The energy of the quasi-free electron in near. critical point nitrogen

Transcription

1 The energy of the quasi-free electron in near critical point nitrogen Yevgeniy Lushtak a,b, C.M. Evans a,b,, and G.L. Findley a,c a Department of Chemistry and Biochemistry, Queens College CUNY, Flushing, NY 11367, United States, Tel: (718) ; Fax: (718) b Department of Chemistry, Graduate Center CUNY, New York, NY 10016, United States c Department of Chemistry, University of Louisiana at Monroe, Monroe, LA 71209, United States Abstract Field enhanced photoemission is used to measure the density dependent quasi-free electron energy V 0 (ρ) in the strongly absorbing gas N 2 for the first time. V 0 (ρ) in N 2 was obtained from low density to the density of the triple point liquid, at noncritical temperatures and on an isotherm near the critical isotherm. A novel critical point effect is observed and is accurately explained by the local Wigner-Seitz model. Key words: field enhanced photoemission, local Wigner-Seitz model, repulsive fluids, quasi-free electron energy, critical point effects PACS: i, i, Pv Corresponding author. addresses: cherice.evans@qc.cuny.edu (C.M. Evans), findley@ulm.edu (G.L. Findley). Preprint submitted to Elsevier 11 June 2012

2 1 Introduction The low field electron mobility in gas phase nitrogen decreases sharply as the nitrogen density ρ approaches that of the liquid [1 4]. The proposed explanations for this decrease include the localization of the electron in nitrogen [5, 6] and electron attachment to nitrogen stabilized by the formation of negatively charged van der Waals clusters [3, 4]. However, to begin to develop models for electron mobility and electron localization in a dense fluid, one must first estimate (or determine) the energy V 0 (ρ) of the quasi-free electron in the fluid, since the potential energy of a localized electron and the radius of the bubble (for a repulsive fluid) where the electron is localized are both dependent on the quasi-free electron energy [4]. Since the only measurement of V 0 (ρ) in N 2 is that for liquid nitrogen at 77 K (cf. Figure 1, marker), Sakai et al. [4] estimated V 0 (ρ) using V 0 (ρ) = 2π A m e ρ + 35 α2 a 0 R α ρ 2. (1) In Eq. (1), is the reduced Planck constant, m e is the electron mass, α is the polarizability of nitrogen, a 0 is the Bohr radius, R α is a characteristic molecular radius and A is the electron/nitrogen scattering length. Their calculation [4], which is shown in Figure 1 as a line, assumed that α = 11.8 a 0, A = 0.57 a 0, and R α = 2.4 a 0. Using this estimated quasi-free electron energy, Sakai et al. [4] concluded that the transition between a delocalized (or quasi-free electron) and a trapped electron in dense nitrogen should occur around 115 K. However, Figure 1 clearly shows that the calculated V 0 (ρ) and the single experimental point are far from agreement. Thus, additional information about V 0 (ρ) in N 2 is vital for understanding electron mobility and localization in this simple molecular fluid. 2

3 The dearth of experimental data for the quasi-free electron energy in molecular nitrogen arises from the difficulty in measuring V 0 (ρ) in strongly absorbing fluids. Two methods for determining V 0 (ρ) have been photoemission [8, 10] from an electrode immersed in the fluid and field ionization [9 11] of a dopant dissolved in the fluid. Photoemission has yielded V 0 (ρ) data with significant experimental scatter, while dopant field ionization requires a dopant that dissolves in the fluid and that also ionizes in an energy region where the fluid is transparent. Within these limits, dopant field ionization has been successful in obtaining V 0 (ρ) for various rare gases [12 20] and for the molecular gases CH 4 [21] and C 2 H 6 [21], at noncritical temperatures and on isotherms near the critical isotherms of the different fluids. A novel critical point effect has been observed that, in turn, led to the development of a new model for the quasifree electron energy (i.e., the local Wigner-Seitz model [12, 21]). However, N 2 absorbs significantly in the vacuum ultraviolet energy region and, therefore, dopant field ionization is not a viable technique for determining V 0 (ρ) in this fluid. Recently, we developed field enhanced photoemission [22] as a new technique for directly measuring V 0 (ρ) in fluids that are unable to solvate a dopant across a broad fluid density range (e.g., He [23]), and in fluids that are opaque to vacuum ultraviolet radiation (e.g., N 2 ). In this letter, we present the first extensive, high precision study of the quasi-free electron energy in N 2 from low density to the density of the triple point liquid at noncritical temperatures and on an isotherm near the critical isotherm. These data are then used to extend the local Wigner-Seitz model to repulsive molecular fluids (i.e., molecular fluids with A > 0). 3

