PHOTOELECTRIC EMISSION MEASUREMENTS ON THE ANALOGS OF INDIVIDUAL COSMIC DUST GRAINS

Transcription

1 The Astrophysical Journal, 645: , 2006 July 1 # The American Astronomical Society. All rights reserve. Printe in U.S.A. A PHOTOELECTRIC EMISSION MEASUREMENTS ON THE ANALOGS OF INDIVIDUAL COSMIC DUST GRAINS M. M. Abbas, 1 D. Tankosic, 2 P. D. Craven, 1 J. F. Spann, 1 A. LeClair, 2 E. A. West, 1 J. C. Weingartner, 3 A. G. G. M. Tielens, 4 J. A. Nuth, 5 R. P. Camata, 6 an P. A. Gerakines 6 Receive 2005 July 13; accepte 2006 March 10 ABSTRACT The photoelectric emission process is consiere to be the ominant mechanism for charging of cosmic ust grains in many astrophysical environments. The grain charge an equilibrium potentials play an important role in the ynamical an physical processes that inclue heating of the neutral gas in the interstellar meium, coagulation processes in the ust clous, an levitation an ynamical processes in the interplanetary meium an planetary surfaces an rings. An accurate evaluation of photoelectric emission processes requires knowlege of the photoelectric yiels of iniviual ust grains of astrophysical composition as oppose to the values obtaine from measurements on flat surfaces of bulk materials, as it is generally assume on theoretical consierations that the yiels for the small grains are much ifferent from the bulk values. We present laboratory measurements of the photoelectric yiels of iniviual ust grains of silica, olivine, an graphite of m raii levitate in an electroynamic balance an illuminate with UV raiation at nm wavelengths. The measure yiels are foun to be substantially higher than the bulk values given in the literature an inicate a size epenence with larger particles having orer-of-magnitue higher values than for submicron-size grains. Subject heaingg: ust, extinction Online material: color figures 1. INTRODUCTION It is well recognize that submicron/micron-size cosmic ust grains play an important role in the evolution an ynamical processes in the galaxy, the interstellar meium ( ISM), an the interplanetary an planetary environments. The ust grains in various astrophysical environments are generally charge, an their equilibrium charge an surface potential influence the ynamical an physical evolutionary processes (e.g., Bailey & Williams 1988; Harwit 1998; Fiel & Cameron 1975; Draine 2004). The ust grains in space environments may be charge by a variety of mechanisms that inclue collisional processes with electrons an ions, triboelectric charging, an photoelectric emissions (e.g., Wyatt 1969; Feuerbacher et al. 1973; Draine 1978; Draine & Sutin 1987). The photoelectric emission process is believe to be the ominant process in many astrophysical environments with nearby ultraviolet (UV) sources, such as the ISM, iffuse clous, outer regions of the ense molecular clous, interplanetary meium, ust in planetary environments an rings, cometary tails, etc. The photoelectric emission from ust grains is assume to be an important mechanism for heating of the neutral gas in the iffuse interstellar clous, as well as in the surface regions of the molecular clous, an is believe to play an important role in the ynamical evolution of the ISM (e.g., Watson 1972, 1973; Draine 1 NASA Marshall Space Flight Center, Huntsville, AL 35812; mian.m.abbas@nasa.gov, paul..craven@nasa.gov, james.f.spann@nasa.gov, ewar.a.west@nasa.gov. 2 University of Alabama, Huntsville, AL 35899; tankos@uah.eu, anre.leclair@msfc.nasa.gov. 3 George Mason University, Fairfax, VA 22030; joe@physics.gmu.eu. 4 Kapteyn Astronomical Institute, Groningen, Netherlans; tielens@astro.rug.nl. 5 NASA Goar Space Flight Center, Greenbelt, MD 20771; joseph.a.nuth@ nasa.gov. 6 Department of Physics, University of Alabama, Birmingham, AL 35294; camata@uab.eu, gerakines@uab.eu ; Mukai 1981; Bakes & Tielens 1994; Dwek & Smith 1996; Weingartner & Draine 2001). The charge an equilibrium potentials of ust grains influence the coagulation an conensation processes in molecular clous. The photoelectric emission process is also the ominant ust-charging process on the lunar sunlit environment leaing to levitation an transportation of ust on the lunar surface observe uring the Apollo missions (e.g., Feuerbacher et al. 1972; Pelizzari & Criswell 1978; Horanyi et al. 1995, 1998, 1998b; Stubbs et al. 2006). An evaluation of the charge an equilibrium surface potential of ust grains of various astrophysical compositions inuce by photoelectric emissions requires knowlege of the photoelectric yiel efine as the electrons emitte per photon absorbe. Accurate theoretical moels for calculation of the yiels of iniviual ust grains are not yet available, an the require information has to be obtaine by laboratory measurements. However, the only measurements of photoelectric yiels available in the literature for ust materials of astrophysical composition are those mae on bulk materials with flat surfaces. This situation exists even though it has long been postulate on theoretical consierations that the photoelectric yiels of iniviual ust grains woul be substantially ifferent from those for the corresponing bulk materials (e.g., Watson 1972, 1973; Gallo & Lama 1976a, 1976b; Draine 1978). The photoelectric yiels of small nanometersize gol an silver particles suspene in He gas an irraiate by UV were measure in a series of papers (Schmit-Ott et al. 1980; Burtscher & Schmit-Ott 1982; Burtscher et al. 1984). The measurements apparently inicate strong enhancements in the yiels compare with the bulk values for Ag particles, but no enhancement for the Au particles. However, the latter paper (Burtscher et al. 1984) showe that for clean Ag particles, the yiel curve was similar to that for the bulk values, inicating that the measure enhancement was affecte by the surface contaminants. The existing moels have not provie a satisfactory explanation for the observe ata.

