Anal. Chem. 1998, 70, 2213-2217
Thermally Activated Electrostatic Injection of Solvated Ions by a Track Membrane Interfaced Vacuum Feedthrough Vladimir V. Gridin and Israel Schechter*
Department of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
Electromembrane ion sources are considered as potential techniques for direct mass spectrometric sampling from ambient conditions. Interfacing of a time-of-flight mass spectrometer by means of a poly(ethylene terephthalate) track membrane requires investigation of the thermally activated processes involved. In this study, we directly attempt substantiating an activation-like performance of such track membrane-mediated interfaces. A number of KCl/glycerol solution samples were tested. A wide range of fixed, externally applied, potential drops was covered. For the charge extraction processes studied, we observe and discuss an activation term, exp(-∆F/kBT), with a free-energy barrier ∆F ) ∆F0 - ∆FΦ. The potential dropdependent ∆FΦ, was found to be sensitive to the varying salt concentration.
Various aspects of advances made in membrane-based analytical techniques have been recently reviewed.1 Several mass spectrometric applications were proposed, for instance, in a number of kinetic studies of chemical and biological reactions, for analysis of environmental samples, in monitoring fermentation and electrochemical processes, etc. Among these is found a high electric field-mediated introduction of ions into mass spectrometers. This approach was pioneered by Simons et al. in early 1970s 2. Since then, various applications of electrospray and electrohydrodynamic processes in MS have evolved. Many relevant features of these analytical schemes have been recently evaluated and reviewed by Cook.3 An innovative usage of track membrane inlets for a direct introduction of cluster ions and their subsequent MS analysis was first reported by Yakovlev et al.4 The, so-called, electromembrane ion source (EMIS) technique offers both the on-line sampling and the MS characterization of inorganic ions. It even appears quite suitable for studying by far larger organic entities, such as biomolecules. In various EMIS applications, a dense network of quite long (10-20 µm), yet very narrow (submicrometer), channels4,5 present in the track membrane governs the transport of charged species, as well as the field structure. (1) Lauritsen, F. R.; Kotiaho, T. Rev. Anal. Chem. 1996, 15, 237-264. (2) Simons, D.S.; Colby, B. N.; Evans, C. A., Jr. Int. J. Mass Spectrom. Ion Phys. 1974, 15, 291. (3) Cook, K. D. Mass Spectrom. Rev. 1986, 5, 467-519. (4) Yakovlev, B. S.; Talrose, V. L.; Fenselau, C. Anal. Chem. 1994, 66, 17041707. S0003-2700(98)00031-6 CCC: $15.00 Published on Web 05/01/1998
© 1998 American Chemical Society
Charge extraction processes at the vacuum/liquid interface of EMIS are subjected to an effective local electrostatic field, E (average per channel). Moreover, in such a multichannel network, a feedback charging of the vacuum-facing side of the track membrane is believed to be of a prime importance in producing high local fields at the liquid/vacuum interface.6 In a steady-state extraction regime, there exists a complex interplay between the current density and the field strength there. Therefore, similar to its predecessors, EMIS utilizes high electrostatic field conditions for extraction of charged species. Yet, this approach should be distinguished from the traditional methods of electrohydrodynamic ionization (EHDI).3,7,8 Note that no ionization of the liquid matter is associated with either the EHDI or EMIS approach. Instead, in both of them the evaporation into vacuum occurs for those ions that are, ab initio, present in the liquid phase. In EHDI applications,7 such ion transfer is stimulated by the high-field conditions, which are known to develop at the very edge of a fine metallic capillary. The liquid phase is in a highly unstable state there.8 Hence, the emission of charged species is stipulated and monitored by the instability itself. On the contrary, only a minute disturbance of the liquid/ vacuum interface is expected to occur for EMIS. In accordance with the Rayleigh stability criterion,9 such ionic sources could sustain (given an appropriate choice of the polymer/liquid wetting angle) quite severe electrostatic fields, i.e., of the order of 107 V/cm. 4,10 Indeed, by means of
∆p + E2/8π - 2γ/r ) 0
(1)
one obtains a stable liquid surface provided that the channel radius, r, is less than 1 µm. Here, such typical figures as ∆p ) 1 atm for the hydrostatic pressure head, E ) 106 V/cm for the local field strength, and γ ) 60 dyn/cm for the surface tension, were applied. Recently reported interfacing of TOF-MS with EMIS4 suggests a working layout for m/z identification of charged material species. (5) Balakin, A. A.; Dodonov, A. F.; Novikova, L. I.; Talrose, V. L. Rapid Commun. Mass Spectrom. 1996, 10, 515-520. (6) Balakin, A. A.; Dodonov, A. F.; Novikova, L. I.; Talrose, V. L. J. Electrost. 1997, 40, 615-620. (7) Stimpton, B. P.; Evans, C. A., Jr. J. Electrost. 1978, 5, 123-144. (8) Du ¨ lcks, T.; Ro ¨llgen, F. N. Int. J. Mass Spectrom. Ion Phys. 1995, 148, 123144. (9) Lord Rayleigh Philos. Mag. 1882, 14, 184-190. (10) Yakovlev, B. S. High Energy Chem. 1995, 29, 389.
