Theta density

For sub-micron silica particles with grafted PDMS (up to 22 K), a different result was obtained (Yates and Johnston, 1999). The particles were unstable and flocculated well above the UCSD of the PDMS-C02 binary system. These results may suggest that it is necessary to raise the density to the UCSD for PDMS at infinite molecular weight (theta density). Another possibility is that the parameters used in the theory and simulation are not applicable to PDMS, since the polymer-polymer interactions are far stronger than the polymer-C02 interaction, unlike the case for PFOA. 

It is important to note that the UCSD above is for the actual finite molecular weight stabilizer, not an infinite molecular weight stabilizer (theta density). Many experimental stability studies of emulsions and latexes in liquid solvents indicate a correlation between the critical flocculation temperature and the theta temperature, 7 0.[68]. However, the difference between Tq and the UCST is often only a few degrees... 

The theta (0) conditions for the homopolymers and the random copolymers were determined in binary mixtures of CCl and CyHw at 25°. The cloud-point titration technique of Elias (5) as moaified by Cornet and van Ballegooijen (6) was employed. The volume fraction of non-solvent at the cloud-point was plotted against the polymer concentration on a semilogarithmic basis and extrapolation to C2 = 1 made by least squares analysis of the straight line plot. Use of concentration rather than polymer volume fraction, as is required theoretically (6, 7 ), produces little error of the extrapolated value since the polymers have densities close to unity. 

If the polymer concentration increases so that the number of high order bead-bead interactions is significant, c>>c =p, (when c is expressed as the polymer volume fraction. Op), the fluctuations in the polymer density becomes small, the system can be treated by mean-field theory, and the ideal model is applicable at all distance ranges, independent of the solvent quaUty and concentration. These systems are denoted as concentrated solutions. A similar description appHes to a theta solvent, but in this case, the chains within the blobs remain pseudoideal so that =N (c/c ) and Rg=N, i.e., the global chain size is always in-... 

Fig. 2. Bead density profiles. Solid line Brushes, mean-field and scaling theory (step function) dashed-dotted line generalization of the Milner et al. theory for brushes in the theta state dashed-double dotted line Milner et al. theory for brushes (EV chains) dashed line EV stars dotted line EV combs. Variable r is scaled to give zero bead density for the smooth curves of brushes at r=l. The brush curves are normalized to show equal areas (same number of units). The comb and star densities are arbitrarily normalized to show similar bead density per volume unit as the step function and EV curves for brushes at the value ol r where these curves intercept...

Fig.22a,b. Bead density profiles in a brush of grafted chains in a theta solvent with N=200, and two different values of the grafting point densities. The smooth curves correspond to the elliptical theoretical prediction. Reprinted with permission from [199]. Copyright (1993) American Chemical Society... 

In particular it has been conjectured that the terminal relaxation of star polymers might be the most sensitive test of the dilution exponent P in Go theta solvents suggest a mean value of nearer 2.3 [32]. A physically reasonable scahng assumption for the density of topological entanglements in a melt of Gaussian chains leads to a value of 7/3 [31]. 

For a theta solvent (V2 = 0) the relevant interaction is described by the third virial coefficient using a simple Alexander approach similar to the one leading to Eq. 13, the brush height is predicted to vary with the grafting density as h pa in agreement with computer simulations [65]. 

White crystals exists in three crystalline modifications alpha-, beta-, and gamma-Ga203 while the alpha-form is analogous to the corundum form of alumina, the beta-Ga203 is isomorphous with theta-alumina alpha-form converts to beta-modification on calcination at high temperatures (600°C) gamma form is stable at low temperatures density 6.44 g/cm (alpha-Ga203),... 

Temperature affects all the physical properties relevant in mass transfer viscosity, density, surface tension, and diffusivity. The empirical factor most often used to account for temperature changes in all these parameters is the theta factor, 0,... 

Initiation of a second round of replication leads to a replication eye at the initiation site of replication (fig. 26.3). As synthesis proceeds the size of the replication eye becomes larger at this stage the replicating chromosome is referred to as a theta structure because it has the appearance of the Greek letter d. Semiconservative replication is consistent with the density of the autoradiographic tracks made by different parts of the chromosome after one and two rounds of replication in [3H]thymidine (see fig. 26.3). 

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