- Email: [email protected]
Modelling of penetration of ions through a shutter grid in ion mobility spectrometers
Sensors and Actuators B 135 (2008) 116–121
Contents lists available at ScienceDirect
Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb
Modelling of penetration of ions through a shutter grid in ion mobility spectrometers Jarosław Puton ∗ , Andrzej Knap, Bogusław Siodłowski Faculty of New Technologies and Chemistry, Military University of Technology, Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 2 October 2007 Received in revised form 19 June 2008 Accepted 6 August 2008 Available online 22 August 2008 Keywords: Ion mobility spectrometry (IMS) Ion shutter Computer simulation of ions movement
a b s t r a c t Phenomena occurring in vicinity of the shutter grid are important for resolving power of ion mobility spectrometers and also for magnitude of the signal from these detectors. In this paper we present results of computer calculations concerning electric field and ion concentration distributions in neighbourhood of grid electrodes. Proposed model and methods of calculation give possibility for estimation of permeability of the grid and for determination of ion concentration profile behind the grid in dependence of grid dimensions and parameters of controlling voltage. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Ion mobility spectrometers (IMS) are analytical instruments used as detectors for investigation of composition of gas mixtures [1]. The basis of spectrometer operation consists in two phenomena: an ionisation of the sample and an identification of ionisation products by their separation according to ion mobility. These phenomena occur in two different parts of spectrometer. The first of them is an ion reactor in which sample ions are produced. The second part is a drift region designed for separation of different ion products. In the classic IMS detectors, operation of which is similar to time of flight mass spectrometers, it is necessary to produce small portions of ions, which then are moving along the drift region. Production of such ion portions is executed with special “ion valve” known as a shutter grid or a shutter gate, which is placed between the ion reactor and the drift region. The gate is closed for most of the time. It is opened only for a short moment, with suitable electric signals (pulses). These pulses change electric field in neighbourhood of the grid only. At some distance from the grid ions are moving under the influence of electric field Edrift , which is uniform and constant. There are two classic solutions of shutter gate. The first one is Tyndall’s gate [2], which consists of two grids (see Fig. 1a). They produce electric field Eblock , direction of which is opposite to the
∗ Corresponding author. Current address: University of Kuopio, LAEC, Patteristonkatu 1, FIN-50100 Mikkeli, Finland. Tel.: +358 15 355 6236; fax: +358 15 355 6363. E-mail address: jaroslaw.puton@uku.fi (J. Puton). 0925-4005/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2008.08.011
field in which drift of ions occurs. This field stops ions and prevents their penetration to the drift region. At present, Tyndall’s gates are not practically used in IMSs. It is a consequence of the fact that their permeability for ions is limited and that these gates are not suitable for production of well shaped narrow ion portions. The most often applied technical solution is Bradbury–Nielsen gate (BNG) [3]. Similarly to Tyndall’s gate, BNG consist of two sets of electrodes (Fig. 1b). The electrodes are placed in one plane or in two planes lying close to each other. If potential difference between successive electrodes is suitably high, electric field Eblock created by grid electrodes can block penetration of ions from reaction to drift region. In that case all ions become discharged on grid electrodes. Equalisation of potential of successive electrodes makes gate permeable. There are several technologies of shutter gates fabrication. It is possible to weave or put wires on special frames. This technology is laborious and requires special instruments [4,5]. It is much easier to use an etching method for grid production. In this case, material of the grid can be a semiconductor plate [6] or a thin metal sheet (see Fig. 2a). A set of two plates separated by insulator creates a complete BNG (Fig. 2b). Area of the plates in surrounding of grid electrodes is usually relatively large; therefore electric capacity of the system can also be significant. It can cause some difficulties in realization of fast changing of electrode polarisation. Precise, small grids can be fabricated with laser technology [7]. This method is useful for large-scale production, and offers low unit price. Similar technical solutions to those used in case of shutter gates for IMS are also applied in mass spectrometry. It is necessary to understand a fundamental difference in the way ions move in both
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
117
Fig. 1. Principles of operation of Tyndall (a) and Bradbury–Nielsen (b) gates.