2 PHOTOELECTRIC MEASUREMENTS ON DUST GRAINS 325 Several theoretical moels base on classical electrostatics have been propose that inicate an inverse size epenence of 1/a for ionization threshol energy or the work function ( WF). A consierable amount of ata now exists for experimental etermination of the ionization threshol energy of particles extening in size over the range of clusters of a few atoms, nanometer/ micron-size particles, an progressively merging with the bulk materials (e.g., Gallo & Lama 1974, 1976a, 1976b; Ekart 1985; Seil et al. 1991; Bréchignac et al. 1992; Dugour et al. 1992; e Heer 1993; Wong et al. 2003). No irect photoelectric yiel measurements on iniviual ust grains of astrophysical interest have been reporte as yet. In this paper, we present the first measurements of the photoelectric yiels of iniviual submicron/micron-size ust grains of astrophysical interest. The yiels reporte here were etermine by irect measurements of the ischarge rates of negatively charge ust grains of silica, olivine, an carbonaceous composition, with sizes in the range of m raii. The measurements were mae by levitating iniviual grains of known size an composition in an electroynamic balance an illuminating them with UV raiation of known intensity at wavelengths of 120, 140, an 160 nm. In x 2, a escription of the experimental apparatus employe in the measurement is given with a brief review of the electroynamic balance. The basic equations an the methoology employe for photoelectric emission an yiel calculations are given in x 3. Experimental results of the photoelectric efficiencies an yiels of silica, olivine, an carbonaceous ust grains are given in x 4, with a etaile iscussion of the possible sources of errors in the measurements in x 5. In x 6, we iscuss some theoretical consierations relevant to photoelectric emissions. A summary an conclusions of the measurements are given in x EXPERIMENTAL APPARATUS 2.1. Electroynamic Balance The photoelectric emission measurements reporte here were performe on an electroynamic balance, also referre to as a quarupole trap, that permits levitation of a single micron-size ust grain in simulate astrophysical environments. An electroynamic balance consists of a top an a bottom electroe of hemispherical configuration, an a ring electroe of cylinrical configuration. The top an bottom electroes are kept at positive or negative DC potentials (V DC ) with respect to the groun, epening on the polarity of the ust grain charge, an an AC potential (V AC ) is applie to the cylinrical electroe. The net effect of the AC fiel is to prouce a null potential at the geometric center of the cavity with the DC electric fiel balancing the gravitational force on a charge ust grain. The ust grains may be kept trappe in the balance for extene perios as long as the require AC an DC potentials an the AC frequency ( ¼ 2f ) satisfy the stability conitions for keeping the particle at the balance center. The stability conitions are etermine by the fiel an rag factors an, respectively, efine as ¼ 2g C 0 z 0 2 V AC V DC ; ¼ 18 D 2 ; where is the viscosity of air, is the mass ensity of the particle, g is the gravitational acceleration, C 0 is a geometric constant experimentally etermine to be 0.68, z 0 ¼ 0:750 cm is ð1þ ð2þ the istance from the trap center to the DC electroes, an D is the effective particle iameter. A particle is trappe only uner a certain range of values of an as etermine by stable solutions of the equations of motion of the particle. A etaile escription of the principles, basic equations, an the require apparatus has been given in previous publications (e.g., Davis 1985; Spann et al. 2001; Abbas et al. 2002a, 2002b, 2003, 2004). A basic quantity that is experimentally etermine on the electroynamic balance with a particle stably trappe is the chargeto-mass ratio given by q m ¼ gz o : C o V DC With irect measurements of V DC, the charge-to-mass ratio of a trappe particle given by equation (3) is a irectly measurable quantity an forms the basis of all measurements on an electroynamic balance Experimental Setup an Proceure for Photoelectric Emission Measurements The experimental setup for photoelectric emission measurements is shown in a schematic in Figure 1 an consists of the following main components: 1. Electroynamic balance: Top an bottom hemispherical electroes, an a cylinrical ring electroe in a vacuum chamber with suitable viewing ports. 2. Electric power supplies: Consisting of an AC voltage source (V AC V, at f AC Hz), a low DC voltage source (V DC 0:01 50 V), an a DC high-voltage source (V h V) power supply for inuctive charging of the ust particles. 3. Particle injector: A pressure impulse evice to inject an inuctively charge particle ( positive or negative) of known composition an ensity in the balance through a port at the top (Spann et al. 2001). 4. Particle imaging system: A 15 mw, He-Ne laser with an optical magnifying system to project the image of the levitate particle on a monitor. 5. Vacuum system: With leak valves an pressure gauges for controlle evacuation of the chamber pressures to 10 4 to 10 5 torr. 6. Far-UV source: A euterium lamp with MgF 2 winow, focusing equipment, an a vacuum monochromator with FWHM resolution of 8 nm. The UV beam is collimate an focuse with amgf 2 lens to limit the beam iameter mm (FWHM) size, smaller than the 6 mm entry/exit apertures in the balance ring electroes, thus eliminating or minimizing photoelectrons emitte by the walls ue to any stray UV raiation. 7. Photomultiplier tube ( PMT ): With spectral response in the nm wavelength region. The size or the effective iameter of a trappe particle is etermine from a few spring-point measurements at pressures of 1 10 torr. The size calculations are base on marginal instability of the levitate particle involving the fiel an viscous rag factors efine in equations (1) an (2), an are iscusse in more etail in x 5.1 an in previous publications (e.g., Davis 1985; Spann et al. 2001). Estimates or upper limits of the particle sizes may also be obtaine from the monitor images using scale factors evelope from particles of known sizes k5 m. After stable trapping an size eterminations at pressures of 1 10 torr, a controlle evacuation proceure is starte to allow ð3þ

3 326 ABBAS ET AL. Vol. 645 Fig. 1. Schematic of the setup of an electroynamic balance for UV photoelectric yiel measurements. the chamber pressure to reach 10 4 to 10 5 torr, at which the photoelectric emission measurements on the levitate particles are carrie out. The levitate particles in the trap are charge positively or negatively by an inuctive process with a high DC potential in the particle injector, the sign of the charge being selecte by the polarity of the charging voltage. A negatively charge particle may be ischarge by exposing it to UV raiation, an a positively charge one ischarges through exposure to a low-energy electron beam. The initial magnitue of charge on a grain is controlle to a egree by the DC potential employe for the charging process. A typical charge for measurements on silica grains, for example, varie from electrons for particles of 0.1 m raii to >200,000 electrons for particles of >3 5 m raii. When the UV raiation beam is turne on, the particle begins to ischarge by ejecting electrons at a rate that epens on the raiation intensity, the size, an the charge state of the particle. The DC voltage is continuously ajuste to balance the gravitational force an keep the particle at the trap center. The UV raiation may be turne on or off, with the particle ischarging or maintaining a constant charge, respectively. The particle is ejecte from the balance when it is nearly or completely ischarge. A positively charge polystyrene particle of 2.3 m raius was kept trappe in the electroynamic balance for a perio of about 8 ays for test purposes an was perioically ischarge an charge by exposure to an electron beam of evan a UV raiation beam, respectively. A cycle of ischarging an charging of the trappe particle selecte from a portion of the ata obtaine over a perio of about 5.5 hr is shown in Figure 2. With UV raiation at 160 nm wavelength turne on at t 1060 minutes, the particle charge increases from an initial charge q 840e to 880e at t 1170 minutes. At this time, the UV raiation intensity is change to a much stronger value consisting of white light covering all wavelengths in the visible to 120 nm spectral region, an the particle charge rapily increases to an equilibrium value of q 1280e at t 1270 minutes. At t 1360 minutes the particle is now expose to an electron beam at 2500 ev, an the particle ischarges to q 880e at t 1380 minutes. At this time the electron beam is turne off, the white light with UV raiation is turne on, an the particle charge increases again to the equilibrium value of 1280e at t 1500 minutes. It shoul be note that the scatter in the grain Fig. 2. Variation of charge with time of a positively charge polystyrene particle of 2.3 m raius perioically ischarge with an electron beam an charge with a UV photon beam. [See the electronic eition of the Journal for a color version of this figure.]

