Phenomenology

Different theoretical models were proposed by Schultze et al. [3.120, 3.226-3.228], Kolb and Gerischer et al. [3.229, 3.230] and Trassati [3.231, 3.232] to explain the physical nature of Me UPD phenomena. Quantum-mechanical approaches, which were recently started by Schmickler and Leiva [3.233-3.239] as well as by Neckel [3.240, 3.241], give a better insight into the complicated Me UPD phenomena. 

A current compilation of investigations on Me UPD systems using monocrystalline substrates and different electrolytes is presented in Section 8.1 with a special reference list. Typical examples of Me UPD systems are discussed in the following sections. 

Me UPD processes involving formation of 2D Meads phases, 2D Me-S surface alloy phases and 3D Me-S bulk alloy phases in the underpotential range (cf. eq. (1.7)) are due to a strong Me-S interaction and represent the initial step of metal electrocrystallization. 

The formation of 2D Meads phases on a foreign substrate, S, in the underpotential range can be well described considering the substrate-electrolyte interface as an ideally polarizable electrode as shown in Section 8.2. In this case, only sorption processes of electrolyte constituents, but no Faradaic redox reactions or Me-S alloy formation processes are allowed to occur, The electrochemical double layer at the interface can be thermodynamically considered as a separate interphase [3.54, 3.212, 3.213]. This interphase comprises regions of the substrate and of the electrolyte with gradients of intensive system parameters such as chemical potentials of ions and electrons, electric potentials, etc., and contains all adsorbates and all surface energy. Furthermore, it is assumed that the chemical potential //Meads is a definite function of the Meads surface concentration, F, and the electrode potential, E, at constant temperature and pressure Meads (7 , ). Such a model system can only be 

The formation of Meads on S corresponds to a transfer of solvated Me j ions from the electrolyte phase (El) to the interphase 0P) forming specifically adsorbed metal adions, Me d, which are partially desolvated and located in the inner part of the electrochemical double layer  

There are at least four crystalline forms of cellulose, based on different packing of the primary chain (Blackwell, 1982), and three forms of granular starch, based on the packing of double helices (Noel et al., 1993). The differences are largely in the unit-cell dimensions and the crystallization and precipitation temperatures. One form of starch, precipitated with alcohol, is in a symmetrical molecular arrangement and is readily dispersible in cold water (Kerr, 1950). Mannan and dextran yield different crystals at low and high temperatures, and there was not only a polymorphic difference, but a conformational difference in cellulose (Quenin and Chanzy, 1987). Curdlan appears to have three polymorphs—anhydrous, hydrated, and annealed. 

Mindful of the energy requirement for dispersion of a polysaccharide solute in water, syneresis is the slow, spontaneous separation of liquid from a gel, as the solid phase attempts to return to its energy ground state. This phenomenon is a quality defect, because it foreshadows solute sedimentation. 

Phenomenology is the study of behavior without explanatory structures and mechanisms. The chemically similar polysaccharides lend themselves to phenomenological study, because of the commonality of many of their properties and responses to ambient stimuli for example, irrespective of their chemistry, polysaccharides are generally dispersible in water and indis-persible in acetone their nry is concentration dependent within a critical range, and, with few exceptions, they respond identically to heat. 

The effect of spillover plays an important role in heterogeneous catalysis and was extensively studied during recent years. It was first noticed in the 1950s by Kuriacose.62 Work in this area has been reviewed by Teichner63 and by Conner et al.64 

The spillover effect can be described as the mobility of sorbed species from one phase on which they easily adsorb (donor) to another phase where they do not directly adsorb (acceptor). In this way a seemingly inert material can acquire catalytic activity. In some cases, the acceptor can remain active even after separation from the donor. Also, quite often, as shown by Delmon and coworkers,65 67 simple mechanical mixing of the donor and acceptor phases is sufficient for spillover to occur and influence catalytic kinetics leading to a Remote Control mechanism, a term first introduced by Delmon.65 Spillover may lead, not only to an improvement of catalytic activity and selectivity but also to an increase in lifetime and regenerability of catalysts. 

