Local electrostatic potential

Protems can be physisorbed or covalently attached to mica. Another method is to innnobilise and orient them by specific binding to receptor-fiinctionalized planar lipid bilayers supported on the mica sheets [15]. These surfaces are then brought into contact in an aqueous electrolyte solution, while the pH and the ionic strength are varied. Corresponding variations in the force-versus-distance curve allow conclusions about protein confomiation and interaction to be drawn [99]. The local electrostatic potential of protein-covered surfaces can hence be detemiined with an accuracy of 5 mV. 

By covalently attaching reactive groups to a polyelectrolyte main chain the uncertainty as to the location of the associated reactive groups can be eliminated. The location at which the reactive groups experience the macromolecular environment critically controls the reaction rate. If a reactive group is covalently bonded to a macromolecular surface, its reactivity would be markedly influenced by interfacial effects at the boundary between the polymer skeleton and the water phase. Those effects may vary with such factors as local electrostatic potential, local polarity, local hydrophobicity, and local viscosity. The values of these local parameters should be different from those in the bulk phase. 

In the following chapters, we will concern ourselves with the nature of the interfacial microenvironments of some polyelectrolytes whose functionality controls photoinduced ET. Emphasis will be placed on the local electrostatic potential and also on the microphase structure of some amphiphilic polyelectrolytes in aqueous solution. 

A merocyanine dye, l-ethyl-4-(2-(4-hydroxyphenyl)ethenyl)pyridinium bromide (M-Mc, 2), exhibits a large spectral change according to the acid-base equilibrium [40, 41]. The equilibrium is affected by the local electrostatic potential and the polarity of the microenvironment around the dye. Hence, this dye is useful as a sensitive optical probe for the interfacial potential and polarity when it is covalently attached to the polyelectrolyte backbone. 

Fig. 3 Transition energy for S0 — Sj (red) and S0 — CT(black) for a tryptophan during a 2 ns QM-MM trajectory of the human eye lens protein yD-crystallin showing typical fluctuations due to rapid changes in local electrostatic potentials at the atoms of the chromophore. This Trp has a low quantum yield because the CT state is near the Sj state much of the time. Heterogeneity in lifetime and wavelength are evident in both states because regions of 100 ps are seen having distinctly different average energies...

Since the energy of electrons in a material is specified by the Fermi level, ep, the flow of electrons across an interface must likewise depend on the relative Fermi levels of the materials in contact. Redox properties are therefore predicted to be a function of the Fermi energy and one anticipates a simple relationship between the Fermi level and redox potential. In fact, the Fermi level is the same as the chemical potential of an electron. Clearly when dealing with charged particles, the local energy levels e are increased by qV, where q is the charge on the particle and V is the local electrostatic potential. The e, should therefore be replaced by e,- + qV and so... 

A solution of any polyelectrolyte-enzyme system might be considered as consisting of two phases in equilibrium, although, within limits, the polyelectrolyte is soluble. Owing to the local electrostatic potential, the inner polyelectrolydc phase, or environment, possesses its own local physicochemical parameters which differ from those of the bulk phase. 

The enzyme activity in the system is therefore controlled by the local electrostatic potential. 

The average local electrostatic potential V(r)/p(r), introduced by Pohtzer [57], led Sen and coworkers [58] to conjecture that the global maximum in V(r)/p(r) defines the location of the core-valence separation in ground-state atoms. Using this criterion, one finds N values [Eq. (3.1)] of 2.065 and 2.112 e for carbon and neon, respectively, and 10.073 e for argon, which are reasonable estimates in light of what we know about the electronic shell structure. Politzer [57] also made the significant observation that V(r)/p(r) has a maximum any time the radial distribution function D(r) = Avr pir) is found to have a minimum. 

Alternatively, there has been a revival of Debye-Hiickel (DH) theory [196-199] which provides an expression for the free energy of the RPM based on macroscopic electrostatics. Ions j are assumed to be distributed around a central ion i according to the Boltzmann factor exp(—/ , - y.(r)), where y(r) is the mean local electrostatic potential at ion j. By linearization of the resulting Poisson-Boltzmann (PB) equation, one finds the Coulombic interaction to be screened by the well-known DH screening factor exp(—r0r). The ion-ion contribution to the excess free energy then reads... 

If the pearl-necklace structure contains only a few pearls, there are always pearls at the end of the chains and these pearls are slightly larger than the inner pearls. This can be proved by doing an explicit calculation of the local electrostatic potential along the necklace very similar to that done in the following section on annealed polyelectrolytes. 