4 No. 1, 2006 PHOTOELECTRIC MEASUREMENTS ON DUST GRAINS 327 where i PMT (k) is the current measure by the PMT at wavelength k,eis the electron charge, q is the quantum efficiency, G is the gain of the PMT, an R represents the reflectance of the mirror (Fig. 1). To etermine the number of photons per secon incient on a ust grain levitate at the trap center, we assume the raial istribution of photons in the beam to be of the Gaussian form as n ph B ¼ nph max (0) exp r2 re 2 ; ð5þ where r e ¼ w e /2 represents the half-with of the beam where the photon flux ensity n ph B is 1/e of the maximum value nph max (0) at the beam center. The above assumption implies that the total integrate photon flux in the beam an measure by the PMT is represente by N ph B ¼ (r 2 e )nph max (0): ð6þ Fig. 3. Variation with time of the charge an DC voltage of a 0.35 m raius silica particle, with the UV raiation beam turne on at t 5minutes,off at 11 minutes, an on again at 18 minutes. The charge remains constant with the UV raiation off an ischarges when it is turne on. The particle is ejecte from the trap when the charge approaches zero. [See the electronic eition of the Journal for a color version of this figure.] charge seen in Figure 2 reflects only the ranom variability of the DC voltage V DC, the measurement accuracy of which is limite to 1 mv. An example of the ischarging of a 0.35 m raius silica particle with an initial negative charge of 300e is shown in Figure 3. The particle maintains constant charge for about 5 minutes until it is expose to UV raiation at 160 nm wavelength when it ischarges to about 50e in 6 minutes. With the UV raiation turne off, the charge remains constant until the UV is turne on again at t 18 minutes when the particle ischarges to <10e when it is ejecte from the trap. All photoelectric emission measurements reporte in this paper were mae on negatively charge ust grains. The choice of negative charge was mae in view of the ease with which negatively charge particles may be ischarge over a range of potentials from high to negligibly small values. Measurements on positively charge grains over a esire range of potentials may be mae with a sequence of charging an ischarging processes with UV an an electron beam, respectively, an are planne in the future. 3. CALCULATION OF PHOTOELECTRIC YIELDS The photoelectric yiel calculations are base on measurements of the ischarge rate of a particle irraiate with a UV beam of known photon flux ensity. The photon flux in the beam is etermine by reflecting it to a PMT an measuring the collecte current, with the beam with etermine by irect measurements at the trap center, as well as by moeling calculations using the ZEMAX optical software. With the beam with smaller than the projecte area of the PMT, the number of photons per secon in the beam N ph B an incient on the PMT is given by N ph B ¼ i PMT(k) e q (k)gr ; ð4þ Since the beam with w e 3:5 4:5 mm is much larger than the particle iameters, equations (4) an (6) may be use to calculate the number of photons incient on the ust grain per secon with n ph ¼ i PMT(k) Dm 2 e q (k)gr we 2(k) : Using numerical values of the PMT use in the photoelectric emission experiments iscusse in this paper, with the gain G ¼ 600 an R ¼ 0:6, equation (7) may be written as n ph ¼ 1:73 ; 1016 i PMT(k) q (k) D 2 m w 2 e (k) : To calculate photoelectric efficiencies an yiels, the number of electrons emitte by a grain with the incient UV photons nees to be etermine. This information may be obtaine from the grain charge q(t) measure as a function of time (eq. [3]) an can be written in terms of the current i to the grain as n e ( s) ¼ i e ¼ : ð9þ The photoelectric efficiency of the ust grain is efine as the number of electrons emitte by the ust grain per incient photon, is a function of the surface potential s, an is written as E pe ¼ ne ( s) n ph : ð10þ The photoelectric yiel, however, is generally efine in the literature as photoelectrons emitte per photons absorbe with the grain potential approaching zero an may be written as ð7þ ð8þ Y ¼ E pe ¼ ne ( s! 0) ; ð11þ Q abs n ph Q abs where Q abs is the absorption efficiency of the grain an may be obtaine by using Mie scattering theory calculations, assuming spherical particles with effective iameters D an a complex refractive inex corresponing to the grain material. The use of effective iameters for nonspherical, irregularly shape particles leas to an uncertainty in evaluation of Q abs in the Mie theory calculations an is expecte to prouce scatter in the measure yiel ata representing the ranomness of the particles. Equations (8) (11) form the basis for measurement an calculation

5 328 ABBAS ET AL. Vol. 645 of the photoelectric efficiency an yiel of iniviual ust grains suspene in the trap an illuminate by UV raiation. 4. EXPERIMENTAL RESULTS OF PHOTOELECTRIC YIELDS Measurements of photoelectric efficiencies an yiels have been carrie out on micron/submicron-size grains of silica, olivine, an graphite levitate in the electroynamic balance with the proceure outline above. An emitte electron from the negatively charge grains employe in all experiments iscusse in this paper experiences a repulsive Coulomb force that is a function of the grain charge or its surface potential. A repulsive force is exerte on an ejecte electron in aition to a force ue to image potential that is attractive regarless of the polarity of the ust grain charge. The photoelectric efficiency is thus expecte to be higher for heavily charge negative grains at high surface potentials compare with the values when the grain is close to being completely ischarge with the surface potential approaching zero. The photoelectric efficiency efine in equation (10) is a function of the particle surface potential, an the measurements generally show an upwar tren with higher potentials. The photoelectric yiel, however, is generally efine for neutral bulk materials with zero surface potential an is represente by the photoelectric efficiency with the surface potential approaching zero. To etermine the photoelectric yiel from the measurements, we aopt the proceure of least-squares regression to etermine the efficiency for the potential approaching zero. This value of photoelectric efficiency when convolve with the absorption efficiency Q abs represents the photoelectric yiel in accorance with the efinition of equation (11). The