Isotherm dynamic methods

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Arabosse, P., Rodier, E., Ferrasse, J.H., Chavez, S., and Lecomte, D. 2003. Comparison between static and dynamic methods for sorption isotherm measurements. Drying Technol. 21, 479-497. 

Figure 12.4 shows a typical DSC curve for the study of an endothermic process by the dynamic method. The heating program is started at the time fst, after an isothermal baseline has been recorded, and ends at the time fend- The reaction or... 

Analogously to the dynamic method, the energy equivalent of the calorimeter, k.Q, can be obtained by performing calibration experiments in the isothermal mode of operation, using electrically generated heat or the fusion of substances with well-known A us//. Recommendations for the calibration of the temperature scale of DSC instruments for isothermal operation have also been published [254,270]. 

In principle, any system studied by the dynamic method can also be studied by the isothermal method, provided that the kinetics of the process is not too slow at the onset temperature. Very slow events result in shallow and broad peaks, which may be difficult to integrate accurately. 

The consequences of this type of activated physical adsorption is not only that the quantity adsorbed can lie off the isotherm but also that the measured quantity of adsorption is far less than the equilibrium value. No experiments have been conducted to illustrate whether or not the quantity adsorbed lies within the hysteresis loop. The occasional failure of the vacuum volumetric method to agree with the dynamic method, which is not subject to any pressure overshoot, may in part be attributed to this phenomenon. 

Bockhorn, H., Homung, A., Homung, U., and Weichmann, J. Kinetic study on the non-catalysed and catalysed degradation of polyamide 6 with isothermal and dynamic methods. Thermochimica Acta 1999 337 14. 

The porous properties of mesoporous layers can be characterized conveniently using classical methods based on the N > adsorption-desorption isotherm at 77 K. However, it is important to use additional techniques based on transmembrane transport properties in order to characterize the passing-through pores. Moreover, these dynamic methods will easily detect the... 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

Similar to studies reported by Litwinienko and co-workers discussed above, a recent report (Dunn, 2006b) demonstrated that non-isothermal (conventional) DSC, static mode P-DSC and dynamic mode P-DSC may be employed to study kinetics of the oxidation of SME. OT results obtained at ambient pressure for DSC and P = 2000kPa for P-DSC and with varying p = 1-20 °C/ min were analyzed by the Ozawa-Flynn-Wall method to calculate activation energies and rate constants. This work concluded that rates of the oxidation reaction could be calculated at any temperature based on accurate measurement of kinetic parameters from analysis of non-isothermal dynamic mode P-DSC scans. 

In this paper solubility measurements of synthetic and natural dyestuffs are presented using VIS-spectroscopy. The investigations concentrate on two different methods. I. P-carotene was measured as a function of temperature and pressure in near- and supercritical C02 (289 to 309 K, 10 to 160 MPa) and CC1F3 (297 to 326 K, 12 to 180 MPa), respectively, using a static method. II. Additionally, the solubilities of l,4-bis-(n-alkylamino)-9,10-anthraquinones (with n-alkyl = butyl, octyl) were determined with a dynamic method in temperature and pressure ranges from 310 to 340 K and 8 to 20 MPa, respectively this method permits a continuous purification from better soluble impurities as well as the measurement of solubilities at the same time. For both anthraquinone dyestuffs intersection points of the solubility isotherms were found in the plot of concentration versus pressure. This behavior can be explained by a density effect. 

From a practical point of view the dynamic method is fast and relatively simple. It has the intrinsic advantage over any equilibrium technique that disjoining pressure isotherms with dYl/dh > 0 can be monitored. It has been successfully applied to measure van der Waals attraction and retardation effects in foam films [80,235], The dynamic method has been applied to foam films of liposomal suspensions [234] and quite recently surface forces of oscillating nature were monitored in foam [235] and pseudoemulsion [236] films. 

The most detailed information about the interaction of two interfaces can be obtained from the disjoining pressure vs. thickness isotherm. Disjoining pressure isotherms were obtained for foam films from 0.7-1.410 5 mol dm 3 F108 aqueous solutions. A disjoining pressure range encompassing 4 orders of magnitude (1 -104 Pa) has been monitored by two complementary techniques the dynamic method and the Thin Liquid Film-Pressure Balance Technique [128,129] (see Section 2.1.8). 

Bergeron and Radke [235] have performed precise measurement of TT(/x) isotherms of NaDoS foam films at high surfactant concentrations employing both the Pressure Balance Technique and the dynamic method of Scheludko-Exerowa [73]. The disjoining pressure isotherms were established down to pressures of 10 Pa with specially constructed film holders and careful pressure isolation and control. 

