Robert S. Hansen

Damping of waves on monolayer-covered surfaces: II. Influence of bulk-to-surface diffusional interchange on ripple characteristics☆

Abstract The theory of capillary ripple propagation with bulk-to-surface diffusional interchange is extended. Methods are developed which permit diffusion coefficient and surface equation of state to be obtained from ripple wave length and damping coefficient measurements. An approximate formula (accurate to within 10% under usual conditions of measurement) for the dependence of damping coefficient on surface elasticity and diffusion is also given; this formula implies that plots of damping coefficient against concentration may possess one and in some cases two maxima for suitable ranges of parameters describing adsorption and diffusional interchange. Wavelengths and damping coefficients were measured at various concentrations for aqueous solutions of pentanoic, hexanoic, heptanoic, and octanoic acids and of pentanol. These data were used to establish parameters in the Frumkin equation of state. The equations of state thus obtained represented very well the dependence of surface tension on concentration in these systems. Apparent diffusion coefficients were also obtained from the same data; these agreed well with bulk diffusion coefficients for pentanol, pentanoic acid, and hexanoic acid, but were an order of magnitude higher for heptanoic and octanoic acids. It is shown that the apparent elasticity of a surface film in the presence of bulk-to-surface diffusional interchange has a strong analogy to the Gibbs elasticity of a film whose thickness is 2D/ω .

Diffusion and the kinetics of adsorption of aliphatic acids and alcohols at the water-air interface☆

Hansen and Wallace (1) and Defay and Hommelen (2) have recently published independent studies of the time-dependent surface tensions of aqueous solutions of aliphatic acids and alcohols. Whereas experimental results in systems studied by both sets of workers appear to be in reasonably close agreement, Hansen and Wallace interpreted their results in terms of a barrier-limited adsorption process, Defay and Hommelen in terms of a diffusion-limited process. A treatment of adsorption kinetics is presented which takes explicit account of the diffusion process without presupposing the absence of an adsorption barrier, a new equation suitable for the treatment of experimental data is derived, and its utility is discussed. It is shown that available data point to a substantial depletion of the subsurface concentration at intermediate times and that the treatment of Hansen and Wallace, presupposing exclusive barrier limitation, cannot be correct. On the other hand, the initial proportionality of spreading pressure to time cannot be explained by an adsorption process limited exclusively by diffusion if it is supposed that the spreading pressure depends on the number of solute molecules in the surface layer in the same manner in the dynamic process and at equilibrium. Two hypotheses are advanced to account for the apparent barrier limitation at low times and diffusional limitation at intermediate times. First, the mechanism of transfer from subsurface to surface may be fast but not infinitely so (small barrier hypothesis). For the linear isotherm it is shown that this hypothesis leads to an adsorption proportional to time at low times, and to that given by diffusion theory with a time lag at long times. Reasons for expecting this behavior to be fairly general are given. Second, adsorption may be exclusively diffusion-controlled, but the concentration depletion near the surface contributes in the initial period of adsorption an effective spreading pressure — nRT, where n is the number of moles of solute per square centimeter in the surface layer. A model giving rise to this correction term is suggested and its plausibility discussed.

Flash Desorption and Isotopic Mixing of Hydrogen and Deuterium Adsorbed on Tungsten, Iridium, and Rhodium

Flash desorption of hydrogen from tungsten, iridium, and rhodium dosed at 100° and 300°K was investigated together with isotope mixing in coadsorbed mixtures of hydrogen and deuterium.The desorption of hydrogen from tungsten, iridium, and rhodium dosed at 300°K proceeds by a second‐order process with an activation energy of desorption well represented by ΔH=ΔH0—αn. At low surface coverages, values of 35, 24, and 18 kcal/mole, respectively, were obtained for ΔH0; the parameter α was determined from desorption curves at higher initial coverages and was found to be 28±2, 14±1, and 24±2 kcal/mole (1015 molecules/cm2)−1, respectively.The desorption spectrum of hydrogen from these metals dosed at 100°K contains two peaks, α and β. The distribution of the isotopes in the desorbed phase formed from coadsorbing H2 and D2 indicates that the α peak is due to an atomic species in the case of iridium and rhodium and a molecular species in the case of tungsten.