absorption efficiency is calculate by using the Mie scattering theory (e.g., Bohren & Huffman 1983; Wiscombe 1979) for the measure effective raius of the particle etermine by the spring-point metho. The photoelectric yiels in the composite yiel plots given in xx have been etermine from the efficiency measurements with the proceure inicate above Photoelectric Yiels of Silica Grains The silica grains employe in the measurements presente here were obtaine from the Bangs Laboratories, Iniana, an have been use for raiation pressure measurements as reporte in a previous publication (Abbas et al. 2003). These grains of spherical configuration, with known ensity an complex refractive inex, are calibrate to the nominal sizes an are thus particularly suitable for investigating the effects of grain size on photoelectric emissions uner UV irraiation. In particular, the experiments were performe on grains selecte from five bins calibrate to sizes of 0.13, 0.35, 0.75, 1.5, an 3.4 m raii. The accuracy of the nominal particle sizes was verifie by carrying out spring-point measurements with stanar eviations of 5% 6% in the nominal raii. Photoelectric emission measurements were mae on several negatively charge particles of each size selecte from each bin, with UVraiation at 120, 140, an 160 nm wavelengths. The measurements are repeate in cycles at several ifferent particle surface potentials ( s ) as the particles ischarge an the surface potentials change with time. The results presente here represent measurements on 21 silica particles of raii in the m range. The average values of the photoelectric efficiencies calculate as a function of surface potentials generally inicate higher values at higher potentials. The plotte yiels, however, represent the efficiency measurements at the grain charge Z or potential approaching zero as iscusse above. Figures 4a 4c represent plots of the average photoelectric efficiencies of silica particles of raii 0.35, 1.5, an 3.4 m atuv Fig. 4a Fig. 4b Fig. 4c fig. 4a fig. 4b fig. 4c Fig. 4. (a) (c): Average photoelectric efficiencies as a function of the particle surface potential base on measurements on a number of silica particles of 0.35, 1.5, an 3.4 m raii illuminate with UV raiation at 120, 140, an 160 nm wavelength. The error bars inicate the 1 stanar eviation ue to the variability of the particles size, as well as the measurement errors. [See the electronic eition of the Journal for a color version of this figure.]

6 No. 1, 2006 PHOTOELECTRIC MEASUREMENTS ON DUST GRAINS 329 Fig. 5. Photoelectric yiels ( Q abs ) vs. photon energy average over measurements on several silica particles. wavelength of 120, 140, an 160 nm, corresponing to photon energies of 10.3, 8.9, an 7.9 ev, respectively. Each plot is base on measurements on four to five particles of the same nominal raius, an the error bars inicate the 1 variability in the measure ata representing the measurement errors, as well as the variability in the particle size. Figure 5 represents the photoelectric yiels ( Q abs ) euce from the photoelectric measurements on all silica particles an plotte as a function of the photon energy. The measurements inicate an exponential increase in the yiels ( Q abs ) with photon energy an a general tren of higher yiels for larger size particles. The photoelectric yiel, efine as the number of electrons ejecte per photons absorbe is etermine by iviing the efficiencies corresponing to zero grain surface potentials by the absorption efficiency Q abs of the particles, is plotte in Figure 6 as a function of the size parameter x ¼ (2a/k), where a is the grain raius an k is the wavelength. This parameter is calculate by using Mie scattering theory (e.g., Bohren & Huffman 1983; Wiscombe 1979) with the complex refractive inices euce from the ata given by Draine & Lee (1984). Using the ata shown in Figure 6, the photoelectric yiels Yof all silica particles Fig. 6. Absorption efficiency Q abs of silica particles as a function of the size parameter (2a/k), using Mie scattering theory, with complex refractive inices from the ata in Draine & Lee (1984). Fig. 7. Photoelectric yiels Y of all particles of 0.13, 0.35, 0.75, 1.5, an 3.4 m raii measure at UV wavelengths of 120, 140, an 160 nm (10.3, 8.9, an 7.9 ev, respectively) as a function of the size parameter x ¼ (2a/k). are shown in Figure 7 as a function of the size parameter. Figure 7 inicates the photoelectric yiels increasing with the particle size for all three wavelengths reaching asymptotic values for large particles. For large particles, the yiels for all three wavelengths of 120, 140, an 160 nm, with photon energies of 10.3, 8.9, an 7.9 ev, respectively, are seen to approach asymptotic values that may be assume to correspon to the bulk values Photoelectric Yiels of Carbonaceous Grains The carbonaceous grains employe in the measurements were synthesize in a laboratory at the University of Alabama at Birmingham an are of nonspherical an irregular configuration with sizes in the range of m raii. The particle sizes were etermine by the spring-point measurements as iscusse in x 3.2, an the ensity was estimate to be 2.0 g cm 3, consistent with the irregular shape an porous nature of the particles. Typical examples of the photoelectric efficiency measurements as a function of the particle surface potentials are shown in Figures 8a an 8b for two particles of 0.44 an 4.5 m raii. A composite plot of the photoelectric yiel measurements on all carbonaceous particles is shown in Figure 9 as a function of the size parameter. Also shown for comparison are the measurements by Feuerbacher & Fitton (1972) mae on a bulk carbonaceous material for three photon energies of 10.3, 8.9, an 7.8 ev (120, 140, an 160 nm, respectively). The plotte bulk measurements have been correcte by using the reflectivities inicate by Feuerbacher & Fitton (1972) to correspon with the yiels presente here as electrons emitte per photon absorbe. The measurements shown for the iniviual ust grains are seen to be higher than the corresponing bulk values by factors of 90, 40, an 10 for wavelengths of 120, 140, an 160 nm, respectively Photoelectric Yiels of Olivine Grains The olivine ust grains employe for the photoelectric efficiency measurements reporte here were synthesize in the materials laboratory at the University of Alabama at Birmingham. These particles are of highly nonspherical configuration an were measure to be of effective raii in the range of m. Figures 10a an10b exhibit two examples of the measurements of photoelectric efficiency as a function of the surface potential,