kinds of detectors. In case of IMS, ions are moving in gas and their trajectories are practically consistent with electric field lines. “Closing of the grid” is equivalent to such potential distribution, for which no field lines penetrate the grid plane. In case of mass spectrometry, ions move in vacuum. Therefore, ions can achieve great velocities. Inertia of ions causes that their trajectories considerably differ from electric field lines. Therefore, in some cases in mass spectrometers grids do not stop ions but only deflect their beam. The phenomena related to transport of ions through a shutter grid influence magnitude and shape of output pulse from IMS detector. Each grid is characterised by a given maximum permeability. Its value determines amplitude of the signal. Grid dimensions and the manner of its electrodes control influence spatial ion density distribution behind the grid, i.e., in the beginning of the drift region. This distribution determines width of output pulses of particular ionic species, and thus also resolving power of the spectrometer. Calculation of the grid permeability is possible on the basis of electric field analysis, i.e., electrostatic considerations. Such calculations were performed for optimisation of the etched silicon grid [6]. Dynamic description of ions penetration through a
grid is possible by computer simulation of ions movement. Similar problem was solved by one of us 18 years ago [8]. Mathematical methods used then have been improved allowing obtaining some new interesting results. 2. Electric field of the grid Calculation of electric field for the model arrangement of electrodes of the grid is not complicated. Widely known computer software can be used for solving problems of the electric field [9] and the movement of ions [10], and also universal mathematical program packs [11] can be applied for these purposes. Results of the calculations presented in the further part of the study were obtained using the computer programme IMS SG 01 developed by us. Input data for the programme are matrixes of electric field potential calculated for definite geometries of the grid. The programme IMS SG 01 is designed for drawing electric field lines, computing permeability of the grid and for simulation of ions movement. The results obtained with the simulation allow investigation of dynamic phenomena that is those kinds of problems in which potentials of the grid electrodes change in time. Upon request
Fig. 2. Single etched electrode (a) and a set of components (b) of the Bradbury–Nielsen gate.
118
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
Fig. 3. Illustration of the method of electric field calculation. Fig. 5. Effect of the electrode diameter on value of the blocking voltage.
the programme with several files of electric field potential data can be made available by the authors. Electric field in the neighbourhood of metal grid electrodes can be considered as a sum of two components. The first one is a uniform electric field disturbed by introduction of the set of conductors (grid electrode wires). The second component is a result of accumulation of electric charges on particular electrodes under influence of differences in electric potential. These two components can be found by solving the Poisson’s equation with boundary conditions corresponding to fixed values of electric fields or potentials on the borders of interesting region. Because of superposition rule, the resulting electric field for any electrode polarisation can be easily calculated as a linear combination of both component fields (Fig. 3). Field lines for three values of electric potential differences between consecutive electrodes ϕgrid are presented in Fig. 4. Permeability of the grid can be computed as a ratio of the number of field lines passing through the grid and the number of lines in front of the grid. The shutter gate is closed when there are electric field lines joining the successive electrodes (Fig. 4c). The value of potential difference for which the grid reaches a “closed state” ϕblock , depends on geometry of the grid. Calculations carried out for different grids built from cylindrical electrodes placed in one plane allowed estimation of the dependence between grid wire diameter and the voltage necessary to close the grid (Fig. 5). For grids with diameters ranging from 5 to 20% of a distance between the elec-
Fig. 4. Electric field lines for open (a), partially closed (b) and closed (c) shutter grid. Grid wires diameter is equal to 0.16 mm, distance between centres of electrodes is 1.0 mm and value of electric field far from grid’s plane is equal to 200 V/cm. ϕgrid is a difference of electric potential between successive grid electrodes.
trodes, a potential difference of 2.0 to 1.2, respectively, of the value of drift field multiplied by a distance between the grid electrodes is necessary to close the grid. Permeability is a function of voltage between grid electrodes. As a rule, permeability decreases with increasing blocking voltage. This dependence for typical grids has a form similar to the curve calculated for a grid consisting of wires with rectangular cross-section placed in two planes (Fig. 6a). Such arrangement corresponds to grid built from two etched thin metal plates separated by thin insulator foil (see Fig. 2a). Results of calculation were compared with experimental data obtained for ion mobility spectrometer MedIMS constructed and used in the Military University of Technology in Warsaw. The shutter grid of this instrument is built from 0.08-mm thick etched beryllium bronze plates separated by 0.10-mm thick teflon foil. For comparison of theoretical and experimental data,
Fig. 6. Permeability of the grid as a function of the difference of grid electrode potentials. Theoretical and experimental dependences for the grid made from etched plates (a) and permeability calculated for the grid with electrodes placed in two relatively distant planes (b).
