Thermal events, timescale

The reaction given in Eq. 3 represents ionization and electronic excitation of water molecules this occurs on the timescale of an electronic transition. The positive radical ion H20 + is known to undergo the ion-molecule reaction (Eq. 4) in the gas phase with a rate constant of 8 x 10 dm mol s [2], which sets the lifetime of the ion at less than 10 s in the liquid. The electronically excited states H2O are known to dissociate in the gas phase, as shown in Eq. 5, and the electron released in the ionization event is known to become thermalized and solvated in less than... 

The model being proper yields a structurally solvable index 1 DAE model. Though what if we do not know it all for example a flow is not known, kinetics are not all known or some properties are missing Some of it can be handled, but for a price information must be added in the form of assumptions. There are simple assumptions, such as property is constant, thus not a function of the state. Those are easy to handle and do only remove algebraic complexity and reduce the fidelity of the model at obvious places. The more complex ones are if the lack of information makes it impossible to compute flows or reactions. At this point it is necessary to resort to more restrictive measure and make timescale assumptions. There are three commonly made assumptions, which are (i) Steady state assuming a system to exhibit a very fast dynamic relative to the modelled dynamic window, thus shifting this system out at the top end, the short time scale and assume event-dynamics. (ii) (Phase) equilibrium in which one assumes very fast communication of extensive quantity such that the two coupled systems are in equilibrium with respect to the affected extensive quantity. The most common case is thermal equilibrium and phase equilibria, (iii) (Reaction) equilibrium in which one assumes very fast reactions, such that the reactions are viewed as instantaneous. 

In atomic scale simulations, there is often a clear separation of timescales. The rate of rare events, e.g., chemical reactions, in a system coupled to a heat bath can be estimated by evaluating the free energy barriers for the transitions. Transition State Theory (TST) [9] is the foundation for this approach. Due to the large difference in time scale between atomic vibrations and typical thermally induced processes such as chemical reactions or diffusion, this would require immense computational power to directly simulate dynamical trajectories for a sufficient period of time to include these rare events. Identification of transition states is often the critical step in assessing rates of chemical reactions and path techniques like the nudged elastic band method is often used to identify these states [10-12,109]. 

The third calibration parameter, which is needed when rapidly changing processes are studied, is the time constant. This is a measure of the thermal inertia of the sample that blurs details in rapid events. The time constant is used in the Tian equation - named after a pioneer in isothermal calorimetry - to correct for this. Typical time constants in isothermal calorimeters are 100-1000 s. As the main hydration has timescales much longer than this, the Tian equation is not needed in cement calorimetry when the main hydration is studied, but it is needed when early reactions are studied. Further information on the Tian equation is given by Wadso (2005), and other similar methods are discussed by Evju (2003). 

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