The equilibrator

A great variety of effective designs of equilibrators for continuous piCOz) systems have been described in the literature. Essentially three different families of equilibrator design can be distinguished  

The flow rate of seawater is adjusted to 1.5-2.0L/min. The air flow (total air volume approximately 400 mL) is maintained at a flow rate of about l.OL/min. The time constant of this equilibrator with respect to CO2 is 75 6 s, as determined from laboratory experiments under the above flow conditions (Kortzinger et al., 1996). For measurements of seawater temperature, the equilibrator is equipped with a platinum resistance thermometer (Pt-100). 

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A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The heating phase is used to take a molecular system smoothly from lower tern peratiires, indicative of a static initial (possibly optim i/ed ) structure, to th e temperature T at which it is desired to perform the molecular dynamics simulation. The run phase then consLitn tes a sim n lation at tern peratnre T. If th e heating h as been done carefully, it may be possible to skip the equilibration phase... 

Variation in Verlet order parameter during the equilibration phase of a molecular dynamics simulation of... 

The radial distribution function can also be used to monitor the progress of the equilibration. This function is particularly useful for detecting the presence of two phases. Such a situation is characterised by a larger than expected first peak and by the fact that g r) does not decay towards a value of 1 at long distances. If two-phase behaviour is inappropriate then the simulation should probably be terminated and examined. If, however, a two-phase system is desired, then a long equilibration phase is usually required. 

To reach equilibrium temperature quickly before starting the equilibration phase of a simulation (see Equilibration and Data Collection on page 74). 

Dg remains constant over a wide range of resin to liquid ratios. In a relatively short time, by simple equilibration of small known amounts of resin and solution followed by analysis of the phases, the distribution of solutes may be followed under many different sets of experimental conditions. Variables requiring investigation include the capacity and percent cross-linkage of resin, the type of resin itself, the temperature, and the concentration and pH of electrolyte in the equilibrating solution. 

In both of these pieces of apparatus, isothermal operation and optimum membrane area are obtained. Good temperature control is essential not only to provide a value for T in the equations, but also because the capillary attached to a larger reservoir behaves like a thermometer, with the column height varying with temperature fluctuations. The contact area must be maximized to speed up an otherwise slow equilibration process. Various practical strategies for presetting the osmometer to an approximate n value have been developed, and these also accelerate the equilibration process. 

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... 

In practice, for fluids of viscosities below 1000 centistokes, the equilibration reaction will take a number of hours at 100-150°C. Residual esters and siliconates which may occur during the reaction are hydrolysed by addition of water and the oil is separated from the aqueous acid layer and neutralised as before. 

The randomization stage refers to the equilibration of the nonequilibrium conformations of the chains near the surfaces and in the case of crack healing and processing, the restoration of the molecular weight distribution and random orientation of chain segments near the interface. The conformational relaxation is of particular importance in the strength development at incompatible interfaces and affects molecular connectivity at polymer-solid interfaces. 

The method has been applied to the reduction of cholestanone. Red uction of this ketone with the mixed reagent and no additional ketone gave 17% of the a-epimer under the equilibration conditions only 3p-ol and unreduced ketone are obtained. Reduction of coprostanone with the mixed reagent gives 94% of the 3a-ol. ... 

A convenient synthesis of A -3-ketones in the 5 5 series uses DDQ in one step. This introduction has to be done indirectly because of the unfavorable direction of enolization. In this scheme, advantage is taken of the equilibrated formylation at C-2 of 5i5-3-ketones. Dehydrogenation of the 2-formyl derivative (72) proceeds rapidly with DDQ and deformylation is achieved in the presence of a homogeneous catalyst. A related approach involves preparation of the 2i -bromo-5i5-3-ketone by bromination of the 2-formyl compound (72). ... 

The product is predominantly the A -olefin, which is neither the more stable isomer (the equilibrated mixture is 2 1, A A ) nor the product expected from 1 elimination (this would be the A -olefin). It is noteworthy that this elimination was conducted in the absence of pyridine. 

Extensions of this concept have utilized enamine hydrolysis (171, X = R N) and the quenching of the enolate anion (171, X = O ) e.g. ref. 353). a,(i-Un-saturated ketones are usually more stable than their p,y counterparts, but there are notable exceptions to this, and in such cases the deconjugated ketone may be isolated from the equilibrated system. For example, retro steroids (9, 10a) have a large proportion of A -3-ketone at equilibrium, and 17-ketones yield the more stable A -system on treatment with acid. ... 

Typical runs consist of 100 000 up to 300 000 MC moves per lattice site. Far from the phase transition in the lamellar phase, the typical equilibration run takes 10 000 Monte Carlo steps per site (MCS). In the vicinity of the phase transitions the equilibration takes up to 200 000 MCS. For the rough estimate of the equihbration time one can monitor internal energy as well as the Euler characteristic. The equilibration time for the energy and Euler characteristic are roughly the same. For go = /o = 0 it takes 10 000 MCS to obtain the equilibrium configuration in which one finds the lamellar phase without passages and consequently the Euler characteristic is zero. For go = —3.15 and/o = 0 (close to the phase transition) it takes more than 50 000 MCS for the equihbration and here the Euler characteristic fluctuates around its mean value of —48. 

Potentiometric titration curves The procedure involves the addition of a salt of a weak acid to the resin and the determination of the pH of the equilibrated solution. Table 9 shows the pK values of the OH groups and dissociation constants of the studied resin. The first ionization occurs at a pH slightly higher than that of sul-... 

The effect of thermal pre-strain treatment on the torsional ductility of the alloys is shown in Figure 9. The curve numbers correspond to the sample series numbers. The basic alloy, a = 0, is represented for comparison as series 4. The series 1 samples had the highest ductility. That of the j9-treated series 2 samples showed a similar thermal dependence below 970 K, but it was lower at 1000 to 1100 K. Ductility of the equilibrated series 3 samples did not show a maximum in its thermal dependence, but it exceeded ductility of the basic alloy. 

The procedure employs a readily available starting material and produces the pure trans isomer in high yield. The method described is an improvement on that used by Eliel and Rerick2 in that it is not necessary to use a clear solution of lithium aluminum hydride in ether for the preparation of the mixed hydride. It is not necessary to know the precise amount of lithium aluminum hydride used so long as a slight excess is present. The excess hydride is destroyed by adding /-butanol the excess /-butanol has no effect on the subsequent equilibration and purification. The equilibration of the 4 / butylcyclohexanol is effected by adding a small amount of 4-/-butylcyclohexanone. 

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