Ising mixture

Caylor et al. [134] performed ellipsometric measurements at the liquid-liquid interface of Pitzer s system. The experiments yielded a decrease in ellipticity, when approaching the critical point. This is in clear contrast to a (/ — v) divergence predicted theoretically [135] and observed experimentally [136] for nonionic Ising mixtures. The results point toward an anisotropic interface caused by an orientation of ion pairs perpendicular to the interface. A rough model for such an interface captured some of the observed features. 

The second term on the right-hand side of Equation (1) is the residual Helmholtz energy of mixing for an Ising mixture (AmixFrIsing). Its expression will be discussed below. 

Residual Helmholtz energy of mixing for multicomponent Ising mixture... 

The additional Helmholtz energy responsible for this secondary lattice can be expressed by using Equation (12) for binary Ising mixture with Xi, x2 replaced by and (1 — Finally, we obtain the temperature-dependent interchange energy that is quadratic to the inverse temperature. 

Deutsoh H-P and Binder K 1993 Mean-field to Ising orossover in the oritioal behavior of polymer mixtures—a finite size sealing analysis of Monte Carlo simulations J. Physique II 3 1049... 

Reflux gently in a test-tube under a short air condenser 1 g. of the base with 2 5 mols or 3 0 g. (3 0 ml.) if the molecular weight is unknown of redistilled acetic anhydride for 10-15 minutes. Cool the reaction mixture and pour it into 20 ml. of cold water (CAUl ION). Boil to decompose the excess of acetic anhydride. When cold, filter the residual insoluble acetyl derivative and wash it with a little cold water. Recrystal-/ise from water or from dilute alcohol. 

In some systems, known as continuous-flow analy2ers, the reaction develops as the sample —reagent mixture flows through a conduit held at constant temperature. In such systems, the reaction cuvettes are replaced by optical reading stations called flow cells. In most analy2ers, whether of discrete- or continuous-flow type, deterrnination of electrolyte tests, eg, sodium and potassium levels, is done by a separate unit using the technique of ion-selective electrodes (ISE) rather than optical detection. 

The theoretical foundation for describing critical phenomena in confined systems is the finite-size scaling approach [64], by which the dependence of physical quantities on system size is investigated. On the basis of the Ising Hamiltonian and finite-size scaling theory, Fisher and Nakanishi computed the critical temperature of a fluid confined between parallel plates of distance D [66]. The critical temperature refers to, e.g., a liquid/vapor phase transition. Alternatively, the demixing phase transition of an initially miscible Kquid/Kquid mixture could be considered. Fisher and Nakashini foimd that compared with free space, the critical temperature is shifted by an amoimt... 

The graphite paste electrode, introduced into voltammetry by Adams [1], has an analogue in an ISE where a mixture of graphite powder with an ion-exchanger solution functions as the electrode membrane, into which a platinum contact is immersed [16, 129, 149]. 

The individual activity coefficients calculated from (4.12), suitable for calibration of ISEs for chloride ions, the alkali metal and alkaline earth ions, are given in tables 4.1 and 4.2. Ion activity scales have also been proposed for KF [141], choline chloride [98], for mixtures of electrolytes simulating the composition of the serum and other biological fluids (at 37 °C) [106,107], for alkali metal chlorides in solutions of bovine serum albumine [132] and for mixtures of electrolytes analogous to seawater [140]. 

The use of ISEs in non-aqueous media(for a survey see [125,128]) is limited to electrodes with solid or glassy membranes. Even here there are further limitations connected with membrane material dissolution as a result of complexation by the solvent and damage to the membrane matrix or to the cement between the membrane and the electrode body. Silver halide electrodes have been used in methanol, ethanol, n-propanol, /so-propanol and other aliphatic alcohols, dimethylformamide, acetic acid and mixtures with water [40, 81, 121, 128]. The slope of the ISE potential dependence on the logarithm of the activity decreases with decreasing dielectric constant of the medium. With the fluoride ISE, the theoretical slope was found in ethanol-water mixtures [95] and in dimethylsulphoxide [23], and with PbS ISE in alcohols, their mixtures with water, dioxan and dimethylsulphoxide [134]. The standard Gibbs energies for the transfer of ions from water into these media were also determined [27, 30] using ISEs in non-aqueous media. 

