used.

IAis the mass-analyzed current of A+, corrected for massdependent transmission and converted from counts per second to amperes. Equation 6 predicts a straight line when ZIIAis plotted versus the solution concentrationsratio [B]/ [A]. The predicted intercept is llpf and the slope is kdk4pf. The experimental plot shown in Figure 2c demonstrates that a good straight line relationship is observed. The intercept provides pf = 1.2 x 10-6 and the Slope kB/kA = k",+/kC,dH+ = 3.4. These two parameters were used to obtain the predicted intensities in Figure 2b. For this system, the agreement between the predictions of eq 4 and the experimental results can be considered as very good. Similarly good agreement was observed" for B+ = NH4+ in plots analogous to those in Figure 2 but involvingthe other AX electrolytes. A summary of these results is given in Figures 3 and 4. Figure 3 gives the plots obtained with the linearized form, eq 6, while Figure 4 gives the observed and predicted ZA as in Figure 2b but for all AX electrolytes used. The kdkA ratios obtained are summarized in Table I. The pf values were found to be relatively close to each other and in the range 1.2 X 10-6-2.5 X 1W. Considering the difficulties of the extrapolations to the intercept (see Figure 2c and Figure 31, the differencesprobably reflect experimental scatter rather than real trends. These pf values are in agreement withapf = 1Wobtainedwith amore directmethod

Figure 5. (a)Capillary current I. (b) Ion intensity for Cs+ when [Cs'] = M and [B+] = [NH4+] Is increased, or [B+] = K+ Is increased in separate experiments. Ions K+ and NH4+, which have cbse to same coefficient k (Table I), have the same effect in decreasing lon intensity of Cs+.

(see Experimental Section). An estimate of f = 0.3 (see Experimental Section) leads t o p = 3 X 1W. The very small p is mostly a consequence of the small orifice, 100 pm in diameter, which separates the atmospheric and vacuum regions in the TAGA instrument. It is clear from Figure 4 that the decrease of I A is dependent on the nature of A. Thus, Cs+experiences the largest decrease and (Bu)~N+ the smallest. At [NH4+]= lW3 M, the decrease for Cs+ is 10 times larger than that for (Bu)4N+. The extent of decrease is dependent on the kdkA ratio, the bigger the ratio, the bigger the decrease of anal@ ion intensity; thus kdkA = 1.1for Cs+ and 0.1 for (Bu)4N+ (see Table I). It is convenient instead of working with the k d k B ratios to assign an arbitrary value to one of the constants and then evaluate the other relative to that value. We have assigned a normalization value k = 1 for Cs+. The resulting other normalized values are given in Table I. A+ and B+ in eq 4 can be interchanged, and it is of interest to examine the validity of the equation for B different from NH4+. On the basis of eq 1, one expects that replacing NH4+ (k = 1)with potassium, K+ (k = l),will lead to decreases in I A + with increase of [B] which are very close to those observed for B+ = NH4+. The plots shown in Figure 5 for A+ = Cs+, B+ = K+and A+ = Cs+,B+= NH4+ exhibit a nearly identical decrease of A+ in agreement with the near equal k values for NH4+ and K+. A more interesting case is the replacement of NH4+ with an ion with much larger k, such as BUN+ ( k = 10). In this case a much M e r decrease of the A+ intensity with increasing concentration of [BwN+] is predicted by eq 1. Experiments where A = MorH+,shown in Figure 6, demonstrate that this prediction is upheld. At the highest concentration of [Bl = 103M, the MorH+ intensity with B = BwN+ is close to 50 times smaller than that with B = NH4+.

3858

ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993 io 3

I

10B=NH4+

CocH+

a

z

D

10':

E c

* "

0

0

z 0 0

0

0

s

j;

0

a

-

lo3

C

:

0

4

102

IO'

PI

I 10.6

0 '

'

' " " " I

10.5

' " " " I

"

1

o - ~

'

"""I

1

o . ~

".....I

10-2

[B'I (MI

(a) Capillary current I. (b) Ion intensity for MorH+ when [MorH+] = 10" M and [B'] = [",+I is increased, or [BbN+] is increased, in separateexperiments. Data show that B+ = B U N wlth hlgh, k = 9,coeffldent leads to very much h m suppression on MorH+ Intensity than NH4+ whose k = 1. Flgure 8.

The results in Figure 6 illustrate that by choosing buffer cations with the low coefficient k one can minimii the adverse effect of the buffer on the sensitivity of the analyte. Results of additional experiments where BQN+ = B+ and A+ are various electrolytes can be found in ref 17. (b)Experiments Where Concentration Is Increased and [A] = [BI. An alternate method of evaluatingthe kdkB ratio is to use the I ~ Iratio, B whose concentration dependence predicted by eq 4 is given by

(7) Shown in Figures 7-9 are results where the concentrations of two electrolytes Ax and BY, present at [AX] = [BY1 are increased from 10-8 to 103 M. For the logarithmic plots shown, a constant ratio I ~ I B corresponds to a constant distance: log IA - log IB.Because [A] = [B], a constant k d k B requires a constant vertical distance in the intensity plots. This is observed at high concentrations C > 106 M. At low concentrations, the two log I curves exhibit a different behavior, which is considered in subsequent sections. The kdkB obtained from the highconcentration region are given in Table I. The coefficients are expressed relative to kc8 = 1. A comparison of the k values given in Table I obtained from the plots in Figures 2-5 and the [A+] = [B+] results in Figures 7-9 shows that the data are in fair agreement and indicate the same trends. Differences between the two sets of data are to be expected. The plots in Figures 2-6 were obtained for [A+] = 106 M. This is a concentration that is barely part of the high-concentrationregion. Therefore, theae data are partly affected by phenomena which become typical for the low-concentration region; see next section. The coefficients in Table I have lowest values, k = 1,for the alkali and NH4+ cations. The tertiary ammonium ions MorH+ to CocH+ have intermediate values, and the quaternary ammonium ions such as BQN+ have high values. The

-

10'

4 -

106

tE*

..

G 10':

--

CS+

D

0

D

C

-

10'

io3

....-- .

.

.

.

i


I

10'

io7

-. VI

i

8658

b

8

C7NH3+

8

10;

. E

106

E

I-

~

t

h

="

L

VI

VI C

C

0

105

8

0

E 105 I

J

c

-0 io4

1

8

lo4 I

I

1

n

10

.

-.

VI

YI

106

PrO+

I

i

I

a

1

I

-c B

C

io3

io7

3

i

. -i / 106

I

Et4N+

8

E

.

. . '

104 1\-9

1b-8

103 1b.7

1;-6

1b.S

i b - 4

1b.3

10.2

10.1

tA+l=[B+l (MI Flgure 8. Same

as Figure 7.