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
which is shown in Fig. 6a, a value of electric field Edrift in the vicinity of grid was needed. This value depends on a magnitude of high voltage used for supplying the IMS detector and was estimated by solving the Laplace equation for electric potential existing in the space surrounded by the real system of detector’s electrodes. An interesting effect can be shown for the grid in which electrodes are placed in two relatively distant planes. In that case equalisation of potential of electrodes does not guarantee achievement of the maximal permeability (Fig. 6b). It is a consequence of the fact that disturbance of electric field by introduction of that system of the grid electrodes is rather significant. Using a small positive potential difference increases permeability because it flattens the course of electric field lines. The effect of closing the grid is obtained by production of a big potential difference between successive electrodes. Opening of the grid takes place by equalisation of potentials of electrodes. Practically it is performed by supplying square voltage pulses to the electrodes from a special generator or by short-circuiting of successive electrodes. The “open” or “closed” state of the grid does not depend on the potential difference only. The deciding factor is a ratio of this difference to the drift field value. Therefore a situation, in which the grid is opened by temporary increase of external (drift) field while all the time potential difference between electrodes remains constant is possible. All calculations, which results are presented here, were made with an assumption that drift field Edrift at some distance from the grid is constant and its value is the same on both sides of the grid. This simplification allows using relatively simple mathematical model for describing static and dynamic phenomena occurring near grid. In reality electric field inside IMS detectors is more complicated. It results mainly from real shapes of detector’s electrodes and distribution of electric potential on them. Another phenomenon which can be taken into account as source of possible inaccuracy is an effect of space charge. As it was mentioned earlier, shutter grid separates ion reactor (reactant section) from drift region. The reactor is filled by ions produced there in complex processes of ionisation while drift region is practically empty, i.e., only very small portions of ions are present there as a result of opening the shutter grid for short time. It means, that electric field on both sides of the grid is shaped by potentials on detector’s electrodes, but only in reaction section one can find additional source of field which is space charge. Diameter of reactant section in MedIMS spectrometer is equal to 1.0 cm and the region in which ions are
Fig. 7. Probability distributions for place (a) and time (b) of the beginning of ion track used in the ion swarm movement simulation. Symbols used on graphs are—t: time, t0 : time of beginning of ions tracking, tg : gating time, tobs : time of observation of ions distribution, y: vertical coordinate, a: distance between centres of electrodes.
119
present is about 2 cm long. On the basis of static current measurements a charge density was estimated to be approximately equal to 1.6 × 10−12 C cm−3 . This value corresponds to ions concentration of 107 cm−3 , which is typical for IMS detectors with 63 Ni ionisation sources. The electric field generated by such space charge was calculated using PDE Toolbox which is the part of MATLAB software [11]. Maximal value of this field is equal to about 3.5 V/cm, what is negligible in comparison with field generated by detector’s electrodes, which value for MedIMS was changed in range 180–250 V/cm. 3. Ionic movement simulation A method of an ion concentration distribution determination consists in tracking of ions movement along their trajectories. The algorithm of the method is very simple. Ions are generated far away from the grid, where influence of the grid electrodes potential on electric field is negligible. In practice, this condition is fulfilled for the distance equal to 2.5 of the spacing between grid electrodes, and in the simulation all ions are generated in such a distance. Value of the vertical coordinate of the point in which ion trajectory begins is pseudo-randomly selected. Ions concentration distribution in the specified time after opening the grid is the result of the simulation. In this connection, it is necessary to select the time of the beginning of ion motion using also the pseudo-random method.
Fig. 8. History of the ion swarm movement—a result of computer simulation.
120
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
Fig. 9. Average ion concentration distribution along spectrometer axis (a) and relative peak area (b) for different times of the opening of shutter grid.
Probability distributions for the initial location and time of ions movement are shown in Fig. 7. During ion movement tracking, status of the grid is checked on every time step. If a change of this status takes place, i.e., grid was opened or closed, an electric field is also changed. The IMS SG 01 programme allows consideration of the influence of diffusion on ions movement. The diffusion coefficient D is calculated from the Nernst–Einstein formula (K = eD/kT), where K is the ion mobility, k the Boltzmann constant, T absolute temperature, e is the elementary charge. For the trajectory modification, the procedure shown in [12] was used, consisting in addition of a small ion displacement in random direction after each time step t. The length of this displacement r is equal to the diffusion length (2Dt)1/2 . Besides diffusion, a mutual electrostatic repulsion can influence ions concentration distribution in the drift region of IMS detectors [13,14]. In our calculations we neglected this effect because electric field produced by swarms of ions in detectors such as MedIMS is very small. On the basis of simple calculation we estimated that the value of this field does not exceed 1.5 V/cm. Phenomena which are described here, i.e., movement of ions in neighbourhood of shutter grid last less than 0.5 ms. During this time displacement of ions with mobility of 2.5 cm2 /Vs in field generated by space charge is not greater than 0.0019 cm. Diffusion length for the same time is equal to 0.0081 cm, i.e., is more than four times greater than displacement related to mutual repulsion. It means that for small times and charge density typical for radioionisation sources space charge effects can be neglected in comparison with diffusion. Number of tracked ions depends on the time of observation. The IMS SG 01 programme working on the medium class PC enables tracking of about 20 000 ion trajectories per 1 min. If a shape of ionic swarm is the only expected result of simulation, it is sufficient to collect information concerning location of 100 000 ions. However, if the quantitative information relating to ion concentration distribution is required the much greater number of trajectories should be analysed. Output data from the program are text files containing concentration distribution of ions. Numerous “computer experiments” were performed enabling obtaining some interesting qualitative and quantitative results. In
Fig. 8 history of the dislocation of the ion swarm in vicinity of the grid is shown. This simulation was carried out for the grid, for which electric field drawing was presented in Fig. 4. The drift field value was 200 V/cm, the voltage blocking the grid 27.5 V and the gating time 200 s. It is clearly seen that shapes of ion swarms are not rectangular. Shape deformation is greater for shorter gating times. Therefore, comparison of the gating time and the time necessary for ions to travel the distance equal to the electrode spacing is of crucial importance. Investigation of the gating time influence on the shape of average concentration distributions along spectrometer axis were also performed (Fig. 9a). These distributions were obtained by integration of the ion concentration along the coordinate perpendicular to drift direction. Next integration, along drift direction, enables obtaining information on total number of ions in the swarm that is about the electric charge carried by ions (Fig. 9b).
