Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 11

Take the dipoles to point along $+z$, and let their surface number density be $n_s$. An annulus of radius $\rho$ and width $d\rho$ contains $n_{s}2\pi \rho d\rho$ dipoles. The electron's electrostatic potential energy is thereforeFor $z\ne 0$, the integral without $2\pi$ equals $z/|z|$, givingThus the jump's magnitude isFor the chosen outward dipole orientation the electron-energy change from the negative to positive side is negative. The electrostatic voltage jump has the opposite sign. This distinguishes the requested magnitude from the sign of the work function change.

Let $\Gamma$ be coverage in $\mathrm{mol}{\mathrm{m}}^{-2}$. Then $n_s=N_A\Gamma$ and the Helmholtz surface-dipole relation iswhere a voltage in volts has the same numerical value as the electron-energy change in electronvolts. Converting the slope from square centimeters to square meters gives $-5\times 10^5\mathrm{V}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$. ThereforeEach added molecule produces an effective outward surface dipole of about $2.2$ D, lowering the electron work function. This is the incremental adsorbate-plus-surface dipole, not necessarily the isolated molecular electric dipole moment.

Nitrogen-down adsorption places the positive hydrogen end farther from the metal, producing an outward molecular electric dipole moment and the observed decrease in work function. Its maximum normal component, however, is only $1.42$ D. Tilting alone can only reduce that component; it cannot explain an effective $2.20$ D.

The adsorbed molecule and metal therefore undergo appreciable electron density. Lone-pair donation into the metal, polarization of the substrate, image response and distortion of the adsorbate can change the effective interface dipole. The inferred increase relative to an upright isolated molecule is about $0.78$ D. For scale, transferring about $0.16$ elementary charges over $1$ Å would produce that dipole increment:This scale illustrates a plausible interfacial polarization; the work-function measurement alone does not uniquely determine a transferred charge or adsorption geometry.

At higher coverage, neighboring outward dipoles generate a local field opposing each other's polarization. This dipole depolarization reduces the incremental dipole per added molecule, so the work function becomes less sensitive to additional adsorption.

Crowding can also tilt the molecules, alter their coordination or make them occupy less strongly donating sites. Any of these changes can decrease the normal dipole increment. A reduced slope is consistent with coverage-dependent depolarization and geometry changes; it is not evidence that coverage has stopped increasing.

A plausible explanation is partial dissociation leaving a residual surface species, such as an NH${}_x$ fragment, adsorbed nitrogen or hydrogen, after molecular ammonia has finished desorbing. A small residual population can maintain a surface electric dipole moment and a $0.2$ eV work function offset. Heating farther can remove, recombine or rearrange those species.

Test this hypothesis by recording temperature-programmed desorption signals for hydrogen and nitrogen as well as ammonia, and by measuring residual nitrogen with X-ray photoelectron spectroscopy. A surface-sensitive vibrational spectrum could distinguish NH${}_x$ groups from atomic nitrogen. Isotopically labelled ammonia would help assign desorption products. Correlating disappearance of the residual spectral signal with recovery of the clean-surface work function would be more diagnostic than the absence of an ammonia signal alone. This is a proposed explanation, not a uniquely established identification.