7 Fig. 8a Fig. 10a Fig. 8b fig. 8a fig. 8b Fig. 8. (a) (b) Same as Fig. 4, but for two iniviual carbonaceous particles of 0.44 an 4.5 m raii.[seethe electronic eition of the Journal for a color version of this figure.] Fig. 10b fig. 10a fig. 10b Fig. 10. (a) (b) Same as Fig. 4, but for two iniviual olivine grains of 0.09 an 1.6 m raii.[see the electronic eition of the Journal for a color version of this figure.] Fig. 9. Photoelectric yiel measurements on all carbonaceous particles as a function of the size parameter. Also shown are the measurements by Feuerbacher & Fitton (1972) mae on bulk carbonaceous material for three photon energies of 10.3, 8.9, an 7.8 ev (120, 140, an 160 nm, respectively). Fig. 11. Photoelectric yiels of all olivine particles of raii in the m range as a function of the size parameter representing measurements at UV photon energies of 10.3, 8.9, an 7.8 ev (120, 140, an 160 nm, respectively).

8 PHOTOELECTRIC MEASUREMENTS ON DUST GRAINS 331 conucte on two iniviual particles of 0.09 an 1.6 m raii. As in the previous cases, the measurements inicate a general epenence on the surface potential, in particular, for the smaller 0.09 m particle. A composite plot of the photoelectric yiels as a function of the size parameter, representing measurements on eight particles of m raii is shown in Figure 11 at UV photon energies of 10.3, 8.9, an 7.8 ev (120, 140, an 160 nm, respectively). A general tren of higher yiels for large size particles at all three wavelengths is inicate by the olivine particles, consistent with the silica an carbonaceous particles. To our knowlege, no photoelectric yiel measurements on bulk materials for this material are available for comparison. 5. AN EXAMINATION OF POSSIBLE SOURCES OF ERRORS IN MEASUREMENTS In view of the novel nature of the results presente in paper, we examine the potential sources of errors that may rener the experimental values unreliable. In particular, sources of experimental errors that may lea to systematic effects relevant to the particle size are consiere. As iscusse in xx 2 an 3 the measurement proceure an the analytical technique for etermination of photoelectric efficiencies an yiels are base on irect measurements of the quantities i PMT (k), the UV beam with w e (k), the effective iameter D m of the grain, an the charge as a function of time. The number of photons incient per secon on the ust grain n ph is etermine by using equation (8). Also, the number of electrons emitte per secon by the grain n e efine by equation (9) is evaluate by irect measurement of the charge q an the ischarge rate (@q/@t). The photoelectric efficiency an yiel is finally base on measurement of the quantities n ph an (@q/@t) as efine in equations (8) (11) Measurement of Photons Incient on a Grain, n ph Evaluation of this quantity requires irect measurements of the following: 1. The total number of photons per secon in the UV beam N ph B : It is etermine by projecting the beam on a PMT an measuring i PMT (k). This is a irect measurement an provies an accurate value of n ph B with no systematic effects relevant to the particle size. 2. The UV beam with w e (k): It is evaluate by using the optical moeling program ZEMAX, with the calculate values valiate by irect measurements by using the knife-ege metho in the trap uner vacuum. The measure beam with is mm an has no systematic size-epenent effect. The above two measurements are mae at pressures of 10 4 torr. The nearly constant measurements of i PMT (k)ateach wavelength inicate the consistency of n ph from one particle to another, ensuring that the calculation of the number of photons per secon in the beam remains nearly the same. With small variations in the measure values being incorporate in the calculations, there is no possibility of systematic size effects. 3. Determination of grain effective iameter D m : For measurements of the photoelectric efficiency an yiel of silica grains, spherical particles of preetermine iameters of m, prepare an calibrate by Bangs Laboratory, Iniana, were employe. For other nonspherical particles, the effective iameters were etermine by using the spring-point metho that is base on marginal stability conitions as a function of the atmospheric rag at pressures of 1 10 torr. This methoology was evelope by acquiring a atabase with measurements of viscous rag factor as efine in equation (2), on calibrate micron-size spherical particles of silica an polystyrene of preetermine size. The valiity of the measure atabase was evaluate with iameter measurements of particles of preetermine size by the spring-point metho. The valiation proceure involve laboratory prepare polystyrene particles of known size, large-size particles with approximate iameters etermine by imaging on a monitor with magnification optics, an small-size particles with the size range limite by one-electron etection. The springpoint technique employe for size etermination in the measurements presente here was valiate by employing blin tests an foun to provie effective iameters with uncertainties of less than 10%. It shoul be note that a ranom uncertainty in knowlege of the effective iameters only contributes to the scatter in the measurements of photoelectric emissions cause by the irregular shape of the particles as well as uncertainties in the measurable quantities. Systematic uncertainties in effective iameters, on the other han, only lea to systematic shifts in the photoelectric yiels with respect to the size parameter. A systematic uncertainty in size etermination oes not lea to a size-epenent effect in the photoelectric yiels. The effect of uncertainties in the size parameter is clearly much smaller than the size epenence of the yiels inicate by the measurements Measurement of the Grain Charge q an Discharge Rate (@q/@t) This measurement is most crucial for accurate evaluation of the photoelectric yiels an requires careful scrutiny. The results on photoelectric emissions presente in this paper were mae on negatively charge particles with a high initial charge q ¼ Ze an ischarge with UV raiation in sequences at three wavelengths of 120, 140, an 160 nm. The particles are ischarge to Z values approaching zero at which they are ejecte from the trap. The DC voltage V DC require to keep the particle at the trap center is recore as a function of time (Fig. 3), an the ischarge rate is calculate in accorance with equation (9). In the following, we examine the accuracy of the charge measurements in view of the following potential sources of errors. 