Further Refinements

The a factor makes usage of equations (4.34) and (4.36) difficult inasmuch as the distance of closest approach is not truly measurable. It also assumes, incorrectly, that all of the ions in the system have equal radii. By setting a standard value for a = 3.04 so that the quantity 0a in the denominator becomes unity, equation (4.34) can be simplified, as suggested by Giintelberg (6)  

This version of the Debye-HUckel equation holds quite well up to an ionic strength of. 1 molal. 

In 1935, Guggenheim (7) proposed another version of this equation based on the mole fractions scale (rational coefficients) and published values for the Interaction coefficient 0. This interaction parameter B is unrelated to the B of equation (4.36). With the advent of improved data, Guggenheim published revised 

3 s (8), based upon the more widely used ionic strength scale, coefficient for an electrolyte with cation c and anion a is  

I - ionic strength in molality scale - nuirber of charges an the cation z - nintber of charges cn the anion 3 - interaction coefficient 

---

The initial step is to identify which database, from a few thousands worldwide (about 10 000 in 2002), provides the requested information. The next step is to determine which subsection of the topic is of interest, and to identify typical search terms or keywords (synonyms, homonyms, different languages, or abbreviations) (Table 5-1). During the search in a database, this strategy is then executed (money is charged for spending time on some chemical databases). The resulting hits may be further refined by combining keywords or database fields, respectively, with Boolean operators (Table 5-2). The final results should be saved in electronic or printed form. 

Model optimization is a further refinement of the secondary and tertiary structure. At a minimum, a molecular mechanics energy minimization is done. Often, molecular dynamics or simulated annealing are used. These are frequently chosen to search the region of conformational space relatively close to the starting structure. For marginal cases, this step is very important and larger simulations should be run. 

Use the HyperChem Model Builder to construct an approximate geometry. If you want to look at the relative energies of a set of molecules, you may want to carry out the calculations using fully optimized molecular geometries. These geometry optimization calculations can use either molecular mechanics or quantum mechanics to further refine the molecular geometry beyond that given by the Model Builder. 

Alcohol autoxidation is carried out in the range of 70—160°C and 1000—2000 kPa (10—20 atm). These conditions maintain the product and reactants as Hquids and are near optimum for practical hydrogen peroxide production rates. Several additives including acids, nitriles, stabHizers, and sequestered transition-metal oxides reportedly improve process economics. The product mixture, containing hydrogen peroxide, water, acetone, and residual isopropyl alcohol, is separated in a wiped film evaporator. The organics and water are taken overhead and further refined to recover by-product acetone and the... 

Rotar Furnace. The rotary furnace, which has more flexibiUty than either the blast or reverberatory furnace, can produce either a single metal product or a high and a low antimonial alloy. The rotary furnace, like the reverberatory furnace, allows for the option of producing low antimony lead for further refinement. 

The lead—copper phase diagram (1) is shown in Figure 9. Copper is an alloying element as well as an impurity in lead. The lead—copper system has a eutectic point at 0.06% copper and 326°C. In lead refining, the copper content can thus be reduced to about 0.08% merely by cooling. Further refining requites chemical treatment. The solubiUty of copper in lead decreases to about 0.005% at 0°C. 

The highest purity (>99.99%) oxygen is obtained through further refinement. At 99.99% the impurities total only 100 ppm. This grade of oxygen is used in the manufacture of electronic components, fiber optics (qv), etc, or for gas chromatograph calibration or research appHcations. 

PGM Concentration. The ore mined from the Merensky Reef in South Africa has a maximum PGM content of 8.1 g/1, of which 50—60% is platinum, and 20—25% palladium. The PGMs are in the form of a ferroplatinum alloy, or as their sulfides, arsenides, or teUurides. The aim of the concentration process is to separate from the ore a cmde metal concentrate, having a PGM content of 60%. The majority of other metals, such as nickel and copper, are separated out at this stage for further refining. 

Several processes are available for the recovery of platinum and palladium from spent automotive or petroleum industry catalysts. These include the following. (/) Selective dissolution of the PGM from the ceramic support in aqua regia. Soluble chloro complexes of Pt, Pd, and Rh are formed, and reduction of these gives cmde PGM for further refining. (2) Dissolution of the catalyst support in sulfuric acid, in which platinum is insoluble. This... 

