Tests for Equilibration

In systems with solvent molecules, many properties may still show fluctuations even after equilibration periods lasting several tens of picoseconds. 

Molecular dynamics simulations of proteins often begin with a known structure (such as an X-ray diffraction structure) that you want to maintain during equilibration. Since the solvent may contain high energy hot spots, equilibration of the protein and solvent at the same time can change the protein conformation. To avoid this, select only the water molecules and run a molecular dynamics equilibration. This relaxes the water while fixing the protein structure. Then deselect the water and equilibrate the whole system. 

Caution During a simulation, solvent temperature may increase while the solute cools. This is particularly true of small solvent molecules, such as water, that can acquire high translational and rotational energies. In contrast, a macromolecule, such as a peptide, retains most of its kinetic energy in vibrational modes. This problem remains unsolved, and this note of caution is provided to advise you to give special care to simulations using solvent. 

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The Pectolyase Y-23 and the purified yeast PG were immobilised as described by Coletti-Previero et al. [14]. 5 g of y-alumina spheres, previously equilibrated in 200 ml of a buffered solution at pH 6.0, was treated first with 30 ml of 0.04 M o-phosphorylethanolamine and then with 30 mL of 0.56 M glutaraldehyde. These two reactions were performed at 25 C and pH 6.0, for 1.5 h and were followed by several washings with abundant distilled water. Finally, 15 mL of 10 mg/mL Pectolyase Y-23 solution or 25 mL of 0.5 mg/mL of purified yeast PG solution, both buffered at pH 6.0, were added and left to react for 2 h at 25 C. y-alumina spheres were then washed with 450 mL of distilled water. The reaction solution was tested for protein content and enzymatic activities. 

Most thermodynamic data for solid solutions derived from relatively low-temperature solubility (equilibration) studies have depended on the assumption that equilibrium was experimentally established. Thorstenson and Plummer (10) pointed out that if the experimental data are at equilibrium they are also at stoichiometric saturation. Therefore, through an application of the Gibbs-Duhem equation to the compositional dependence of the equilibrium constant, it is possible to determine independently if equilibrium has been established. No other compositional property of experimental solid solution-aqueous solution equilibria provides an independent test for equilibrium. If equilibrium is demonstrated, the thermodynamic properties of the solid solution are also... 

A solvent at this step is omitted since this may result in a misleading homogeneity at an early stage of equilibration. If a statistical distribution of the functio nalized siloxy-units is not achieved the properties of the resulting polysiloxane are unfavorable. After the reaction the mixture is diluted with 20 volume percent of water and shaken for another hour. The two phases are separated by centrifugation, the polysiloxane is diluted with 1 volume of ether and extracted with water until the test for sulfate is negative. The solvent is removed in vacuo. 

The data shown in Fig. 7 are for the dry specimens. When the specimens had been exposed to boiling water for 1 h and then tested after equilibration at room temperature, the results shown in Fig. 8 were obtained. Here, the differences in... 

Soil sorption coefficients are most often determined using a batch technique (Organization for Economic Cooperation and Development, 1983 American Society for Testing and Materials, 1993 2001), whereby a small quantity of the soil is agitated for a period of time (e.g., 18 hours) with an aqueous solution of the chemical under investigation the phases are then separated and the concentration of chemical measured in one or both of the phases. While in principle the method is simple, problems can arise due to, for example, incomplete phase separation, lack of time for equilibration, volatilization loss, and chemical instability. 

The additional charge and the corresponding additional surface tension are time-dependent quantities in which the equilibrium between the bulk and the interface is not established. The irreversible contribution can be separated from the reversible by considering the time dependence, if the experimental time scale allows for such a test. Time-dependent effects can be observed by impedance measurements at different frequencies. For gold, as an example, impedance measurements showed spectra characteristic for equilibration processes at least over a time scale of 0.1 ms to 100 s. Gold also shows a surface reconstruction depending on the potential [148]. Fortunately, the variation of the interfacial strain with potential is usually so small that the original Lippmann equation (41) for a solid is practically the same as for a liquid electrode 1149]. 

Procedure. The test for dried products shall consist of measuring the maximum loss of weight in a weighed sample equilibrated over anhydrous phosphorus pentoxide at a pressure of not more than 1 mm. of mercury, and at a temperature of 20° to 30° C for as long as it has been established is sufficient to result in a constant weight. 

Data Quality Normally, it is not possible to evaluate LLE data for thermodynamic consistency [Sorenson and Arlt, Liquid-Liquid Equilibrium Data Collection, Binary Systems, vol. V, pt. 1 (DECHEMA, 1979), p. 12]. The thermodynamic consistency test for VLE data involves calculating an independently measured variable from the others (usually the vapor composition from the temperature, pressure, and liquid composition) and comparing the measurement with the calculated value. Since LLE data are only very weakly affected by change in pressure, this method is not feasible for LLE. However, if the data were produced by equilibration and analysis of both phases, then at least the data can be checked to determine how well the material balance closes. This can be done by plotting the total... 

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