Blob theory

The smooth change in the polymer coil dimension passing through the 6-temperature is exemplified by the data of Pritchard and Caroline (1981) shown in Fig. 6.4. Here the hydrodynamic expansion factor is plotted as a fimction of the temperature. Contrary to the predictions of the blob theory, da /dr is clearly non-zero at the 0i -temperature, irrespective of the molecular weight. Its positive value is consonant with the predictions of the cluster series... 

The theory based on this assumption is expected to give zeroth order predictions of global polymer properties, and is usually called the blob theory. However, this nomenclature does not seem relevant to the author (see Section 1.4). Hence, in this book, we call it the Weill-des Cloizeaux theory. 

The Weill-des Cloizeaux theory assumes that no expansion takes place within subchains shorter than aN. On this assumption we may consider a chain model which consists of Gaussian subcoils, each being made of Nc beads and interacting with one another. With such a subcoil viewed as a blob, this model is often referred to as the blob model. However, it is important to recognize that the Weill-des Cloizeaux theory concerns interactions between beads but not those between blobs. Therefore, contrary to many other authors, the author does not consider it relevant to call it the blob theory. 

The dashed line is expected by the blob theory explained in Chapter 7. 

Since the blob theory based on e is not concerned with the correlation of density fluctuations, it gives no information about In their derivation of eq... 

For the reason mentioned above, the Dc drita of Figure 7-4 show the behavior of D near and in the semi-dilute regime. The dashed line in the figure has been drawn to fit the data points for 0.002 < < 0.03. Its slope 0.65 is compared with the blob theory in Section 2.3. 

Summarizing, we may conclude that reported sedimentation and diffusion data on semi-dilute solutions do not always lend support to the predictions of the Brochard-de Gennes blob theory. Certainly, this theory oversimplifies the complex hydrodynamic interactions involved in many-chain systems. Nonetheless we should not underestimate its merit that has sparked off many sedimentation and diffusion measurements on concentrated polymer solutions in recent years. 

Either the blob theory or the scaling theory predicts only in proportionality form the dependence of various static properties of a polymer solution on concentration and molecular weight. Naturally it is more desirable to have a theory which is capable of predicting the prefactors in the proportionality relations. Efforts toward such a theory have been made notably by Edwards and collaborators, starting from Edwards paper [42] in 1966, but the theories reported so far leave much to be desired. 

Tanaka et and by Weill and co-workers. In the recent modified blob theory, the change from Gaussian to excluded volume statistics is not as sudden as was at first surmized, and an estimate of the width of the cross-over region can be made and compared with experimental data. 

The measurement of D from a QELS experiment allows calculation of a dynamic hydrodynamic radius for the polymer coil. This parameter is not identical with the static radius of gyration R. and an understanding of why this situation exists is given by the so-called blob theory or the more recent modified blob theory proposed by Weill and des Ctoizaux, which has been tested extensively for polyacrylamide solutions. Han has used the blob theory to describe the temperature and molecular dependence of [ 1 over a wide range of conditions and demonstrated that a corresponding change in vfrom 0.5 to 0.8 could be predicted. Another consequence of this analysis was that it would be more accurate if the parameter tj M, used for the piurpose of universal calibration in GPC was replaced by tj M (/ /R ). ... 

The behavior of PE chains can be analyzed in more detail by the scaling approach based on the concept of thermal and electrostatic blobs. The blob theory assumes that, on small length scales shorter than the correlation length (called also the blob size ), the energy of random thermal motion counterbalances the excluded volume effect of segments, and short parts of the chain behave as ideal chains. Therefore, it holds that where gn is the number of segments per... 

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