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However, any analytically reliable development in this field requires a full-scale consideration of the underlying physical processes involved in such ionic feedthroughs. In particular, there have been no attempts, so far, to directly and conclusively substantiate an activation-like performance5 of these membrane-mediated interfaces. To be specific, forthcoming eqs 2-4 are often introduced5 to consolidate a typical theoretical description of EMIS. A single-channel contribution to the collector current, I, is given by
I ) qNν
(2)
where q is an ion charge, N is a number of ions present at the liquid/vacuum interface, and ν is the effective escaping frequency. Within this approach, the collector current is expected to increase as a function of N and the increasing field strength, E. An explicit field dependence is introduced as follows. Within a single-particle approach, the probability of finding charged species at the vacuum side of the track membrane is set proportional to 1/ν; here the effective escaping frequency, ν is set by
ν ) ν0 exp(-∆F/kBT)
(3)
In the above, ν0 ∼ 1014 s-1, kB is the Boltzmann constant, and T is the absolute temperature. In polar liquids, both the polarization and the evaporation energy terms are expected to contribute to the activation energy, ∆F ) ∆F0 - ∆FΦ, of eq 3. Here, the barrier depression term, ∆FΦ, arises from the application of the electrostatic field. It is usually set to follow a Schottky-type behavior,11 namely,
∆FΦ ∼ q(qE)1/2
(4)
In this work, we aimed to experimentally substantiate applicability of several theoretical concepts in describing track membrane-mediated charge extraction processes. For this purpose, we investigated thermally activated performance of such membranes. We have considered two separate cases of interest. Our first objective was to collect data on glycerol, which has been the most frequently utilized solvent in track membrane-mediated charge extraction applications. Second, several KCl/glycerol solutions were tested in thermally activated regime. EXPERIMENTAL SECTION Our experimental setup is schematically shown in Figure 1. The dynamic vacuum (down to 6 × 10-8 mbar) conditions were produced by a pumping array with a Turbo pump (STP-400, SeikoSeiki, Japan), which was positioned just beneath the track membrane inlet. Throughout the study, such inlets were cut from 10 µm-thick poly(ethylene terephthalate) track membranes6 for which the typical channel density and the mean channel diameter were, respectively, 107 cm-2 and 0.07 µm. High dc fields were set by means of a Branderburg high Voltage power supply and (11) Condon, E. U., Odishaw, H., Eds. Handbook of Physics; Ch. 8 McGraw-Hill: New York, 1958; Chapter 8.
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Figure 1. Schematics of track membrane assembly for air-tovacuum charge extraction, applying high electric field. Inset: a model diagram for thermally activated charge extraction processes.
