Characteristic temperature isothermal

Folded proteins can be caused to spontaneously unfold upon being exposed to chaotropic agents, such as urea or guanidine hydrochloride (Gdn), or to elevated temperature (thermal denaturation). As solution conditions are changed by addition of denaturant, the mole fraction of denatured protein increases from a minimum of zero to a maximum of 1.0 in a characteristic unfolding isotherm (Fig. 7a). From a plot such as Figure 7a one can determine the concentration of denaturant, or the temperature in the case of thermal denaturation, required to achieve half maximal unfolding, ie, where... 

Symbol (0) for characteristic temperature. 2. Symbol (0) for degree of saturation of binding sites as defined in the Langmuir isotherm treatment for adsorption of a ligand onto a surface. See Langmuir Isotherm. 3. Symbol (0) for plane angle. 4. Symbol (0) for one of the space coordinates in the three-dimensional, spherical polar coordinate system. 5. Symbol (0) for Celsius temperature. 

The phenomenon of polymer swelling, owing to sorption of small molecules, was known even before Staudinger reported [1] in 1935 that crosslinked poly(styrene) swells enormously in certain liquids to form two-component polymer gels. The physical state of such systems varies with the concentration (C) and molecular structure of the sorbed molecules thus, the system undergoes transition at constant temperature from a rigid state (glassy or partially crystalline) at C < Cg to a rubbery state at Cg (the transition state composition). When C > Cg and the second component is a liquid, its subsequent sorption proceeds quickly to gel-saturation and of course a solution is produced if the polymer lacks covalently bonded crosslinks or equivalent restraints. Each successive physical state exhibits its own characteristic sorption isotherm and sorption kinetics. 

Knowledge regarding the two characteristic temperatures, the and the SADT, which are used to express the thermal instability of a chemical of the TD type and that of a chemical of the AC type, having each an arbitrary shape and an arbitrary size, placed each in the atmosphere under isothermal conditions, respectively, is indispensable in temperature control to prevent such a chemical from exploding thermally. 

The general procedure followed will be outlined briefly here for the thermal conductivity. All available experimental data for the saturated liquid for each molecular species is first plotted in reduced forms vs. the reduced temperature, as shown by the solid lines in Fig. 2. Associated with each molecular species is, of course, a characteristic A. Isotherms are then cross-plotted for /c vs. A, as shown in Fig. 3, from which additional values of k can be obtained for any given A. Then by iteration, the existing data for each molecular species is extrapolated to consistent triple- and critical-point values. In both Figs. 2 and 3 the classical critical and triple points have become lines, since for light molecules the reduced parameters of the critical state are also functions of A as mentioned above. 

Under polymerization fast processes when R < R [28, 35], when intensive longitudinal and cross mixing average temperature in reaction zone so that MMD and average MM are turned to be close to characteristic for isothermal conditions at temperatures corresponding to adiabatic mixture initial heating. However, polymerization possibilities in adiabatic conditions are usually limited by... 

Fig. 40. Scaling of the volume magnetostriction of (a) CeCug, and (b) mixed-phase CeCu Sij with H T + 0)] at different temperatures (Zieglow-ski et al. 1986). H is the applied magnetic field and 0 a characteristic temperature chosen to make all the isotherms coincide as well as possible. Large differences between superconducting and non-superconducting CeCujSij are found.

The prediction of miscibility requires knowledge of the parameters T" (the characteristic temperature), p (the characteristic pressure) and V (the characteristic specific volume) of the corresponding equation of state which can be calculated from the density, thermal expansivity and isothermal compressibility. The isobaric thermal expansivity and the isothermal compressibility can be determined experimentally from p-V-Tmeasurements where these values can be calculated from V T) and V(p)j. The characteristic temperature T is a measure of the interaction energy per mer, V is the densely packed mer volume so that p is defined as the interaction energy per... 

Efficient desorption is accomplished at temperatures above the characteristic temperature, Tq. The characteristic temperature is equal to the temperature at which the slope of the adsorption isotherm at the origin is equal to CpsICpb, the ratio of the heat capacities of the soUd phase and the inert carrier gas. For a... 

As the alkyl chains assume an ordered arrangement with weak intermolecular forces, the thermal liberation of rotational freedom around the chains takes place at a relatively low temperature. Molecular motion within the chain increases gradually as the temperature increases until, at characteristic temperatures, there is a considerable increase in the molecular motion, causing the formation of various polymorphs. Polymorphic crystals may be defined as crystals that are formed from the same molecule and have the same composition but are different in crystal structure. During a phase transition the crystal that exists at low temperatures may be tfansformed on heating into a different structure. Two different kinds of polymorphs exist equilibrium and metastable [14,15]. A form that has a range of temperature over which it is stable with respect to other polymorphs is said to be an equilibrium polymorph. An equilibrium polymorph exhibits thermodynamically reversible isothermal phase fiansitions. Metastable polymorphs are kinetically stable states whose existence depends on the presence of a kinetic barrier to the attainment of equilibrium polymorphs. The fiansformation of a metastable polymorph to the corresponding equilibrium polymorph is an irreversible process. 

At temperatures higher than a characteristic temperature, Tc, the critical temperature, the vdW pressure isotherms monotonically decrease with the molar volume. The slope of the curve is always negative... 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

The three general states of monolayers are illustrated in the pressure-area isotherm in Fig. IV-16. A low-pressure gas phase, G, condenses to a liquid phase termed the /i uid-expanded (LE or L ) phase by Adam [183] and Harkins [9]. One or more of several more dense, liquid-condensed phase (LC) exist at higher pressures and lower temperatures. A solid phase (S) exists at high pressures and densities. We briefly describe these phases and their characteristic features and transitions several useful articles provide a more detailed description [184-187]. 

The curve of Fig. XVII-15 is essentially a characteristic curve of the Polanyi theory, but in the form plotted in might better be called a characteristic isotherm. Furthermore, as would be expected from the Polanyi theory, if the data for a given adsorbate are plotted with RTln P/f ) as the abscissa instead of just ln(P/P ), then a nearly invariant shape is obtained for different temperatures. The plot might then be called the characteristic adsorption curve. 

To generate characteristic velocities and bring a molecular system toequillbrium at th e sim illation temperature, atom s are allowed to in teract W ith each other through the equation s of motion. For isothermal simulations, a temperature bath" scales velocities to drive the system towards the simulation temperature,. Scaling occurs at each step of a simulation, according to equation 2S. 

Adsorption is invariably an exothermic process, so that, provided equilibrium has been established, the amount adsorbed at a given relative pressure must diminish as the temperature increases. It not infrequently happens, however, that the isotherm at a given temperature Tj actually lies above the isotherm for a lower temperature Ti. Anomalous behaviour of this kind is characteristic of a system which is not in equilibrium, and represents the combined effects of temperature on the rate of approach to equilibrium and on the position of equilibrium itself. It points to a process which is activated in the reaction-kinetic sense and which therefore occurs more rapidly as temperature is increased. 

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