The effect of spillover was observed for different species such as H,68 O69 n,70 NO64 or CO.69 Most of the research has been carried out with hydrogen spillover. 

The simplest example of oxygen spillover is found in the adsorption of oxygen on carbon. The spillover oxygen migrates from the basal carbon (donor) to carbon atoms exposed at steps between layers of the graphite surface, where it reacts with the edge carbons (acceptor).71 In this case the donor and acceptor phase consist of the same material with different surface properties. 

Examples of reverse spillover (or backspillover) are the dehydrogenation of isopentane and cyclohexane on active carbon. Deposition of a transition metal on the active carbon accelerates the recombination of H to H2 due to a reverse spillover or backspillover effect.72 

In a crystal, the electronic and ionic conductivities are generally tensor quantities relating the current density Iq to the applied electric field E in accordance with Ohm s law. The scalar expression for the mobile-ion current density in the different principal crystallographic directions has the form 

If we place an ionic conductor between parallel-plate blocking electrodes that produce an electric field E parallel to the x-axis, the electrostatic potential varies as — xE on passing from one electrode at x = 0 to the other. At equilibrium, the mobile-ion concentration Cj(x) is proportional to exp(qEx/kT), and the ionic drift-current density (7(E in the field is balanced by a diffusion current due to the concentration gradient (Fick s law)  

To obtain a more complete description, we need to find an analytic expression for the pre-exponential factor Dq of the diffusion coefficient by considering the microscopic mechanism of diffusion. The most straightforward approach, which neglects correlated motion between the ions, is given by the random-walk theory. In this model, an individual ion of charge q reacts to a uniform electric field along the x-axis supplied, in this case, by reversible nonblocking electrodes such that dCj(x)/dx = 0. Since two 

In a stoichiometric material at T 7J, an = 0.5exp —AHJ2kT) introduces an additional term into the activation energy . of Eqn. (3.12) Eqn (3.13) becomes 

Experiment shows that the magnitude of the electric field between two plates depends on the medium contained between them. The quantity dielectric constant is used as a measure of the effect of the medium in reducing the field that exists if nothing is there. Water has a particularly large dielectric constant (ca. 78 at 25 °C). This means that if the field between two plates separated by a vacuum amounts to Xq, the field would be reduced to if water were used to fill the space between the plates. 

What are the phenomena characteristic of dielectric breakdown The first six in importance are  

The time between application of an electric field sufficiently high to cause the breakdown phenomena and their occurrence is about 1 /rs. 

An increase in pressure applied to the liquid suppresses the formation of streamers, which are the most telling sign of breakdown. 

The critical applied volts (and the associated electric field at the interfaces concerned) that cause breakdown depend upon the conductance of the solution (Fig. 2.72). 

Bar sky and Robbins performed NEMD simulations of the interfacial structiue and rheology of binary blends of symmetric polymers which were made immiscible to various degrees by adjusting the cross-interaction parameters. A liquid film was sheared by sliding boundaries. They found that there was a difference in velocity of the two species at the interface, suggesting a partial slip boundary condition. They attributed this to a difference in the positions of the centres of mass of the species on opposite sides of the interface. The viscosity in the interfacial region was lower than the bulk viscosity. 

There is much current simulation activity in studying supercooled liquids and the glass transition. There are a number of themes of investigation which are highlighted below. 

There are several recurring themes that appear in and have motivated the simulation studies. The first is that there is some distinguishing feature of the potential energy landscape which can lead to a quasi-equilibrium or solid model for the glassy state. This perspective on the glassy state is discussed in the next section. 

By far the most interesting and significant feature of CAM plant stomatal behavior is that they may open at night and close during the day. 