1Oa-103 M, discussed in the preceding section. There are two important differences: (a) The ion intensities ZA and ZB experience a large decrease as [A] = [B] is decreased below lod M; (b) the ratio Z ~ Z gradually B decreases and becomes close to unity (Figures 7 and 8) as the concentration is decreased much below 106 M. The cause for the decrease of the intensities ZA and ZB as [A] = [B] are decreased is easily e~plained.'~Due to the presence of an electrolyteimpurity in the pure methanol used which is equivalent to 1.3 X 106 M NH&l or NaCl = C (see Experimental Section), we have actually a three-component system where at low [A+] = [B+] the dominant electrolyte is the impurity electrolyteC whose concentration ia constant. Therefore, as [A] and [B] are decreased below 1od M, the presence of C becomes more and more important, and since the C+ ions compete in the conversion process to gas-phase ions, they lead to a decrease in the observed ZA and ZB. This type of behavior is analogous to that observed in section Ia and in accord with eq 4, which can be extended in order to include a third electrolyte

I

..

10.9

. 10.8

-

16.7

10.6

10.5

10"

..--.I

.. 1 0 - 3 10.2 I

I

10.1

[ A + l = [ B + l (MI Flguro 0. Ion intensitiesobservedin experimentswhere [A+] = [e']. I n Figures 7 and 8, the intensity ratio approaches IA/fB = 1 at low concentrations. In the present figure, IA > I, even at low concentrations.

under conditions where [Cl

>> [AI

= [Bl, eq 8 reduces to

and since pf, I, and kc[Cl are constant, ZA becomes proportional to [AI. This equation predicta a linear region with a slope of -1 for the logarithmic plots in the low [AI = [Bl regions, and such a region is observed in Figures 7 and 8. The observation that the ratio I ~ I decreases B and comes close to unity as [A+] = [B+] is decreased much below 1V M means that kdkB is not constant in this range (see eq 10, which is obtained from eq 8).

The reasons for this are explored in the next section. It is shown there that, at low concentrations, the unipolar (+) ions on the surface of the droplets from which ion evaporation

3660


1

10'

J IAI (M) Flgurs 10. Observed ion intensltles from separate experiments where [A+] is increased from to lo-* M. Solid lines are predicted intensitiesof A+ evaluated witheq 4 and coefficients in Table I. Although no B is added, electrolyte impurity in the methanol used must be taken

into account.

is assumed to dominate over the charge-paired electrolyte ions in the bulk of the droplet. Under these conditions of no resupply of the surface ions by ions from the bulk, a depletion of the surface ions A+ with the higher ion evaporation coefficient (kA) occurs which reduces the ratio IdIg of the gas-phase ion products; i.e., this is a situation where the production of gas-phase ions is limited by the low total number of A+ ions present in the droplets and not by the relative efficiency of conversion of ions in solution to ions in the gas phase. The ion intensities IA and Ig where B+ = Cs+, shown in Figure 9, do not become close to equal at very low concentrations. The ions A+ can be expected to be surface active while Cs+ is not. Under conditions where the surface ion populationexceedsthe bulk of droplet ion population, surface enrichment of A+ due to surface activity w i l l be especially important in leading to higher intensities IA. As shown in section IIIf, it is probably differences due to surface activities that leads to the observation k A > kg at low concentrations. A somewhat simpler situation, where the same effecte can be expected, occurs in experiments where there is only one added electrolyte, AX, apart from the constant-concentration impurity electrolyte C. In a series of experiments, the concentration [AX] was varied over a wide range. Results from such experiments are shown in Figure 10, where AX = MorHC1, CodHC1, HerHC1, CocHC1, and CsCl. The experimental points at low [AX] show considerable scatter. This is unavoidable since absolute intensities IA are difficult to reproduce exactly in separate electrospray experiments.Also shown in the f i i e are calculated I Aobtained with eq 4. The required parameters kA and kg, were taken from the data in Table I, which were obtained from the linearized plots, eq 6, involving the same analyte A and the electrolyte B = NH4+. Because the impurity C in methanol is mostly NHd+X and Na+X and since the coefficients k for NH4+ and Na+ are expected to be very similar, the k from Table I for B = NH4+ should be suitable. The current I required for the evaluation of IA (see eq 4)was measured in each experiment. It should be noted that I is constant for [A] = 10-8-10-6 M for all A since in this region C is the dominant electrolyte. Furthermore, I increases very slowly as [A] surpass 106 M and is essentially independent of the nature of A; see eq 1and Figure 2a. The calculated curves in Figure 10 show clearly the predicted order of IA+,dependent on the magnitude of kA (Table I), which is CocH+ > HerH+ > CodH+ > MorH+ > Cs+. The scatter in the experimental data prevents a very (19) Iribarne, J. V.; Thomson, B. A. J. Chern. Phys. 1976, 64, 2287.

good comparison, but it is very clear that the experimental data do not obey the predicted order and are much more compatible with nearly equal IA currents at low [A+]. This result is in agreement with the observations presented in Figures 7 and 8 which involved the simultaneouspresence of two analytes [A] = [Bl, and the failure of eq 4 in the present case must be due to the causes already indicated for Figures 7-9. 111. Physical Background and Significance of Coefficients k and Equation 4. In this section we will examine phenomena concerning the mechanism of gas-phase ion production by electrospray and their relationship to the present experimental findings and the significance of eq 4. ( a )Properties of the Iribarne Ion Evaporation Equation. We w i l l assume that the mechanism of ion evaporationfrom small highly charged droplets proposed by Iribarne and T h o m s ~ nis~at~ ~ least ~ ~ qualitatively correct. After an examination of the properties of this equation, it will be shown that eq 4 can be derived from the Iribarne theory and that the coefficients k of eq 4 obtained at high concentrations should correspond to the (relative) ion evaporation rate constanta of the Iribame equation, when ions of similar surface activities are involved. The ion evaporationrate constants of the Iribarne equation k, = (kT/h)e-AG*/RT (11) are based on transition-state theory and AG*stands for the free energy of the transition state, where an ion-solvent molecule cluster M+(Sl)mleaves a small charged droplet. A basic assumption of the Iribarne treatment is that the transition complex occurs late, Le., at a state where the ion cluster M+(Sl), is fully free of the droplet and at some distance x , from it. The advantage of this assumption is that the free energy of this state can be evaluated with a closed classical expression:

AG*=

(AG,' +

4 m oNe2 (R-d)

) (12)

The terms in the first parenthesis give the energy of the transition state while the terms in the second parenthesis give the energy of the initial state; see Figure 11. The zero level for both states is the charged droplet and the ion cluster at infiiite distance. The first term expresses the electrostatic potential energy due to the repulsion between the ion cluster and the charged droplet, which has N elementary charges. The second term expresses the potential due to attraction between the charge of the ion and the polarizable drop. This term is approximately by the electrostatic attraction due to the image force. The third term represents the solvation energy of the ion cluster M+(Sl), in the neutral drop, while the last term corrects for the fact that the drop is not neutral but has N elementary charges. Thus, Ne2/4arpO(R - d ) correspondsto the electrostatic repulsion energy required to bring the ion cluster from infinity to a distance d inside the drop and the ion cluster is assumed to travel through vacuum. Thus,the assumption is made that once the ion cluster has arrived at R - d , the solvation energy A G,," is released. The expressions in the second parenthesis make sense; however, they do not represent a rigorous expression for the energy change of the process. AG*can be obtainedby treating the distance x as parameter and finding the value xmfor which AG*is maximum. Iribarne and Thomeon19 provided a very useful figure that gives the charge of the droplet N a n d the radius R for AG* = 9 k d / mol, which leads to the rate constant k~ = 106 s-l at T = 298 (20) Thomson, B. A.; Iribarne, J. V. J. Chern. Phys. 1979, 71, 4461.

