Kinetics evolutions

An overreaching theme of the present chapter, besides broken ergodicity, has to do with the fact that most of the enhanced sampling methods that we shall discuss address situations in which one cannot clearly identify a reaction coordinate that can be conveniently used to describe the kinetic evolution of the system of interest. While methods for enhanced sampling are designed to yield accurate results faster than regular molecular dynamics or Monte Carlo (MC) methods, it is our belief that there is no perfect method, but that, rather, there are methods that perform better for particular applications. Moreover, it should be noted that, while in instances when a proper reaction coordinate can be identified methods described in other chapters are probably more efficient, they could still benefit by sampling in conformational directions perpendicular to the reaction coordinate. 

LFP gives us the time resolution needed to follow the kinetic evolution of many carbenic reactions.9 However, if the carbene lacks a readily accessible UV chromophore, its reactions must either be followed indirectly or, as has recently become practical, by LFP with IR detection of the carbenic intermediates.10... 

This model for the modulated state of tubules leads to an interesting speculation on the kinetic evolution of flat membranes or large spherical vesicles into tubules.68,132 In this scenario, when a flat membrane or large spherical... 

Figure 5.51 Scenario for kinetic evolution of flat membranes into tubules.68,132 (a) When membrane is cooled into tilted phase, it develops stripes in tilt direction and then breaks up along domain walls to form ribbons, (b) Each ribbon twists in solution to form helix, (c) Helical ribbon may remain stable or may grow wider to form tubule. Reprinted with permission from Ref. 139. Copyright 2001 by the American Chemical Society.

Low Angle Light Scattering Photometry Static Envelopes. We shall first consider the final scattering envelopes obtained after gelation is complete. The next subsection will be devoted to the kinetic evolution of the scattering envelopes ... 

Helfferich, F. (1983). Ion exchange kinetics—Evolution of a theory. In Mass Transfer and Kinetics of Ion Exchange (L. Liberti and F. Helfferich, eds.), pp. 157-179. Matinus Nijhoff Publishers, Dordrecht, The Netherlands. 

Figure 8. Kinetic evolution of CdS band-gap energy (A) and Co2+ ligand-field absorption intensity ( ), collected in situ during the synthesis of Co2+ CdS nanocrystals in inverted micelles.

A description of a kinetic evolution for point defects can be carried out directly through above specified kinetic schemes and equations for elementary processes which were employed regarding the absorbed species. For describing a kinetic evolution of two- and three-dimensional macrodefects, it is necessary to construct models for connection of elementary processes with a change of structural macrodefects [196]. 

Figure 10.9 Polycyclooctene irradiated in the photoDSC system at 35°C under air. Left ordinate ( ) IR kinetic evolution of carbonyl band (1721 cm-1). Right ordinate ( ) change in crystallization heat. Reproduced from reference [59], 2005 with permission from Elsevier.

The aim of this first section is to describe the rupturing mechanisms and the mechanical conditions that have to be fulfilled to obtain monodisperse emulsions. A simple strategy consists of submitting monodisperse and dilute emulsions to a controlled shear step and of following the kinetic evolution of the droplet diameter. It will be demonstrated that the observed behavior can be generalized to more concentrated systems. The most relevant parameters that govern the final size will be listed. The final drop size is mainly determined by the amplitude of the applied stress and is only slightly affected by the viscosity ratio p. This last parameter influences the distribution width and appears to be relevant to control the final monodispersity. 

In addition to the constraint on concentrations imposed by Equation (9.27), a reaction network s stoichiometry imposes a set of constraints on certain conserved concentration pools [2], These constraints follow from the equation for the kinetic evolution of the metabolite concentration vector ... 

The authors also studied the kinetic behavior of the 11 member library DCL2 by plotting the concentration of the constituents as a function of time (Fig. 4). This kinetic evolution is biased compared to the reference non-self-duplicating DCL1... 

Figure 4. Kinetic evolution of SANS at high Q of Silica S2M after exposure to matched cyclohexane (50% CgDu) at 289 K.

Figure 8. Kinetic evolution of the diffraction peak (100) of mesoporous silica during capillary condensation of benzene (59 % CbD ), corresponding to the incremental increase in P/Po from 0.54 to 0.62. (Time interval between measurements is 130 s.)...

Three mixtures with weight fractions of silicone oil of 0.01,0.02 and 0.03 were prepared. The temperature quenches were performed in the same way as described earlier. The kinetic evolution of the phase separation is recorded on videotapes from which series of digitized pictures taken at different times can be extracted. The time origin t=0 is chosen when the initial coalescence stops and uniformly-sized drops start to aggregate. In each picture, the mean chain length, S(f), is calculated. It is defined as... 

Kinetic Evolution of Thermal CO2 Dissociation Products During Quenching Phase... 

To better understand the pattern formation dynamics, the morphological and kinetic evolution of the surface pattern during swelling was studied extensively... 

Tanaka, H., et al. Morphological and kinetic evolution of surface patterns in gels during the swelling process - evidence of dynamic pattern ordering. Phys. Rev. Lett. 68(18), 2794-2797 (1992)... 

White JDL, McClintock MK (2001) Immense vent complex marks flood-basalt eruption in a wet, failed rift Coombs Hills, Antarctica. Geology 29(10) 935-938 Wilson M (1989) Igneous petrogenesis a global tectonic approach. Unwin Hyman, London Wilson TJ (1992) Mesozoic and Cenozoic kinetic evolution of the Transantarctic Mountains. In Yoshida Y et al. (eds) Recent progress in Antarctic earth science. Terra Scientific, Tokyo, Japan, pp 304-314... 

The kinetic evolution is usually represented by a sigmoid-type curve. Such a typical curve is given in Figure 9 for the case of displacement reaction, Ni + CuO Cu -F NiO realized in planetary ball mill [58]. Author of this overview analyzed these experimental results by one of the most frequently used kinetic model applied to various solid-state reactions, namely Johnson-Mehl-Avrami equation ... 

After this first detection and quantification in red wine, the kinetic evolution of the concentrations of the native oak-derived C-glucosidic ellagitannins and their... 

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