Abstract:
A micro-fabricated double condenser method and apparatus for the measurement of number-size distribution of airborne nanoparticles is provided. The invention is an instrument which can measure particle size under 100 nanometers in-situ. The present invention includes features such as a small nanoparticle airborne particulate analyzer, with a voltage-stable and feedback-controlled instrument package. The invention features also include a micro-fabricated nanoparticle charging and sorting device (NCaS). The present invention provides a portable, lightweight, and efficacious particle-sizing instrument that is able to effectively count and size nanoparticles over a wide range of operating conditions.

Description:
REFERENCE TO U.S. GOVERNMENT INTEREST 
       [0001]    “The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Grant USDOT DTRT06-G-0018 CFDA 20.701, UTC Core award, awarded by U.S. Department of Transportation.” 
     
    
     CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0002]    The present application is related to, claims the earliest available effective filing date(s) from (e.g., claims earliest available priority dates for other than provisional patent applications; claims benefits under 35 USC §119(e) for provisional patent applications), and incorporates by reference in its entirety all subject matter of the following listed application(s) (the “Related Applications”) to the extent such subject matter is not inconsistent herewith; the present application also claims the earliest available effective filing date(s) from, and also incorporates by reference in its entirety all subject matter of any and all parent, grandparent, great-grandparent, etc. applications of the Related Application(s) to the extent such subject matter is not inconsistent herewith. 
         [0003]    U.S. provisional patent application 61/319,352, entitled “Microfabricated Device For The Measurement Of Number-Size Distribution Of Airborne Nanoparticles”, naming Terence Barrett, as inventor, filed 31 Mar. 2010 
       BACKGROUND 
       [0004]    1. Field of Use 
         [0005]    Unregulated nanoparticles are the largest component by number fraction of the particulates in late model vehicle tailpipe exhaust, and are responsible for numerous adverse pulmonary and cardiovascular health effects. Expense, size and weight, and vibrations sensitivity confine the industry standard-instruments able to ascertain the size and number of these fine particulates to lab bench use. To effectively regulate and reduce nanoparticle emissions, inexpensive, small, light, and vibration insensitive nanoparticle analyzing instruments are needed. 
         [0006]    This application relates to the measurement of air pollution and in particular to the rapid measurement of the quantity and size distribution of aerosol particles. As vehicle engines become more complex and varied, it becomes necessary to have better systems to determine motor vehicle emissions inventories. To develop accurate ultrafine particle models, the common practice of using engine dynamometers and in-lab testing will need to be replaced with in-situ monitoring of vehicles on the road. However, measurement of engine exhaust particle size is currently done using instruments which are bulky, expensive, and energy inefficient to easily adapt to on-board, in-situ particle measurement. 
         [0007]    2. Description of Prior Art 
         [0008]    Mobile emission inventories have traditionally been based on average emission performance of small data sets of new car, small-scale used car, or road side measurements. However, these methods are only approximations to the continuously varying emissions of real-world vehicles. 
         [0009]    There is a lack of truly portable instruments that can both size and count aerosol particle emissions directly on-board vehicles in real time. For example, starting in 2012, heavy-duty diesel on-board vehicle particle emission monitoring will be required in the United States. One particle emission monitoring system is a partial-flow constant volume sampling system that weighs 120 kg and is available to capture particle emissions via a bag collection system which is available for post particle emission analysis (e.g., particle size and count) in a laboratory. 
         [0010]    There are other limitations with current systems for measuring engine exhaust particles, in particular ultrafine particles, or particle sizes less than 100 nanometers. Measuring ultrafine particles is typically done in a laboratory setting. As noted earlier, particulate monitoring instruments are bulky and not designed for in-situ (i.e., on board or real-time) particle monitoring. Those particulate sizing instruments are generally connected to engine dynamometers which are run at loads to roughly simulate on-road conditions and are not suitable for in-situ fleet-wide monitoring of engine exhaust particles. 
         [0011]    Additionally, particles are measured by measuring the mass of particles below a certain aerodynamic size collected on a filter. This method has the advantage of simplicity but does not distinguish between large particles, i.e., particles above 100 nm, ultrafine particles (&lt;100 nm), and nanoparticles (&lt;50 nm) which correlate with significant adverse health impacts. Often, the total mass of the smaller particles are often minuscule and indeterminate when compared to that of the larger particles. However, it is the smaller ultrafine and nanoparticles that have a higher mobility into the human lung than the larger particles; and can pass from the lung directly into the bloodstream. 