the dc current readouts were detected using a nano-Ampermeter (Yokogawa, Japan). Temperature readings (referred to the ice point) were obtained using a calibrated differential Cu-Co thermocouple. The measuring joint of this thermocouple was directly immersed into the glycerol droplet. Precautions were undertaken to disallow any charge leakage through the thermocouple circuit. The uncertainties of the temperature readouts (due to the finite thermal conductivity and heat capacity of the thermocouple joint) have been estimated to fall within 0.4-0.6 K. The temperature of the glycerol droplets, T ) T0 + ∆T, has been monitored to increase at the rate of 1.2 K/min from its ambient value, T0, of ∼291 K. Analytical purity glycerol (Frutarom Ltd.) was used. The glycerol samples’ droplets were changed ones in 12 h and the entire experiment was performed under open and ambient laboratory conditions. The appropriate glycerol solutions (in a form of ∼200-µL droplets) were applied to the ambient pressure side of the track membrane. A negative high-voltage bias to the droplets was supplied by means of a metal electrode (gold ring) immersed there. The negatively charged species were extracted into the TOF-MS vacuum chamber, held at various operational pressures ranging from 10-2 to ∼10-7 mbar. Track membranes were used here to interface between these two pressure-conditioned space regions as well as to allow the high-field regimes to be developed and maintained thereof. The experimental readouts, in terms of the dc currents, I, were recorded and analyzed. The extrinsic charge carrier concentration (of dissolved KCl), ∆C, was varied from 0 to 0.02 M. The former figure corresponds to a pure solvent, for which case our electroconductivity measurements suggest the intrinsic carrier concentration (in a form of deprotonated glycerol molecules) CG = 5 × 10-5 M (or n = 2.5 × 1022 m-3). Clearly, in this notation the total carrier concentration, C, is just C ) CG + ∆C. For the KCl/glycerol solutions, however, since ∆C . CG, C = ∆C. In what follows, we also make use of a unitless quantity X ≡ C/CG. Thus, for a pure solvent case, X ) 1 and rises up to ∼400 for ∆C ) 0.02 M.
RESULTS AND DISCUSSION This section is organized in accord with our main objectives. First, several relevant interrelations are introduced. These are followed by the data presentation and interpretation. Theoretical Considerations. Any EMIS extracted charged species in our study is essentially composed of a charged entity (e.g., a negative ion or a deprotonated glycerol molecule) and a certain number of the solvent neutrals attached to it.4 Consider this as a subsystem of the total system, which includes the entire droplet sample and the glycerol-wetted track membrane. The possibility of establishing a thermally activated steady-state charge extraction regime is based on the forthcoming thermodynamic considerations. Let both the externally applied potential drop, ∆Φ, and X be fixed. The corresponding free energy of the system is assumed to be such that F ) FJ(∆Φ, X). Here, J ) L, R stands for the two possible configurations of the system, where the subsystem is found either (a) to the left or (b) to the right of the interface boundary provided by the track membrane; refer to the inset of Figure 1. Clearly, then, F ) FL in a former and F ) FR in a latter case. The corresponding grand partition functions are ZL and ZR. That is, with the usual notation involved, FJ ) -kBT ln ZJ, J ) L, R. Also Z ) ZL + ZR. The probability of finding the system with its subsystem in either one of the above-mentioned states is then PJ ) ZJ/Z; J ) L, R. Hence, for the conditional probability of a single charge extraction event, f ≡ PR/PL , and with ∆F ≡ FR - FL, we arrive at
f ) exp(-∆F/kBT)
(5)
Clearly such ∆F plays a role of an activation energy for the charge extraction events. Recalling eqs 2 and 3, we observe that I ∼ f. Hence, constructing I/I0 ) f(T)/f(T0) and letting ∆(1/kBT) ≡ 1/kBT0 - 1/kBT one obtains
I/I0 ) exp[∆F∆(1/kBT)]
(6a)
ln(I/I0) ) ∆F∆(1/kBT)
(6b)
Figure 2. Typical temperature dependence of the normalized track membrane current, I/I0, at different fixed values of externally applied potential drop, ∆Φ. Note that ∆T ) T - T0, T0 ) 291 K.
