Molecular numbers

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

It is noteworthy that some terms originating from lateral interactions are once summed over molecular numbers j and merely renormalize, in this sense, the adsorption potential u j,other terms to be summed... 

For the superior performance design with consecutive, multiply furcated capillaries using conventional manifolds, flow distribution quality was determined. Polydispersity indices for eight capillaries ranged from 1.66 to 1.71, i.e., it showed a low spread, demonstrating that flow distribution was reasonably achieved. The molecular number average was... 

In a dilute solution of M identical molecules, the sum over all of the beads in the system may be restricted to a sum over aU beads of a single molecule, if the prefactor of l/V is replaced by the molecular number density M/V. 

Because all electron decays for O2-M mixtures in the above-mentioned experimental conditions show pseudo-first-order behavior, each decay curve gives an electron lifetime To, which is related to molecular number densities [O2] and [M] as ... 

It is worth noting that averaging in Eq. (4.18) is possible for the MWD only. Therefore, if the molecular number distribution qn(n) is known, it is necessary to derive the MWD by the usual... 

Choose RMS Fit and Overlay on the Display menu and pick the desired overlaying option (Molecular numbering or Selection order). This places one molecule on top of another (Figure 14.12). 

Component Molecular Number of Naphthalene Biphenyl recovered weight D atoms Relative abundance... 

Eckbreth, et al. (16) have studied saturation in CH and CN and verified that under saturation conditions reasonable estimates of molecular number density can be obtained. 

Single-shot integrated Q-branch intensity measurements were performed to obtain the N2 and O2 molecular number densities from the reaction products. These data were reduced with the averaged CARS temperatures to obtain the species-concentration profiles also shown in Figs. 3-5. 

In the last equations A(n) is the Helmholtz free energy of the total NVT system fully defined by the vector n = nm, n 2,... providing the molecular number in each tiny volume and iq) is the chemical potential at a given iq position, i.e., within the corresponding tiny volume. Note that the molecular number can be used as a continuous variable, given the fact that for any thermodynamic property in a macroscopic system the variation due to a single molecule is virtually equivalent to a differential. From the definition of the chemical potential and probability density in the r) space p(t, ti), we readily have... 

In the CME framework of discrete molecular numbers, X changes one by one stochastically. The stochastic CME model follows the master equation graph of Figure 11.5 ... 

A spherical embryo of radius r is bombarded by vapor molecules at a rate 4wrWc/4 where N(= P/k ) is the molecular number density of the vapor and C (= VSksTl n-m) is the mean molecular speed. As a result of using kinetic theory of gasses for the mean molecular speed we can write the condensation rate, CR, as... 

Finally, we note that the last combination is the change in the physical field potential energy upon incrementing the molecular number by one, so... 

Reactions in which the molecularity number (number of molecules) decreases when starting materials are converted to products cycloadditions, condensations. 

The chemical stability of PVN was extensively studied by Poulain, Michaud and Poulard [29]. They examined polymers with the molecular weight M and molecular number M of the order of 150,000 320,000 and 120,000-140,000 respectively. They aged PVN at 90 and 65 C. Tliey followed (1) the decomposition of the nitrate groups, (2) the degradation of the chains followed by chromatography. 

Furthermore, it has recently been found that the discrete nature of a molecule population leads to qualitatively different behavior than in the continuum case in a simple autocatalytic reaction network [29]. In a simple autocatalytic reaction system with a small number of molecules, a novel steady state is found when the number of molecules is small, which is not described by a continuum rate equation of chemical concentrations. This novel state is first found by stochastic particle simulations. The mechanism is now understood in terms of fluctuation and discreteness in molecular numbers. Indeed, some state with extinction of specific molecule species shows a qualitatively different behavior from that with very low concentration of the molecule. This difference leads to a transition to a novel state, referred to as discreteness-induced transition. This phase transition appears by decreasing the system size or flow to the system, and it is analyzed from the stochastic process, where a single-molecule switch changes the distributions of molecules drastically. 

Note that for each species the molecular number and mass average velocities are equal, as all the molecules have the same mass. 

A. The molecular number A. Replacement of univalent FROM ISOSTERISM... 

Allen, in 1918 defined the molecular number of a compound in a similar way of the atomic number ... 

Example Comparison of the ammonium and the sodium cations. The atomic number of nitrogen is 7 and that of hydrogen is 1. Thus the molecular number of the ammonium... 

Possessing the same molecular number, the ammonium cation should resemble the sodium cation. This is roughly true. More generally, two compounds with identical molecular numbers present at least some similar physical properties (e.g. specific heat). 

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