         [0012]    One model of a particle measuring device can measure particle mobility (from which particle diameter is derived) diameters from 0.0025 um to 1.0 um and produce a size vs. count distribution in approximately two minutes. However, the instrument is not ideal for non-laboratory use because it is expensive, requires a high watt source, and takes 2 minutes to make a single size distribution measurement. 
         [0013]    In one optical system for measuring particle concentration, light is directed through aerosol particle-laden smoke and the attenuation of the light is measured on a detector to indicate total particle concentration. This method does not measure particle size distribution, however. Another optical method uses light scattering to measure particle size by causing the particles to pass one at a time through a chamber so that scattered light amplitude depends on the particle size. The amplitude is measured by a photomultiplier which produces an electrical signal dependent upon particle size. To isolate single particles for detection, gas sampling must be done at low velocity, and the system is usually provided with very narrow pipes which are subject to contamination, require frequent cleaning, and tend to collect the larger particles before their entry into the sensing chamber. Further, such method of measuring the size of a single particle is very slow, requiring perhaps as much as an hour for a typical measurement. 
         [0014]    Electrical methods have the advantage that they can be operated nearly continuously with the results available to the operator after a very short interval of time. In one electrical method described in U.S. Pat. No. 3,114,877 to Dunham, a charging device operates to charge separate groups of aerosol particles passing the device. The particles then flow in a random manner through a field-free region, pass an ion trap and flow to a detector. At the detector, the particles lose their charge and produce a current. Although the detector current in the Dunham apparatus is said to be an index of the number of particles, it is clear that the amplitude of the current is a function of the total charge on all of the particles sensed by the detector at a given moment. Thus, the amplitude of the current is a function of the total surface area of the particles. Because the particles flow in a random manner to the detector, particles having different surface areas (and thus different sizes) lose their charge at the same moment of time to produce the current. Therefore, the output current in the Dunham apparatus is not indicative of the number of particles except when they are of uniform size. 
         [0015]    Another method which indicates aerosol particle size distribution is based on the mobility of charged particles in an electric field extending radially across a tube in which the particles flow. Mobility is a measure of the velocity of a charged particle in an electric field, and generally speaking, the higher the charge on the particle the higher the mobility. For a given method of charging a particle, the amount of charge on the particle is a function of the size of the particle. Therefore, mobility is a function of particle size and methods based on particle mobility utilize the difference in mobility to measure particle size distribution. In one such device described in U.S. Pat. No. 3,413,545 to Whitby, clean air is caused to move downwardly in an annular flow path surrounding an elongated electrode extending axially in a cylindrical housing. Charged aerosol particles are introduced around the outer periphery of the flow path of clean air and an electric potential is applied across the elongated electrode and the cylindrical housing. For any given potential, particles having mobility below a certain value will not move radially enough to contact and lose their charge to the elongated electrode before passing its downstream end. An electrometer detects these charged particles which generate a current, the amplitude of which is a function of the total charge on the detected particles. By varying the potential applied to the elongated electrode, more or fewer charged particles will reach the detector and induce the current. By relating the current produced when various potentials are applied to the elongated electrode, a measure of particle size distribution can be obtained. However, a number of factors limit the usefulness of this device for monitoring effluents in stacks of industrial installations, for example. Due to the method of charging, known as diffusion charging, only particles less than about 2 microns diameter can be measured whereas in a typical stack, particles up to 100 microns or more will be present. Further, the diffusion charging method is also inconvenient because it requires a source of compressed air and various thin pipes which are subject to clogging. 
         [0016]    Another apparatus for measuring particle size and distribution is described in U.S. Pat. No. 7,098,462 to Chua et al. That micro-fabricated device describes a series of condensers in a fixed electric field, each attached to its own electrometer circuit. The distribution of particle sizes in an aerosol is determined by the fraction collected and measured by each of the condenser/electrometer circuits. However, it will be appreciated that characterizing an aerosol of unknown particle size distribution would require a Chua et al. apparatus having enough condensers and corresponding electrometer circuits for any possible particle size; thus leading to a bulky and inefficient method for measuring particle sizes. 
         [0017]    Accordingly, there is a need for a method and apparatus for a compact, low-cost, low power system capable of discriminating and measuring in-situ particle size distribution based on particle mobility in electric fields generated by multiple condensers. 