1. How accurate is evaluation of the ischarge rate (@q/@t)? The ischarge rate is etermine from measurements of the change in the particle charge with time as shown in Figure 3. The particle charge q may be etermine accurately with high sensitivities, approaching the etection limit of a single electron emission at a time in sufficiently low charge regimes. The ischarge rate is calculate with a computer program that permits a running average over a variable interval of time or alternatively over a number of ata points, etermine by the nature of the measure ata. The accuracy of this measurement is basically etermine by the accuracy of the measurements of V DC. 2. Coul the vibrational motion of a trappe particle moveit in an out of the UV beam with systematic effects for large an small particles? The effective particle iameters are m, whereas the beamwith is m. The UV beam is aligne with the horizontal axis through the trap center. With amplitue of the vibrational motions being limite to maximum lengths of a few microns, the particle remains near the beam center as valiate by the projecte image on the monitor. 3. Coul the ischarge rate be influence by collisional processes with the ambient gas? This effect is completely negligible since with the UV raiation turne off at pressure levels of 760 to 10 5 torr, a charge particle may be kept trappe for several ays at a time without any measurable change in the charge. The ionization potential (IP) of major gases in the trap (N 2,O 2 )is much higher than the UV photon energies. In aition, the mean

9 332 ABBAS ET AL. Vol. 645 free path at pressures 10 5 to 10 4 torr is so large that any effect ue to the presence of positive ions woul be completely negligible. A typical example of the effect of UV raiation on the ischarge of a particle with charge q is shown in Figure 3 as a function of time with the corresponing DC voltage V DC. 4. What are the effects of ifferences in particle shapes an surface features on photoelectric emissions? In our analysis, the particles of irregular shape an known ensity, with measurements of charge-to-mass ratio, are characterize by effective iameters. The photoelectric emission process is etermine mainly by the particle size, with ranom ifferences in shapes an surface features reflecte by the scatter in the ata. This is inee what is observe. 5. Are there any effects of electron emissions from the walls illuminate with UVraiation? The entrance an exit apertures for the UV beams are 6 mm, while the beam size is mm. The effects of any electrons emitte from the walls with incient UV raiation an colliing with negatively charge ust grains are expecte to be negligible uner a repulsive force of the negatively charge particles. Nevertheless, for cases in which the UV beam with is wier than the exit aperture, using equations (8) (11), we estimate the fractional change Y in the photoelectric yiel ue to electrons emitte from the walls as Y ¼ 3:9 ; 10 9 Y W Y stick S A ; ð12þ where Y W an Y are the photoelectric yiels for the trap walls an the ust materials, respectively; stick is the efficiency of the photoelectrons for sticking to the negatively charge ust grains; an S A (m 2 ) represents the surface area of the walls expose to UV raiation. It shoul be note that any particle size epenence of Y in equation (12) enters only through Y, an there is no irect epenence on the particle size. If the Y is not size epenent, the electron emission from the walls woul not prouce a size-epenent effect. If, on the other han, Y is higher for submicron-size particles, as expecte by the current theory, the fractional change ue to emission from the walls woul be smaller for small-size particles, an effect contrary to the measure tren. In any case, the numerical values for Y for the beam iameter larger than the aperture by, say, 2 4 mm, Y w ¼ Y, an sticking efficiency 0.1 for the negatively charge particles is inicate to be <1%. From equation (12), we fin the effect of electron emission from the walls to be negligibly small, for any realistic values of beam iameters, sticking efficiencies, an the relative yiels of the grain an wall materials. 6. What are the effects of the electrical fiels of the DC voltage V DC an the AC voltage V AC on the measure photoelectric emission rates? The role of the DC potential ( V) applie to the top an bottom electroes is only to prouce a vertical fiel to balance the gravitational force an keep the particle at the trap center. The AC potential applie to the ring electroe, however, prouces a null fiel at the trap center, an the suspene particle is confine to a region of relatively small electric fiel at frequencies of Hz. The external AC an DC fiels woul influence the photoelectric emission rates only if they moify the WF or the thresholenergyrequireforejectionofanelectronfromtheust particle. Fiel emission phenomenon occurs at electric fiel strengths several orers of magnitue higher than the AC or DC fiels involve in the experiments reporte here, an consequently we fin the fiel emission effect ue to applie potentials to be completely negligible. The above conclusion is valiate by the ata relating to a whole series of experiments on a large number of particles involving a wie range of values of V DC, V AC, an f AC, where the particles ischarge only when the UV raiation is turne on, with no significant ifference in the ischarge rates for similar particles at ifferent values of V AC. Figures 12a 12c exhibit three plots of measurements of the photoelectric efficiency, the AC potential V AC as a function of grain-surface potential s, carrie out on three similar silica grains at UV wavelength of 160 nm: (a) a ¼ 0:33 m, V AC V, s ¼ 0:1 1:4 V; (b) a ¼ 0:37 m, V AC V, s ¼ 0:2 1:8 V; an (c) a ¼ 0:38 m, V AC V, s ¼ 1 9 V. The plots in the above figures inicate epenence of the photoelectric efficiency on grain surface potential or the charge as iscusse previously. However, the efficiencies at similar surface potentials exhibit only small ifferences that are inicative of ifferences in the particle size an shape. The photoelectric yiels corresponing to efficiencies for s! 0 inicate values of (1:7 2:6) ; 10 4 espite significant ifferences in the values of V AC. Also, it is significant to note that the photoelectric efficiencies inicate a ecreasing tren with increasing values of V AC, which is opposite to what woul be expecte for enhance emissions for higher AC potentials. We therefore conclue that the external fiels have no influence on ischarge rate of a trappe particle uner UV illumination. 