Although the early work of De Saussure (see Chap. 5.1.1) clearly showed dark CO2 uptake by cacti (see Chap. 5.1.1), it was not until the early reports of Gregory et al. (1954) and Nuernbergk (1961) showing nocturnal rather than daytime CO2 uptake that the significance of the reverse phase gas exchange became of general interest (see Chap. 6). 

Subsequently, reports such as Nishida (1963, see also Nishida, 1977) and Joshi et al. (1965) confirmed and emphasized nocturnal stomatal opening in succulents. 

Following the classification of CAM gas exchange patterns as suggested by Neales (1975) and discussed above (see Chap.5.1.2 see Fig.5.1), three types of transpiration patterns in CAM plants (i.e., three types of stomatal movement patterns) can be distinguished  

For a given antifoam-surfactant solution combination, the main practical concern is simply to ensure that sufficient antifoam is present to produce the desired diminution in foam volume given the nature and intensity of the relevant aeration processes involved. If this is to be achieved with a minimal level of empiricism, some knowledge of the relation between antifoam concentration and foam volume under given conditions of foam generation is required. Despite the evident importance of this fundamental aspect of antifoam behavior, there have been relatively few attempts to understand it [1]. This of course derives from the complexity that we have shown characterizes the overall process of antifoam action on foam volume. We may, however, derive useful generalizations if we make some simple, but realistic, assumptions. 

Antifoams are often conveniently dispersed into foaming systems in the form of emulsion drops or individual particles. Here we assume that the concentration, state of dispersion and the effectiveness of each antifoam entity in such antifoam dispersions remain constant during foam generation. These assumptions therefore 

We first deduce the effect of antifoam concentration on generated foam volumes, which should result if we make the simple assumption that the relative effectiveness of different antifoams is independent of both antifoam concentration and foam volume for a given method of foam generation and surfactant solution. Comparison with the experiment is made. 

The molecular weight range achieved with these methods spans 10,000-450,000 Da, with larger polymers typically formed by incorporating the saccharides during 

Ligand Lectin Ligand valency Assay Method Ref. 

Bivalent and trivalent Serum-type mannose 2-3 1-2 X 10 precipitation 105 

NAcYD(GG-ah-GlyC) Bivalent glycopeptide based YEE (ah-GlyC) Chicken hepatic lectin 2 2.6 X 10 precipitation 1 

Tris-GlcNAc glycocluster Chicken hepatic lectin 3 5.1 X 10 precipitation 1 

If the stress-strain curve extends considerably beyond the yield point one speaks of a tough polymer the shape of the curve depends on the strain hardening behavior of the polymer and on the tendency to neck formation. Curve d) is characteristic for soft polymers, e.g. for thermoplastics at a temperature close to their glass transition temperature or plasticised polymers, which do not yet show rubber elastic behavior. 

As indicated earlier the different stress-strain curves are not characteristic for particular, chemically defined species of polymers but for the physical state of a polymeric solid. If the environmental parameters are chosen accordingly transitions from one type of behavior (e.g. brittle, curve a) to another (e.g. ductile, curve c) will be observed. These phenomenological aspects of polymer deformation are discussed in detail in [14], [52—53], [55—57], and in the general references of Chapter 1. A decrease of rate of strain or an increase of temperature generally tend to increase the ductility and to shift the type of response from that of curve a) towards that of curves c) and d). At small strains (between zero and about one per cent) the uniaxial stress o and the strain e are linearly related (Hooke s law)  

Even at these small deformations the apparent Young s modulus E is a function of the rate of strain. This shows that E is not solely determined by the energy elastic deformation of bond angles, bond lengths, and intermolecular distances but also involves time-dependent displacements of atoms and small atom-groups. In the fol- 

The shear modulus G is proportional to the absolute temperature T, Boltzmann constant k, and the number N of subchains between cross-links  

When a small current or potential is applied, the response is in many cases linear. The effective resistance can, however, vary over a wide range. When this resistance is high, we have a polarizable interface, meaning that a small current generates a high potential across it (i.e., the interface is polarized to a large extent). 