       BRIEF SUMMARY 
       [0018]    The foregoing and other problems are overcome, and other advantages are realized, in accordance with the presently preferred embodiments of these teachings. The invention provided is a robust and field deployable instrument. The present invention includes features such as a small nanoparticle airborne particulate analyzer, with a voltage-stable and feedback-controlled instrument package. The invention features also include a micro-fabricated nanoparticle charging and sorting device (NCaS). The present invention provides a portable, lightweight, and efficacious particle-sizing instrument that is able to effectively count and size nanoparticles over a wide range of operating conditions. 
         [0019]    In accordance with one embodiment of the present invention a portable apparatus for measuring aerosol particle concentration and particle size distribution is provided. The apparatus includes a corona charger for ionizing the aerosol particles; a first condenser for ion trapping aerosol particles charged by the corona charger, and a second condenser connectable to the first condenser, wherein the second condenser is adapted to trap aerosol particles having a plurality of mobilities. 
         [0020]    In accordance with another embodiment of the present invention a portable apparatus for measuring aerosol particle concentration and particle size distribution is provided. The apparatus includes a corona charger for ionizing the aerosol particles and a first condenser for ion trapping aerosol particles charged by the corona charger, wherein the first condenser is adapted to trap aerosol particles having a first plurality of mobilities. 
         [0021]    The invention is also directed towards a portable apparatus for measuring aerosol particle concentration and particle number size distribution. The apparatus includes a corona charger for ionizing the aerosol particles and a first condenser for ion trapping aerosol particles charged by the corona charger, wherein the first condenser is adapted to trap aerosol particles having a first mobility. Also included is a second condenser connectable to the first condenser, wherein the second condenser is adapted by an adjustable power supply to trap aerosol particles having a plurality of mobilities. Included is a measurement board for determining particle sizes and number concentrations in the aerosol; and a control board for: monitoring measurements by the measurement board, adjusting the pump controller, adjusting the first adjustable high voltage power supply, adjusting the second adjustable high voltage power supply, and adjusting the third adjustable high voltage power supply. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0022]    The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other objects, features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
           [0023]      FIG. 1  is pictorial illustration of one embodiment of the miniaturized micro-fabricated double condenser in accordance with the present invention; 
           [0024]      FIG. 2  is an operational control system diagram for the measurement of number-size distribution of airborne nanometer-particles in accordance with the present invention shown in  FIG. 1 ; 
           [0025]      FIG. 3  is a graphical depiction of calculations verifying scalability of design to nanometer dimensions and operating parameter ranges in accordance with the present invention shown in  FIG. 1 , where critical mobilities on the y-axis are plotted as a function of flow rate (I/min)-Voltage (V) ratio on the x-axis (shown in  FIG. 3  as (Q/Phi)); 
           [0026]      FIG. 4A  is a graphical depiction of electrical mobility versus particle diameter in accordance with the present invention shown in  FIG. 2 ; 
           [0027]      FIG. 4B  is a graphical depiction of types of particle charging as a function of electrical mobility and particle diameter in accordance with the present invention shown in  FIG. 2 ; 
           [0028]      FIG. 5A  is a graphical depiction of current reading/condenser voltage versus critical mobilities for multiple concentrations of isopropanol (IPA) in accordance with the present invention shown in  FIG. 2 ; 
           [0029]      FIG. 5B  is a graphical depiction of slopes of current/voltage versus critical IPA mobilities in accordance with  FIG. 5A ; 
           [0030]      FIG. 5C  is a graphical depiction of current reading/condenser voltage versus critical mobilities for multiple oleic acid particle diameters in accordance with the present invention shown in  FIG. 2 ; 
           [0031]      FIG. 5D  is a graphical depiction of slopes of current/voltage versus critical oleic acid particle mobilities in accordance with  FIG. 5C ; 
           [0032]      FIG. 6A  is a graphical depiction of a number distribution of IPA and oleic acid particles in IPA versus particle diameter in accordance with the present invention shown in  FIG. 2   
           [0033]      FIG. 6B  is a graphical depiction of a fraction of oleic acid particles in IPA versus particle diameter in accordance with the invention shown in  FIG. 2 ; 
           [0034]      FIG. 7  is a graphical depiction of size distribution measurements for IPA and oleic acid aerosols; 
           [0035]      FIG. 8  is a pictorial illustration of an alternate charger+series/parallel aspiration capacitor embodiment of the present invention shown in  FIG. 1 ; and 
           [0036]      FIG. 9  is a pictorial illustration of an alternate switchable series condenser configuration of the present invention shown in  FIG. 1 . 
       