ANALYTICAL CHEMISTRY, VOL. 85, NO. 24, DECEMBER 15, 1993 ion

solvent cluster

( a ) I n i t i a l state

0.0

k.0.031

d=3

A,

k=1.2x104 s-l

6x5

A, k=9.6x1OSs.1

loo

1 .o

0.5

7

A,

d -= ,l

s.’

1.5

2.0

x (nm)

-

/

N=50, k.0.24

5.’

20

,N=55, k=15 S.’

p

( b ) Transition state

P

5

50

X u

10

CI Q

80, k=4.1x10gs” 0 0.0

0.5

1 .o

”,

0 1.5

2.0

x (nm)

18.05

8.05

0

-1.95

-50

0.5

1 .o

1.5

I.11.95 2.0

x (nm)

I

,AGs=-62

kcallmole k=474 s.’

--

AGs=-58 kcallmole

s

: AGs=-54 kcallmole

0.0

al

x

‘1

I-

-

al

0

Flgur. 11. Schematic representation of Initial state (a) and transltlon state (b) proposed by Irlbame and Thoms~n.‘~ Evaporatlnglon leaves as a cluster M+(sL),,,, where SL are solvent moiecuies.

0.0

-a2

3661

0.5

1 .o

1.5

= u

-10

7-0 2.0

x (nm)

Flgwe 12. Free energy as a function of distance x of M+(SI)~ from surface of drop predicted by eq 1 2 N = 70; d = 3.85 A. (a, top) R is used as a parameter and A&” = -57 kcal/mol. (b, bottom) A&” is used as a parameter for R = 80 A. Values of k~obtained at A&” are given beside each curve.

“C(see eq 11). Iribarne reasoned that ion evaporation would become important only after kl reaches such large values corresponding to microsecond lifetimes for ion evaporation. Two curves for AG,1° = -56 kcaUmol and AG,1° = -64 kcal/ mol were shown. An additional illustration of results obtained with the Iribarne equation is given in Figure 12. The change of AG* and kr for a constant, AG,1° = -57 kcal/mol, N = 70, and a droplet radius treated as a parameter is shown in Figure 12a. These results illustrate the extremely rapid change of k1 with R. Thus, for a change from R = 100 to 70 A, k~increases from 10-3 to 1.4 X 1013s-l, i.e., by 16 orders of magnitude! This

Flgure 13. Same as Figure 12. (a, top) dis used as a parameter while R = 80 A, N = 70, and A&’ = -57 kcal/mol. (b, bottom) N is uwd as a parameter whlle R = 80 A, d = 3.85 A, and A&” = -57 kcal/mol.

very strong dependence on the radius of the droplet supports Iribarne’s decision to assume that ion evaporation for a given charge N will be completely unimportant relative to Rayleigh fission for conditions where the Rayleigh fiiion radius RR is larger than the radius RI, which leads to ion evaporationwith k~ = 106 8-l. Iribarne showed that the ion evaporation condition RI > RR occurs when the droplets become very small, R = 80 A and N = 70 as typical values. The results given in Figure 12b illustrate the change of AG* and k~ for constant N and d with AG,1° as a variable parameter. It is interesting to note that the distance xm which corresponds to the transition state remains essentially constant for different AG,IO. An examination of eq 12 shows that, for a constant xm and constant d, the difference between AG* for two given AGaolois given by AAG* = AG,*(A+) - AG,*(B+) =

- (AG,,,~(A+)- AG,”(B+)) which means that the rate constant ratio for two different ion species that have different ion cluster solvation energies and the same value for d will be given by

The plot shown in Figure 13a illustrates the change of AGI* and k~when d is changed at constant R, N , and AG,IO. It is seen also that in this case xm remains essentially constant for substantial changes of d. The independence of xm on d and AG,1° allows an important simplification.

Thus, when more than one ion species is present in a droplet, k1 for each species can be factored into a function k(N,R), which represents the droplet state R, Nand is independent of the nature of the ion and a function k’A(dA,AG,lO(A)), which expresses the nature of the ion A and is independent of R and

9662


N. Furthermore, kAo(dA,AGsom)can also be factored into two indpeendent functions as shown in eq 14b. Equation 14 is based on the results given in Figure 12 and 13 and is valid for the range of parameters covered in these figures. (b) Ion Evaporation and SolventEvaporation. The results presented in Figure 13b illustrate the rapid decrease of the ion evaporation rate constant kI with decrease of droplet charges N. Thus, the actual ion evaporation rates from a droplet will be controlled also by the solvent evaporation rate, which will shrink the droplet and increase kI. The droplets undergoing ion evaporation are very small, and for the volatile solvents normally used, such as methanol and water, the evaporation rate will be under surface rather than diffusion control.21 This means that the evaporation rate will be controlled by the rate of liquid-to-vapor conversion at the surface, since the recondensationof evaporated solvent molecules is negligible relative to the surface evaporation. The rate of solvent evaporation under surface control is expressed byz1

where the dmldt is the rate of change of droplet mass, ij is the average thermal velocity of the vapor molecules of the solvent,R is the radius of the droplet,po is the vapor pressure of the solvent, M is the molar mass of the solvent, and R, and Tare the gas constant and temperature in degrees kelvin. a is the condensationcoefficient equal to the fraction of solvent vapor molecules which, on collision with the droplet surface, condense on the droplet. The value a = 0.04 has been determined for water and ethanol.22We make the assumption that the same value also holds for methanol. Using the relationship between mass m, density a, and volume of the droplet, m = 4/3uR3p, eq 15 can be recast in the form (16) which on integration leads to a relationship between the radius R of the droplet and time t ,

R = R, - 1.2 X 10-3t

(17b)

where the numerical factor of eq 17b was evaluated for methanol @" = 1.66 X lo4 Pa, M = 0.032 kg/mol, 0 = 4.5 X 102m/s,p = 0.8 X lo3kg/m3,a = 0.04, T = 298 K). The radius of the droplet at t = 0 is Ro, and both R and ROare in meters. According to eq 17, the time required for the complete solvent evaporation of an Ro = 1 0 - l O m (W0m = 100 A) methanol droplet is t = 8 pa, which is very short relative to the time scale of droplet residence between the ES capillary and the orifice to the mass spectrometer. Thus, once a droplet of Iribarne ion evaporation size is formed, it will evaporate and lead to gas-phase ions within a few microseconds. It should be noted that the temperature of the evaporating droplets will be lower than that of the ambient gas because of cooling of the droplet by evaporation. For methanol, the droplet's temperature was estimated to be 8 OC lower than that of the ambient gas. Thus, the results provided are for a droplet temperature of 298 K and an ambient gas temperature of -306 K. For the basis of the estimate, see the Appendix. (21) Davies, C. N. Evaporationof AirbomeDropleta. InFundamentals of Aerosol Science; Shaw, D. T., Ed.; Wiley Interscience: New York, 1978; p 154. (22) Pound, G. M . J . Phys. Chem. Ref. Data 1972,1,135.