4 2 Experimental All data were measured with monochromatic vacuum ultraviolet synchrotron radiation using the University of Wisconsin Synchrotron Radiation Center stainless steel Seya-Namioka beamline equipped with a high energy (5 35 ev) grating [11]. The radiation, having a resolution of 10 mev in the energy region of interest, enters a copper sample cell fitted with a MgF 2 window capable of withstanding up to 100 bar of pressure. A 10 nm thick strip of sputter deposited platinum along the window diameter serves as the photoemitting electrode. A stainless steel electrode is attached to the window perpendicular to this strip of platinum, with the spacing between the two electrodes being 0.1 cm. The electric field is applied to the stainless steel electrode, while the photocurrent is detected at the platinum electrode using a Keithley 6514 electrometer. (The high voltage power supply and the electrometer drew power through an AC line conditioner to remove electrical line noise.) The flux from the Seya beamline was monitored for consistency using a nickel mesh intersecting the beam prior to the sample cell. However, the photoemission spectra were normalized to monochromator flux using a GaAsP diode adjusted for the beamcurrent in the Aladdin storage ring, since the lowest photoemission threshold of the nickel mesh occurs in the spectral region of interest. The cell temperature was adjusted, and maintained to within ±0.05 K, using an Advanced Research Systems DE-204SB 4K closed cycle helium cryostat system. Nitrogen (Matheson Gas Products or Airgas, %) was used without further purification. Prior to the introduction of N 2, the gas handling system was baked to a base pressure of at least low 10 8 Torr. The number density was determined from the modified Benedict-Webb-Ruben equation of state 4

5 for nitrogen [24]. At temperatures below the critical temperature of K, where the density of N 2 is varied by adjusting the temperature, the N 2 pressure was maintained at a minimum of 5 bar above the vapor pressure, as determined from the vapor pressure equation developed by Jacobsen et al. [25]. This ensured that the N 2 in the sample cell remained in the gas phase. The experimental technique of field enhanced photoemission [22, 23] requires that photoemission spectra for at least four different applied electric fields be measured for each N 2 density and for each isotherm. The difference i in the near threshold photoemission from the platinum electrode in the presence of nitrogen and under the influence of two different electric fields is [22, 23] where i ( ) B(T, ρ) = [hν ϕ(ρ)] Λ H Λ L (Λ H Λ L ), (2) Λ i = e3 E i ε r (T, ρ), (3) with i = L, H for the low and high applied electric field E i, respectively. In eqs. (2) and (3), B(T, ρ) is an empirical constant that depends on the fraction of electrons that can absorb a photon and escape, hν is the photon energy, e is the electron charge, ϕ(ρ) is the platinum work function in the presence of nitrogen, and ε r ε(t, ρ)/ε 0 is the temperature and density dependent nitrogen relative permittivity, with ε 0 being the permittivity of the vacuum. Additional rearrangement of Eq. (2) gives [22, 23] hν = b i E + a, (4) with a slope of b = 1/B(T, ρ) and an intercept of a(ρ) = ϕ(ρ) 1 2 ( Λ H + Λ L ), (5) 5

