Angle of tetrahedral rotation

Figure 6. Stability of illite layers formed by WD mechanism percentage of change in percentage illite layers between 1 and 3 Sr-exchanges is plotted against Of, the angle of tetrahedral rotation. Data from Table V.

Figure 5,44 Sketch of tetrahedral rotational angle a, for two limiting conditions, = 0° and = 12°. From Hazen and Wones (1972). Reprinted with permission of The Mineral-ogical Society of America.

Table 2. Axial thermal expansion coefficients (ax in ° C ) for the cell edges and the volume, and the first derivative of tetrahedral rotation angle a versus T in dioctahedral micas.

Figure 5.44 shows the conformation of the hexagonal rings on the tetrahedral sheet for limiting values of the rotational angle = 0° and 12°, respectively). Due to structural constraints, the value of depends directly on the mean cation-to-oxygen distances in [TO4] tetrahedra (4) and in octahedra (4,), according to... 

As already noted, the structural limits of the rotational angle are 0° and 12°. This implies that the ratio of mean octahedral and tetrahedral distances is restricted in the range... 

They explained the fit of the dioctahedral and trioctahedral sheets by the thinning of the dioctahedral sheet (2.05 A) and the thickening of the trioctahedral sheet (2.15 A), giving a mean lateral octahedral edge of 3.02 in both sheets. To compensate for the thinning of the dioctahedral sheet the tetrahedral sheet thickened slightly. The tetrahedral rotation is in the same direction as for the other chlorites, but the angle is somewhat less than expected. 

The unperturbed dimensions of various condensation polymers obtained by the present method are listed in Table 10. A polyelectrolyte chain, sodium polyphosphate, has been included because theta-solvent results are available. The freely-rotating chain dimension (Lzyof of poly(dimethylsiloxane) in the table is due to Flory and his coworkers (705), that for the polyphosphate chains is taken directly from the paper of Strauss and Wineman 241 ), while most of the others have been calculated in the standard manner with the convenient and only negligibly incorrect assumption that all the aliphatic bond angles are tetrahedral. The free-rotation values for the maleate and fumarate polyesters are based on parameters consistent with those of Table 6 for diene polymers. 

While the freely jointed chain is a simple model from which to begin predictions of chain dimensions, it is physically unrealistic. Since each carbon atom in a real polymer chain is tetrahedral with fixed valence bond angles of 109.5°, the links are subject to bond angle restrictions. Moreover, the links do not rotate freely because, as we have seen earlier, there are energy differences between diflferent conformations (cf. Fig. 2.3). Both of these effects cause to be larger than that predicted by the freely jointed... 

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