I

70 O o

60

0

i

0 0

0 0

55

0.00

0.10

0.20

0.30

0.40

t (PSI

Flgurr 14. Change of number of charges N with tlme for a droplet undergdng Irlbame ion evaporation and solvent evaporation. Evaluated with eqs 17 and 18 for N = 70 and Ro = 80 Kat t = 0 A Q O = -57 kcal/mol, d = 3.85

1.

On the basis of eq 17 and the Iribarne rate constants, it is possible to evaluate the gas-phase ion yield as a function of time. The results shown in Figure 14give the residual charge N on a droplet with NO= 70, Ro = 80 A at t = 0. The data were obtained with the equation

by selecting AiV = -1. The At1 required for evaporation of the first charge is obtained with the kI(No,Ro) as predicted by the Iribarne equations (see Figures 12and 13). At2 for the loss of the second charge is then obtained with N1 = 69 and RI, which correspond to the droplet radius after At, (see eq 16) and so on. The results in Figure 14 indicate that about half of the charge N is converted to gas-phase ions in 1MS. For more detail see ref 17. ( c ) Competitive Ion Evaporation. When the total charge N is due to two different ion species A and B, eq 18 can be reformulated with inclusion of eq 14a as shown:

-

where N ~ ( N + ANB)is the ratio of ions A to total ions N at the surface of the drop. There will be situations where the ratio NAI(NA+ NB)will not change (significantly) during the ion evaporation process. This will be the case when the number of ions nA and ne in the bulk of the droplet, due to electrolyte in the droplet, is very much higher than the number NA+ NBof ions at the surface. In this case the surface ratio NJNB will be maintained by rapid exchange with ions from the bulk. An approximate time constant for the exchange rate, time for diffusion of the ion to the surface, is given by

~ ~ D where D is the diffusion coefficient of the ion in the given solvent.23 Choosing R = 500 A and a typical diffusion coefficient for alkali ions in water, D = 1.7 X 10-5 cm2/s, one obtains tDiff= 1ps. The time required for smaller droplets will be much shorter. Furthermore,in methanol, the diffusion coefficients are higher. Since the Iribarne droplets are very small, diffusion will be able to maintain an approximately constant NdNB ratio on a submicrosecond time scale. When the ions are not surface active, this ratio will be equal to the concentration ratio C ~ C in B the bulk of the droplet. For the condition where NJ(NA + NB) = C ~ ( C A+ CB) remains constant during the Iribarne droplet evaporation, t,

=R

(23) McDaniel, E. W. Collision Phenomena in Ionized Gases; John Wiley: New York, 1964; p 502.

9669

ANALYTICAL CHEMISTRY. VOL. 65, NO. 24, DECEMBER 15, 1993

one can obtain the total number of gas-phaseions A+produced by the droplet by integration of eq 19 over a time, tf, required for the complete evaporation of all ions from the droplet.

The value of the integral is the same for all ion species since k ( R m is independent of the chemical nature of the evaporating ions. Assuming that the gas-phase ion current Z A , ~is proportional to NA,g,the number of gas-phase ions produced by the average drop, the ratio of gas-phase ion currents can be obtained with application of eq 21 and since the integrals cancel

1.5-

-s E

a

1.0

(10

t

-a

a

I

s-r

-6

? L

E

c

Y

-4

Q

0 200

0

400

600

t (PSI

Furthermore,assumingthat the droplet bulk ratio cA/mequals the solution concentration ratio, NAINB = c A / c B = [AI/[Bl

(23)

one obtains, (24) Equation 24 represents a derivation of the empirical eq 4 on the basis of the Iribarne relationships. It will be shown in the next section that the condition eq 23 is valid only at higher electrolyte concentrations; i.e., [AI = [Bl > 5 X 1od M.For that concentration range, and in the absence of differential surface activitybetween A and B, the experimentalcoefficient ratio kA/kB is predicted to be identicalwith the ion evaporation rate constants ratio k’dk‘B. ( d )Charge,Radiw, Concentration, and Time Dependence for Droplets Evolving toward Gas-PhcrseZon Emission. An estimate of the charge Q and radius R of the droplets from the time they are produced by the electrospray to the point where they become gas-phase ion emitters is possible on the basis of recent experimental observations of ES droplets by Davis et aLZ4and Gomez and Tang.2533 Reliable data are availableonly for droplets larger than 1pm. The assumptions listed below are closely based on the work of Gomez and Tang.m (1)The initial droplets produced by ES, particularly at low flow rates, -3 pllmin, have a narrow size and charge per droplet distribution. Typical values are RO= 1.5 pm and QO = 8 X 10-15C. This QO corresponds to a charge that is -40% of the charge, QR,required to lead to the Rayleigh droplet stability limit.27

Flgure 15. Changes of radius R and charge 0 with time of a droplet produced by electrospray which undergoes successivenot symmetric boplet flssbn (seeFigwe 16). Fisslon occurs at 80% of the Raylelgh limit, and parent drop loses 2 % of Its mess and 15% of Its charge.

-

smaller, offspring droplets each of which has a radius 10% of the radius of the parent droplet. The occurrence of fission below the Rayleigh limit seems to be associated with the observed presence of elastic deformations of the droplets, which oscillate between oblate and prolate shapes.2e (3) Process 2 repeats itself when the parent droplet, after radius shrinkage due to evaporation, is again at 80% of the Rayleigh stability limit. In this manner, a succession of droplet emissions occur from the gradually shrinking parent droplet. The graph given in Figure 15 illustrates the described process. The change of the parent droplet radius R with time was evaluated with eq 17. The radius of the parent droplet Ro = 1.5 pm is small enough such that eq 17, which is based on surface-controlled evaporation, can be expected to apply for solvents as volatile as methanol.21 The change of mass and thus also radius of the parent droplet when fission occurs is very small and thereforejust perceptible for the data shown in Figure 15. The time required for the fist fission is -460 pa, and a t this point RI = 0.94 pm. A second fission occurs after a shorter time, -70 pa, and further fissions occur at similar but gradually shortening intervals. The number ne and the charge Q, of the offspring droplets created from the parent droplet at a fission event can be estimated from assumptions 2; Le., the parent droplet uses 2 % of its mass and 155% of its charge and the offspringdroplet radius R, is 10% of the parent radius R. Applying conservation of mass where p is the density of the solvent

Q$ = 6 4 ~ ~ ~ y R ~ ~ (25a) Q$ = 1.25 X 10-’ORR3

n,FR, 4 3p = 0.02yR3p 4

(25b)

where eo = 8.8 X 10-l2is the permittivity of vacuum and y is the surface tension. For methanol, y = 0.0226 N/m2, eq 25a leads to eq 25b. Gomez and Tang found that larger droplets have initial chargee Ro which are closer to the Rayleigh stability

and since R, = O.lR, one obtains n, = 0.02/(0.1)~= 20 The charge Q, of each droplet is given by

limits.26

Q, =

YQ

= 7.5 x 10-36

(2) The droplets shrink due to solvent evaporation while the charge Q remains constant. Due to the decrease ofradius, the droplets undergo fission when the radius has shrunk to a value for which Q equals 80% of QR. The parent droplet loses 15% of its charge and 2 % of its mass,producing several

Thus, the first litter of -20 droplets will have

(24) Taflin, D. C.; Ward,T. L.; Davis, E. J. Langmuir 1989, 5, 376. Davis, E. J. ISA Trans. 1987,26,1. (25) Gomez, A.; Tang, K. Proceedings of the Fifth International Conference on Liquid Atomization and Spray S y s t e m I CLASS-91; Smerjians, H. G., Ed. NIST Spec. Publ. 1991, No. 813. (26) Gomez, A.; Tang, K. Phys. Fluids A, in press. (27) Lord Rayleigh, Philos. Mag. 1882, 14, 184.

