Lindemann type

Conventional wisdom concerning thermal unimolecular reactions would seem to dictate that this must then be a Lindemann-type collisionally activated dissociation reaction scheme such as is in Equation (17). Application of the steady-state... 

Given that the apparent rate constants for complex reaction systems might strongly deviate from Lindemann-type rate expressions, the concept of correcting the Lindemann expression for k(T, p) leads to problems. Based on this conclusion, Venkatesh et al. [110] proposed the use of a purely mathematical approximation, Chebyshev polynomials, to represent the temperature and pressure dependences of apparent rate constants. Briefly, a Chebyshev polynomial of degree i— is defined as... 

The ion-molecule reactions show a characteristic behavior they present a very small or even no activation barrier. This behavior can be understood by considering a Lindemann type formalism [4, 5]. According to this model, an intermediate activated molecular complex is formed through a bimolecular collision. A subsequent collision of the intermediate activated complex (A+M)+ with another molecule (third body, N) is necessary in order to release the excited energies. Furthermore, it is well known that ion-molecule complexes stick together by ion/dipole and ion/ induced dipole forces, and these classical electrostatic forces between the components of an ion/molecule complex and the stability of this complex increase with the dipole moment and the polarizability of the neutral component, which varies with its size and the presence of functional groups. 

For converting Cp to Cy data, a Nernst-Lindemann type of equation can be used, since compressibility and expansivity data are usually not available [27]. This equation has the form... 

In terms of a simple Hinshelwood - Lindemann type mechanism this would be... 

According to the Lindemann-Christiansen hypothesis, formulated independently by both scientists in 1921, all molecules acquire and lose energy by collisions with surrounding molecules. This is expressed in the simplified form of the Lindemann mechanism, in which we use an asterisk to indicate a highly energetic or activated molecule, which has sufficient energy to cross the barrier towards the product side, and M is a molecule from the surroundings M may be from the same type as A ... 

In most chemical reactions the rates are dominated by collisions of two species that may have the capability to react. Thus, most simple reactions are second-order. Other reactions are dominated by a loose bond-breaking step and thus are first-order. Most of these latter type reactions fall in the class of decomposition processes. Isomerization reactions are also found to be first-order. According to Lindemann s theory [1, 4] of first-order processes, first-order reactions occur as a result of a two-step process. This point will be discussed in a subsequent section. 

Current studies of unimolecular reactions can be broadly divided into three categories, based on different methods of activation of the decomposing species. The first, most classical, method is that of thermal activation of the type first envisioned by Lindemann to explain unimolecular dissociation phenomena brought about by heat energy. The second method involves chemical activation, ... 

Lindemann (1922) first suggested this type of intermediate. 

Thus the Lindemann theory predicts that a plot of l/kUni versus 1 /[M] should yield a straight line. Experimental data consistently shows downward curvature at high pressure (small values of 1/ [M]) in plots of this type. The predicted v-intercept (1 /kam) is too large (i.e., the theory underpredicts the extrapolated infinite-pressure rate constant kUni,oo)- This is the second general breakdown of the Lindemann theory that motivated further theoretical analysis. 

The simplest type of system that obeys equation (17) is the unimolecular process 95li products. Since a stable molecule should not spontaneously break up into reaction products, the mechanism by which the unimolecular process occurs must be explained. Many unimolecular reactions are believed to follow the mechanism proposed by Lindemann, namely. 

This equation predicts that a graph of 1/ uni against 1/[M] (or /p) will be a straight line whose intercept is 1 /ho and whose slope is 1 /k. This type of plot is called a Lindemann plot, and provides, in principle, an elementary method for determining both the high and low-pressure limiting rate coefficients and for testing the theory. Unfortunately, as discussed below, Lindemann plots are often not linear. 

In the early days of the work, this phase transition was mainly analyzed from the structures of Ar7 including the conformation change of the isomers, the various energy profiles, and the fluctuation of these properties [1-9,11]. Among these analyses, Lindemann s 8 was often used to monitor the phase transition. Most of these calculations carried out in these days are the Molecular Dynamics and the Monte Carlo calculations since the quantum effect was expected to be small for argon atoms [21,22,26]. These types of analyses can be categorized as the analysis of the potential energy features from the various directions. 

If we further take fe = 0 this becomes the Lindemann mechanism that is used to explain the observation that many gas-phase reactions of the type A product that appear unimolecular at high pressure change their character to bimolecular at low pressure. Lindemann has postulated that such unimolecular reactions proceed... 

If one role of PKG is to decrease smooth muscle intracellular Ca levels, then the mechanism by which this occurs is still not completely defined. Several protein substrates that are known to be phosphorylated by activation of PKG have been identified in SMCs, platelets, and other tissues. Interestingly, some of these proteins have been shown by others to regulate intracellular Ca levels in various cell types. For example, phospholamban, when phosphorylated by PKA in cardiac myocytes, dissociates from sarcoplasmic reticulum (SR) Ca -ATPase resulting in the enhanced sequestration of Ca into the SR (Lindemann et al., 1983). A similar effect of PKG activation has been shown in SMCs (Cornwell et al., 1991 Karczewski et al., 1992 Raeymaekers et al., 1988 Sarcevic et al., 1989). Using another example, Supattopone et al. (1988) reported that PKA-dependent phosphorylation of the inositol 1,4,5-trisphosphate (IP3) receptor in broken-cell fractions decreased Ca release from brain microsomes. Our laboratory has recently shown that the IP3 receptor is also phosphorylated by PKG in vitro on the major PKA phosphorylation site (i.e., Ser-1755) (Komalavilas and Lincoln,... 

In this section the results obtained from AIMD-B-LYP simulations by energizing three isomers of Li9" clusters will be analyzed [39]. For this purpose three types of quantities will be used. One of them is the root-mean-square (RMS) bond-length fluctuation 8 [25], which is calculated at the end of trajectories. A sharp increase of the 8 value is known as the Lindemann criterion for bulk melting, while in the context of finite-size clusters it can be taken as an indication of transition from solid-like to liquid-like state. We find it particularly instructive to analyze the trajectories in terms of atomic equivalence indexes ,... 

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