When the effective resistance is low, the interface is said to be nonpolarizable. In this case a significant current can be passed with only minimal change in the 

A good reference electrode is always a reversible electrode. The inverse is not necessarily true. Not every reversible electrode is suitable as a reference electrode. For example, the correct thermodynamic reversible potential of a metal/metal-ion electrode may be hard to reproduce, because of impurities in the metal or complexing agents in the solution, even when the interface is highly nonpolarizable. 

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While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. 

The classic theory due to van der Waals provides an important phenomenological link between the structure of an interface and its interfacial tension [50-52]. The expression... 

The preceding material of this section has focused on the most important phenomenological equation that thermodynamics gives us for multicomponent systems—the Gibbs equation. Many other, formal thermodynamic relationships have been developed, of course. Many of these are summarized in Ref. 107. The topic is treated further in Section XVII-13, but is worthwhile to give here a few additional relationships especially applicable to solutions. 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

The interface between a solid and its vapor (or an inert gas) is discussed in this chapter from an essentially phenomenological point of view. We are interested in surface energies and free energies and in how they may be measured or estimated theoretically. The study of solid surfaces at the molecular level, through the methods of spectroscopy and diffraction, is taken up in Chapter VIII. 

The function of this chapter is to review these methods with emphasis on the types of phenomenology involved and information obtained. Many of the effects are complicated, and full theoretical descriptions are still lacking. The wide variety of methods and derivative techniques has resulted in a veritable alphabet soup of acronyms. A short list is given in Table VIII-1 (see pp. 313-318) the lUPAC recommendations for the abbreviations are found in Ref. 1. 

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

There is a large volume of contemporary literature dealing with the structure and chemical properties of species adsorbed at the solid-solution interface, making use of various spectroscopic and laser excitation techniques. Much of it is phenomenologically oriented and does not contribute in any clear way to the surface chemistry of the system included are many studies aimed at the eventual achievement of solar energy conversion. What follows here is a summary of a small fraction of this literature, consisting of references which are representative and which also yield some specific information about the adsorbed state. 

The traditional, essentially phenomenological modeling of boundary lubrication should retain its value. It seems clear, however, that newer results such as those discussed here will lead to spectacular modification of explanations at the molecular level. Note, incidentally, that the tenor of recent results was anticipated in much earlier work using the blow-off method for estimating the viscosity of thin films [68]. 

These concluding chapters deal with various aspects of a very important type of situation, namely, that in which some adsorbate species is distributed between a solid phase and a gaseous one. From the phenomenological point of view, one observes, on mechanically separating the solid and gas phases, that there is a certain distribution of the adsorbate between them. This may be expressed, for example, as ria, the moles adsorbed per gram of solid versus the pressure P. The distribution, in general, is temperature dependent, so the complete empirical description would be in terms of an adsorption function ria = f(P, T). 

As stated in the introduction to the previous chapter, adsorption is described phenomenologically in terms of an empirical adsorption function n = f(P, T) where n is the amount adsorbed. As a matter of experimental convenience, one usually determines the adsorption isotherm n = fr(P), in a detailed study, this is done for several temperatures. Figure XVII-1 displays some of the extensive data of Drain and Morrison [1]. It is fairly common in physical adsorption systems for the low-pressure data to suggest that a limiting adsorption is being reached, as in Fig. XVII-la, but for continued further adsorption to occur at pressures approaching the saturation or condensation pressure (which would be close to 1 atm for N2 at 75 K), as in Fig. XVII-Ih. 

I. Adsorption Heats and Entropies. It is not necessary, phenomenologically, to state whether the process is adsorption, absorption, or solution, and for the adsorbent-adsorbate complex formal equations can be written, such as... 