Another reason for a deviation from relationships expected for a homogeneous nonconducting medium is the difference in reorganization energy for the same Ru-complexes located in the protein-water interface of different local dielectric constant and local electrostatic potentials. 

The physical basis of the second type of approach rests upon the effect of the local electrostatic potential upon dynamic interactions at encounters with charged quenching molecules resulting in fluorescence (phosphorescence) (Vogel et al., 1986 Anni et al., 1994) or between a stable radical, e.g. nitroxide, and another charged paramagnetic species (Likhtenshtein et al., 1972 Likhtenshtein, 1976, 1988,1993). In such cases, the relaxation parameters, i.e. the life-time of the fluorescence (phosphorescence) chromophore or spin-spin and spin-lattice relaxation rates of paramagnetic species are dependent upon the frequency of encounters, and, therefore, on local electrostatic fields... 

A new experimental approach has been developed to study the distribution of local electrostatic potential around specific protons in biologically important molecules. The approach is the development of a method denoted as "spin label/spin-probe" proposed in... 

The proposed method is based upon the quantitative measurement of the contribution of differently charged nitroxide probes to the spin-lattice relaxation rate (1/T i) of protons in a particular molecule, followed by the calculation of local electrostatic potential using the classical Debye equation (Likhtenshtein et al., 1999 Glaser et al., 2000). In parallel, the theoretical calculation of potential distribution with the use of the MacSpartan Plus 1.0 program has been performed. 

Apparent local electrostatic potential U(Ro) can be determined from the experimental dependence of the proton spin-lattice relaxation rate on the concentration of the nitroxide probes [R ]... 

The method used in this investigation did not reveal a local electrostatic potential for the glycine a-H nuclei located close to the zwitterionic environment. 

Miteva, M.A., Kossekova, G. P., Villoutreix, B O., and Atanasov, BP. (1997), Local electrostatic potentials in pyridoxal phosphate labeled horse heart cytochrome c, J. Photochem. and Photobiol., B Biology 37, 74-83. 

An insulator, on the other hand, has an ill-defined Fermi level which does not equilibrate with the spectrometer. Instead, the vacuum level of the insulator (E ) aligns with the local electrostatic potential surrounding its surface. An insulator more than a micron thick (which is the case for most catalyst samples analyzed by XPS) will not be within the local potential of the metal sample holder. The insulator will be separated from the spectrometer vacuum level (EJ) by some voltage (Vp) (30). This voltage will depend on the geometry of the sample holder and on the energy and flux of electrons from the x-ray source, the flood gun, the sample itself, and all other sources within the chamber. The potential Vp cannot be reliably measured. 

To calcualte the repulsive force between two plates, we need the local electrostatic potential, ift, which creates a local stress. The local stress can be calculated from the osmotic pressure caused by the local ionic concentration, which is in turn caused by the local electrostatic potential [17]. 

The irmer potential is an important property of individual phases. Much more will be said about this property when the interface between two phases is discussed in chapter 8. For the moment, < ) is regarded as a property of phase a which is the same throughout the phase with a value defined with respect to charge-free infinity. On the other hand, in the case of an electrolyte solution, the local electrostatic potential varies from point to point due to the presence of discrete charges on the ions. Thus the electrostatic potential is more positive at a cation and more negative at an anion. These fluctuations occur about the average value, < ) . This can be seen more clearly by writing out the chemical potential of ion i in terms of its concentration c, and activity coefficient y,. Thus, from equation (6.6.1)... 

At the present time, when the structure of the proton pumping protein and the membrane s surface can be gained at atomic resolution, when the dissociation of a proton can be recorded with sub-nanosecond resolution and molecular dynamics can be extended to tens of nanoseconds, it seems that a combination of these methods will be required to elucidate the mechanism of the reaction. Thus, combination of specific labeling of sites of interest by a photoacid or indicator, coupled with time-resolved measurements and molecular dynamics of the reaction, will be the next step in the research. Once these combined experiments are available, the generalization of the process, like the role of local electrostatic potential, orientation of water and the relative motion of side-chains, will be quantitated, with a subsequent improvement in the theoretical predicting power. 

Here represents all the chemical interactions between the ion of type i its surroimdings and (fi represents the electrostatic part of the electrochemical potential. Thus, Z is the valence of the ion, F is the Faraday, and (ji is the local electrostatic potential. Actually, the separation of chemical and electrostatic components in this way is based more on conceptual preference than on operational meaningfulness(35, 36). but the separation has a great deal of historical precedence and is mentioned here for that reason. But the approach used here does not make use of such distinctions eind in this sense at least would be in accordance with the recommendations elaborated by Guggenheim (35) it may be called the local equilibrim approach and may be simimarized as follows. 

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