the field-dependent term
∆FΦ,X ) [q3∆Φ/D4π0]1/2 ) AX[∆Φ]1/2
(7)
where 0 and are, respectively, the permittivity of vacuum and the static dielectric constant of glycerol () 42); AX ≡ [q3/ D4π0]1/2. The subscript, X, is implicitly indicative of the carrier concentration dependent features of ∆F. Our last entry in this subsection is the carrier concentration dependence of ∆F. Quite generally, both the concentrationdependent entries of eq 7, namely, D and , become smaller as the electrical conductivity of the ionic solution increases. On a qualitative footing, therefore, ∆FΦ,X(for ∆Φ * 0) is expected to increase as a function of increasing X. One’s anticipation, then, would be a smaller activation barrier, ∆F. Due to the complexity of the general treatment, we consider only the limiting case of ∆Φ f 0. Clearly, then, ∆F f ∆F0,X. In this regime, the charge extraction is a pure fluctuation process. To the first order in ∆T ) T - T0, we may then write
or
∆F0,X ) ∆F0,1 - kBT0 ln X
We utilize eq 6b in the forthcoming presentation of our experimental results. At this stage, however, let us introduce another relation, which allows the possibility of a field-dependent ∆F to be tested in terms of eq 4. Worth noting is that for a typical gap, G ) 0.4 ( 0.1 mm, between the track membrane (held at ∆Φ of, 2-3 kV) and the grounded stainless steel grid the externally applied fields, ∆Φ/G, are of the order of 105 V/cm only. This is more than 1 order of magnitude smaller than the local (nearby the track membrane) electrical field, E.6 On the other hand, it is well established that the extraction of ions is more intense larger is the potential drop ∆Φ applied.6 At this stage, with no microscopic knowledge of the processes involved in causing such a discrepancy, we interrelate ∆Φ and E by means of an “effective length” parameter, D, such that E ) ∆Φ/D. In other words, with ∆F ) ∆F0,X - ∆FΦ,X, we write in SI units for
(8)
whereby ∆F0,1 stands here for X ) 1, i.e., for the pure glycerol case. This relation is quite readily derived upon using a largely simplifying assumption that the electrochemical potential of the extracted charged species remains nearly the same irrespective of any atomic (or molecular) properties of the associated chargecarrying core (being either a deprotonated glycerol molecule or the monovalent ion) involved. Experimental Results. We now present the experimental results supporting the above theoretical considerations. A typical variation of the normalized track membrane current, I/I0 ) I(T,∆Φ)/I(T0,∆Φ), as a function of the temperature rise, ∆T, is shown in Figure 2 for two fixed values of the externally applied potential drop, ∆Φ. A substantial increase of I/I0 for increasing T is observed. Although, at fixed T0, the current is known to increase with ∆Φ, it appears that the higher the potential drop applied, the smaller would be the variation of I/I0 obtained. Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
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Figure 3. Plot of ln[I/I0] versus ∆(1/kBT); refer to eq 6b. The slopes provide the field-dependent values of the activation energy, ∆F ) ∆F(∆Φ).
Figure 5. Plot of ∆F versus [∆Φ]1/2 for X ) 0. Refer to eq 7.
Figure 6. Values of ∆F recorded for different ∆C cases for the smallest ∆Φ () 0.3 kV) applied. Figure 4. Plot of ∆F ) ∆F(∆Φ) for the minimal (∆C ) 0) and maximal (∆C ) 0.02 M) KCl concentrations.
In Figure 3 the left-hand side of eq 6b is plotted versus ∆(1/kBT) so that a positive slope of the linear regression line drawn through the data points provides ∆F. The thermally activated nature of charge extraction by EMIS is self-evident, therefore. The data of this figure also suggest that ∆F should depend on ∆Φ. Our measurements for ∆F ) ∆F(∆Φ) are shown in Figure 4. For all the solution samples studied (X ) 1 inclusive), ∆F was found to decrease with increasing ∆Φ. Even though I0 tends to increase with X, the sensitivity of I/I0 to ∆Φ appears to be smaller for the higher ionic concentrations than for the lower ones. Unfortunately, the quite substantial experimental uncertainties of Figure 4 do not permit any conclusive data processing for testing eq 7. Recall that as a function of the potential drop applied, a square-root-type reduction of the activation barrier is anticipated for. In this regard, we were successful in extending our measurements only for glycerol. Any attempt of doing so with ∆C . CG has eventually resulted in a malfunctioning of the track membrane. In this case, the charge extraction was so intense that the liquid droplets formed at the vacuum-facing side of the membrane were short-circuiting it, inevitably, to the grid. In Figure 5 we plot our data for ∆F as a function of [∆Φ]1/2. The calculated slope was S = 0.01 eV1/2 and since S ) A ≡ 2216 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