4. Conclusion A shutter grid is very important constructional element of an ion mobility spectrometer. Simple electric field analysis in the neighbourhood of the shutter grid allows determination of the grid permeability and estimation of the difference of electrode potentials, which ensures closing the grid for given value of the drift field. Very interesting results were obtained with ion movement simulation in the vicinity of the grid. Ions concentration distributions behind the grid in the beginning of the drift section significantly differ from the rectangular. That influences the shape of output peak as well as the spectrometer resolving power.
References [1] G.A. Eiceman, Z. Karpas, Ion Mobility Spectrometry, 2nd ed., CRC Press, Boca Raton, 2005. [2] A.M. Tyndall, The Mobility of Positive Ions in Gases, Cambridge University Press, New York, 1938. [3] N.E. Bradbury, R.A. Nielsen, Absolute values of the electron mobility in hydrogen, Phys. Rev. 49 (1936) 388–393.
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121 [4] J.R. Kimmel, F. Engelke, R.N. Zare, Novel method for the production of finely spaced Bradbury–Nielson gates, Rev. Sci. Instrum. 72 (2001) 4354–4357. [5] O.K. Yoon, I.A. Zuleta, M.D. Robbins, G.K. Barbula, R.N. Zare, Simple templatebased method to produce Bradbury–Nielsen gates, J. Am. Soc. Mass Spectrom. 18 (2007) 1901–1908. [6] M. Salleras, A. Kalms, A. Krenkow, M. Kessler, J. Goebel, G. Mueller, S. Marcoa, Electrostatic shutter design for a miniaturized ion mobility spectrometer, Sens. Actuators B: Chem. 118 (2006) 338–342. [7] M. Teepe, J.I. Baumbach, A. Neyer, H. Schmidt, P. Pilzecker, Miniaturized ion mobility spectrometer, Int. J. Ion Mobility Spectrom. 4 (2001) 60–64. [8] J. Puton, Static and dynamic properties of the shutter grid for the ion mobility spectrometer, Nauch. Apparat.-Sci. Instrum. 4 (1) (1989) 29–41. [9] http://www.fieldp.com. [10] http://www.simion.com. [11] http://www.mathworks.com. [12] A.H. Brittain, J.L. Brokenshire, Quantitative Investigation of the Ion Mobility Spectrometry (IMS) Detection of Nitro-Compounds Over a Wide Temperature Range, and The Effects of Dopants. In: 5th International Workshop on Ion Mobility Spectrometry, Jackson, Wyoming, 1996. [13] J. Xu, W.B. Whitten, J.M. Ramsey, Space charge effects on resolution in a miniature ion mobility spectrometer, Anal. Chem. 72 (2000) 5787–5791. [14] G.E. Spangler, Space charge effects in ion mobility spectrometry, Anal. Chem. 64 (1992) 1312.
121
Biographies Jarosław Puton obtained his PhD degree from Military University of Technology in Warsaw, Poland in 1980. From this time he is working in the field of instrumentation for analysis of gaseous mixtures. His research involved problems of construction and theory of ionisation detectors. Most of his works are dedicated to Ion Mobility Spectrometry. Presently he is working in the Laboratory of Applied Environmental Chemistry at University of Kuopio, Finland. Andrzej Knap received his MC degree in protection against contamination in 1996 and PhD in instrumental chemistry in 2004. He is lecturer and researcher in the Department of Chemistry, Military University of Technology, Warsaw, Poland. His present research interests are analysis of air pollution using instrumental techniques and signal processing. Bogusław Siodłowski received his MC degree in protection against contamination specialty from Military University of Technology in 1998. Presently he is pursuing his PhD in Institute of Chemistry, Faculty of New Technologies and Chemistry, Military University of Technology, Warsaw, Poland. His current research interests cover analysis of air pollutions using Ion Mobility Spectrometry.
