Potential energy curve physisorption

Figure 14 Potential energy curves for the H-graphite interaction for three cases physisorption on a rigid lattice (dotted line, filled squares), chemisorption where the lattice is allowed to relax (solid line, open circles), and chemisorption where the bonding carbon is fixed in the puckered position (dashed line, filled circles). The symbols correspond to the DFT calculations, and the lines correspond to the model PES. Taken from Ref. [90],...

Figure 39 Some calculated characteristics of H2 on Mg(0001), after Ref. 87. Top schematic potential energy curve. P = physisorption minimum M = chemisorbed molecule B = chemisorbed atoms A and D are transition states for chemisorption and dissociation. Bottom development of the one-electron density of states at certain characteristic points. M and M2 correspond to two molecular chemisorption points, different distances from the surface. The dashed line is the au density, moving to lower energy as the dissociation proceeds.

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

The activation energies of most chemisorptions are very low, sometimes even zero. The reason for this low activation energy is shown in Fig. 2.7 which illustrates the potential energy curves for both the physisorption (curve P)... 

Fig. 2. Crossed potential energy curves for physisorption and chemisorption, (a) Non-activated adsorption (b) activated adsorption.

Figure 2.23. Potential energy curves for chemisorption and physisorption.

The isolated H2 molecule possesses an occupied lOg, bonding level well below the bottom of most metal bands and a luu, antibonding level above Ep. At large distances from the metal surface, the electronic stmcture of H2 is little affected by the presence of the surface. The physisorption well is determined by the dynamic polarization properties of H2 (van der Waals attraction) and the steep rise in energy due to Pauli repulsion as the separation is reduced. H2 acts as a neutral but polarizable adsorbate. A physisorbed state of that nature is expected on all simple and noble metal surfaces. The corresponding potential energy curves were calculated for the simple metals Al, Mg, Li, Na and K and for the noble metals Cu, Ag and Au [101-106]. They compare weU with the few available experimental results [107,108]. 

Fig. 4.1 Potential energy curves for (7) physical and (2) chemical adsorption (a) non-activated (b) activated. Epot - potential energy, Qc - heats of chemisorption, Qp - heats of physisorption, Ead -energy of activation for desorption, Ediss - dissociation energy for the diatomic molecule. The sum AEdes = Ead + Qc is the the heat of hemisorption, in the activated processes [8]...

The difference between physisorption and chemisorption can be explained using a potential-energy diagram. The potential-energy diagram for physisorption and chemisorption of an A-A molecule (e.g., H2) is shown in Figure 10.1. Curve P in... 

Fig. 5-11 Potential energy and interatomic distances in the adsorption of hydrogen on nickei Curve 1 physisorption (0.32 nm, AHp = —A k)/moi)...

Different potential energy (Epot) curves can be drawn to represent an adsorption process, but one of the most frequently used for physisorption... 

Fig. 2.13 Schematic cross-section of the physisorption potential V(r. z) by the plane r = const corresponding to an adsorption site. The minimum of this curve determines the equilibrium position and the binding energy of an adsorbed atom.

The shapes of the interatomic potential curves are approximations chosen for mathematical convenience. Such potential functions are generally used in discussions on a variety of properties of molecules and lattices optical absorption and luminescence, laser action, infrared spectroscopy, melting, thermal expansion coefficients, surface chemistry, shock wave processes, compressibility, hardness, physisorption and chemisorption rates, electrostriction, and piezoelectricity. The lattice energies and the vibration frequencies of ionic solids are well accounted for by such potentials. On heating, the atoms acquire a higher vibrational energy and an increasing vibrational amplitude until their amplitude is 10-15% of the interatomic distance, at which point the solid melts. 

Fig. 3. Potential curves, describing adiabatic and non-adiabatic adsorption mechanisms, 22, 11 - diabatic terms, responsible for the configurations c -f- S and c-t- 5, respectively for z -> oo (c and S being adsorbed molecule of the sort c and surface) 21, 2 T - adiabatic terms responsible for the scune configurations for z oo Ech, Eph, E t, - energies of chemisorption, physisorption and chemisorption activation A. - nonadiabatic terms interaction parameter z. - term crossing point E, Ez - normal energies of translational motion of molecule in initial and final states. Term 1 corresponds to the chemisorptional state while the term 2 - to the phisisorptional one for z < z,.

Figure 3.6 The Lennard-Jones curve-crossing model for dissociative chemisorption, left without and right with an energy barrier. The undissociated A2 molecule is physisorbed at the surface. The A atoms are chemisorbed. The energy of the two new metal—A bonds suffices to compensate for the A-A bond energy e and the depth of the physisorption well. Therefore the interaction potential of the undissociated A2 molecule with the surface is asymptotically lower, by the A—A bond energy. But near the surface this potential curve is crossed by the interaction of two A atoms with the surface. The limitation of the two-body point of view is evident in this plot. The A—A bond distance, that is surely a key variable, is not represented in this simple view. More on this topic in Chapter 12.

Chemisorption is characterized by binding energies of a few eV, i.e., much larger than in physisorption. The corresponding equilibrium distances are about 1-3 A, i.e., shorter than for physically adsorbed species. If one draws on the same plot, the adsorption potentials for a physically adsorbed molecule and for chemically adsorbed atoms of which it consists, then the two potential curves cross each other at some intermediate distance from the surface (see Fig. 2.15). This means that a molecule approaching the surface has a certain probability to transfer to the other electronic term through a Landau-Zener... 

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