The Q, and R,of second, third, etc., litter of droplets can be evaluated in an analogous manner. In order to obtain an estimate of the process and properties leadingto an *average” ion-emitting droplet, we select a third litter of offsprings. At this point the parent droplet charge Q is down to 75 % of the

Q, = 6.12

X

10-17C

R, = 0.094 pm N , = 382 elementary charges

3684

ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993 ~ ~ = 8 . 2 x 1 0 - 1c5 Ro=l.5 prn

n u

Q ,=8.2~10-15C

~ , = 0 . 9 4prn

At=462

-

20 droplets

Qs=4.4~10-17C,N d 7 6 Rs=0.076 pm Rs=0.029 pm (290

A),

N=276

W

+

ocoo

I

At=39 ps

R ~ 1 8 A, 0 Nw70

gas phase ion Changes of radius R and charge 0 with time in droplet fissions of parent droplet and offspring droplets. Required time for solvent evaporation evaluated with eq 17. Time for lon evaporation invoMng Iribarne size droplet from Flgure 14.

Flgure 16,

initial charge Qo (see Figures 15 and 16). We do not select the litter where Q = 0.5Q0 because it is likely that a full conversion of the parent droplet to offspring droplets does not occur due to time or other limitations. The evolution of a third litter offspring droplet to an Iribarne ion-emitting droplet is represented schematicallyin Figure 16. The offspring droplet shrinks through evaporation until it reaches 80% of the Rayleigh limit. At this point its radius is 290 A and its charge consists of N = 276 elementary charges. The fission of such a small droplet has not been observed. It could fiiion in the “uneven”mode of 15 % charge and 2 % mass loss with 20 offsprings or could fission more evenly into two droplets of near equal charge and mass. For convenience, in order to obtain typical Iribarne-size droplets, we assume that even fission occurs twice in succession so that four droplets, each carrying one-fourth of the charge, are formed. Then, each droplet shrinks through evaporation until it reaches the radius typically required for Iribarne ion emission, R = 80 A for N = 70. The situation where the offspring droplets fission unevenly will be considered in section h. ( e )Prediction of the Decrease of Observed kdkB Ratio at Low Concentrations due to Depletion of Ions with Higher Evaporation Coefficient. An estimate of the concentration of the electrolyte ions present in the bulk of the Iribarne droplet can be obtained by assuming that the bulk electrolyte concentration in the offsprings at each fission is equal to the bulk concentration in the parent. With this assumption, because the volume shrinks due to evaporation, the concentration will have increased by the product of the volume ratios (Vi/Vf)l(Vi/Vf)2(Vi/Vf)3= F,whichcan beevaluatedfromthe data in Figure 16. The result is F = 7.6 X 17.3 X 11 = 1450. This means that the concentration in the Iribarne droplet has increased by a factor of -1450 relative to the initial concentration. From the known volume VI of the Iribarne droplet (Figure 15), one can evaluate n, the total number of

-

paired electrolyte ions in the bulk of the droplet. nM= [M+lFVIL= 1.86 X 10e[M+]

(26)

where [M+l is the concentration of the electrolyte ions in the electrosprayed solution and L is Avogadro’s constant. The numberid factor given is for a droplet of 80-Aradius and [M+l in moles per liter. For [M+]= l t 5mol/L, the calculated number of bulk ions is n M = 18. Since the number of ions on the surface is N = 70, the solution in the bulk has few additional ions to supply. It is easy to see that at such low initial concentrations the experimentally determined ratio kdkB will be smaller than the theoretical ratio k’dk’B (when k’A > k’B). To illustrate, we assume [AI = [Bl and k’dk’B 03. There will be 35 A and 35 B ions on the surface and 9 A and 9 B ions in the bulk. After all 44 surface and bulk A ions are used up due to the rapid evaporation of A, 70 - 44 = 26 B ions will evaporate, leading to k d k e = 44/26 = 1.7, which is much smaller than k’dk‘B = w. Repeating the same type of calculation for different [A] = [B] concentrations, one obtains the resulta shown in Figure 17; see curve k’dk’B = m, It is also possible to evaluate the change of the kdkB with concentration for other k’dk’B ratios. Two such curves for k’dk’B equal to 5 and 2 are also shown in Figure 17. These data were evaluated” with eq 19 using a numerical procedure similar to that used for the data shown in Figure 14. At for AN = -1 was obtained for each step; then ANd ANB was evaluated for each At. The total A ions available for conversion to gas-phase ions was taken as the sum of A ions on the surface plus the A ions in the bulk of the droplet. Representative curves obtained with the experimentally obtained kdkB (see Figures 7 and 8) are also shown in Figure 17. There is considerable correlation between the shapes of the experimental and calculated curves. It should be noted that the data shown in Figures 7 and 8 involve ions A+ and B+, whose surface activities are expected to be similar.

ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993 10

Table 11. Data Used for Evaluation of Iribarne Rate Evaluated 4, and Experimental Coefficients Constants 4, k

I I 1, I

M+

I

I

I

Li+ Na+ K+ CS+ NI&+ (CHs)JV+(CaH&N+ -AG,IO(M+)~ 122 -AGO,' (M+)* 74.4 me 7 -AC.,,I'(M+(H~O),)~ 61.2 -Rdhydratedp = d 3.82 AG* 13.1 kI X 1W S-1 0.02 k 1.6

[AI

=PI(M)

Flgure 17. Predicted kA/kBratio expected for a given ion evaporation ratio k'A/k& in function of concentration [A+] = [e+]. Solid curves are predicted kA/kB fOr kf/kfB values shown beskles the curves. Experimental pointsare from Figures 7 and 8 and ghre kA/kBfor Bu4N+/ CodH', Pen4N+/Bu4N+,and Cs+/K+. Agreement between predicted and observed kdkB supports proposed depletion mechanism. I n calculated curves, A+ and B+ are assumed to have equal surface

activity. The agreement between predicted and experimental kAl kg in Figure 17 supports the depletion of faster evaporating ion interpretation proposed above. cf, Predictions of k'a/k'B from Theory and Experiment. It was shown in the preceding section that the experimental kdkB ratios obtained at high concentrations should correspond to rate constant k'dk'B ratios for the evaporation of ions from the droplets when A and B have no surface activity or the same surface activity. For the alkali cations, M+ (Li+, Na+, K+, Cs+), the experimental results (Table I) provide kdkB = k'A/k'B = 1, which means that the AG* for ion evaporation of these ions should be approximately equal, e.g. AAG* = O for Li+-Cs+ (27) The characteristics of the ions enter AG*through the solvation energy AG,lo(M+(S1),) and the distance d ; see eqs 12 and 14 and Figure 12. Assuming that the changes of d are small, eqs 13 and 27 require that the AAGs,lo be small or close to zero.