Contents lists available at ScienceDirect
Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb
Modelling of penetration of ions through a shutter grid in ion mobility spectrometers Jarosław Puton ∗ , Andrzej Knap, Bogusław Siodłowski Faculty of New Technologies and Chemistry, Military University of Technology, Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 2 October 2007 Received in revised form 19 June 2008 Accepted 6 August 2008 Available online 22 August 2008 Keywords: Ion mobility spectrometry (IMS) Ion shutter Computer simulation of ions movement
a b s t r a c t Phenomena occurring in vicinity of the shutter grid are important for resolving power of ion mobility spectrometers and also for magnitude of the signal from these detectors. In this paper we present results of computer calculations concerning electric field and ion concentration distributions in neighbourhood of grid electrodes. Proposed model and methods of calculation give possibility for estimation of permeability of the grid and for determination of ion concentration profile behind the grid in dependence of grid dimensions and parameters of controlling voltage. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Ion mobility spectrometers (IMS) are analytical instruments used as detectors for investigation of composition of gas mixtures [1]. The basis of spectrometer operation consists in two phenomena: an ionisation of the sample and an identification of ionisation products by their separation according to ion mobility. These phenomena occur in two different parts of spectrometer. The first of them is an ion reactor in which sample ions are produced. The second part is a drift region designed for separation of different ion products. In the classic IMS detectors, operation of which is similar to time of flight mass spectrometers, it is necessary to produce small portions of ions, which then are moving along the drift region. Production of such ion portions is executed with special “ion valve” known as a shutter grid or a shutter gate, which is placed between the ion reactor and the drift region. The gate is closed for most of the time. It is opened only for a short moment, with suitable electric signals (pulses). These pulses change electric field in neighbourhood of the grid only. At some distance from the grid ions are moving under the influence of electric field Edrift , which is uniform and constant. There are two classic solutions of shutter gate. The first one is Tyndall’s gate [2], which consists of two grids (see Fig. 1a). They produce electric field Eblock , direction of which is opposite to the
∗ Corresponding author. Current address: University of Kuopio, LAEC, Patteristonkatu 1, FIN-50100 Mikkeli, Finland. Tel.: +358 15 355 6236; fax: +358 15 355 6363. E-mail address: jaroslaw.puton@uku.fi (J. Puton). 0925-4005/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2008.08.011
field in which drift of ions occurs. This field stops ions and prevents their penetration to the drift region. At present, Tyndall’s gates are not practically used in IMSs. It is a consequence of the fact that their permeability for ions is limited and that these gates are not suitable for production of well shaped narrow ion portions. The most often applied technical solution is Bradbury–Nielsen gate (BNG) [3]. Similarly to Tyndall’s gate, BNG consist of two sets of electrodes (Fig. 1b). The electrodes are placed in one plane or in two planes lying close to each other. If potential difference between successive electrodes is suitably high, electric field Eblock created by grid electrodes can block penetration of ions from reaction to drift region. In that case all ions become discharged on grid electrodes. Equalisation of potential of successive electrodes makes gate permeable. There are several technologies of shutter gates fabrication. It is possible to weave or put wires on special frames. This technology is laborious and requires special instruments [4,5]. It is much easier to use an etching method for grid production. In this case, material of the grid can be a semiconductor plate [6] or a thin metal sheet (see Fig. 2a). A set of two plates separated by insulator creates a complete BNG (Fig. 2b). Area of the plates in surrounding of grid electrodes is usually relatively large; therefore electric capacity of the system can also be significant. It can cause some difficulties in realization of fast changing of electrode polarisation. Precise, small grids can be fabricated with laser technology [7]. This method is useful for large-scale production, and offers low unit price. Similar technical solutions to those used in case of shutter gates for IMS are also applied in mass spectrometry. It is necessary to understand a fundamental difference in the way ions move in both
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
117
Fig. 1. Principles of operation of Tyndall (a) and Bradbury–Nielsen (b) gates.