Propagation Characteristics of Capillary Ripples. I. The Theory of Velocity Dispersion and Amplitude Attenuation of Plane Capillary Waves on Viscoelastic Films

The boundary value problem for velocity of propagation and attenuation of capillary ripples over viscoelastic surface films is set up and solved from the viewpoint of continuum hydrodynamics. Both soluble and insoluble films are treated. Successive approximation methods are used to derive explicit formulas for velocity of propagation and amplitude attenuation; formulas for these quantities, accurate to second order, are given for slightly viscoelastic and highly viscoelastic films, and formulas, accurate to first order, are given for films of intermediate viscoelasticity.

A simple quantitative treatment of the spreading of monolayers on thin liquid films

Abstract A simple steady-flow treatment of the spreading of a monolayer over a thin liquid film leads toχ 2 = (2h/μ)π 0 t, where χ is the distance spread in time t, h the liquid-film thickness, μ the coefficient of viscosity of the liquid underlying the monolayer, and π 0 is the spreading pressure of the lens (located at χ = 0 ) generating the monolayer. The spreading of oleic acid on glycerol films was followed by observation of talc markers, and found in remarkably good agreement with this simple equation. Limitations of the equation, associated with neglect of pressure gradients and idealization of flow patterns, are briefly discussed. The equation should be most nearly valid for thin, wide films, but even in this case idealizations involved in the theory are such that its success in representing data is surprisingly good.

Reduction of nitric oxide with carbon monoxide on the Rh(100) single-crystal surface

Abstract The reduction of nitric oxide with carbon monoxide has been investigated on the Rh(100) single-crystal surface. Steady-state kinetic measurements, at 688 K and in the pressure range 1.0 to 1800 Pa, indicate that this process proceeds via a Langmuir-Hinshelwood-type mechanism and is selective toward the production of N2 and CO2. The carbon monoxide kinetic order varied continuously from +1 to −1 as the partial pressure of CO was increased from 1 to 250 Pa, at a constant NO partial pressure of 57.5 Pa. In a similar manner, the nitric oxide kinetic order varied continuously from + 3 2 to −1 as the partial pressure of NO was increased from 1 to 1800 Pa, at a constant CO partial pressure of 44.0 Pa. The catalyst surface was characterized with Auger electron spectroscopy (AES), low-energy electron diffraction (LEED), and thermal desorption spectroscopy (TDS). Initial Auger analysis revealed surface contamination by sulfur, phosphorus, and boron. The boron contaminant was identified by AES and by the formation of boron (3 × 1) or (3 × 3) ordered overlayers. These contaminants were removed via cycles of argon ion bombardment, reactive ion bombardment, and high-temperature annealing. Nitric oxide adsorbed with a high sticking coefficient and formed a c(2 × 2) ordered overlayer at saturation. The nitric oxide adsorbate dissociated upon slow stepwise heating as indicated by the production of a surface oxide and disappearance of surface nitrogen. Thermal desorption experiments at a faster heating rate indicated, however, that most of the adsorbed nitric oxide desorbed molecularly in a first-order process with a peak at 401 K during the temperature flash. Carbon monoxide adsorbs molecularly in two distinct sites with desorption from both following first-order kinetics with TDS peaks at 373 and 425 K. A kinetic model was developed which is consistent with both the steady-state kinetic and surface characterization results. The kinetic data were fit to the steady-state rate law derived from this mechanism involving the reduction of adsorbed nitrous oxide and nitrogen dioxide species by molecularly adsorbed carbon monoxide.

