Crystalline experimental considerations

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

Although the extent of crystallinity is the variable under consideration, time is the experimental variable. Accordingly, what is done is to identify the specific volume of a sample at t = 0 (subscript 0) with V, the volume at t = °° (subscript °o) with and the volume at any intermediate time (subscript t) with the composite volume. On this basis, Eq. (4.39) becomes... 

There has been considerable discussion about the extent of hydration of the proton and the hydroxide ion in aqueous solution. There is little doubt that this is variable (as for many other ions) and the hydration number derived depends both on the precise definition adopted for this quantity and on the experimental method used to determine it. H30" has definitely been detected by vibration spectroscopy, and by O nmr spectroscopy on a solution of HF/SbFs/Ha O in SO2 a quartet was observed at —15° which collapsed to a singlet on proton decoupling, 7( 0- H) 106 Hz. In crystalline hydrates there are a growing number of well-characterized hydrates of the series H3O+, H5O2+, H7O3+, H9O4+ and H13O6+, i.e. [H(0H2) ]+ n = 1-4, Thus... 

Their crystallization behavior compares with natural rubber, as follows (1) their rate of crystallization is more rapid and (2) their amount of crystallinity is temperature dependent, but considerably less strain dependent. These experimental rubbers have excellent green strength and building tack. 

For crystalline compounds, they noted that an important factor to consider is the crystal lattice energy. From theoretical considerations and subsequent empirical studies, they discovered that melting point (mp) serves as an excellent proxy for this factor. While this is a significant advance in our understanding of water solubility, it falls short as a means to predict solubility from the chemical structure alone a compound must be made and a mp determined experimentally. 

The question may then be raised as to whether insoluble monolayers may really be treated in terms of equilibrium thermodynamics. In general, this problem has been approached by considering (i) the equilibrium spreading pressure of the monolayer in the presence of the bulk crystalline surfactant, and (ii) the stability of the monolayer film as spread from solution. These quantities are obtained experimentally and are necessary in any consideration of film thermodynamic properties. In both cases, time is clearly a practical variable. 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

The most recent fairly comprehensive review Of the vibrational spectra of transition metal carbonyls is contained in the book by Braterman1. This provides a literature coverage up to the end of 1971 and so the subject of the present article is the literature from 1972 through to the end of 1975. Inevitably, some considerable selectivity has been necessary. For instance, a considerable number of largely preparative papers are not included in the present article. Tables A-E provide a general view of the work reported in the period. Table A covers spectral reports and papers for which topics related purely to vibrational analysis are not the main objective. Papers with the latter more in view are covered in Table C. Evidently, the division between the two is somewhat arbitrary. Other tables are devoted to papers primarily concerned with the spectra of crystalline samples — Table B — to reports of infrared and Raman band intensities — Table D and sundry experimental techniques or observations - Table E. Papers on matrix isolated species, which are covered elsewhere in this volume, are excluded. 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

The study of crystals and their X-ray patterns is both fascinating and complex. From a known crystal structure, a theoretical diffraction pattern can be constructed using vector algebra, including snch considerations as structure factors which account for disallowed interactions with the crystal lattice and determine the relative intensity of the diffracted beams. For onr pnrposes, it is snfficient to know that a diffraction pattern can be obtained experimentally in a relatively rontine fashion, and the resulting pattern is characteristic of a specific crystalline material. 

We can conclude from these thermodynamic considerations that it is possible to estimate the redox potentials of excited molecules, if we know the equilibrium redox potentials for the molecules in the ground state, as well for reduction as for oxidation, and add or subtract from these redox potentials the excitation energy AE of the lowest singlet or triplet state. For most dye molecules the reduction redox potential is experimentally more easily accessible than the oxidation redox potential. In such cases we have found that an estimation can be made by assuming that the ionisation energy of the dye molecule in crystalline state is similar to the ionisation energy in a polar solvent and gives an approximate value for the absolute redox potential. Such estimations are especially useful for a comparison of molecules with similar structure. 

Just above the melting point the polymer is visually quite viscous and numerous observations have been made that the polymer exhibits a memory effect, that is to say, on recooling the melt crystallites will appear in the same sites where they had been before melting the polymer. Hartley, Lord and Morgan (1954) state It is reasonable to suppose that there will be a few localities in the crystalline polymer which have a very high degree of crystalline order, and therefore the melt can contain, even at considerable temperatures above the observed melting or collapse point, thermodynamically stable minute crystals of the polymer . Especially if the polymer has been irradiated so as to contain a few crosslinks as in irradiated polyethylene, then flow is inhibited and spherulites can be made to appear on recrystallization in the same sites that they had before the polymer was melted, Hammer, Brandt and Peticolas (1957). However, as mentioned above, the specific heat of irradiated polyethylene in the liquid state is identical with that of the unirradiated material, within the limits of experimental error. Dole and Howard (1957). 

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