Fairly accurate estimates for AAG,1° (M+(HzO),), in a small aqueous droplet, can be obtained from the thermodynamic cycle.

&P

The cycle leads to AG,~*(M+(S~),) = AG,O(M+)

3066

- AG,,,YM+) -

nAGvaPo(S1)(29) Data for the solvation of the naked ion, AG,lO(M+), and for the solvation of the naked ion by n solvent molecules,

98.2 56.4 7 56.5 3.58 9.3 9.8 1.6

80.6 36.5 6 55.8 3.3 9.7 4.9 1.0

67.5 23.5 5 54 3.29 7.9 94 1.0

81e

(54)f

-

- 6 55.6' 3.3 9.5 6.8 1.3

-

-(49Y

(52)f -

-0 (49)' (2)* 7.9 98 -5

-

-

a Valuea (inkcal/mol) fromDesnoyer." Values (inkcdmol) from D2idiE.a m is the number of H2O molecules which leads to a minimum in -AG,,I~(M+(H~O),). Evaluated with eq 29 and AGwo(H20) = 1.95 kcal/mol, where AGvapo(H20)= RTln 760/pRD and PRO is the vapor pressure of HzO (inTorr) over a droplet with radius R. was obtained from p e , the vapor pressure over a flat surface with eq ln @RO/PO) = 2yM/RpRgT, where y is the surface tension, M the molar mass, and p the density of water. R, is the gas constant.g0 p o = 23.8 Torr,P R O = 28 Torr at 298 K.e Estimate based on near equality: AGo,sO(K+)= AGo.~O(N&+)~~ and value for K+; see present table. f Rough estimates based on data from refs 31 and 32. 8 Radii (inangstroms) from Conway.% Arbitrarily assumed value based on size of ethyl group.

*

AGo,,O(M+), are available in the literature for S1= H20.2w2 The vaporization energy of SI = water from a small droplet, AGvaPo(S1), is also available. These data are summarized in Table 11. It is found that, -AGsolo(M+(Sl),,)decreases as n increases. A minimum is reached for n = m. These minimum values are given in Table 11. With these data we can evaluate the AA G,lO. The AA Gsol0 for Na+ and Cs+ is found to be -(AG,,,o(Na+(H20),) - A G,,lo(Cs+(H,O)m)) = 2.5 kcaVmol This difference is very much smaller than the difference of the solvation energy of the nakes ions Na+ and Cs+,which is -30 kcal/mol. However, the AAG,,1° is still not equal to zero. It is not clear whether the disagreement is due to errors in the literature data used.28,29The literature data have expected errors in the f3 kcal/mol range. Another problem isthe use of water rather than methanol, for which the required supporting thermodynamic data are not available. However, the trend of higher -AG.,I~(M+(H~O),)for the smaller ions in Table I1 is so consistent that a result of AAG,l= 0 for all the alkali ions appears very unlikely. One needs to examine whether the differences in the parameter d might lead to AAG* = 0. d is the distance of the surface ion from the surface of the drop (see Figure 11). Iribarne assumed that this distance could be approximated by the radius of the ion plus the radius of one water molecule. This would mean that smaller d would have to be used for the smaller ions Li+ and Na+. As evident from Figure 16b, this would lead to a correction in the wrong direction since smaller d lead to even lower kI. It can be argued that the d for the smaller ions should be larger and not smaller, Li+ and Na+ are much more strongly solvated. Therefore, the electric field that forces the ions (28) Desnoyers, J. E.; Jollceur, C. Hydration Effects and Thermodynamic Properties of Ions. In Modern Aspects of Electrochemistry; Bockris, J. 0.M., Conway, B. E., Eds.; Plenum Press: New York,1969; VOl. 5, p 2. (29) DPidib, I.; Kebarle, P. J. Phys. Chem. 1970, 74, 1466. (30) Glasstone, S. Textbook of Physical Chemistry, 2nd ed.; D. Van Nostrand New York, 1956; p 495. (31) Kebarle, P. Annu. Reu. Phys. Chem. 1977,243,467. (32) Arnett, E. M.; Jones, F. M., III; Taagepera, M.; Henderson, W. G.;Beauchamp,J. L.;Holtz, D.; Taft, R. W. J. Am. Chem. SOC.1972,94, 4726.

3666 ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15. 1993

toward the surface will not be able to push the more solvated ions as closely to the surface. More suitable for the values of d should be the ionic radii obtained from ion mobility experiments in solution, the so-called Stokes or hydrated ion radii.33 These radii decrease in the order Li+ Cs+; see Table 11. The AG* for the alkaline cations were evaluated with the Iribarne equation using the AG,010(M+H20),) and d values given in Table I1 for a droplet with N = 70 charges and R = 80 A. The result obtained for Na+ and Cs+ is AG*(Na+)= 9 kcal/mol, AG*(Cs+)= 7.7 kcal/mol at 298 K, and AAG* = 1.3 kcal/mol. This value is not equal to zero, as required, but sufficientlyclose to be consistent with the Iribarne treatment. Examining the complete set of AG* for Li+ to Cs+, one finds that the AAG* are quite close to zero. However, the observed regular decrease of AG* from Li+ to Cs+ is not compatible with random errors in the data used and suggests that the trend observed in the calculated kI is real. Therefore, we consider the calculated AG*and kI to be just barely consistent with the observed experimental coefficients k. The tetraalkylammonium ions (TA) have experimental k values which are much larger than those for the alkali cations (see Table I). This is consistent with expectation on the basis of the Iribarne theory. The solvation energies of the naked TA ions, -AG,,lO(TA), can be estimated from available literature data31932and are found to be very much smaller than those for the alkali cations (see Table 11). In fact, the -AG,,IO for the naked (C5H11)4N+is smaller than the solvation energies for the alkali ion clusters, AGml0(M+(Sl),,,).The cluster (c2H&N+(H20), is expected to have an m 1, so that AG,oio(CzH5)4N+) AGm1°((C~H5)4N+(H~O)m). The low solvation energies for the TA ions given in Table I1 are in line with the observed high k values and with the order Et4N+ < PqN+ < BmN < Pent4N of the experimental coefficients k in Table I. The structures of the alkaloids used in the present work are shown in Chart I. The experimental k values are as follows: morphine -2, codeine -3.8 heroin -5.5 cocaine, -8; see Table I. Morphine, codeine, and heroin are closely related. Morphine has two hydroxyl groups, codeine has one and heroin has none. The hydroxyl groups, particularly in the presence of the positive charge on the nitrogen in the protonated compounds, will be somewhat acidic and therefore engage in stronger hydrogen bondingto the methanolor water solvent molecules.34 This will increase the solvation of the ion. Therefore, the observed order of k values for these three compounds follows the order of expected decreasing solvation and is in line with the ion evaporation theory. Although the cocaine structure is very different, this compound is also a tertiary amine. It is also devoid of hydroxyl groups and its high k value is consistent with expected relatively weak solvation. (g) Ion Solvation and Ion Surface Activity It was shown in the preceding section that the magnitudesof experimentally observed coefficienta k for ions other than the alkali cations are consistent with the ion evaporation theory of Iribarne and Thomson. However, so far we have not taken into account the surface activity of the ions. Since surface-active ions will have relatively higher concentrations on the surface than in the bulk of the droplet, eq 22, which assumes equal surface activity, i.e.,

Chart I Ho /

-

-

-

NA/NB = nAinB will not be applicable. The surface population will be (33)Conway, B. E.Ionic Hydration in Chemistry and Biophysics; Elsevier Publishing: New York, 1981; p 73. (34)Davidson,W .R.;Sunner,J.; Kebarle, P. J. Am. Chem. SOC.1979, 101, 1675.