6. THEORETICAL MODELS AND COMPARISON WITH EXPERIMENTS 6.1. Theoretical Moels on Size Depenence of Photoelectric Yiels In this section, we examine laboratory measurements of the photoelectric yiels presente in this paper in view of the existing theoretical moels an preicte values for micron/submicronsize ust grains. Detaile escriptions of the basic theory of photoelectric emissions are given in stanar texts on soli-state physics (e.g., Cusack 1958; Kittel 1996). The electrons at the surface regions of neutral ust grains are consiere to be confine to a potential well prouce by a ouble layer of equal an opposite charges forme at the bounary of the grain an the surrouning meium. The ouble layer of atomic imensions is assume to be of orer a few angstroms. The absorption of a UV photon in a ust grain leas to an excite electron moving towar the surface. The excite photoelectron may be ejecte from the grain provie its energy is sufficiently high to overcome the energy lost in the inelastic scattering, penetrate or tunnel through the barrier forme by the ouble layer at the surface, an in aition is enough to overcome the attractive force ue to the image potential of the ejecte electron. With a positively charge grain of charge Ze (Z > 0), an ejecte electron experiences a strong attractive force at short istances, e.g., a few hunre angstroms from the surface ue to the image potential, an is subjecte to a long-range attractive Coulomb force at longer istances. With a negatively charge grain (Z < 0), the ejecte electron also experiences an attractive force at short istances from the grain ( ), ue to the image potential, but is subjecte to a repulsive Coulomb force at larger istances. A neutral insulating grain has all valence ban energy levels occupie, an the excess electrons occupy the first available vacant energy levels in the conuction ban, with the ifference in the energy levels referre to as the ban gap. Consequently, the energy require for ejection of an excess electron from the conuction ban, also referre to as photoetachment, is less than that require for ejection of an electron from the valence ban.

10 No. 1, 2006 PHOTOELECTRIC MEASUREMENTS ON DUST GRAINS 333 Fig. 12a No rigorous theoretical moels of the photoelectric yiels of iniviual small ust grains are available as yet. In the following we examine the preictions of the current theoretical moels on size epenence of the WF, IPs, or ionization energies, an experimental valiations of the moels by measurements of the photoelectric yiels. 1. Accoring to a moel aopte by Watson (1972), the probability of an electron being emitte from a soli after photon absorption at a istance x below the surface is proportional to expð x/l e Þ, where l e is the electron escape length. The electrons that are excite eep insie the soli at istances larger than the attenuation length l a, corresponing to an e-foling length of the raiation, o not reach the surface. The yiel of small grains is assume to be enhance relative to the bulk values as the istance x of electron excitation to the surface is limite for small grains. Several reviews of theoretical evaluations of the photoelectric emissions have been given in the literature, in particular, on expecte enhancements of the photoelectric yiels of small ust grains in comparison with measurements for the corresponing bulk materials (e.g., Watson 1972, 1973; Draine 1978, 2004; Bakes & Tielens 1994; Weingartner & Draine 2001). Base on this consieration, Draine (1978) evelope an expression for the yiel enhancement factor for small grains of raii a, given by y 1 ¼ þ 2 2 exp ( ) 2 2 þ 2 2 exp ( ) ; ð13þ Fig. 12b Fig. 12c fig. 12a fig. 12b fig. 12c Fig. 12. (a) Photoelectric efficiency of a negatively charge 0.33 m raius particle ischarge with UV raiation at 160 nm wavelength from an initial surface potential of V, at AC ring electroe peak potentials of 1000 an 2000 V. (b)sameasin(a), but for a particle of 0.37 m raius at AC ring electroe peak potentials of 1000 an 2000 V varie at ifferent particle surface potentials of V. (c)sameasin(a), but for a particle of 0.38 m raius at AC ring electroe peak potentials of V varie at ifferent particle surface potentials of 9 1 V. [See the electronic eition of the Journal for a color version of this figure.] where ¼ a/l a þ a/l e an ¼ a/l e. The typical values for the two lengths l e an l a, from experimental ata, are estimate to be 10 an 100 8, respectively, although the value for l e is uncertain (e.g., Bakes & Tielens 1994; Hino et al. 1976; Pope & Swenberg 1982). For particle sizes corresponing to polycyclic aromatic hyrocarbon molecules, Bakes & Tielens (1994) estimate the yiel enhancement to be 11 with the above choice of parameters. However, for particle sizes in the range of m raii employe in the experiments reporte here with the parameters iscusse above, equation (13) oes not preict any enhancement an the factor y 1 approaches unity. This moel preicts a constant value of the photoelectric yiels with no variation over the size range consiere, whereas the measurements inicate a size epenence with a sharp ecrease in the yiels for smaller sizes. The moel escribe by equation (13) is thus not in agreement with the measurements mae on iniviual ust grains presente in this paper. 2. Weingartner & Draine (2001) provie estimates of the threshol energy h pet for the photoelectric ejection of electrons from the valence ban, as a function of grain charge an size. Here we reprouce their results but ignore quantum effects that are unimportant for the grains in our trap. For Z 1, h pet ¼ W b þ Z þ 1 e 2 2 a : ð14þ Van Hoof et al. (2004) slightly moifie the Weingartner & Draine result for Z < 1, fining h pet ¼ W b e 2 2 e þ (Z þ 1) 2a a 1 1 : 1 þ ( Z 1) 1=2 ð15þ From equation (15), the threshol energy ecreases as the grain becomes more negatively charge. This is in qualitative agreement with our result that the photoemission efficiency increases