[q3/D4π0]1/2, we estimate D = 350 nm. This figure is ∼10 times smaller than the interchannel spacing (there are ∼107 channels/ cm2). On the other hand, consider a characteristic length scale for approximating the extent of the local field region. This could be done using the Debye and Huckel theory of electrolytes,12 where the free carriers redistribute themselves in such a way as to screen out the Coulomb field of a probe charge in a distance of the order of LD ) (0kBT/2nq2)1/2. On physical grounds, the balance between thermal kinetic energy and electrostatic energy is used to determine the magnitude of such an effective (at times called as the Debye length) screening distance, LD. Since, in our case n ) 3 × 1022 m-3, such D appears to be 1 order of magnitude larger than LD. Note also that D is ∼5 times larger than the mean channel diameter (=70 nm), yet by far smaller than a typical channel length (=10 mm). At this stage, we have no satisfactory explanation for this value of D. Nevertheless, our major goal of experimentally establishing the principal [∆Φ]1/2 field dependence has been reached so far. Our last experimental entry is concerned with the carrier concentration dependence of ∆F when ∆F f 0. In our study the smallest ∆Φ, for which a stable stationary charge extraction was still possible, was 0.3 kV. Such data might be used to assess the limiting behavior of ∆F(∆Φ f 0) ) ∆F0,X. (12) Eggers, D. F.; Gregory, N. W.; Halsey, G. D.; Rabinovitch, B. S. Physical Chemistry; Wiley: New York, 1964; Chapter 12.
the enthalpy of evaporation, which for a single glycerol molecule is ∼0.92 eV13 and is reasonably close to the above estimated ∆F(∆F f 0, C f 1 M). Finally, according to Figure 7, the polarization energy contribution, P, for a pure glycerol would be given by P = (1.19 eV - 0.92 eV) ) 0.26 eV. This corresponds, for ) 42 and r = q2/8π0P, to a characteristic polarization length, r = 2.8 nm. Taking it as a radius of the cluster ion provides, on average, 4-6 glycerol neutrals attached to each deprotonated glycerol molecule extracted by EMIS.4
Figure 7. Fitting the data of Figure 6 to eq 8. The slope of the linear regression line through the data points is quite close to kBT0.
In Figure 6, we plot such ∆F data for the entire range of X covered in this work. The dependence is far from a linear one: for ∆C f 0 (i.e., X f 1), the activation barrier is seen to rise sharply to ∼1.2 eV. In Figure 7, these data are replotted in terms of ln X. Thus, in accordance with eq 8, there exists a reasonable least-mean squares linear fit through the data with the slope value of 0.024 eV = kBT0. Observe that ∆C ) 1 M results in ln X ) 9.9. This, in turn, when substituted into the fit equation of Figure 7, produces ∆F(∆Φ f 0, ∆C f 1 M) = 0.96 eV. Within our model case, it would equally well correspond to a hypothetical situation where a “salt” of deprotonated glycerol molecules was added to a neutral glycerol solvent, so that the ∆C f 1 M limit had been realized. In such a case, a very minute contribution to ∆F would have been expected to come off the polarization effects. Hence, roughly speaking, the activation barrier would have solely been due to
CONCLUSIONS Several analytically relevant characteristics of the electromembrane ion source were investigated. The studied features are related to direct ambient condition sampling into high-vacuum mass spectrometers. First, theoretical considerations regarding the temperature dependence of these membranes were developed and examined. Experimental results revealed the nature of the activation barriers related to the multichannel extraction processes involved. The effects of the substrate concentration, as well as those of the applied electrical field upon the barriers and the resulted EMIS currents, were presented for the first time. The experimental results are shown to fit the theoretical mainframe for operational functioning of electromembrane ion sources. ACKNOWLEDGMENT This research was supported, in part, by the James-Franck Program for Laser Matter Interaction and by the Technion VPR Fund. We are grateful to A. A. Balakin for assisting in interfacing our TOF-MS with EMIS facility. Received for review January 7, 1998. Accepted March 30, 1998. AC9800311 (13) Gallant, R. W. Hydrocarbon Process 1967, 46, 201-215.
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