kinds of detectors. In case of IMS, ions are moving in gas and their trajectories are practically consistent with electric field lines. “Closing of the grid” is equivalent to such potential distribution, for which no field lines penetrate the grid plane. In case of mass spectrometry, ions move in vacuum. Therefore, ions can achieve great velocities. Inertia of ions causes that their trajectories considerably differ from electric field lines. Therefore, in some cases in mass spectrometers grids do not stop ions but only deflect their beam. The phenomena related to transport of ions through a shutter grid influence magnitude and shape of output pulse from IMS detector. Each grid is characterised by a given maximum permeability. Its value determines amplitude of the signal. Grid dimensions and the manner of its electrodes control influence spatial ion density distribution behind the grid, i.e., in the beginning of the drift region. This distribution determines width of output pulses of particular ionic species, and thus also resolving power of the spectrometer. Calculation of the grid permeability is possible on the basis of electric field analysis, i.e., electrostatic considerations. Such calculations were performed for optimisation of the etched silicon grid [6]. Dynamic description of ions penetration through a
grid is possible by computer simulation of ions movement. Similar problem was solved by one of us 18 years ago [8]. Mathematical methods used then have been improved allowing obtaining some new interesting results. 2. Electric field of the grid Calculation of electric field for the model arrangement of electrodes of the grid is not complicated. Widely known computer software can be used for solving problems of the electric field [9] and the movement of ions [10], and also universal mathematical program packs [11] can be applied for these purposes. Results of the calculations presented in the further part of the study were obtained using the computer programme IMS SG 01 developed by us. Input data for the programme are matrixes of electric field potential calculated for definite geometries of the grid. The programme IMS SG 01 is designed for drawing electric field lines, computing permeability of the grid and for simulation of ions movement. The results obtained with the simulation allow investigation of dynamic phenomena that is those kinds of problems in which potentials of the grid electrodes change in time. Upon request
Fig. 2. Single etched electrode (a) and a set of components (b) of the Bradbury–Nielsen gate.
118
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
Fig. 3. Illustration of the method of electric field calculation. Fig. 5. Effect of the electrode diameter on value of the blocking voltage.
the programme with several files of electric field potential data can be made available by the authors. Electric field in the neighbourhood of metal grid electrodes can be considered as a sum of two components. The first one is a uniform electric field disturbed by introduction of the set of conductors (grid electrode wires). The second component is a result of accumulation of electric charges on particular electrodes under influence of differences in electric potential. These two components can be found by solving the Poisson’s equation with boundary conditions corresponding to fixed values of electric fields or potentials on the borders of interesting region. Because of superposition rule, the resulting electric field for any electrode polarisation can be easily calculated as a linear combination of both component fields (Fig. 3). Field lines for three values of electric potential differences between consecutive electrodes ϕgrid are presented in Fig. 4. Permeability of the grid can be computed as a ratio of the number of field lines passing through the grid and the number of lines in front of the grid. The shutter gate is closed when there are electric field lines joining the successive electrodes (Fig. 4c). The value of potential difference for which the grid reaches a “closed state” ϕblock , depends on geometry of the grid. Calculations carried out for different grids built from cylindrical electrodes placed in one plane allowed estimation of the dependence between grid wire diameter and the voltage necessary to close the grid (Fig. 5). For grids with diameters ranging from 5 to 20% of a distance between the elec-
Fig. 4. Electric field lines for open (a), partially closed (b) and closed (c) shutter grid. Grid wires diameter is equal to 0.16 mm, distance between centres of electrodes is 1.0 mm and value of electric field far from grid’s plane is equal to 200 V/cm. ϕgrid is a difference of electric potential between successive grid electrodes.
trodes, a potential difference of 2.0 to 1.2, respectively, of the value of drift field multiplied by a distance between the grid electrodes is necessary to close the grid. Permeability is a function of voltage between grid electrodes. As a rule, permeability decreases with increasing blocking voltage. This dependence for typical grids has a form similar to the curve calculated for a grid consisting of wires with rectangular cross-section placed in two planes (Fig. 6a). Such arrangement corresponds to grid built from two etched thin metal plates separated by thin insulator foil (see Fig. 2a). Results of calculation were compared with experimental data obtained for ion mobility spectrometer MedIMS constructed and used in the Military University of Technology in Warsaw. The shutter grid of this instrument is built from 0.08-mm thick etched beryllium bronze plates separated by 0.10-mm thick teflon foil. For comparison of theoretical and experimental data,
Fig. 6. Permeability of the grid as a function of the difference of grid electrode potentials. Theoretical and experimental dependences for the grid made from etched plates (a) and permeability calculated for the grid with electrodes placed in two relatively distant planes (b).
