Blob radius

Size and energy release. The terminal blob consists of about n0 30 overlapped ion-electron pairs. Spatial distribution of these species may be described by Gaussian function where the blob radius ... 

It turns out that there is a simple rescaling possible, by which all curves superimpose (at least approximately) on a master curve (Fig. 13b) A b is rescaled by Sbiob. the number of monomers per blob, motivated by the idea that the bottlebmsh polymer is viewed as a pearl-necklace chain of blobs, the blob radius being the cross-sectional radius of the cylindrical brush. From this condition, biob is easily derived numerically from the simulation data. 

The scaling theory discussed above for stars can also be apphed to chains grafted to a hne. Each branch or arm is again treated as a series of spherical blobs. Since the volume accessible at a radial distance r from the grafting line increases, the monomer density decreases and the size of the blobs increases with r. At a distance r from the grafting line, a cylinder of length L has piL blobs of radius (r) covering a cross-sectional area of Lr. Therefore the blob radius,... 

Nj,=N/f is the number of beads per branch or arm). For larger chains, however, the solvent can penetrate in outer regions of the star and the situation within these regions is more Hke a concentrated solution or a semi-dilute solution. These portions of the arms constitute a series of blobs, whose sizes increase in the direction of the arm end. The surface of a sphere of radius r from the star center is occupied by f blobs. Then the blob size is proportional to rf. Most internal blobs are placed in conditions similar to concentrated solutions and, consequently, their squared size is proportional to the number of polymer units inside them as in an ideal chain. This permits one to obtain the density of units inside the blob, as a function of r ... 

Scaling theory also derives such results in another, more intuitive way, based on some heuristic picture of the internal structure of the polymer solution. Consider some piece of length nB within a chain of length n. It is natural to assume that this piece forms a subcoil, a blob1, of typical extension R, which scales like the coil radius for a polymer molecule of segments Rb nB- Thus the local density of segments due to the blob is estimated as... 

According to this definition dilute solutions of long macromolecules are critical. The role of the correlation length is played by the radius of gyration Rg rsj Nu — oo N — oo, and by virtue of the chain structure a polymer coil shows density fluctuations on all scales r < Rg. Indeed, a blob of size r is just a correlated fluctuation of the density. 

Here Ry stands for a typical ionization potential. Equation (2) indicates that the terminal positron blob is a spherical nanovolume, which confines the end part of its trajectory. This is where ionization slowing down is the most efficient (the thermalization stage of the subionizing positron is not included here). The mathematical formulation of this statement is twofold. Just after the first blob formation step , which is ltr Wu) (the thick arrow in Fig. 5.1), the positron reaches the center of the blob. After that, the end part of the ionization slowing-down trajectory is embraced by the blob i.e., the slowing-down displacement of the positron, Rion Wbi, Ry) — au is equal to the radius of the blob, au-... 

The relationship between volume, maximum thickness and radius gives a measure of the flatness of the blob away from its leading edge. That is, the volume is a constant times ttR Aq. Tfie constant is unity for a flat blob with vertical sides, 0.79 for the inviscid blob, and 0.67 for the lubrication theory blob (Huppert 1982). The central region of the inviscid blob is flatter than that of the lubrication theory blob as expected, but the difference is not large. 

Fig. 9 Schematic representation of (sections of) multi-arm star polymers in semidilute solution in good solvent. The three different length scales, the radius ofthe star R, the coat ri, hard core are indicated. The open circles denote the correlation length blob size)...

The experimental form factor P( ) shown in Fig. 12a can be expressed as P q) = [bcFc q,rc) + bsFs q,rc,R )], where bc,bs are the contrast factors for the core (c) and shell (5) with core radius and overall micelle radius R, whereas Fc q), F q) aiQ the scattering amplitudes of the core and shell, respectively. Under core contrast conditions (Z s 0), the expected first minimum for the compact sphere at high q values falls outside the ("/-range, whereas under shell contrast conditions the power-law behavior arising from blob (swollen PEO shell) scattering is observed. Hence, the dual colloid-polymer character of the particle is clearly reflected in Fig. 12a. 

In order to estimate the first contribution from the elastic adsorption, a C gel picture is used, in which the gel is a collection of adjacent blobs of radius that has a characteristic relaxation time Ti / >coop, where Dcoop r/bnrji is the cooperative diffusion constant of the gel, T is temperature and t] is the viscosity of the solvent [80]. Each blob is associated with a partial polymer chain (the polymer chain between two next-neighboring cross-linking points). The scaling theory relates this molecular structure of the gel with its elastic modulus E by the equation [80]. 

The blob size relative to the mean-square radius of gyration is... 

It is necessary to consider different regimes dependent on the dimensions of polymer chains. A long chain collapses into a globule consisting of close-packed blobs of size The blobs are either Gaussian or swollen depending on the second virial coefficient value. In a 0 solvent, the chain radius in the collapsed state is given by ... 

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