    
    
     DESCRIPTION 
       [0037]    The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. 
         [0038]    Referring to  FIG. 1  there is shown a pictorial illustration of one embodiment of the miniaturized micro-fabricated double condenser in accordance with the present invention. This embodiment includes a charger  101 D and two aspiration capacitors in series  102   a ,  102   b  and  105   a ,  105   b . Both aspiration capacitors would nominally be held at the same voltage, but optionally may use separate high voltage power supplies to reduce the likelihood that the current signals to the respective electrometers would be confounded; only one differentiation of the I/V curve of the second condenser  10 B would give the number of particles in a given size bin. (See  FIG. 5A .) 
         [0039]    The first condenser  102   a ,  102   b  serves two critical functions: it acts like the sheath air, separating the response of the different particle sizes so they are not confounded, and it serves as an ion trap, reducing the prevalence of combined charging. With this design, the I/V vs. mobility (k) characteristic is the same for a given set of design parameters, and so various settings of potential (V) and flow rate (Q) can be selected that will maximize the possible range of sampled critical mobilities; discussed in more detail herein. 
         [0040]    The size distribution is determined from the I/V vs. k characteristic as shown by Eq. 8. (See paragraph 49.) Differentiating Eq. 8 with respect to critical mobility k c  results in Eq. 9. (See paragraph 49.) Plotting I 3 /V 3  vs. k c  for all settings of V 3  and Q a , results in a curve where the slope of the curve at each selected value of k c  provides the number of particles in the mobility range k d  to k c . See  FIGS. 5A-5D  and  FIGS. 6A-6B . 
         [0041]    The series embodiment of the present invention supports a sweep V and/or Q operation. This embodiment supports the linear sweep of voltage and/or flow rate, and is able to measure a continuously varying I/V response. This embodiment could be extended in this way to give a direct (non-differentiated) measurement of the particle size distribution. The linear sweeping of V and Q will obviate the need to differentiate the resulting IN curve. 
         [0042]    There are four parameters of interest to the characterization of charging efficiency: intrinsic charging efficiency (ε i ), the fraction of originally neutral particles which become charged within the charger; extrinsic charging efficiency (ε e ), the fraction of originally neutral particles which emerge out of the charger carrying at least one unit of charge; diffusion loss (LD), the fraction of particles lost in the charger through diffusion to the walls; and electrostatic loss (LE), the fraction of particles lost in the charger through electrical attraction to the plates that create the corona-inducing field. The four parameters are represented as: 
         [0000]      ε i =( C   1   −C   3 )/ C   1   EQ. 1
 
