Gaussian blobs

In fact, in a recent work on poly(vinylethylene), the size of the Gaussian blob has been found to correspond to about 20 bonds [39]. 

First, primary particles were created computationally in the form of so-called Gaussian blobs (Stepanek and Rajniak, 2006), as illustrated in Fig. 7.24. This method distorts more or less strongly the surface of a sphere towards different primary... 

Fig. 7.24 Reconstruction of primary particles of different morphology as Gaussian blobs according to Stepanek and Rajniak (2006) (a) field of independent random variables, (b)...

Decreasing viscosity upon increasing PE concentration for some strong PEs, whereas the viscosity increases in the case of neutral polymers [2, 17]. Eormation of electrostatic and Gaussian blobs, necklace-like structures or linear rods, depending on the solvent quality and PE charge [2, 18]. Eormation of complexes with oppositely charged PEs [19]. 

Equation (22) has been confirmed by a variety of techniques including neutron scattering, dynamic light scattering, and osmotic pressured measurements [23]. As concentration increases the concentration blob decreases in size until the Kuhn length is reached and the coil displays concentrated or melt Gaussian structure. The coil accommodates concentrations between the overlap and concentrated through adjustment of the concentration blob size. 

Thus the chain can be viewed a a Gaussian chain of n/n B n B-blobs, consistent with the above discussion. 

Now consider an isolated chain of length n n. Parts nt < raj intrinsically should show only weak interaction effects, the effective -parameter zb tnj2 being small (We ignore three-body interactions.) Thus nj-blobs should be random walk-like intrinsically. A long chain should show a swollen configuration, built from Gaussian temperature blobs. This yields... 

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 ... 

Starting from the Poisson equation and assuming Gaussian spatial distributions for ions and intrablob electrons with the dispersions and ae, prove that ae — cn <3C a and estimate A a = ae —on numerically. Assume the initial number of ion-electron pairs in the blob are no 30 and a, 40 A and e - is the dielectric permitivity of the medium. Note that at r a, out-diffusion flux of electrons is compensated for by their drift in the electric field of the ions (quasi-equilibrium condition). 

The linear relation between force and end-to-end distance (Hooke s law) is valid as long as there are many Kuhn monomers in each tension blob. As the end-to-end distance R approaches a significant fraction of its maximal value R ay.. a deviation from Hooke s law is expected. Note that the Gaussian approximation assumes Rx < i max and always leads to Hooke s Law. Below we derive the non-linear relation between force and elongation for strongly stretched chains. The limit of the linear regime corresponds to a force of the order of... 

The effect of this interaction on the conformations of an A chain can be analysed using the scaling approach described in detail in Chapter 3. On small length scales (smaller than the thermal blob size < 7), the excluded olume interactions barely affect the Gaussian statistics of the chain where gj- is the number of monomers in a thermal blob. The thermal blob is defined as the section of the chain with excluded volume interactions of order of the thermal energy ... 

Within the electrostatic blob the electrostatic interaction can be considered as a weak perturbation, and a polymer chain on the scale D obeys the Gaussian statistics ... 

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 ... 

---