The plan of this chapter is as follows. We discuss chemisorption as a distinct topic, first from the molecular and then from the phenomenological points of view. Heterogeneous catalysis is then taken up, but now first from the phenomenological (and technologically important) viewpoint and then in terms of current knowledge about surface structures at the molecular level. Section XVIII-9F takes note of the current interest in photodriven surface processes. 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

Here we have neglected derivatives of the local velocity of third and higher orders. Equation (A3.1.23) has the fonn of the phenomenological Newton s law of friction... 

Onsager postulates [4, 5] the phenomenological equations for irreversible processes given by... 

Hamiltonian, but in practice one often begins with a phenomenological set of equations. The set of macrovariables are chosen to include the order parameter and all otlier slow variables to which it couples. Such slow variables are typically obtained from the consideration of the conservation laws and broken synnnetries of the system. The remaining degrees of freedom are assumed to vary on a much faster timescale and enter the phenomenological description as random themial noise. The resulting coupled nonlinear stochastic differential equations for such a chosen relevant set of macrovariables are collectively referred to as the Langevin field theory description. 

The phenomenology of model B, where (j) is conserved, can also be outlined simply. Since (j) is conserved, it obeys a conservation law (continuity equation) ... 

Smoluchowski theory [29, 30] and its modifications fonu the basis of most approaches used to interpret bimolecular rate constants obtained from chemical kinetics experiments in tenus of difhision effects [31]. The Smoluchowski model is based on Brownian motion theory underlying the phenomenological difhision equation in the absence of external forces. In the standard picture, one considers a dilute fluid solution of reactants A and B with [A] [B] and asks for the time evolution of [B] in the vicinity of A, i.e. of the density distribution p(r,t) = [B](rl)/[B] 2i ] r(t))l ] Q ([B] is assumed not to change appreciably during the reaction). The initial distribution and the outer and inner boundary conditions are chosen, respectively, as... 

Here E(t) denotes the applied optical field, and-e andm represent, respectively, the electronic charge and mass. The (angular) frequency oIq defines the resonance of the hamionic component of the response, and y represents a phenomenological damping rate for the oscillator. The nonlinear restoring force has been written in a Taylor expansion the temis + ) correspond to tlie corrections to the hamionic... 

The focus of the present chapter is the application of second-order nonlinear optics to probe surfaces and interfaces. In this section, we outline the phenomenological or macroscopic theory of SHG and SFG at the interface of centrosymmetric media. This situation corresponds, as discussed previously, to one in which the relevant nonlinear response is forbidden in the bulk media, but allowed at the interface. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

We now consider how one extracts quantitative infonnation about die surface or interface adsorbate coverage from such SHG data. In many circumstances, it is possible to adopt a purely phenomenological approach one calibrates the nonlinear response as a fiinction of surface coverage in a preliminary set of experiments and then makes use of this calibration in subsequent investigations. Such an approach may, for example, be appropriate for studies of adsorption kinetics where the interest lies in die temporal evolution of the surface adsorbate density N. ... 

Petukhov A V 1995 Sum-frequency generation on isotropic surfaces general phenomenology and microscopic theory for ]ellium surfaces Phys. Rev. B 52 16 901 -11... 

Sipe J E, Moss D J and van Driel H M 1987 Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals Phys. Rev. B 35 1129-41... 

Phenomenologically, the FNDOR experiment can be described as the creation of alternative relaxation paths for the electron spins, which are excited with microwaves. In the four-level diagram of the system... 

One can regard the Hamiltonian (B3.6.26) above as a phenomenological expansion in temis of the two invariants Aiand//of the surface. To establish the coimection to the effective interface Hamiltonian (b3.6.16) it is instnictive to consider the limit of an almost flat interface. Then, the local interface position u can be expressed as a single-valued fiinction of the two lateral parameters n(r ). In this Monge representation the interface Hamiltonian can be written as... 

In tire limit of a small defonnation, a polymer system can be considered as a superjDosition of a two-state system witli different relaxation times. Phenomenologically, tire different relaxation processes are designated by Greek... 

Here A, C and E are phenomenological coefficients in the Landau expansion in tenns of the smectic ordering ... 

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