         [0000]      ε e =( C   2   −C   3 )/ C   O   EQ. 2
 
         [0000]        LE=ε   i −ε e   EQ. 3
 
         [0000]        LD =(1−ε i )(1 −C   1   /C   O )  EQ. 4
 
         [0043]    Four measurements are undertaken for each corona voltage (V 1 ), flow rate (Q a ), and particle size (Dp) combination to be characterized in order to calculate the above four parameters: First, the CPC measured concentration (C O ) when the charger and an electrostatic precipitator (ESP) are bypassed; second, the CPC measured concentration (C 1 ) when the voltages of both charger and ESP are zero; third, the CPC measured concentration (C 2 ) when the charger is at its set point voltage and the ESP is set at voltage (V IR ) sufficient to remove the free ions only; and fourth, the CPC measured concentration (C 3 ) when the charger is at its set point voltage and the ESP is set a voltage (V PR ) sufficient to remove all charged particles. 
         [0044]    Testing the present embodiment of the miniaturized micro-fabricated double condenser  10  shown in  FIG. 2  includes a radioactive neutralizer in order to re-neutralize the charged mono-disperse aerosol provided by a Differential Mobility Analyzer (DMA). First, an optimum corona voltage (V 1 ) can be selected. Then, over the range of condenser voltages (V 2 =V 3 =V) and aerosol flow rates (Q a ) for each particle diameter (Dp), the curve of I 3 /V 3  vs. k c  will be recorded, and then numerically differentiated once to determine the number of particles in a given size bin (as described earlier), where the bin extent is defined by the mobility range k d  to k c , with the capacitances determined by the direct measurement method and the relative measurement method. The bins can be adjusted until each mono-disperse aerosol is detected by a single bin. This will provide the relationship between D p  and k c  that will be used for calculating the size distribution of a poly-disperse aerosol. 
         [0045]    It will be appreciated that the present invention also enables a size distribution measurement of a poly-disperse aerosol. (See  FIG. 7 ). The size distribution measurement is made by measuring the mobility distribution of a poly-disperse aerosol; assigning a D p  to each mobility bin; correcting the counts in each bin using the charger extrinsic efficiency for each bin&#39;s Q a  and D p ; and correcting the counts in each bin with the charge distribution (which will shift the multiply-charged fraction of a bin to larger D p  bins). The system may be further extended with a single new NCaS device that implements the series/parallel design for direct measurement of the size distribution or a NCaS device and electronic circuit suitable to implement the V and/or Q sweep method. 
       DETAILED DISCUSSION 
       [0046]    Referring still to  FIG. 1  there is shown pictorial illustration of one embodiment of the miniaturized micro-fabricated double condenser  10  in accordance with the present invention. The components of the micro-fabricated corona ionizer are deposited on an insulating substrate  103 . One possible material for insulating substrate  103  is glass; although it will be appreciated that any suitable insulating substrate may be used. Anchor  101  is deposited on substrate  103 . A typical material for anchor  101  is copper; although it will be appreciated that any suitable anchoring material may be used. Grids  101   a ,  101   b  are suitably deposited and anchored on the substrate  103  such that they are parallel to probe  101   d  and equidistant from probe  101   d . In this configuration, the corona ionizer forms a flow-through ionizer, which is useful for creating micro-fabricated particulate sensors. 
         [0047]    Probe  101   d  is deposited with anchor  101   c  but is undercut so that it is suspended above substrate  103 . The radius of the tip of probe  101   d  is typically less than approximately 20 μm, while the suspension height of probe  101   d  above substrate  103  is typically less than 500 μm. 
