Potential Technique

Suppose that a component of the potential energy between two particles i and j can be written as a product of a strength parameter and an inverse power of the interparticle separation r,y, 

In the Monte Carlo system with periodic boundary conditions the corresponding contribution to the total energy of the system is then the infinite sum 

Several workers have attempted to evaluate the exact Ewald pair potential directly in the Monte Carlo program. The practicality of this approach clearly depends on a judicious choice of both the convergence parameter w and the number of terms to be included in each of the two series. The value w = in (B6) leads to equal asymptotic rates of convergence for the two series but it is far from obvious that this would be the most efficient choice. In fact, the most satisfactory algorithm of this type takes w 5 with this choice only the large spherically synunetric term in the summation over real lattice vectors needs to be included (i.e., A = 0 if r is determined by the minimum image distance convention). The summation over reciprocal lattice vectors now becomes very slowly convergent, with terms up to = 14 (125 

The change in the right-hand side of (B8) as the result of a single particle displacement involves the interaction of the old and new coordinates of the moved particle only with each wave vector k[viz. sin(2irk r,), cos(2 irk ry), etc.]. This reduces the computation of this part of the Ewald potential to an amount comparable to that required for determining the energy change after a trial move in a system of 125 particles with a spherically s)mimetric potential. 

We are happy about many conversations with those who share our delight in the Monte Carlo game. We would like to thank Glenn Torrie for contributing the appendix on Ewald potentials. The financial assistance of the National Research Council of Canada is gratefully acknowledged. 

---

Biopolymer Extraction. Research interests involving new techniques for separation of biochemicals from fermentation broth and cell culture media have increased as biotechnology has grown. Most separation methods are limited to small-scale appHcations but recendy solvent extraction has been studied as a potential technique for continuous and large-scale production and the use of two-phase aqueous systems has received increasing attention (259). A range of enzymes have favorable partition properties in a system based on a PGE—dextran—salt solution (97) ... 

I.A. Abrikosov and H.L.Skriver, Self-consistent linear-muffin-tin-orbitals coherent-potential technique for bulk and surfaces calculations Cu-Ni, Ag-Pd, and Au-Pt random alloys, Phys. Rev. B 47, 16 532 (1993). 

The advantages of controlled-potential techniques include high sensitivity, selectivity towards electroactive species, a wide linear range, portable and low-cost instrumentation, speciation capability, and a wide range of electrodes that allow assays of unusual environments. Several properties of these techniques are summarized in Table 1-1. Extremely low (nanomolar) detection limits can be achieved with very small sample volumes (5-20 pi), thus allowing the determination of analyte amounts of 10 13 to 10 15 mol on a routine basis. Improved selectivity may be achieved via the coupling of controlled-potential schemes with chromatographic or optical procedures. 

The charging of the double layer is responsible for the background (residual) current known as the charging current, which limits die detectability of controlled-potential techniques. Such a charging process is nonfaradaic because electrons are not transferred across the electrode-solution interface. It occurs when a potential is applied across the double layer, or when die electrode area or capacitances are changing. Note that the current is the tune derivative of die charge. Hence, when such processes occur, a residual current flows based on die differential equation... 

Dynamic techniques are those in which electrolytic processes occur at the electrodes and therefore a finite current is passed through the electrochemical cell. Thig discussion will be limited to controlled-potential techniques, namely voltammetry and ampero-metry. While other dynamic electrochemical techniques have been developed, these two are by far the most commonly used for bioelectroanalytical studies. 

The difficulties in conventional polarography as mentioned in Section 3.3.1.1, especially the interference due to the charging current, have led to a series of most interesting developments by means of which these problems can be solved in various ways and to different extents. The newer methods concerned can be divided into controlled-potential techniques and controlled-current techniques. A more striking and practical division is the distinction between advanced DC polarography and AC polarography. These divisions and their further classification are illustrated in Table 3.1. In treating the different classes we have not applied a net separation between their principles, theory and practice, because these aspects are far too interrelated within each class. 

I. Controlled-potential techniques II. Controlled-current techniques ... 

Wawzonek, S., Potentiometry oxidation reduction potentials, Techniques of Chemistry, (Eds. A. Weissberger and B. W. Rossiter), Vol. I, Part Ha, Wiley-Interscience, New York, 1971. 

Despite their vast untapped potential, techniques like fluorous biphasic catalysis still have limitations. These limitations center on solubility and emanate directly from the strengths of the technique heavily fluorous compounds tend to be highly insoluble in organic solvents while organic compounds (especially polar ones) tend to be highly... 

Selecting an approach To check for chlorine in the river water, there are many potential techniques. The simplest one would be a total chlorine test strip, in which the chlorine in the water reacts with chemicals on the paper to change the color. 

Chemical potential techniques. Phase diagrams can be determined by chemical potential methods such as EMF. In this case the activity of one or both of the components is measured during a cooling or heating cycle and a series of characteristic breaks define phase boundaries. Figure 4.6 shows a series of Al-Sn... 

Controlled double-potential techniques have also allowed measurement of relative emission intensity as a function of the time in which each of the potential steps is allowed to proceed. Comparisons of the emission intensities obtained with those predicted by mathematical models68,69 have been used as mechanistic evidence,85,67 see Sect. IV-B. 

---