CycIohexanediamine s commercial origin is its presence as a minor 0.1 <1% coproduct of hexamethylenediamine [124-09-4] produced by hydrogenation of adiponittile [111-69-3]. Fractional distillation by up to four columns in a series is routine commercial practice to purify nylon grade acychc diamine the cmde cycloahphatic diamine requires further refining before use as a specification intermediate. 

Raw lac is first treated to remove water-soluble carbohydrates and the dye that gives lac its red color. Also removed are woody materials, insect bodies, and trash. It is further refined by either hot filtration or a solvent process. In the heat process, the dried, refined lac is filtered molten through cloth or wine screens to produce the standard grades of orange shellac. In the solvent process, lac is dissolved and refluxed in alcohol solvents, filtered to remove dirt and impurities, and concentrated by evaporation. The lac can be further decolori2ed in this process to produce very pale grades. Bleached shellac is prepared by treatment with dilute sodium hypochlorite and coalesced into slabs. 

In the case of low temperature tar, the aqueous Hquor that accompanies the cmde tar contains between 1 and 1.5% by weight of soluble tar acids, eg, phenol, cresols, and dihydroxybenzenes. Both for the sake of economics and effluent purification, it is necessary to recover these, usually by the Lurgi Phenosolvan process based on the selective extraction of the tar acids with butyl or isobutyl acetate. The recovered phenols are separated by fractional distillation into monohydroxybenzenes, mainly phenol and cresols, and dihydroxybenzenes, mainly (9-dihydroxybenzene (catechol), methyl (9-dihydtoxybenzene, (methyl catechol), and y -dihydroxybenzene (resorcinol). The monohydric phenol fraction is added to the cmde tar acids extracted from the tar for further refining, whereas the dihydric phenol fraction is incorporated in wood-preservation creosote or sold to adhesive manufacturers. Naphthalene Oils. Naphthalene is the principal component of coke-oven tats and the only component that can be concentrated to a reasonably high content on primary distillation. Naphthalene oils from coke-oven tars distilled in a modem pipe stiU generally contain 60—65% of naphthalene. They are further upgraded by a number of methods. 

I Jnqiiaternized DMAEMA copolymers afford resins that are mildly cationic and less hydroscopic. They provide more moisture-resistant fixatives (146). further refinements have been accompHshed by adding a third comonomer such as A/-vinylcaprolactam (V Cl). In this case, replacement of VP with VCl results in a terpolymer (VP/VCl/DMAEMA) with even greater high humidity moisture resistance and cud retention. 

Approximately 1 kg of biphenyl per 100 kg of benzene is produced (6). Because of the large scale, HD A operations provide an ample source of cmde biphenyl from which a technical grade of 93—97% purity can be obtained by distillation (35). Zone refining or other crystallization techniques are requited to further refine this by-product biphenyl to the >99.9% purity requited for heat-transfer appHcations. 

U.S. Sieve Series The American Society for Testing and Materials in cooperation with the National Bureau of Standards and the American National Standards Institute has further refined the U.S. sieve series, combining the former coarse and fine series into a single series series with a fourth-root-of-2 ratio (Table 19-6). The openings in the individual sieves have remained unchanged except for minor adjustments in sieves coarser than 0.00673 m (6.73 mm). In the revised series, sieves 1 mm and coarser are identified by opening in millimeters, and those finer than 1 mm by their openings in microns. 

Additional gasoline and diesel fuel can be produced through further refining, such as hydrocracking or catalytic cracking of the wax product. 

The simplest method that keeps the temperature of a system constant during an MD simulation is to rescale the velocities at each time step by a factor of (To/T) -, where T is the current instantaneous temperature [defined in Eq. (24)] and Tq is the desired temperamre. This method is commonly used in the equilibration phase of many MD simulations and has also been suggested as a means of performing constant temperature molecular dynamics [22]. A further refinement of the velocity-rescaling approach was proposed by Berendsen et al. [24], who used velocity rescaling to couple the system to a heat bath at a temperature Tq. Since heat coupling has a characteristic relaxation time, each velocity V is scaled by a factor X, defined as... 

---