         [0048]    Still referring to  FIG. 1 , differential mobility separator plates  102   a  and  102   b  are deposited on the substrate  103  such that airflow passing the ionizer is directed between mobility separator plates  102   a  and  102   b . When a potential difference is applied between mobility separator  102   a  and  102   b , an electric field is created between them. 
         [0049]    When charged particulates enter the space between mobility separator plates  102   a  and  102   b , they are deflected by the electric field. The amount of deflection is dependent upon the mobility of the particulates and the strength of the applied field. By varying the voltage applied to mobility separator plates  102   a  and  102   b , particulates of different mobility can be made to impinge on mobility separator plates  102   a  and  102   b  and the resultant current can be measured as discussed herein to determine the concentration of particulates with a given mobility. It will be understood that a relationship can be established between a particle&#39;s mobility and its diameter. (See  FIG. 4A  and  FIG. 4B .) With general regard to aerosol technology and particle measurement, reference can be had to Flagan, R. C. (1998). “History of electrical aerosol measurements.” Aerosol science and technology 28(4)“; and, Hinds, W. C. (1999). “Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles.” New York, John Wiley &amp; Sons. See also  FIG. 3 , where there is shown a graphical depiction of calculations verifying scalability of design to nanometer dimensions and operating parameter ranges in accordance with the present invention shown in  FIG. 1 . 
         [0050]    Charged particles not collected by mobility separator plates  102   a  and  102   b  flow into the second series connectable condenser  10 B. Condenser  10 B includes mobility separator plates  105   a  and  105   b  deposited on substrate  104 . Mobility separator plates  105   a  and  105   b  are suitably charged to collect charged particles of interest. 
         [0051]    Referring also to  FIG. 2  there is shown an operational control method diagram for the measurement of number-size distribution of airborne nanometer-particles in accordance with the present invention shown in  FIG. 1 . The control board  214  applies a control voltage to the high voltage power supply (HVPS)  211  driving a high voltage output (V 1 ) to the micro-fabricated corona charger  26 . A corona develops on the end of the probe pin  101   a , and electrons from the corona, propelled by the electrical field, drift between the condenser plates  102   a ,  102   b . This establishes a leakage current between pin  101   d  and plates  101   a ,  101   b  which is amplified by a corona electrometer  22  and recorded by measurement board  21 . The average number of charges acquired by each particle can be determined based on a function of charger voltage, aerosol flow rate, and particle diameter. 
         [0052]    Still referring to  FIG. 2 , pump  210  is adjusted to pull aerosol at a desired flow rate (Q) thru the miniaturized micro-fabricated double condenser  10 . Flow rate is monitored by flow meter  29 . 
         [0053]    Still referring to  FIG. 2 , HVPSs  212 ,  213  provide high voltage outputs (V 2  V 3 ) establishing electric fields in condenser  27  and condenser  28 , respectively. 
         [0054]    The inertial impactor  25 , filters the aerosol  217  to pass particle diameters of interest to the corona charger  26 . It will be appreciated that any suitable method for filtering particles of interest may be used. 
         [0055]    The aerosol then passes thru the corona charger  26  and its particles are ionized. 
         [0056]    The charged particles of the aerosol then flow into the first condenser  27  and begin to flow toward the condenser plate  102   a  or  102   b  with the opposite charge. Charged particles with an electrical mobility greater than the critical mobility of the condenser for this flow rate and voltage are collected on the condenser plate  102   a  or  102   b . (This includes the air molecules ionized by the corona.) The critical mobility of the first condenser is: 
         [0000]        k   c   =Q   a /(4π C   1   V   2 )  Eq. 5
 