HO@N-CH3 CH3

Caffeine

Morphine CH3COO

-%

CH,COO'$N+2H3

Codeine

Heroin AH3

;r Cocaine dependent on equations of the type N A = KsAnA NB = KsBnB where Ks is an equilibrium constant expressing surface activity. Such distribution equilibria are observeda6 in conventionalsolution at concentrationswhere a formation of micelles in the solution has not yet occurred. For the high-concentrationES experimenta,where depletion has not occurred, the observed ES coefficient ratio should be given by

-=k~ K S A ~ A surface-active ions k~ K S B ~ B Therefore, the question of which is more important, surface activity or ion cluster solvation energies, can be asked. Unfortunately, due to the lack of accurate ion cluster solvation energies and of the parameters d, the k' values for these ions cannot be predicted quantitatively with the Iribarne equations. Quantitative surface activity information is also scarce. Therefore, one has to resort to qualitative comparisons, and with these, the difficulty arises that ion cluster solvation energies and surface activities are often clmely correlated. Ions with low ion cluster solvation energies for which a high k'I is expected are generally also of high surface activity. For example, the solvation energies -AG,1° for the tetraalkylammonium ions decrease in the order Me4N+, EhN+,Pr4N+ (see Table 11),leading to expected higher k' in that order, but the surface activities also increase in the same order.35 The k values for the tetraalkylammonium ions are much higher than those for the alkali cations. The cluster solvation energies for these ions are lower than those for the alkali cations (see Table 11). However, the surface activities are also much higher. The previous discussion of the phenomena involved suggests at least a partial solution for this dilemma. It was shown in section d that, as the initial concentration C is decreased, (35)Tamaki, K. Boll. Chem. SOC.Jpn. 1967,40,38.


one reaches the condition where the number of unipolar ions on the surface exceeds the number of charge-paired ions in the bulk of the ion-emitting droplet. This condition holds for C < 106 M. At such concentrations, the observed gasphase ions reflect directly the surface population of the droplet. In a solution with [AI = [BI,the observed kdkB evaluated with eq 10 were found to approach the limit kdkB = 1,for any expected value of the Iribarne constants, k'dk'e, provided that the surface activity of A and B was expected to be approximately equal (see Figure 17). The data given in this figure did not include compounds whose surface activities were expected to be very different. Measured ion intensities IAand IB for pairs with expected large surface activity differences, BmN+/Cs,C ~ H ~ S N HCs+, ~+/ and C ~ ~ H ~ ~ N H ~ + were / C Sshown + , in Figure 9. In all three cases one finds that the observed intensities I Aand IB do not come together at low concentrations; i.e., the ratio I ~ I =B kdkB remains quite large, k d k B 1 5, even at the lowest concentrations. We can conclude that the kdkB ratios observed in the low concentration range C < lO-5M reflect surface activities while those observed in the high concentration range C = 10-3-10-2 M, reflect the ion evaporation constants k'dk'B and also enrichments due to surface activity, i.e., K s ~ K s B . The enrichment of the droplet surface on the more surfaceactive component probably occurs in the evaporation stages of the parent droplets between the Rayleigh instability explosions. As illustrated in Figure 15, these evaporation stages are relatively long, t 1 50 ps, and this should allow the enrichment of the surface with surface-active ions. Consideringthat for the alkali ions which have no surface activity the experimental ratio kdkB was close to unity while the calculated Iribarne ratios k'dk'B were found to change significantly (Table 11),one could ask the following question. Could it be that the Iribane equation does not apply and the different experimental ratios kA/kB observed for ions other than the alkali ions (Table I) are largely or even exclusively due to surface effects? ( h )Alternate Mechanisms for Gas-Phase Ion Formation. A Modified Ion Evaporation Model. In the preceding discussion it was shown that the experimental results are consistent with the Iribarne ion evaporation theory. It was also shown that the surface ion population should be corrected for enrichment with ion species which are surface active. However, possibly due to lack of accurate literature data (Table II), a quantitative proof of the Iribarne equation could not be obtained. We consider the relatively narrow range of coefficients k (1-16, Table I) surprising from the standpoint of the Iribarne theory. A AG* difference of only 5 kcal/mol leads to a k'dk'B c 500 at 298 K (see eq 11). From the standpoint of electrospray mass spectrometry,the relative lack of selectivity is an advantage. All types of ions are expected to be detectable with ESMS. It is possible that the relative lack of selectivity is due to a gas-phase ion production mechanism that is somewhat different from the Iribarne ion evaporation model as represented by eq 12. An alternative is suggested from an examination of the time required for the different processes leading to ion emission. A complex series of solvent evaporation and droplet fissions lasting hundreds of microseconds leads to the Iribarne-size droplet. According to the model, ion emission then occurs and requires some 1ps (see Figure 14). However, even if the Iribarne ion emission did not occur, the droplet itself will lose most of ita solvent molecules, due to solvent evaporation, in only -8 ps (see eq 17b). This time difference is not very large. Suppose that the Iribarne emission did not occur as predicted. Then solvent evaporation will continue until a much more disorderly gas-phase ion production occurs that may not follow eq 12 of the model. For

3667

this type of ion emission, solvation energy differences, surface effects, and the effect of temperature may have a much reduced importance relative to the functionalities predicted by eqs 11 and 12. One reason why eq 12may not apply is the assumed 'late" transition state which occurs after the ion cluster has 'broken through" the surface of the droplet. An "early" transition state which occurs just as the cluster disrupts the surface may lead to a higher AG*. In such a case a higher electric field will be required, i.e., a smaller more highly charged droplet. One would expect a decreased functional dependence on parameters like AG,l0. Rayleigh fissions will also remain competitive down to a smaller radius. The small highly charged offsprings of such fissions may also lead to gas-phase ions so rapidly that diffusion is not able to maintain a constant bulk-to-surface concentration ratio even for high, above 5 X 10-5 M, initial concentrations. In this case a resupply with bulk ions will not occur and a depletion effect similar to that observed at low concentrations will reduce the observed kd kg ratios even at high [A+] = [B+] concentrations. ( i ) Single Ion in Droplet Theory (SIDT). Riillgen% has criticized the derivation of the Iribarne equation. While we do not agree with all the points raised by Riillgen, we noted above that the last two terms in eq 12 do not constitute a rigorous expression. Riillgen stated that the Iribarne equation predicts to high ion emission rates and that Rayleigh fission rates remain faster than the ion emission rates. Riillgen et al.37 have proposed that Rayleigh fission continues, leading ultimately to very small droplets, 1nm in diameter, which contain only one ion. Evaporation of solvent from such droplets leads to gas-phase ions. This mechanism, which we will call SIDT, is similar to one proposed earlier by Dole.38 No details were provided37on whether there should be any selectivity for ions A+ relative to B+ and what the criteria for such a selectivity should be. Because the Iribarne model provided predictions on the basis of ion solvation energies and a number of authors starting with Iribarne and T h o m s ~ nfound ' ~ ~ ~qualitative ~ agreement with these p r e d i c t i o n ~ , 2 J the ~ J ~Iribarne ~ model was favored in the literature. However, these authors did not take into account that a correlation between surface activity and solvation energies of the ion can be expected. Also not considered was the possibility that selectivity in the SIDT can be expected on the basis of differential surface activity. More surface-active ions should be more abundant on the surface and therefore also in the final single-ion droplets. With these additions, the SIDT is also in qualitative agreement with experimental results such as those shown in Table I. A difficulty of the SIDT concerns the expected presence of other solutes in the droplet containing the single ion. Solutions containing a single electrolyte such as NaCl, particularly at higher concentrations (1W M), should lead to single-ion (Na+)droplets which also containavariable number of solute molecules, in this case charge-paired ions Na+ and C1-. Evaporation of the solvent from the droplets should lead to Na+(NaCl), ions.13 Yet no such ions, not even Na+-NaClwere observed from such solutions.13 This appeared as decisive evidence against SIDT. However, the fission leading to small droplets was assumed to be always "even".

