Equilibrium times

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

Because of this heat generation, when adsorption takes place in a fixed bed with a gas phase flowing through the bed, the adsorption becomes a non-isothermal, non-adiabatic, non-equilibrium time and position dependent process. The following set of equations defines the mass and energy balances for this dynamic adsorption system [30,31] ... 

The equilibrium time required for adsorption of metals on biomass was studied for various initial metal concentrations and the results were shown in Figure 2. The adsorption increases rapidly with time in the initial period of adsorption and approaches an equilibrium at about 120min for all the concentrations studied (10-100 mg/L). The slow but gradual increase of metal biosorption after 120min indicates that the adsorption occurs through a continuous formation of adsorption layer in the final period of adsorption. 

Long equilibrium time required (for static mode)... 

Characterisation of matrix influences requires determination of equilibrium times... 

Geissler, P. L. Dellago, C., Equilibrium time correlation functions from irreversible transformations in trajectory space, J. Phys. Chem. B 2004,108, 6667-6672... 

Linear calibration curves were obtained over a range of 4.5 to 1500 ng/mL for cyclosporine A (r = 0.999), 0.2 to 100 ng/mL for tacrolimus (r = 0.998), and 0.4 to 100 ng/mL for sirolimus (r = 0.995). Within-run coefficients of variation were less than 8% for cyclosporine A, tacrolimus, and sirolimus. Between-run coefficients of variation were less than 2.7% for cyclosporine A, 8.4% for tacrolimus, and 9.3% for sirolimus. The total run time of an injection was 3 min including equilibrium time. The online extraction column worked for 800 injections without loss of cleaning capacity. The analytical column was good for at least 2000 injections. 

Equilibrium times of sorption experiments for different surfactants in different environmental matrices... 

The titration procedures described in the literature can be classified as continuous or incremental, depending on the mode of titrant addition. In the first case the titrant is continuously introduced in the reaction vessel at a programmed (not necessarily constant) rate during a run. The application of this method requires apparatus with quick response to temperature changes and can be used only to study fast reactions. Slow reactions (i.e., those with a reaction time longer than the equilibrium time of the reaction vessel) may be accurately studied by the... 

The test, theoretical relationship between the non-dimensional relative concentration (cRC), and the root time factor (r) may be seen in Fig. 5. Mohamed and Yong [142] analyzed the results obtained from the diffusion experiment shown in Fig. 5 a, b, using the information from solution of the equation above. The theoretical correlation in Fig. 5 c shows a linear relationship up to a relative concentration of 0.2 (80% equilibrium). At a relative concentration of 0.1 (90% equilibrium), the abscissa is used to determine the point on the experimental curve corresponding to a relative concentration of 0.1 (i.e., 90% of the steady state equilibrium time). 

Adsorption of metobromuron onto ACC was monitored spectrophotometrically at 244 nm by the procedure described above. Absorbance data, obtained in 1-min intervals until equilibrium, were converted into concentration data using the corresponding calibration relation and then plotted as a function of time in Fig. 22.2. Initial concentration of pesticide in the solution was 7.64 x 10 M and adsorption equilibrium time using 18 mg ACC, determined as the time after which the concentration of the pesticide solution remained unchanged during the course of adsorption process, was 1,156 min. The decrease in concentration of pesticide is fast at the early stages, while it slows down toward the end of adsorption period. Concentration... 

The time-dependent behaviors of metal ions adsorption were measured by varying the equilibrium time between the adsorbate and adsorbent in the range of 30-300 min. The concentration of Pb(ll) and Zn(ll) were kept as 50 ttg/mL while the amount of resin added was 0.5 g. The experiments were performed at pH 4 for Pb L... 

Various adsorption parameters for the effective removal of Pb + and ions by using new synthesized resin as an adsorbent from aqueous solutions were studied and optimized. Time-dependent behavior of Pb + and ions adsorption was measured by varying the equilibrium time between in the range of 30-300 min. The percentage adsorption of Pb + plotted in Fig. 26.2 as a function of contact time... 

The time-dependent behavior of ions adsorption was measured by varying the equilibrium time between the adsorbent (ground sumac leaves) and adsorbent (Cu " ions) in the range of 30 min and 24 h. The concentration of was kept 40 pg ttiL , particle size 710 pm, and amount of adsorbent 0.1 g. 

Time-depended behavior of Cu + ion adsorption was measured by varying the equilibrium time between in the range of 0.5-72 h. The percentage adsorption of Cu + ions plotted in Fig. 28.2 as a function of contact time. The percentage adsorption of Cu + indicates that the equilibrium between the Cu + ions and sumac leaves was attained 4 h. Therefore, 4 h stirring time was found to be appropriate for maximum adsorption and was used in all subsequent measurement. The effect of temperature and pH the adsorption equilibrium of Cu + on sumac leaves was investigated by varying the solution temperature from 283 to 303 and pH from 6 to 10. The results are presented in Fig. 28.3. The results indicated that the best adsorption results were obtained at pH 8 at 293 K. 

The test is recommended to be operated with a small pressure difference (less than 3 cm Hg) across the membrane and a low mole fraction (0.05-0.1) of the condensable gas. The time to complete an analysis is dictated by the temperature and pressure equilibrium times which are typically a few hours. The test can accommodate membrane samples of various shapes and sizes... 

The presence of color in many industrial effluent streams is highly undesirable. LDHs have been found to be particiflarly effective at removing various synthetic dyes (Table 1) [158]. For example. Acid Blue 29 could be adsorbed on the surface or enter the interlayer region of the LDH by anion exchange an equilibrium time of 1 h with 99 % dye removal was obtained. Furthermore,... 

Some BGE or sample components can adsorb strongly to capillary wall, resulting in permanent changes or very long equilibrium times. Therefore, keep track of your capillary s history, or better, dedicate the capillary to a certain method or BGE. Always check the final method conditions after method optimization on a fresh capillary. 

MRR) to recover platinum. The extraction of palladium by the sulfide is slow with 2-3 hr to achieve equilibrium, which inhibits flow sheet design. However, it has been shown that tertiary amines can act as a kinetic accelerator, reducing equilibrium times to minutes, but no information has been published on the effect of these amines on palladium-platinum separation. High loading of the sulfides is possible, and stripping is easy with aqueous ammonia. The overall extraction and stripping equations are as follows ... 

Classical thermodynamics is based on the concept of equilibrium. Time is not involved in conventional engineering thermodynamic textbooks. Heat transfer deals with rate of energy transfer, but does not cover cycles. There is a gap between thermodynamics and heat transfer. The chapter Finite-Time Thermodynamics bridges the gap between thermodynamics and heat transfer. 

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