Isotropic temperature

TABLE 2.16 Melting Point, Tm (°C), and Isotropization Temperature, I) (°C), of Poly(l,4-phenylene terephthalate) LCPs Containing Various Substituents... 

Isotropic temperature factors (B) are in A standard deviations are given in parentheses. 

A review of the literature demonstrates some trends concerning the effect of the polymer backbone on the thermotropic behavior of side-chain liquid crystalline polymers. In comparison to low molar mass liquid crystals, the thermal stability of the mesophase increases upon polymerization (3,5,18). However, due to increasing viscosity as the degree of polymerization increases, structural rearrangements are slowed down. Perhaps this is why the isotropization temperature increases up to a critical value as the degree of polymerization increases (18). 

There are also some trends when looking at the main chain flexibility. Table II demonstrates that when the main chain flexibility decreases from cyanobiphenyl containing polymethacrylates to polysiloxanes, not only does the Tg drop, but the isotropization temperature increases. However, the trend is the opposite when the mesogen is methoxyphenyl benzoate (18). Therefore, this effect of the main chain flexibility is still ambiguous. 

Symmetric polysiloxanes having m — 2—9 have also been investigated, with some properties listed in several articles in a handbook [158], and elsewhere [20]. The isotropization temperatures reported in these studies show a very interesting increase with increase in the number m of methylene groups in the side chains... 

Polysiloxanes in this category typically contain cyclics of -Si(CH3)2-0- siloxane units of various sizes, or such siloxane units mixed with some carbosiloxanes (with additional -CH2- sequences) [163-165]. The cyclic portions can add considerable stiffness, resulting in isotropization temperatures above the polymers decomposition temperatures. 

One aspect of this type of behavior involves the already mentioned increase in the isotropization temperatures with increase in elongation [169-171], Also of... 

The second consideration, anticipated in Sect. 3.1, is that whereas Sm and Sc increase little with temperature (see Fig. 8) so that in the literature the temperature dependence of Gc and Gm is often approximated by straight lines, Sl varies moderately up to the glass transition temperature Tg but will increase substantially between Tg and the isotropization temperature. The behavior of Sl is due to the fact that, as the temperature increases, polymer chains are progressively more likely to bend sharply in the melt, whereas they are forced to remain straight in the mesophase and in crystals. The downward curvature of Gl in Fig. 8 shifts to lower temperatures with inherently more flexible chains. With very flexible polymers Tml becomes therefore smaller than the crystal-melting temperature Tcl and a stable mesophase cannot form. 

Refinement takes place by adjusting the model to find closer agreement between the calculated and observed structure factors. For proteins the refinements can yield R-factors in the range of 10-20%. An example taken from reference 10 is instructive. In a refinement of a papain crystal at 1.65-A resolution, 25,000 independent X-ray reflections were measured. Parameters to be refined were the positional parameters (x, y, and z) and one isotropic temperature factor parameter... 

Correa, S. M., A. Gulati, and S. B. Pope (1994). Raman measurements and joint pdf modeling of a nonpremixed bluff-body-stabilized methane flame. In Twenty-fifth International Symposium on Combustion, pp. 1167-1173. Pittsburgh, PA The Combustion Institute. Corrsin, S. (1951a). The decay of isotropic temperature fluctuations in an isotropic turbulence. Journal of Aeronautical Science 18,417 -23. 

Reflection intensity in the SAED negatives was measured with a microdensitometer. The refinement of the structure analysis was performed by the least square method over the intensity data (25 reflections) thus obtained. A PPX single-crystal is a mosaic crystal which gives an "N-pattem". Therefore we used the 1/d hko as the Lorentz correction factor [28], where d hko is the (hkO) spacing of the crystal. In this case, the reliability factor R was 31%, and the isotropic temperature factor B was 0.076nm. The molecular conformation of the P-form took after that of the P-form since R was minimized with this conformation benzene rings are perpendicular to the trans-zigzag plane of -CH2-CH2-. 

For vanadium, the ratios are smaller, and the dynamic density maps do not show a distinct maximum in the cube direction. The difference is attributed to anharmonicity of the thermal motion. Thermal displacement amplitudes are larger in V than in Cr, as indicated by the values of the isotropic temperature factors, which are 0.007 58 and 0.00407 A2 respectively. As in silicon, the anharmonic displacements are larger in the directions away from the nearest neighbors, and therefore tend to cancel the asphericity of the electron density due to bonding effects. 

Evaluate the bias in the isotropic temperature factor of the hydrogen atom of problem 1.1 as a function of the true k value, if k is arbitrarily set to 1 in a refinement. 

An interesting fact is that in the case of K Cu[Fei cCo c(CN)6], the potassium ions occupy statistically one-half of the eight cubes of one unit cell, but with a high value of the isotropic temperature factor indicating a smudgy position of the potassium ions. In the compound K Ni[Fei xCox(CN)6], an eccentric position of potassium ions was found. Such an eccentric position of the countercation was also described by Bo-carsly et al. for sodium-containing nickel hexacyanoferrate(II) [34]. 

Isotropic temperature factors were used for 0(2) through 0(9) This compound Is a superconductor with Tc 40 K. 

The polymers of 284 are hydrogels and can take up a moderate amount of water. The ROMP of 285 only proceeds to completion if the polystyrene side chains are kept reasonably short (n = 4, 7 or 9). Polymers of monomers such as 286 exhibit a nematic or smectic mesophase resulting from side-chain crystallization. Isotropization temperatures increase with increasing MW, becoming constant at about 30-50 repeat units. Side-chain crystallization tends to be suppressed as the MW increases. 

We arrive at this conclusion from the lack of more than a slight atropisomeric excess (ca. 0.1% in all but one anomalous experiment) after equilibration of racemic BN in the cholesteric phases at several temperatures (TablelV). The lack of change in the ratio of atropisomers in the cholesteric phases is consistent with our observation that liquid-crystal induced circular dichroism spectra (67) of ISN in cholesteric mixture D are due to a macroscopic property of the solvent the LCICD spectra disappear when mixture D is heated to an isotropic temperature. 

---