-

(36) Rcllgen, F. W.; Bramer-Weger,E.;Biitfering, L.J. Phys. 1989,48, C6-253. (37) Schrnelzeisen-Redeker, G.; Biitfering, L.; Rdllgen, F. W. Znt. J. Mass Spectrom. Ion Processes 1989,90, 139. (38) Dole, M.; Mack, L. L.; Hines, R.; Mobley, R. C.; Ferguaon, L. D.; Alice, M. B. J. Chem. Phys. 1968,49,2240. (39) Sakairi, M.; Yergey, A. L.; Lise, K. W. M.; LeBlanc, J. C. Y.; Guevremont, R.; Berman, R. S. Anal. Sci. 1991, 7,199. (40) Rafaelli, A.; Bruins, A. P. Rapid Commun.Mass Spectrom. 1991, 5, 269. (41) Hiraoka, K. Rapid Commun. Mass Spectrom. 1992,6, 463.

8688


Solvent evaporation when even fission is present leads to high solute concentrations in the droplets. Uneven fission, with 15% of the charge but only 2% of the mass going into the offspring droplets, leads to an expected decrease by a factor of 7.5 of solute concentration relative to charge in the offspring droplets, while for even fission there is no change in their ratio. The occurrence of uneven fission, demonstrated by Davis% and Gomezs thus provides not only a mechanism for the rapid formation of very small droplets which are close to the SIDT condition but also a partial removal of the solute problem. If one assumes that the offspring droplet in Figure 16 does not undergo even fission, but uneven fisoion, the resulting second-generation offsprings will have a radius of 0.003 nm and only N = 2 charges. The calculated factor F by which the concentration increasesin these droplets relative to the initial concentration C of the solution is only F = 140. If even fission had occurred throughout, the factor would have been -(7.5)2 = 56 times higher. With uneven fission, F = 140,and the known volume of the droplets, one obtains the prediction that the number of charge-paired ions is only n = 2 for an initial concentration C = 10-4 M and n = 20 for C = 109 M. Solvent evaporation from a droplet with N = 2 charges will lead to a split into two single charges. For C = 1o-L M a fair yield of MX free ions M+ can be expected, but not so for a concentration of C = 103 M,where the typical ion expected would be M+(MS), with x = n/2= 10. Since no Na+(NaCl), ions were observed with 1V M NaCl solutions,13 the SIDT still faces a discrepancy but the discrepancy is now very much smaller.

CONCLUSIONS (1)Equation 4 provides useful predictions, both in the low, 1085 X 10-6 M, and in the high, 106-10-2M, concentration range. However, the coefficientsk have different significance in the tworanges. At low concentration, k d k B express relative surface activities of A+ and B+. When A+ and B+ have equal surface activity, kJkB = 1. In this range, the unipolar ions on the surface of the ion evaporating deoplet dominate over the charge-paired electrolyte ions in the drop. At high concentrations, kJkB express the relative surface activities and relative ion evaporation rates provided that the ion evaporation theory holds. (2)The relative values k d k e obtained at high concentrations are consistent with predictions of the Iribarne theory. It was shown that the theory should be extended to include surface effects, since ion species which are enriched on the surface will experience higher evaporation rates. The theory could not be proved or disproved on the basis of quantitative comparison with experiment. The observed range k = 1-16, for the relative values of the coefficients,is smaller than could be expected on the basis of the Iribarne theory, and this suggests that the functional dependence, eq 12,is not exact. The observed uneven fiision of the droplets24lBprovidesstrong support for the single ion in droplet theory of Rollgen.3' It is proposed that ion selectivity in this model should be based on the surface activity of the ions. (3) The formation of the ion evaporating droplets is preceded by a long (hundreds of microseconds) and complex process of shrinkage by solvent evaporation and droplet fission. The ion evaporation stage is short-a few micro-

seconds. Since the solvent evaporation rate is proportional to the vapor pressure of the solvent (eq 16)ES with lees volatile solvents such as water @" = 24 Torr relative to methanol (p" = 125 Torr at 25 "C)) may lead to higher intensities IA and IB when operated above ambient temperature. (4) Solvent evaporation leads to a large volume shrinkage which increases the concentration of solutes like A+ and B+ in the offspring droplets by a large factor. When uneven fission is involved,the factor is much smaller than is the case for even fission. (5)The Coefficients in Table I provide a guide to choice for cations in buffers which will lead to the smallest suppression of the intensity of the analyte ion. (6)In cases where quantitative information is to be obtained by the addition of an intend standard to the solution, the internal standard B+ should have the same surface activity and the same ion evaporation coefficient as the analyte A+, as is the case for K+/Cs+(Figure 7 and Table I). Only in this case will IA/IB

= [A+I/EB+l

Furthermore, this equality will hold only when both [A+] and [B+l are in the 10810-6 M range or in the 5 X 106-10-9 M range; i.e., both concentrations should be in the low or in the high range.

APPENDIX Estimate of Temperature Difference between Evaporating Droplet and Ambient Gas. The temperature of the evaporating droplet will be lower than the temperature of the ambient gas because of cooling due to evaporation. For methanol the temperature difference can be estimated as -8 "C. The temperature difference can be estimated aa follows: collisionds of gas molecules with drop evaporating solvent molecules/s

~

a!po

~

160 for MeOH wherep"(Me0H) = 120 Torr and a! = 0.04;for definition and value of a! see refs 21 and 22. Heat gained from ambient gas is equal to heat lost by evaporation PgcpAT= ap"AHva,(MeOH)

7 c,(air) = 2R = 7 cal/K-mol AHvap(MeOH)= 9OOO cal/mol The assumption was made that every gas molecule wumes the temperature of the droplet on collision (Le., accommodation coefficientof 1). A smaller accommodation coefficient will lead to higher AT.

RECEIVED for review May 12, 1993. Accepted September 17,1993.' ~

0

~~

Abstract published in Aduance ACS Abstracts, October 16, 1993.

Dependence of ion intensity in electrospray mass spectrometry on the

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