6 where i E is defined as i E i ΛH Λ L. (6) Thus, the field enhanced photoemission signal is a plot of photon energy as a function of i E. When the linear region of this signal is fitted by least squares analysis, the intercept a(ρ) yields the work function ϕ(ρ) in the zero field limit. The quasi-free electron energy is then determined from V 0 (ρ) = ϕ(ρ) ϕ 0, (7) where ϕ 0 is the zero density work function. Because ϕ(ρ) is temperature dependent, and in order to minimize error introduced by nitrogen/electrode interactions, a series of photoemission spectra were obtained at low nitrogen pressures at various voltages for each isotherm. The nitrogen density for these low pressure measurements was approximately cm 3 and, therefore, ϕ 0 = ϕ( cm 3 ) for all isotherms. Since each FEP spectrum, defined by Eq. (4), depends on the relative permittivity in the fluid, this latter parameter was obtained by a least squares analysis of the total charge on the electrodes, in the absence of photons, as a function of voltage across the electrodes at all N 2 densities, temperatures and applied electric fields. The Clausius-Mossotti function [26] for the experimentally determined relative permittivity in N 2 is shown in Figure 2, plotted as a function of N 2 number density ρ. These data indicate that the relative permittivity is independent of temperature for our system and is cubically dependent on ρ. 6

7 3 Results and Discussion Figures 3 5 present representative photoemission spectra of platinum in N 2 at various densities and temperatures and at various electric field strengths. From low density (e.g., Figure 3a) to high density (e.g., Figure 5b), a distinct enhancement of the photocurrent as a function of electric field is observed. Similar series of photoemission spectra were obtained at various nitrogen number densities at noncritical temperatures and on an isotherm near the critical isotherm. The electric fields for each density where chosen to maximize the signal to noise ratio and to maximize the electric field enhancement of the photocurrent, but to minimize electron localization in N 2 [1 4]. Thus, as the density increased and the temperature decreased, the electric fields applied across the cell also increased. At the highest N 2 densities, the minimum field applied was 26 kev/cm, while the maximum field was 50 kev/cm. In contrast, at low N 2 number densities, similar (or better) signal to noise ratios were obtained with electric fields between 4 kev/cm and 18 kev/cm. Thus, at these high field strengths (which are sufficient to prevent electron trapping), the significant decrease in photocurrent between the low density spectra and the high density spectra in Figures 3 5 is caused by multiple scattering effects changing B(T, ρ), rather than by electron localization in the fluid. The spectra presented in Figure 4, which were measured at the near critical temperature of 127 K, were obtained in succession to the data sets measured on the two noncritical isotherms of 132 K (e.g., Figure 3) and 137 K. The small variance in the total photocurrent emitted from the electrode for the low density spectra (cf. Figures 3a and 4a) indicates that oxide layer formation on the electrode from any residual impurities in nitrogen is negligible. (The larger 7

8 difference in the total photoemitted current in Figure 5a in comparison to those in Figures 3a and 4a was caused by the replacement of the Pt electrode between these measurements due to a crack in the MgF 2 window. High pressures and low temperatures place significant stress on the MgF 2 window of the sample cell. Because of this stress, window breakage does occasionally occur during the measurement of V 0 (ρ) in a fluid. When this occurs, the window (including the platinum electrode) is replaced. After baking the vacuum system to ensure a base pressure of low 10 8 Torr, new low density spectra were measured for the isotherm in question. Subsequently, these spectra were used to determine a new reference ϕ 0 for the new electrode on the isotherm.) After obtaining i E from Eq. (6) for all possible pairwise differences between the photoemission spectra taken at various applied electric fields for each density, the linear regions in the i E data were fitted by least squares analysis to Eq. (4). Representative FEP intercepts a(ρ) for the noncritical temperatures of 137 K and 132 K are shown in Figures 6a and 6b, respectively, plotted as a function of Λ H + Λ L. Figure 6c presents a similar graph for the near critical isotherm of 127 K. Extrapolating these data sets to zero field yields the work function ϕ(ρ) and, therefore, the quasi-free electron energy from Eq. (7). (We should note here that plots similar to those presented in Figure 6 also exist for data obtained at temperatures below the critical temperature, but are not shown for brevity. In addition, temperatures below the critical temperature were necessary to achieve densities above cm 3 while maintaining a pressure below 80 bar, since the density change as a function of pressure is small in this thermodynamic region of the N 2 phase diagram [24]. Therefore, only the low density data set (necessary to determine ϕ 0 ) and a single high density data set were measured for each isotherm below the critical isotherm.) 8

