Electrostatic Blob

Figure 4.14 A chain is imagined to be made of electrostatic blobs of linear size 9. Within the blob, electrostatic interactions are weak and the chain statistics appropriate for the uncharged backbone is applicable. Outside the blobs, electrostatic repulsion dominates and the chain is extended into a rod-like conformation.

The pearls are just at the Rayleigh instability threshold, their density is that of a collapsed globule and their size is obtained from the Rayleigh charge. It is the so-called electrostatic blob size... 

Calculate electrostatic potential of the blob if the distributions of the blob species arc the same as in Problem 1. 

An excellent physical model describing the conformation of the polyelectrolyte molecule was proposed by de Gennes et al. in Ref. 14, where the conformation of the polyelectrolyte molecule immersed in an ideal solvent was considered. The molecule has m monomer units of size a. The fraction / of monomer units possesses by charge e (i.e., / is the degree of ionization of the molecule). The macromolecule is presented as a linear sequence of electrostatic blobs of spatial size D (see Figure 1). Each blob contains g charges, i.e., gif monomer units, and thus the size R of the macromolecule is... 

The spatial size D of electrostatic blob can be estimated from the condition that the energy of electrostatic repulsion of two blobs is of the order of thermal energy IcT ... 

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 ... 

A similar presentation of the polyelectrolyte macromolecule as an extended sequence of blobs is valid also in the case of good solvent, when the interaction between neutral monomers has a repulsive character, and the polymer chain within the electrostatic blob has a conformation of the coil with the excluded volume interaction [15]. 

In the course of conformational transition the number g of monomer units forming the electrostatic blob increases. For the case of relatively short chain (small value of m) or relatively weak degree of ionization / the collapse transition is ended by the formation of spherical globules. The condition for spherical globule formation is... 

We will focus here on the transition in a weak polyelectrolyte molecule. We will consider that Ineq. 11 is fulfilled and that the forming globule structure has a spherical shape (we have the only electrostatic blob or the only bead in the necklace). We also will not discuss the effect of counterion condensation [20-26]. Due to this effect the real charge of the macromolecule is somewhat lower than the net charge of the molecule [20,21], At a higher degree of ionization /the condensation of counterions could lead also to the collapse of macromolecules [22-26], This phenomenon is attracting considerable attention in the literature [22-26],... 

The adsorption model described above assumes the existence of different discrete states of protein molecules in the surface layer, with neighbouring states differing from one another by the molar area increment Aco. From the viewpoint of scaling analysis, (Aco) has to be close to the size of an electrostatic blob [132]. In adsorption layers of proteins the flexibility of chains increases due to the high concentration of both protein and inorganic electrolyte [133]. This allows to consider, instead of discrete states, an infinitesimal change do in the molar area. To perform the transition from the discrete to the continuous model one has to replace formally the summations in Eqs. (2.126)-(2.128) by an integration [86]. 

Combining Eqs. (18) and (20) gives the effective electrostatic persistence length for a string of electrostatic blobs. 

In a salt-free solution, the onset of collapse transition in a PE star corresponds to the collapse of individual electrostatic blobs in the uniformly stretched arms of the star. An increase in the number of star branches, p, enhances interbranch Coulomb repulsions, and, thereby, decreases the electrostatic blob size. Therefore, the collapse transition is shifted towards poorer solvent conditions upon an increase in p. 

For crew-cut PE micelles, the coronal chains can be presented as being composed of strings of Gaussian electrostatic blobs of size The average... 

For polyelectrolyte bmshes, a strong confinement of coimterions inside the bmsh was predicted, causing a high osmotic pressure inside SPEB. This condition of quasi-electroneutrality leads to a picture in which the outer regions of the bmsh are composed of electrostatic blobs that do not fill space. The confinement of counterions was experimentally confirmed by van der Maarel et and... 

When C > C, similar to the treatment of neutral polymers in semi-dilute solutions, we can use the blob model to describe the polyelectrolyte segment holding the electrostatic repulsion in semi-dilute solutions. Assuming the blob size as a characteristic length to maintain the chain rigidity, with reference to the critical overlap concentration C, ... 

---