         [0057]    where:
       C, is the capacitance of the condenser, estimated by:       
 
         [0000]        C   1   =A /4π d   Eq. 6
 
         [0059]    where:
       A is the condenser plate area; and   d is the condenser plate separation.       
 
         [0062]    When the charged particles stick to the condenser plate  102   a  or  102   b , the particle transfers it charge, which become a current that is amplified by the electrometer  23  and recorded by measurement board  21 . 
         [0063]    Charged particles not collected by the first condenser flow into the second condenser  28  where they are driven to the opposite charged plate of this condenser as described earlier. Charged particles with a critical mobility greater than the critical mobility k d  of both condensers combined but less than k c , because the particles were not collected in the first condenser  27 , are collected in the second condenser  28 . The critical mobility k d  of both condensers combined is described as: 
         [0000]        k   d   =Q   a /(4π( C   1   +C   2 ) V   3 )  Eq. 7
 
         [0000]    It will be understood that there is also a fraction of charged particles with mobilities less than k d  that gets collected; this can be taken into account, as shown in the data analysis below. 
         [0064]    The current from these collected charges is amplified by electrometer  24  and recorded by measurement board  21 . The aerosol with whatever particles still remain in it passes that the flow meter and pump and exits the instrument. 
         [0065]    This process is repeated over a range of airflow Q a  and voltage (V 2 ,V 3 ) values, with the current from the second condenser  28  recorded at each setting. The airflow and voltage values are selected to provide values of the critical mobilities that will define particle diameter ranges that are of interest. 
         [0066]    The recorded data is arranged as I 3 /V 3  vs. k c  and differentiated once in accordance with Eq. 9. This information, along with Eq. 8 below, and the corrections calculated from the instrument characterization (described above) results in the number vs. diameter distribution, f(k), of the aerosol sample, the desired measurement. 
         [0000]        I   3   /V   3 =4π e[C   1   k   c ∫ k     d     k     c     f ( k ) dk +( C   1   +C   2 )∫ 0   k     d     kf ( k ) dk−C   1 ∫ 0   k     e     kf ( k ) dk]   Eq. 8
 
         [0067]    Where:
       I 3 =second separator current   V 3 =second separator voltage   C 1 =Condenser 1 capacitance   C 2 =Condenser 2 capacitance   e=electron charge   k c =first condenser critical mobility   k d =second condenser critical mobility   f(k)=mobility spectrum of the sample aerosol       
 