9 The quasi-free electron energy V 0 (ρ) in nitrogen is presented in Figure 7 as a function of N 2 number density ρ. As in the case of the repulsive atomic gases Ne [18] and He [23], but unlike the attractive molecular gases CH 4 [21] and C 2 H 6 [21], the quasi-free electron energy in N 2 is strictly positive. However, unlike the quasi-free electron energy in the repulsive atomic gases [18, 23], V 0 (ρ) in N 2 has a significant curvature at medium N 2 number densities. Even with this curvature, a substantial critical point effect is observed. Thus, N 2 acts as a significant test to the local Wigner-Seitz model for the quasi-free electron energy. Within the local Wigner-Seitz approach, V 0 (ρ) = P (ρ) + E k (ρ) k B T, (8) where P (ρ) is the ensemble averaged electron/nitrogen polarization energy, E k (ρ) is the zero point kinetic energy of the quasi-free electron, and (3/2)k B T (k B Boltzmann s constant) is the thermal energy of the quasi-free electron. The ensemble average electron/nitrogen polarization energy is calculated from [11, 12, 21] P (ρ) = 4πρ 0 g(r) w (r) r 2 dr, (9) where g(r) is the nitrogen/nitrogen radial distribution function, and w (r) is the electron/nitrogen interaction potential. Since many of the thermodynamic properties of N 2 across a broad temperature and density range can be modeled using a simple Lennard-Jones 6-12 potential [27 29], dense N 2 may be taken to be approximately spherical. Thus, we chose the electron/nitrogen interaction potential w (r) to be identical to that used by us in the successful modeling 9

10 of V 0 (ρ) in previous atomic and molecular systems [12 18,21,23], namely [30] w (r) = 1 2 α e2 N i r 4 i f (r i ), (10) with a screening function f (r) given by [30] f (r) = 1 απρ ds 1 r+s 0 s g(s) dt 1 2 r s t f (t) θ(r, s, t) (11) 2 to account for the repulsive interactions between induced dipoles in the fluid. (In Eq. (11), s and t represent the distance between the N 2 molecule of interest and all other N 2 molecules, and θ(r, s, t) = [3(s 2 + t 2 r 2 ) (s 2 t 2 + r 2 ) + 2s 2 (r 2 + t 2 s 2 )]/(2 s 2 ).) The zero point kinetic energy E k (ρ) is obtained from solving the Schrödinger equation (with scattering boundary conditions) for the quasi-free electron in a dense fluid. Assuming that the dynamic polarization potential resulting from local interactions of the quasi-free electron with the fluid is short-ranged and has an average translational symmetry allows one to write [11, 12, 18, 21] E k (ρ) = 2 η m e r 2 b, where η 0 is the phase shift induced by the short-ranged potential and r b is the interaction range for the potential. At any density, the minimum distance between a quasi-free electron with low kinetic energy and a single molecule in the fluid is given by the absolute value of the scattering length A. At high fluid number densities, under the assumption that interactions in the first solvent shell dominate the dynamics of the problem, the maximum pairwise interaction distance r l is one-half the spacing between two molecules in the first solvent shell. This maximum spacing, otherwise known as the local Wigner- 10

11 Seitz radius [11, 12, 21], is r l = 3 3 4πg m ρ, (12) where g m is the maximum of g(r). Under these assumptions, the interaction range for the local potential is r b = r l A, and the zero point kinetic energy E k (ρ) becomes E k (ρ) = 2 η m e (r l A ) 2. (13) Previously, we have shown that accurate modeling of V 0 (ρ) within the local Wigner-Seitz approach across the entire density range of a fluid, at noncritical temperatures and on an isotherm near the critical isotherm, allows one to determine suitable intermolecular potentials for the fluid [21, 23], since the only empirically determined parameter within the local Wigner-Seitz model is η 0. Figures 8a and 8b present the ensemble averaged electron/nitrogen polarization energy P (ρ) and the zero point kinetic energy E k (ρ) for the quasi-free electron in N 2 plotted as a function of N 2 density. The radial distribution functions where determined from a direct integration of the Ornstein-Zernike relation with a Percus-Yevick closure [31] assuming a Lennard-Jones 6-12 potential with parameters σ = Å and ϵ/k B = K. (Lemmon et al. [28] obtained these parameters from an optimization to N 2 viscosity data to within 2% of experiment from low density to the density of the triple point liquid.) The scattering length of A = 0.19 Å was obtained by Asaf et al. [32] from the shift of high-n CH 3 I Rydberg states doped into low density N 2 gas. Optimizing η 0 in Eq. (13) to achieve the best fit to the V 0 (ρ) data in Figure 7 using Eq. (8) gave η 0 = This fit is shown in Figure 7 as a solid line for V 0 (ρ) calculated for noncritical temperatures and as a dotted line for that calculated for an isotherm near the critical isotherm. 11