The following section reviews the literature data summarizing the behaviour during carbonization of five individual polymers, i.e. polyethylene (PE), polypropylene (PP), polystyrene (PS), polyvinyl chloride (PVC) and polyethylene terephthalate (PET). Eor each polymer, results will first be presented for flash pyrolysis then for slow pyrolysis by the isothermal and dynamic methods. 

In slow pyrolysis, temperatures are generally lower than for flash pyrolysis, but residence time is longer. Meanwhile, there are two different methods. One method is the isothermal-static method where the charge is directly heated at a given temperature and maintained during a certain time while in the dynamic method (TGA) the charge is progressively heated. 

Application of difiFerential thermal analysis and thermogravimetric analysis techniques to the pyrolysis of cellulose is obviously complicated by the complexity of the reactions involved, and the corrections and simplifying assumptions that are required in calculating the kinetic parameters. Consequently, these methods provide general information, instead of accurate identification and definition of the individual reactions (and their kinetics), which are traditionally conducted under isothermal conditions. The data obtained by dynamic methods are, however, useful for comparing the efiFects of various conditions or treatments on the pyrolysis of cellulose. In this respect, the application of thermal analysis for investigating the effect of salts (and flame retardants in general) on the combustion of cellulosic materials is of special interest and will be discussed later (see p. 467). 

Figure 6. Equilibrium water vapor sorption isotherms obtained on female stratum corneum (age 29) using salt solutions ( ) and the dynamic method (O) at 23.3 0.5°C...

S. Nose, An Extension of the Canonical Ensemble Molecular Dynamics Method, Mol. Phys. 57 (1986) 187-191 S. Nose, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys. 81 (1984) 511-519 D. J. Evans and B. L. Holian, The Nose-Hoover Thermostat, J. Chem. Phys. 83 (1985) 4069-4074 B. L. Holian, A. F. Voter and R. Ravelo, Thermostatted Molecular Dynamics How to avoid the Toda Demon Hidden in Nose-Hoover Dynamics, Phys. Rev. E 52 (1995), 2338-2347 Luis F. Rull, J.J. Morales and F. Cuadros, Isothermal Molecular-Dynamics Calculations, Phys. Rev. B 32 (1985) 6050-6052. 

There are various techniques available for molecular dynamics simulation, i.e., adiabatic, isothermal. The constant volume, temperature (isothermal NVT) method (constant number of atoms, volume, and temperature) is most commonly used. The simulated results obtained from the molecular dynamics studies are then coordinate minimized to ensure that the global minimum has been achieved. 

The dynamic methods are based on direct chromatography and are popular because they are faster and easier to automate. Four direct chromatographic methods that are available for determination of adsorption isotherms are frontal analysis (FA) [13, 109] frontal analysis by characteristic points (FACP) [109], elution by characteristic points (ECP) [109] and the perturbation peak (PP) method [118-121], The FACP and ECP methods have... 

Arrelano et al. (1989) evaluated the gel points of various DGEBA-based epoxy-resin systems via the crossover method. They also defined the vitrification point as the maximum in G" in an isothermal dynamic time test. In all these gel-point measurements the frequency must be chosen such that the relaxation of the network is enabled during data sampling. This is represented as... 

A dynamic method for acquiring and treating infrared spectroscopic data from the imidization of a number of polyimide systems is presented. In situ FT-IR analysis of polymer reactions is preferred when doing comparitive studies on a number of polymer systems. For systems where these reactions occur at relatively high temperatures, it is often difficult to obtain good isothermal data for determining kinetic parameters. Kinetic data for several polyimide systems are shown and compared. 

For our DTA tests we use equipment from Adolf Kuhner AG ( 1 ) We run two types of DTA tests. One type is a dynamic heating method with a 2.5 C/min. heating rate, and the other is an isothermal heating method. In the isothermal test we preheat the heating block to a specific temperature, insert the sample, and keep the heating block at the specific temperature for at least eight hours. 

Another reason that isothermal heating methods are used in the initial screen is to identify materials that have time dependent thermal stability. These materials have a thermal decomposition that does not follow a simple Arrhenius relationship in which the reaction rate increases exponentially with an increase in temperature. Instead an extended induction period is required before the decomposition becomes detectable. An example of this behavior is shown in Figure 2. The DTA isothermal test recorder traces of methane sulfonic acid, 3,7-dimethyloctyl ester at different test temperatures are shown. The induction time varies from less than 1 hr. at 180 C to 46 hr. at 130 C. As with this compound, it is not unusual that once decomposition is detected it proceeds very rapidly, releasing all of the heat in a short period of time. Dynamic heating methods do not indicate if this type of thermal instability is present if it is, the initial detection temperature from dynamic tests will be grossly misleading as to the thermal stability of the material. 

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