Catalytic decomposition of ammonia on tungsten (100), (110), and (111) crystal faces

The rates of catalytic decomposition of ammonia on (100), (110), and (111) single crystal faces of tungsten were measured over the temperature range 800–970 °K for ammonia pressures ranging from (0.5–100)× 10−3torr and for nitrogen and hydrogen pressures varying from (0–50) × 10−3torr. In all cases the rate of decomposition was of the form, rate=A+BPNH3(2/3), and was independent of nitrogen and hydrogen partial pressures. The constants A and B varied substantially with crystal face; the values of B for the (111), (100), and (110) faces were in approximate ratio 8.4:1.55:1 and these substantially established the decomposition rate for PNH3>5 × 10−3torr. Rate forms for NH3 and ND3 were compared on the (111) face at 860 °K, with results ANH3=AND3,BNH3≈ 1.47 BND3. The observed rate form is derived from a model involving nearly complete surface coverage by the species WN and small surface coverages by species W2N, W2N3H2, and WNH. The A term in the rate law is generated by the reaction, 2WN→W2N+(1/2)N2. This p...

Propagation characteristics of capillary ripples. II. Instrumentation for measurement of ripple velocity and amplitude

Abstract An instrument for measuring the propagation velocity of capillary ripples to within 0.3% and for measuring the amplitude of such ripples to within 1% to 10% (depending upon amplitude) was designed and constructed. The principal components of the instrument were a Langmuir trough of Teflon (with provision for automatic recording of compression data); generating and receiving probes consisting of a thin rod and a razor blade respectively mounted so that the rod and razor edge were parallel and accurately placed in the surface to be studied. The generator probe was driven sinusoidally by a highly modified audio “tweeter” speaker and the receiving probe was coupled to a crystal phonograph cartridge mounted on a micromanipulator. The standing wave pattern generated between the probes caused a sinusoidal output from the crystal cartridge which was amplified; the signal amplitude was proportional to the amplitude of the ripples, and the phases of generator and receiver oscillations could be compared. Propagation velocity and damping coefficient dispersion could be readily calculated from this information collected as a function of frequency.

Study of the Adsorption of Hydrogen, Ethane, Ethylene, and Acetylene on Iridium by Field Emission Microscopy

A field emission microscope permitting precise control of iridium emitter temperature from 4 to 1700°K was used to study changes in emission patterns and work functions resulting from time and temperature dependent surface reactions in the adsorption of hydrogen, ethane, ethylene and acetylene on iridium.The qualitative character of the emission patterns indicates a rather uniform covering of the high index faces of iridium by all species studies in the temperature range 70–300°K. Hydrocarbon species, once chemisorbed, are substantially immobile at temperatures below 700°K; above 700°K an intensification of emission pattern, probably due to carbonization, occurs around the edges of the 111 planes.Iridium surfaces containing adsorbed species were flashed for controlled periods of time to controlled temperatures; characteristic changes in work function resulted which were both time and temperature dependent. These experiments indicate that hydrogen is readily desorbed by iridium above 400°K, and that a larg...

A molecular orbital investigation of chemisorption. II. Nitrogen on tungsten (100) surface

The relative bonding energies of nitrogen chemisorbed at three symmetric sites on a W(100) surface, represented by finite arrays of tungsten atoms [L. W. Anders. R. S. Hansen, and L. S. Bartell, J. Chem. Phys. 59, 5277 (1973)] were obtained by means of the extended Huckel molecular orbital theory (EHMO). The preferred site for nitrogen chemisorption was found to be the five coordination number (5 CN) site or the fourfold site with a tungsten atom below four tungsten atoms surrounding the nitrogen atom. The 5p orbital repulsive energy, in the case of hydrogen chemisorption, could be adequately approximated by the sum over pairs of empirical exponential repulsive terms; in the case of nitrogen chemisorption, this same method was approximately 10% in error at the equilibrium bond distance, and repulsive energies were therefore obtained from calculations including tungsten 5p orbitals but with smaller arrays.