12 Clearly, the local Wigner-Seitz model accurately fits the quasi-free electron energy V 0 (ρ) for all temperatures. The significant curvature of V 0 (ρ) now can be explained by comparing P (ρ) in Figure 8a with E k (ρ) in Figure 8b. As was observed for the repulsive atomic gases [18,23], the strictly positive E k (ρ) dominates the energetics. However, P (ρ) is significantly larger for N 2 in comparison to Ne [18] and He [23]. In the density range cm 3, P (ρ) and E k (ρ) in N 2 change with equal but opposite rates. Thus, V 0 (ρ) shows almost no variation as a function of density in this region. The success of the local Wigner-Seitz model of V 0 (ρ) in both atomic [12 19,23] and molecular [21] fluids provides significant insight into the energetics of a quasi-free electron in a dense fluid, which in turn can be applied to the development of new models for electron mobility. Whether V 0 (ρ) will be strictly positive, strictly negative, or neither is the result of the competition between the potential energy of the polarization of the fluid by the quasi-free electron (i.e., P (ρ)) and the kinetic energy of the electron (i.e., E k (ρ)). At high densities E k (ρ) will always dominate the energetics, since the interaction range r b for the quasi-free electron with a single fluid constituent becomes small. However, in the low to medium density region, whether E k (ρ) or P (ρ) dominates is subtly determined by a combination of the polarizability of the fluid, the intermolecular interactions within the fluid as defined by the intermolecular potential, the scattering length of the fluid constituents, and the phase shift due to dynamic polarization within the first solvent shell of the fluid. For example, argon and nitrogen have similar polarizability volumes (α = Å 3 for Ar [33] and α = Å 3 for N 2 [33]) and, therefore, similar ensemble average electron/fluid polarization energies (P (ρ) = 0.79 ev [determined here] and 1.04 ev [12] at the triple point density of N 2 and Ar, 12

13 respectively). However, V 0 (ρ) in argon [12 14, 17] is strictly negative, while that in nitrogen is strictly positive. This difference in V 0 (ρ) is determined by η 0, the phase shift arising from dynamic polarization within in the first solvent shell of the fluid. In argon, η 0 = 0.33 [12 14,17], whereas η 0 = 0.83 in nitrogen (as determined here). In fact, we have observed that attractive fluids (i.e., fluids with negative zero kinetic energy electron scattering lengths) tend to have η 0 < 0.5 [12 17, 21], while repulsive fluids tend to have η 0 > 0.6 [18, 23]. Our group is currently in the process of developing molecular dynamics routines to calculate the quasi-free electron energy, so as to probe the origin of the phase shift η 0. 4 Acknowledgments The experimental measurements reported here were performed at the University of Wisconsin Synchrotron Radiation Center (NSF DMR ). This work was supported by a grant from the National Science Foundation (NSF CHE ). We also thank Ms. Samantha Dannenberg, Mr. Holden Smith and Ms. Ollieanna Burke NSF Research Experience for Undergraduate (NSF CHE ) students for their assistance in acquiring the photoemission data, some of which are presented in Figures 3 5. References [1] L. Frommhold, Phys. Rev. 172 (1968) 118. [2] T. Wada, G. R. Freeman, J. Chem. Phys. 72 (1980)

