Spheronization

Everett [5] found Eq. XI-33 to be obeyed by several systems, for example, that of benzene and cyclohexane on Spheron 6. 

For adsorption on Spheron 6 from benzene-cyclohexane solutions, the plot of N N2/noAN2 versus N2 (cyclohexane being component 2) has a slope of 2.3 and an intercept of 0.4. (a) Calculate K. (b) Taking the area per molecule to be 40 A, calculate the specific surface area of the spheron 6. (c) Plot the isotherm of composition change. Note Assume that is in millimoles per gram. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

Fig. XVn-21. (a) Differential heat of adsorption of N2 on Graphon, except for Oand , which were determined calorimetrically. (From Ref. 89.) (b) Differential heat of adsorption of N2 on carbon black (Spheron 6) at 78.5 K (From Ref. 124).

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

Fig. 2.24 Adsorption isotherms of argon at 78 K on Spheron-6 carbon black, heated to various temperatures indicated in °C on each isotherm. (After Polley, Schaeffer and Smith. )...

Fig. 2.25 The differential heat of adsorption of argon on carbon blacks at 78 K, before and after graphitizalion.. Spheron O, Graphon. , and El denote molar heat of sublimation and of evaporation respectively.

Beaded methacrylate polymers, poly(hydroxyethylmethacrylate), Spheron, Separon (29), and poly(glycidylmethacrylate), Eupergin (30,31), are studied extensively at the Czechoslovak Academy of Macromolecular Sciences. An addition to this type of support is poly(oxyethylene-dimethacrylate) (32). Heitz et al. (33) described the preparation of beaded poly(methylacrylates) cross-linked with ethanedimethacrylates. 

SP 75 The Close-Packed-Spheron Model of Atomic Nuclei and... 

The Close-Packed-Spheron Theory and Nuclear Fission 815... 

THE CLOSE-PACKED-SPHERON MODEL OF ATOMIC NUCLEI AND ITS RELATION TO THE SHELL MODEL... 

The Distribution of Spherons in Layers.—Several theoretical and empirical arguments indicate that the nature of spheron-spheron interactions is not such as to limit the ligancy of a spheron to a fixed value, but that, instead, maximum stability is achieved when each spheron ligates about itself the maximum number of neighbors aggregates of spherons, like aggregates of argonon (noble-gas) atoms or metal atoms, assume a closest-packed structure. 

A simple argument leads us to conclude that the spherons in a nucleus are arranged approximately in a series of concentric layers. The energy of a nucleus is... 

To avoid confusion with the shells of the shell model of the nucleus we shall refer to the layers of spherons by special names the mantle for the surface layer, and the outer core and inner core for the two other layers of a three-layer nucleus. 

The Relation between the Shell Model and Layers of Spherons.—In the customary nomenclature for nucleon orbitals the principal quantum number n is taken to be nr + 1, where nr> the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nT + l + 1.) The nucleon distribution function for n = 1 corresponds to a single shell (for Is a ball) about the origin. For n = 2 the wave function has a small negative value inside the nodal surface, that is, in the region where the wave function for n = 1 and the same value of l is large, and a large value in the region just beyond this surface. 

Those subshells that occur (are occupied) with only the value 1 for the quantum number n contribute only to the outer layer of spherons (the mantle). 

In the calculations for the inner core and innermost core the decreased volume of the inner spherons (shift to tritons and dineutrons) has been taken into account. The nature of the spherons is indicated by the chart (Fig. 2) and the Z/N ratio. 

Summary.—The assumption that atomic nuclei consist of closely packed spherons (aggregates of neutrons and protons in localized Is orbitals—mainly helions and tritions) in concentric layers leads to a simple derivation of a subsubshell occupancy diagram for nucleons and a simple explanation of magic numbers. Application of the close-packed-spheron model of the nucleus to other problems, including that of asymmetric fission, will be published later.13... 

The structural interpretation of the principal quantum number of nucleonic orbital wave functions and the structural basis provided by the close-packed-spheron theory for the neutron and proton magic numbers are discussed in notes submitted to Phys. Rev. Letters and Nature (L. Pauling, 1965). 

No simple explanation of the onset of deformation at N = 90 has been advanced. I have found that a simple explanation is provided by the close-packed-spheron theory of nuclear structure. 

The close-packed-spheron theory8 incorporates some of the features of the shell model, the alpha-particle model, and the liquid-drop model. Nuclei are considered to be close-packed aggregates of spherons (helicons, tritons, and dineutrons), arranged in spherical or ellipsoidal layers, which are called the mantle, the outer core, and the inner core. The assignment of spherons, and hence nucleons, to the layers is made in a straightforward way on... 

For icosahedral packing, the transition from an inner core of one spheron to one of two spherons would be expected to take place between V = 90 and N = 92. The effect of the shell structure (completed mantle at 31 rather than 32 spherons) may explain why the transition occurs over the range 88 to 92 rather than more sharply at 90 to 92. 

The onset of prolate deformation is expected at 13 spherons, with two in the inner core. 

That stable nuclear structures should involve stable local structures about each of the inner-core spherons is a reasonable consequence of the mutual interdependence of structure and potential energy function and the short range of internucleonic forces. 

This core, with two spherons as inner core, has a prolate deformation from spherical symmetry. On the basis of the arguments discussed above, we assign this prolate core to Ndg,... 

A core of 13 spherons with an inner core of a single spheron (icosahedral packing) may occur for N = 90 (45 spherons), but not for N s 92. The energy values reported by Barber et al.4 indicate that the change to prolate deformation is about half completed at N = 90. Possibly these nuclei show resonance between the prolate structure and the icosahedral spherical structure.5... 

It is unlikely that mDyg has 13 spherons in its core, because it would then have two pro-... 

F1G. 1. Two-dimensional representation of a nearly spherical close-packed arrangement of spherons, with one in the inner core (left), and of an arrangement with prolate deformation, consequent to having two spherons in the inner core (right). 

A third neutron (second spheron) first appears in the inner core at N = 91 jjGd, has spin and negative parity, corresponding to inner-core neutron configuration Is2 Ip. 

Close packing of spherons provides a simple explanation of nuclear properties, including asymmetric fission. 

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