Molecules, spherical

Inspection of Table III-l shows that there is a wide range of surface tension and E values. It is more instructive, however, to compare E values calculated on an energy per mole basis. The area per mole of spherical molecules of molecular weight M and radius r is... 

Corner J 1948 The second virial coefficient of a gas of non-spherical molecules Proc. R. Soc. A 192 275... 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

Figure 2.6 Model of a particle P, a hole H, and the bottleneck between them in a liquid of spherical molecules.

The bovine serum albumin molecule is known to be nearly spherical and uncharged in a solution of pH 5.37. A plot of n/c2 versus C2 for this polymer at 25°C is linear and has an intercept corresponding to M = 69,000. The slope of the line is 1.37 X 10" Torr liter g . Use this slope to estimate the radius of this spherical molecule. 

Fig. 6.8. Most metals solidify with a dendritic structure. It is hard to see dendrites growing in metals but they con be seen very easily in transparent organic compounds like camphene which - because they have spherical molecules - solidify just like metals.

Consider spherical molecules A and B having radii and Tb and diffusion coefficients Da and Db- First, suppose that B is fixed and that the rate of reaction is limited by the rate at which A molecules diffuse to the B molecule. We calculate the flux 7(A- B) of A molecules to one B molecule. Let a and b be the concentrations (in molecules/cm ) of A and B in the bulk, and let r be the radius of a sphere centered at the B molecule. The surface area of this sphere is Aitr, so by Pick s first law we obtain... 

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

By the last two assumptions the theory, strictly speaking, is only applicable to the monatomic gases A, Kr, Xe, to a somewhat lesser extent to the almost spherical molecules CH4, CF4, SFe, and perhaps to nonpolar diatomic molecules. The rotation of even slightly nonspherical molecules like Q2 and N2 will not be free in the entire cavity when such a molecule comes close to the wall of its cage it will have to orient itself parallel to this wall. Furthermore, some of the cavities are somewhat oblate (cf. Section I.B), and thus the rotation of relatively large, oblong molecules may be seriously... 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

To make evaluations more definite, we use optical and microwave experimental data, as well as calculations of molecular dynamics of certain simple liquids which usually fit the experiment. Rotation is everywhere considered as classical, and the objects are two-atomic and spherical molecules, as well as hard ellipsoids. 

Here u is a unit vector oriented along the rotational symmetry axis, while in a spherical molecule it is an arbitrary vector rigidly connected to the molecular frame. The scalar product u(t) (0) is cos 0(t) in classical theory, where 6(t) is the angle of u reorientation with respect to its initial position. It can be easily seen that both orientational correlation functions are the average values of the corresponding Legendre polynomials ... 

It should be noted that the same method for calculation of isotropic scattering spectra is applied to spherical molecules as well. The only difference between linear and spherical molecules is the shape of the static spectrum, while its collapse proceeds in a qualitatively similar way. 

In the present section the general kinetic equation (3.26) will be solved within the Keilson-Storer model for an arbitrary angular momentum correlation [163], We consider here the case of spherical molecules (for linear molecules see Appendix 5). The corresponding initial condition is the equilibrium distribution... 

According to Eq. (2.13), the spectra we are interested in are given by a Fourier transform of the orientational correlation functions of the corresponding order Similarly to what was done in Chapter 3, the correlation functions for linear and spherical molecules may be represented as a superposition of the partial (marginal) components... 

Derivation of the isotropic Q-branch spectra for the case of linear molecules is analogous to the case for spherical molecules. The integral part of the kinetic equation determines the set of eigenfunctions of the collisional operator... 

Temkin S. I., Suvernev A. A., Burshtein A. I. Pressure transformation of the Q-branch of the CARS spectrum of spherical molecules. Opt. ... 

Suvernev A. A., Temkin S. I. Spin-rotational NMR-relaxation of spherical molecules in gas phase, Chem. Phys. Lett. 154, 49-55 (1989). 

Parker G. A., Pack R. T. Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for non-spherical molecules, J. Chem. Phys. 68, 1585-601 (1978). 

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