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         [0076]    Still referring to  FIG. 2 , control board  214  may be any suitable computer/microcontroller. For example, computer/microcontroller  214  and measurement board  21  may be, or include, a “mote”  215 . As used in this disclosure, the term “mote device” or “mote” typically indicates an autonomous or semi-autonomous computing; communication, actuating, and/or sensing device as described in the mote literature (e.g., Intel Corporation&#39;s, or Crossbow Inc.&#39;s mote literature,). 
         [0077]    Certain embodiments of the mote device(s)  215  can be fabricated to be relatively small (typically less than several inches in dimension, often a fraction of an inch). Certain embodiments of mote systems(s) can be relatively inexpensive to produce, and can be designed to stand up to relatively harsh and/or external environments. 
         [0078]    Many embodiments of mote systems(s)  215 , or simply “motes”, as described in this disclosure can provide a wide variety of parameter sensing and/or actuating functionalities. Such parameter sensing may be controlled (and/or light or display device actuated) using computer-based sensing, electro-mechanical sensing, magnetic sensing, and/or other sensing techniques. Certain embodiments of mote device(s) and networks can be located at remote, hostile, external, or inaccessible location(s); and can be wirelessly networked. 
         [0079]    Still referring to  FIG. 2 , control board  214  may also include a Global Positioning Satellite (GPS) transceiver  216  for determining location information associated with particle measurements. In addition, control board  214  may also include a radio frequency identification tag (RFID)  218 , passive, active, or a hybrid. RFID tags are well known in the art and need not be discussed here. 
         [0080]    It will be appreciated that the invention described herein advantageously provides particle diameter measurement and particle count for a range of nanoparticle diameters over a range of operating conditions suitable for on-board exhaust sampling of spark and compression ignition vehicles and for road-side exhaust sampling in a miniaturized package. The effect of the first condenser is to simplify the data inversion and to improve the signal-to-noise ratio. And, as described above, the two condensers working in tandem sweep through a range of voltage settings, and the particles collected by the second condenser are measured by a single electrometer. 
         [0081]    It will be further appreciated that the miniaturized voltage-stable, and feedback-controlled instrument package includes a novel, micro-fabricated nanoparticle charging and sorting device (NCaS) (see  FIG. 1 ). Using the separator portion of the NCaS device as an aspiration capacitor, also known as an ion condenser) advantageously removes, the requirement for a separate particle separation step using a Faraday cup; this further reduces the size and weight of the device. 
         [0082]    Another advantage of the present invention is that the parallel condenser plates  102   a ,  102   b  and  105   a ,  105   b , are held at a potential voltage difference and the current through that circuit is monitored as the charged particles of the sample aerosol are collected on one of the condenser plates and release their electrons. 
       Alternate Invention Embodiment Discussion 
       [0083]    Referring also to  FIG. 8  there is shown a pictorial illustration of an alternate charger+series/parallel aspiration capacitor embodiment of the present invention shown in  FIG. 1 . This embodiment requires at least three NCaS devices, or one enhanced NCaS device integrating the function of at least three of the NCaS devices. This embodiment allows for the direct (non-differentiated) measurement of the particle size distribution. In essence, the parallel capacitors  8 A,  8 B (held at slightly different voltages) do the work of the double differentiation. 
         [0084]    Still referring to  FIG. 8 , differential mobility separator plates  102   a  and  102   b  are deposited on the substrate  103  such that airflow passing the ionizer is directed between mobility separator plates  102   a  and  102   b . When a potential difference is applied between mobility separator  102   a  and  102   b , an electric field is created between them. 
         [0085]    When charged particulates enter the space between mobility separator plates  102   a  and  102   b , they are deflected by the electric field. The amount of deflection is dependent upon the mobility of the particulates and the strength of the applied field. By varying the voltage applied to mobility separator plates  102   a  and  102   b , particulates of different mobility can be made by control board ( FIG. 2-214 ) to impinge on mobility separator plates  102   a  and  102   b  and the resultant current can be measured by measurement board ( FIG. 2-21 ) as discussed herein to determine the concentration of particulates with a given mobility. It will be understood that a relationship can be established between a particle&#39;s mobility and its diameter. Charged particles not collected by mobility separator plates  102   a  and  102   b  flow into condensers  8 A and  8 B. Condenser  8 A includes mobility separator plates  108   c  and  108   d  deposited on substrate  103   c . Mobility separator plates  108   c  and  108   d  are suitably charged to collect charged particles of interest 
         [0086]    Similarly, condenser  8 B includes mobility separator plates  108   a  and  108   b  deposited on substrate  103   b . Mobility separator plates  108   a  and  108   b  are suitably charged to collect charged particles of interest. 
         [0087]    Referring also to  FIG. 9 , there is a pictorial illustration of an alternate switchable series condenser configuration of the present invention shown in  FIG. 1 . Switching the segmented condenser sections via control board ( FIG. 2-214 ) into varying lengths, for example  9 E and  9 F, allows the overall ratio of critical mobilities to be varied, proyiding for a user-selectable accuracy/precision tradeoff. 
         [0088]    Still referring to  FIG. 9 , condenser stages  9 C and  9 D can be switched off or on in the high voltage and electrometer circuits (See  FIG. 2 ), so that the critical mobility of the two stages  9 C,  9 D can be equally raised or lowered. Also, using one condenser in each stage and then the other would extend the time between cleaning or condenser replacement. 
         [0089]    It should be understood that the foregoing description is only illustrative of the invention. Thus, various alternatives and modifications can be devised by those skilled in the art without departing from the invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications and variances that fall within the scope of the appended claims. 
         [0090]    For example, referring again to  FIG. 1 , it will be understood that in the event of a malfunction of the second condenser  10 B, the invention can operate in Charger+single Aspiration Capacitor mode. This mode uses a single NCaS device plus an electrometer circuit to measure the current induced by the charges collected to the separator plates  102   a  and  102   b . This mode requires a double differentiation, but now of the I/V curve. Operationally this is accomplished as two single differentiations for the tangent intercepts to determine the number of particles in a single size bin. 
         [0091]    In addition, the present invention and embodiments are constricted with suitable materials to withstand and operate in a temperature range of approx. −20 to 300 C (from the ambient temperatures in the winter of northern climates to tailpipe exhaust temperatures); relative humidity from zero to fully saturated (encountered in both the ambient air and in direct vehicle exhaust); particle compositions both hydrophobic and hydrophilic; particle morphologies both simple and agglomerated (to cover both the nucleation and the accumulation modes of the particle spectrum, the latter especially an issue with diesel exhaust, which forms long-chain agglomerates); a particle diameter range of 10-300 nm to cover the high end of the nucleation mode and the low end of the accumulation mode; and a size-bin resolution sufficient to clearly differentiate the two modes.