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
which is shown in Fig. 6a, a value of electric field Edrift in the vicinity of grid was needed. This value depends on a magnitude of high voltage used for supplying the IMS detector and was estimated by solving the Laplace equation for electric potential existing in the space surrounded by the real system of detector’s electrodes. An interesting effect can be shown for the grid in which electrodes are placed in two relatively distant planes. In that case equalisation of potential of electrodes does not guarantee achievement of the maximal permeability (Fig. 6b). It is a consequence of the fact that disturbance of electric field by introduction of that system of the grid electrodes is rather significant. Using a small positive potential difference increases permeability because it flattens the course of electric field lines. The effect of closing the grid is obtained by production of a big potential difference between successive electrodes. Opening of the grid takes place by equalisation of potentials of electrodes. Practically it is performed by supplying square voltage pulses to the electrodes from a special generator or by short-circuiting of successive electrodes. The “open” or “closed” state of the grid does not depend on the potential difference only. The deciding factor is a ratio of this difference to the drift field value. Therefore a situation, in which the grid is opened by temporary increase of external (drift) field while all the time potential difference between electrodes remains constant is possible. All calculations, which results are presented here, were made with an assumption that drift field Edrift at some distance from the grid is constant and its value is the same on both sides of the grid. This simplification allows using relatively simple mathematical model for describing static and dynamic phenomena occurring near grid. In reality electric field inside IMS detectors is more complicated. It results mainly from real shapes of detector’s electrodes and distribution of electric potential on them. Another phenomenon which can be taken into account as source of possible inaccuracy is an effect of space charge. As it was mentioned earlier, shutter grid separates ion reactor (reactant section) from drift region. The reactor is filled by ions produced there in complex processes of ionisation while drift region is practically empty, i.e., only very small portions of ions are present there as a result of opening the shutter grid for short time. It means, that electric field on both sides of the grid is shaped by potentials on detector’s electrodes, but only in reaction section one can find additional source of field which is space charge. Diameter of reactant section in MedIMS spectrometer is equal to 1.0 cm and the region in which ions are
Fig. 7. Probability distributions for place (a) and time (b) of the beginning of ion track used in the ion swarm movement simulation. Symbols used on graphs are—t: time, t0 : time of beginning of ions tracking, tg : gating time, tobs : time of observation of ions distribution, y: vertical coordinate, a: distance between centres of electrodes.
119
present is about 2 cm long. On the basis of static current measurements a charge density was estimated to be approximately equal to 1.6 × 10−12 C cm−3 . This value corresponds to ions concentration of 107 cm−3 , which is typical for IMS detectors with 63 Ni ionisation sources. The electric field generated by such space charge was calculated using PDE Toolbox which is the part of MATLAB software [11]. Maximal value of this field is equal to about 3.5 V/cm, what is negligible in comparison with field generated by detector’s electrodes, which value for MedIMS was changed in range 180–250 V/cm. 3. Ionic movement simulation A method of an ion concentration distribution determination consists in tracking of ions movement along their trajectories. The algorithm of the method is very simple. Ions are generated far away from the grid, where influence of the grid electrodes potential on electric field is negligible. In practice, this condition is fulfilled for the distance equal to 2.5 of the spacing between grid electrodes, and in the simulation all ions are generated in such a distance. Value of the vertical coordinate of the point in which ion trajectory begins is pseudo-randomly selected. Ions concentration distribution in the specified time after opening the grid is the result of the simulation. In this connection, it is necessary to select the time of the beginning of ion motion using also the pseudo-random method.
Fig. 8. History of the ion swarm movement—a result of computer simulation.
120
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121
Fig. 9. Average ion concentration distribution along spectrometer axis (a) and relative peak area (b) for different times of the opening of shutter grid.
Probability distributions for the initial location and time of ions movement are shown in Fig. 7. During ion movement tracking, status of the grid is checked on every time step. If a change of this status takes place, i.e., grid was opened or closed, an electric field is also changed. The IMS SG 01 programme allows consideration of the influence of diffusion on ions movement. The diffusion coefficient D is calculated from the Nernst–Einstein formula (K = eD/kT), where K is the ion mobility, k the Boltzmann constant, T absolute temperature, e is the elementary charge. For the trajectory modification, the procedure shown in [12] was used, consisting in addition of a small ion displacement in random direction after each time step t. The length of this displacement r is equal to the diffusion length (2Dt)1/2 . Besides diffusion, a mutual electrostatic repulsion can influence ions concentration distribution in the drift region of IMS detectors [13,14]. In our calculations we neglected this effect because electric field produced by swarms of ions in detectors such as MedIMS is very small. On the basis of simple calculation we estimated that the value of this field does not exceed 1.5 V/cm. Phenomena which are described here, i.e., movement of ions in neighbourhood of shutter grid last less than 0.5 ms. During this time displacement of ions with mobility of 2.5 cm2 /Vs in field generated by space charge is not greater than 0.0019 cm. Diffusion length for the same time is equal to 0.0081 cm, i.e., is more than four times greater than displacement related to mutual repulsion. It means that for small times and charge density typical for radioionisation sources space charge effects can be neglected in comparison with diffusion. Number of tracked ions depends on the time of observation. The IMS SG 01 programme working on the medium class PC enables tracking of about 20 000 ion trajectories per 1 min. If a shape of ionic swarm is the only expected result of simulation, it is sufficient to collect information concerning location of 100 000 ions. However, if the quantitative information relating to ion concentration distribution is required the much greater number of trajectories should be analysed. Output data from the program are text files containing concentration distribution of ions. Numerous “computer experiments” were performed enabling obtaining some interesting qualitative and quantitative results. In
Fig. 8 history of the dislocation of the ion swarm in vicinity of the grid is shown. This simulation was carried out for the grid, for which electric field drawing was presented in Fig. 4. The drift field value was 200 V/cm, the voltage blocking the grid 27.5 V and the gating time 200 s. It is clearly seen that shapes of ion swarms are not rectangular. Shape deformation is greater for shorter gating times. Therefore, comparison of the gating time and the time necessary for ions to travel the distance equal to the electrode spacing is of crucial importance. Investigation of the gating time influence on the shape of average concentration distributions along spectrometer axis were also performed (Fig. 9a). These distributions were obtained by integration of the ion concentration along the coordinate perpendicular to drift direction. Next integration, along drift direction, enables obtaining information on total number of ions in the swarm that is about the electric charge carried by ions (Fig. 9b).