14 [3] N. Gee, M. A. Floriano, T. Wada, S. S. S. Huang, G. R. Freeman, J. Appl. Phys. 57 (1985) [4] Y.Sakai, W.F. Schmidt, A.G. Khrapak, IEEE Trans. Dielec. Elec. Ins. 1 (1994) 4. [5] A. G. Khrapak, I. T. Iakubov, Sov. Phys. Uspekhi 129 (1979) 703, and references therein. [6] J. P. Hernandez, Rev. Mod. Phys 63 (1991) 675, and references therein. [7] W. Tauchert, H. Jungblut, W. F. Schmidt, Can. J. Chem. 55 (1977) [8] I. T. Steinberger in Electronic Excitations in Liquefied Rare Gases, W. F. Schmidt, E. Illenberger, ed. (Am. Sci. Publ., Valencia, 2005), and references therein. [9] J. Meyer, Ph.D. dissertation, Universitat Hamburg (1992), and references therein. [10] A. K. Al-Omari, Ph.D. dissertation, University of Wisconsin Madison (1996), and referencest therein. [11] Xianbo Shi, Ph.D. dissertation, Graduate Center CUNY (2010), and references therein. [12] C. M. Evans, G. L. Findley, Phys. Rev. A 72 (2005) [13] C. M. Evans, G. L. Findley, Chem. Phys. Lett. 410 (2005) 242. [14] C. M. Evans, G. L. Findley, J. Phys. B: At. Mol. Opt. Phys. 38 (2005) L269. [15] Luxi Li, C. M. Evans, G. L. Findley, J. Phys. Chem. A 109 (2005) [16] Xianbo Shi, Luxi Li, C. M. Evans, G. L. Findley, Chem. Phys. Lett. 432 (2006)

15 [17] Xianbo Shi, Luxi Li, C. M. Evans, G. L. Findley, Nucl. Inst. Meth. Phys. A 582 (2007) 270. [18] C. M. Evans, Yevgeniy Lushtak, G. L. Findley, Chem. Phys. Lett. 501 (2011) 202. [19] Xianbo Shi, Luxi Li, G. M. Moriarty, C. M. Evans, G. L. Findley, Chem. Phys. Lett. 454 (2008) 12. [20] C. M. Evans, Yevgeniy Lushtak, Xianbo Shi, Luxi Li, G. L. Findley, Chem. Phys. Lett. 505 (2011) 16. [21] Xianbo Shi, Luxi Li, G. L. Findley, C. M. Evans, Chem. Phys. Lett. 481 (2009) 183. [22] Y. Lushtak, C.M. Evans, G.L. Findley, Chem. Phys. Lett. 515 (2011) 190. [23] Y. Lushtak, Samantha Dannenberg, C.M. Evans, G.L. Findley, Chem. Phys. Lett. (2012) [24] W. B. Street, L. S. Sagan, J. Chem. Thermodynamics 5 (1973) 633. [25] R. T. Jacobsen, R. B. Stewart, M. Jahangul, J. Phys. Chem. Ref. Data 15 (1986) 735. [26] J. W. Schmidt, M. R. Moldover, Int. J. Thermophys. 24 (2003) 375. [27] J. G. Powles, K. E. Gubbins, Chem. Phys. Lett. 38 (1976) 405. [28] E. W. Lemmon, R. T. Jacobsen, Int. J. Thermophys. 25 (2004) 21. [29] A. Elkamel, R. D. Noble, J. Membrane Sci. 65 (1992) 163. [30] J. Lekner, Phys. Rev. 158 (1967) [31] E. W. Grundke, D. Henderson, R. D. Murphy, Can. J. Phys. 51 (1973) [32] U. Asaf, J. Meyer, R. Reininger, I. T. Steinberg, J. Chem. Phys. 96 (1992) [33] R. H. Orcutt, R. H. Cole, J. Chem. Phys. 46 (1967)

16 Fig. 1. The quasi-free electron energy V 0 (ρ) in molecular nitrogen as a function of nitrogen number density ρ. ( ) determined from photoemission [7] of an electrode immersed in liquid nitrogen at 77 K. ( ) calculated from Eq. (1) [4]. 16