11 334 ABBAS ET AL. Vol. 645 with Z. However, the shift in threshol energy is at most 0.1 ev for the grains consiere here. From equation (14), the threshol energy for neutral grains ecreases with size a.ifthis shift in threshol energy were the only factor influencing the yiel, then the yiel woul increase with grain size. Weingartner & Draine (2001) also inclue the Watson size-epenent yiel enhancement, so their moel yiels ten to increase as the grain size ecreases (for a P 300 8). For the grains consiere here, both the threshol energy shift an the Watson effect are expecte to be negligible. Thus, this moel is not in agreement with the measurements presente in this paper. Parallel to the above evelopments of photoelectric yiels of ust grains for astrophysical applications, a large boy of literature exists on evelopment of theoretical moels for size epenence of the WFs, IPs, or the ionization energies of iniviual atoms, aggregates, or clusters of atoms (e.g., Gallo & Lama 1974, 1976a, 1976b; Ekart 1985; Seil et al. 1991; Bréchignac et al. 1992; Dugour et al. 1992; e Heer 1993; Wong et al. 2003). The basic assumption in the evelopment of these moels is the expectation of evolution of the physical properties of small atomic systems progressing to large clusters an particles of arbitrary size. The moels are esigne to preict the energy require to remove an electron from an atomic system, with a systematic transition of the IP for single atoms to clusters of a few to a large number of atoms, an extening to the WF for bulk materials. In these moels, the effective raii R cl of a cluster of N atoms is assume to vary as R cl / N 1 =3, with the preicte IP epenence on N varying as /N 1/3. With the new techniques for prouction an experiments on atomic clusters, the moels are being teste an valiate for clusters of sizes ranging from a few to thousans of atoms (e.g., Ekart 1985; Seil et al. 1991; Bréchignac et al. 1992; Dugour et al. 1992; e Heer 1993; Wong et al. 2003). The measurements exhibit a clear tren of lower IPs an therefore higher expecte photoelectric yiels for larger clusters. A brief summary of the theoretical ieas relevant to the measurements presente here is given in the following. 3. A classical electrostatic moel for evaluation of the WF an ionization energy of an insulating sphere of arbitrary raius a an ielectric constant K was given by Gallo & Lama (1974, 1976a, 1976b). This formulation for estimation of the ionization energy, efine as the energy require to remove an electron from a sphere of arbitrary raius a to a istance r 0 ¼ a þ x 0, just outsie the surface where all the kinetic energy is issipate against short-range forces. The ejecte electron has to overcome the electrostatic forces ue to the resiual positive charge on the sphere, the polarization of the sphere inuce by the resiual charge, an by the electron itself. The energy require to move an electron from r 0 to infinity is erive as " ¼ Z 1 r 0 e 2 F = r ¼ e 2 ðk 1Þ X1 n r 0 a 1 þ nkþ ð 1Þ n¼0 þ 1 2 e 2 ðk 1Þ X1 n 1þ nkþ1 ð Þ n¼0 a n r nþ1 0 a 2nþ1 r0 2nþ2 : ð16þ The complex expression in equation (16) is approximate by ( " ffi e 2 1 K 1 a x 0 K þ 1 a þ x 0 þ 1 " #) K 1 a 3 2 K þ 1 ð2a þ x 0 Þða þ x 0 Þ 2 : ð17þ In the limit of very large particle raii, equation (17) reuces to " W ¼ e 2 K þ 7 : ð18þ 4x 0 K þ 1 Plots of equations (17) an (18), shown in Figure 1 of Gallo & Lama (1976b), for insulate spherical particles as a function of raius a an ielectric constant K inicate that the ionization energy or the WF monotonically ecreases with raius an approaches asymptotic values for large raii representing bulk materials. Also, the plots inicate the WFs for a particle of raius a ecreasing with increasing values of the ielectric constant K. The size epenence inicate by these plots implies the photoelectric emissions an yiels increasing with particle raii with the asymptotic values approaching the bulk measurements an higher yiels for particles with materials of higher ielectric constant. The size epenence of the yiel measurements presente in this paper, which inicates an orer of magnitue higher yiels for the larger particles compare with the small submicron size, is thus qualitatively consistent with the tren of the above classical electrostatic moel. It is interesting to note that the tren of ielectric constant epenence inicate by the yiel measurements presente in this paper is also qualitatively consistent with the above moel. The measurements for carbonaceous particles ( Fig. 9) with ielectric constant of 12 15, compare with silica (Fig. 7) with ielectric constant of , are measure to be higher by a factor of 2 3 as expecte from the moel. Clearly, the above classical moel is only an approximate representation, an a rigorous theoretical moel remains to be evelope. 4. A moel evelope by Wong et al. (2003) is base on classical electrostatics for stuies of the size epenence of the WFs an IPs. It provies a scaling relation base on the image charge metho for calculation of the energies require for removal of an electron from particles over a size range of iniviual atoms, clusters or small particles, an bulk materials. As in item (3) iscusse above, the interpolation formula is base on the energy require to remove an electron from a istance above the surface to infinity an is written as (Jackson 1975) (R) ¼ e 2 1 þ 4(=R) þ 6(=R) 2 þ 2(=R) 3 4 (1 þ =2R)(1 þ =R) 2 ¼ W ; R ð19þ where (/R) represents the scaling function for particles of raius R. In the limiting cases of R!1, the scaling reuces to unity, an the IP approaches the bulk WF W ¼ e 2 /4. Onthe other han, for particle sizes approaching atomic imensions, /R is 1, (1) ¼ 2, an the expression (R) provies the ratio of the atomic IP to the WF of bulk material by the well-known value of IP/W 2. Equation (19) inicates a size epenence of the photoelectric yiels, with higher values of the IP an lower photoelectric yiels for particles of smaller raii, an is consistent with the measurements presente in this paper. However, the above scaling function for size epenence may be consiere only on a qualitative basis in view of the simple classical electrostatic moel on which it is base, an the IPs of small grains may not be estimate accurately. The size epenence inicate by the scaling function in equation (19) has been generally verifie by a large variety of