4. Conclusion A shutter grid is very important constructional element of an ion mobility spectrometer. Simple electric field analysis in the neighbourhood of the shutter grid allows determination of the grid permeability and estimation of the difference of electrode potentials, which ensures closing the grid for given value of the drift field. Very interesting results were obtained with ion movement simulation in the vicinity of the grid. Ions concentration distributions behind the grid in the beginning of the drift section significantly differ from the rectangular. That influences the shape of output peak as well as the spectrometer resolving power.
References [1] G.A. Eiceman, Z. Karpas, Ion Mobility Spectrometry, 2nd ed., CRC Press, Boca Raton, 2005. [2] A.M. Tyndall, The Mobility of Positive Ions in Gases, Cambridge University Press, New York, 1938. [3] N.E. Bradbury, R.A. Nielsen, Absolute values of the electron mobility in hydrogen, Phys. Rev. 49 (1936) 388–393.
J. Puton et al. / Sensors and Actuators B 135 (2008) 116–121 [4] J.R. Kimmel, F. Engelke, R.N. Zare, Novel method for the production of finely spaced Bradbury–Nielson gates, Rev. Sci. Instrum. 72 (2001) 4354–4357. [5] O.K. Yoon, I.A. Zuleta, M.D. Robbins, G.K. Barbula, R.N. Zare, Simple templatebased method to produce Bradbury–Nielsen gates, J. Am. Soc. Mass Spectrom. 18 (2007) 1901–1908. [6] M. Salleras, A. Kalms, A. Krenkow, M. Kessler, J. Goebel, G. Mueller, S. Marcoa, Electrostatic shutter design for a miniaturized ion mobility spectrometer, Sens. Actuators B: Chem. 118 (2006) 338–342. [7] M. Teepe, J.I. Baumbach, A. Neyer, H. Schmidt, P. Pilzecker, Miniaturized ion mobility spectrometer, Int. J. Ion Mobility Spectrom. 4 (2001) 60–64. [8] J. Puton, Static and dynamic properties of the shutter grid for the ion mobility spectrometer, Nauch. Apparat.-Sci. Instrum. 4 (1) (1989) 29–41. [9] http://www.fieldp.com. [10] http://www.simion.com. [11] http://www.mathworks.com. [12] A.H. Brittain, J.L. Brokenshire, Quantitative Investigation of the Ion Mobility Spectrometry (IMS) Detection of Nitro-Compounds Over a Wide Temperature Range, and The Effects of Dopants. In: 5th International Workshop on Ion Mobility Spectrometry, Jackson, Wyoming, 1996. [13] J. Xu, W.B. Whitten, J.M. Ramsey, Space charge effects on resolution in a miniature ion mobility spectrometer, Anal. Chem. 72 (2000) 5787–5791. [14] G.E. Spangler, Space charge effects in ion mobility spectrometry, Anal. Chem. 64 (1992) 1312.
121
Biographies Jarosław Puton obtained his PhD degree from Military University of Technology in Warsaw, Poland in 1980. From this time he is working in the field of instrumentation for analysis of gaseous mixtures. His research involved problems of construction and theory of ionisation detectors. Most of his works are dedicated to Ion Mobility Spectrometry. Presently he is working in the Laboratory of Applied Environmental Chemistry at University of Kuopio, Finland. Andrzej Knap received his MC degree in protection against contamination in 1996 and PhD in instrumental chemistry in 2004. He is lecturer and researcher in the Department of Chemistry, Military University of Technology, Warsaw, Poland. His present research interests are analysis of air pollution using instrumental techniques and signal processing. Bogusław Siodłowski received his MC degree in protection against contamination specialty from Military University of Technology in 1998. Presently he is pursuing his PhD in Institute of Chemistry, Faculty of New Technologies and Chemistry, Military University of Technology, Warsaw, Poland. His current research interests cover analysis of air pollutions using Ion Mobility Spectrometry.