17 Fig. 2. [Color online] The Clausius-Mossotti function [(ε r 1)/(ε r + 2)], where ε r ε(t, ρ)/ε 0, with ε 0 being the vacuum permittivity, plotted as a function of N 2 number density ρ. The solid markers represent data measured at the noncritical temperatures of ( ) K, ( ) K, ( ) various noncritical temperatures below the critical temperature of T c = K. ( ) are data obtained on the near critical isotherm of K. The solid line is a nonlinear least squares analysis to [(ε r 1)/(ε r +2)] = a 1 ρ+a 2 ρ 2 +a 3 ρ 3, with a 1 = 0.57±0.01 cm 3, a 2 = 1.8± cm 6 and a 3 = 6.7 ± cm 9. 17

18 Fig. 3. [Color online] Photocurrent plotted as a function of photon energy for N 2 number densities of (a) cm 3 and (b) cm 3 at the noncritical temperature of K. In (a), the applied fields are ( ) 1.0 kv/cm, ( ) 1.5 kv/cm, ( ) 2.0 kv/cm, ( ) 3.0 kv/cm, and ( ) 4.0 kv/cm. In (b), the fields are ( ) 4.0 kv/cm, ( ) 7.0 kv/cm, ( ) 10 kv/cm, ( ) 14 kv/cm, and ( ) 18 kv/cm. 18

19 Fig. 4. [Color online] Photocurrent plotted as a function of photon energy for N 2 number densities of (a) cm 3 and (b) cm 3 at the near critical temperature of K. In (a), the applied fields are ( ) 1.0 kv/cm, ( ) 1.5 kv/cm, ( ) 2.0 kv/cm, ( ) 3.0 kv/cm, and ( ) 4.0 kv/cm. In (b), the fields are ( ) 8.0 kv/cm, ( ) 13 kv/cm, ( ) 18 kv/cm, ( ) 25 kv/cm, and ( ) 32 kv/cm. 19

20 Fig. 5. [Color online] Photocurrent plotted as a function of photon energy for N 2 number densities of (a) cm 3 and (b) cm 3 at the noncritical temperature of 90.0 K. In (a), the applied fields are ( ) 1.0 kv/cm, ( ) 1.5 kv/cm, ( ) 2.0 kv/cm, ( ) 3.0 kv/cm, and ( ) 4.0 kv/cm. In (b), the fields are ( ) 26 kv/cm, ( ) 32 kv/cm, ( ) 38 kv/cm, ( ) 44 kv/cm, and ( ) 50 kv/cm. 20

21 Fig. 6. [Color online] The FEP intercept a(ρ) of representative field enhanced photoemission plots measured at (a) K, (b) K, and (c) K. In all graphs, ( ) cm 3. The densities of N 2, in units of cm 3, are from ( ) 2.0 to ( ) 9.9 in (a); from ( ) 1.0 to ( ) 11.1 in (b); and from ( ) 1.1 to ( ) 9.9 in (c). The FEP intercepts for field enhanced photoemission plots measured at temperatures below the critical temperature (such as those obtained from the photoemission data presented in Fig. 5) are not shown for brevity. See text for discussion. 21

22 Fig. 7. [Color online] The quasi-free electron energy V 0 (ρ) in N 2 determined from Eq. (7) using the data in Figure 6 (as well as data at other densities and temperatures that are not shown in Figure 6 for brevity) plotted as a function of N 2 number density ρ. ( ), ( ) and ( ) represent data obtained at K, at K and at various temperatures below the critical temperature, respectively. ( ) represents data obtained at K, which is near the critical temperature of K. The lines are a local Wigner-Seitz calculation. See text for discussion. 22

23 Fig. 8. [Color online] (a) The ensemble average electron/n 2 polarization energy P (ρ) calculated from Eq. (9), and (b) the zero point kinetic energy E k (ρ) obtained from Eq. (13), plotted as a function of N 2 number density ρ. The solid lines represent calculations performed at noncritical temperatures, while the dashed lines represent calculations at K (T c = K). The N 2 /N 2 interaction potential was modeled using a Lennard-Jones 6-12 potential [28]. The zero kinetic energy electron scattering length was A = 0.19 Å [32], while η 0 = 0.83 (as determined here). See text for discussion. 23