Step-ladder Models

This model is usually called the step-ladder model. According to this model, the vibrational relaxation dynamics of the system depends only on Ay-,0 and vibrational frequency o>. 

A step-ladder model may use equations (1.68) and (1.84). Further step-ladder models are discussed in ref. 115. Quantitative results for the continuum model of recombination of atoms have been derived by computer calculation of and P for a rotating Morse oscillator. ... 

Because of the complex, multilevel nature of the NO2 system, simplifying assumptions have to be made in analyzing the quenching. Keyser et chose a step-ladder model to represent the internal relaxation, in which each bimolecular collision is supposed to remove the same amount of rovibrational energy. The experimental observations could then be matched with roughly 3 kcal/mole being removed per collision. 

Table 1 Average energies transferred in up and down collisions and average energies dow transferred in down transitions in kJ mol ). Exponential model used for < A > > d.wn relation except for = step-ladder, t = shifted exponential model). Thermal activation, from relative collision efficiencies at 300 K, ref. 63 CHjNC at 554 K, ref. 65 ...

Third, we must know something about the collisional transition rates between the grains, and many models have been explored in the past, particularly those known as the step-ladder and the exponential models [72.R 73.F 77.T1] I will confine myself almost exclusively in this discourse to the strong collision model, equation (2.26), and for the time being, at least, the apparent rate constant p for the relaxation of the total internal energy can be regarded as an adjustable parameter. 

Equilibrium polymerization is often described by a MSOA scheme such as given in Chapter 2, also known as the ladder model [27], the isodesmic model [28], or the free association model [29], where the equilibrium constants of the sequential back and forward reaction steps are presumed to be equal. (For a discussion of variants of this assumption, e.g., see [30].) Here, we give a statistical-mechanical prescription that is equivalent to it but that allows for a more straightforward generalization. 

Such insoluble ladder products as are obtained by most methods are of uncertain structure and consist mainly of step-ladder sequences. In addition, the claims for stability are not tempered by comparisons with appropriate model single-chain polymers. To further cloud the issues. 

---