An improvement [325] in the properties of the halide ISE, both in increased sensitivity and decreased light sensitivity can be attained by using a mixture of silver halide and Ag2 S, which is far less soluble than any of the silver halides. The other ISE properties do not change. The ise versus log a dependence is thus identical with the dependence for a pure silver halide membrane [288]. This system is used in most commercial ISEs. 

For a detailed study, see [421-424], In general, all-solid-state ISEs are used with an internal silver contact. Selectrodes (see p. 60) can also be prepared from a mixture of halide and silver sulphide [328,329]. 

Ion-selective electrode forPb The commonly used version of the ISE has a pressed or sintered PbS - Ag2 S mixture membrane [ 144, 325], The sintered membrane has the character of a solid solution [181], The dependence of the potential of ISEs with various PbS Agj S ratios on the Pb " activity is depicted in fig. 6.2. An ISE containing a mixture of PbS and Ag2 S in a plastic matrix has been proposed [249, 250]. Several versions of this ISE (PbTe, PbSe, PbS in an Ag2S mixture) were tested in buffers for Pb [242]. Hirata and Higashiyama [154, 156] suggested a mixture of PbS, CuS and Ag2S for a Pb " ... 

The precision of the determination increases in mixed solvents, for example 70% ethanol [119] or dioxan/water [340]. A special ISE with a membrane consisting of a PbS, PbS04, Ag2 S and CuS mixture has been constructed for sulphate determinations [320]. 

Cd ion-selective electrodes The usual version of the Cd " ISE contains a membrane of a sintered or pressed mixture of CdS and Ag2 S [121, 325,408]. Membranes from sintered Ag2S, CuS and CdS mixtures [157] have also been proposed, similarly as forPb ISEs. CdS precipitate in a polyethylene matrix [250] or a CdS-Ag2S precipitate mixture in a silicone rubber matrix [153] can also be used for Cd ISEs. Cd ISEs can be calibrated using a metal diethylenetriamine buffer [66]. Similar substances interfere in the response of the Cd ISE as for the Hg, Ag and Cu electrodes. 

In the electrode with CuS alone, which has negligible conductivity, the precipitate ISE with a silicone rubber matrix has better properties than the electrode with a pressed pellet [314], The ISE with a mixture of CuS and Agi S finds broad application [325]. If the membrane is prepared by pressing, the grains of these two compounds combine to form jalpaite, Agi.55C%.4sS [180], This substance is a mixed conductor with transport numbers of Ag, 0.69 Cu(I), 0.30 and electrons, 0.01, at 25 C [175]. The sintered electrode also contains Ag1.2Cuo.8S or Ago.93Cu1.07S. Oxidation of these phases leads to considerable deterioration in the electrode function [180]. Good electrodes... 

Analytical determinations with the fluoride ion-selective electrode These are based either on direct potentiometry of fluorides [37, 84, 85, 88, 430] or on titration determinations of either fluorides or of other ions and also on titrations with fluoride ions as indicator. The advantages of potentiometry with an ISE over other analytical methods for determining fluorides were pointed out by Crosby etai [67], Further comparison studies [42, 56, 191, 433] came to the same conclusions, confirmed also by a study of 16 methods [365]. Fluoride ions are titrated either with La (for concentrations greater than 1 mM) or Th (in the concentration range 0.2-1 mM F ) [13, 102, 103, 113,233, 234]. Titration with fluoride ions can be used for the determination of Al with formation of the AIF4 complex up to nanomolar concentrations, especially in ethanol-water mixtures [25] (see also [267,384]). Precipitation titrations can also be used to determine La, Th and UOJ [241, 384] as well as Li in... 

Ammonium ISEs have been developed using a mixture of nonactin and monactin XXIII they can be used for the determination of NHj in serum [186] (see fig. 7.6), in urine [80], in water [40, 136], as well as for kinetic study of the decomposition of arginine [159]. Unfortunately the detection limit is 50 times greater than that of the ammonium gas probe [40] (see section 4.4). 

The solid-membrane ISE has certain disadvantages for the determination of chloride inside cells and thus ion-selective microelectrodes containing ion-exchanger Corning No. 477315 (based on a nitroxylene mixture) are used [223]. Reviews of intracellular applications of this electrode can be found in [23, 78, 86, 211,217]. 

Rates were measured polarimetrically and were believed to be those of the methanolyses of anomer-ised a,p-mixtures. 

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