Single-chain blobs

Swollen polymer gels can also be visualised as a collection of adjacent blobs (a kind of network), each blob being associated with one chain and having properties very similar to those of a single chain. 

Both theories of single-chain adsorption, described above, ignore a very important effect—the loss of conformational entropy of a trand due to its proximity to the impenetrable surface. Each adsorption blob has jb contacts with the surface and each strand of the chain near these contacts loses conformational entropy due to the proximity effect. In order to overcome this entropic penalty, the chain must gain finite energy E er per contact between a monomer and the surface. This critical energy Ecr corresponds to the adsorption transition. For ideal chains Ecr A E. The small additional free energy gain per contact kT6 should be considered in excess of the critical value Ecr,... 

The conformation of a single chain in a good solvent (left side) is a self-avoiding walk of thermal blobs while the conformation in a poor solvent (right side) is a collapsed globule of thermal blobs. 

In Section 5.3, the static correlation length was defined for semidilute solutions. This correlation length separates single-chain (dilute-like) conformations at shorter length scales (r < 0 from many-chain (melt-like) statistics at longer length scales (for r > 0. The concentration correlation blob of size contains g monomers of a chain, with conformation similar to dilute solutions ... 

We can now use the blob picture of a single chain to get the scaling relation for the radius of gyration. On average each blob contains g chain units of length a and because excluded volume conditions prevail within the blob, then... 

When C > C, the coils start to interpenetrate into each other. Daoud et al. proposed a blob model to describe such states of polymer chains (Daoud et al. 1975). As demonstrated in Fig. 4.8, they treated the single chain as a string of liquid droplets referred as blobs, which is similar to a pearl-necklace. The blob size is... 

If a stretching force is imposed on the two chain ends of a polymer in a good solvent, the single chain will response with a deformation along the direction of the force. On the other hand, thermal fluctuations tend to restore the local chain conformation to the coil state without any stretching, as illustrated in Fig. 4.14. Let s assume the existence of Njg blobs, each with a linear size satisfying r =... 

Nano-materials of polymers are the important issue in many high-technology fields, such as micro-electronics, dmg delivery and device technology. If polymer chains are compressed into various geometries of nanoscale compartments, such as ultra-thin films, nano-pores and nano-spheres, their deformation causes an entropy loss of chain conformatiOTi. Therefore, deformatiOTi of polymer chains often influences their physical performances. The blob model has been widely applied in the scaling analysis of single-chain crmformation under nano-confinement (Rubinstein and Colby 2003). 

A mainly attractive substrate with a contact-energy gain e will draw a polymer chain closer to the surface, and such a condensation process causes a loss of entropy. Therefore, there exists an equilibrium thickness d f(ff the coil absorbed onto the substrate surface (De Gennes 1976). The blob model can be used again to estimate the chain length dependence of d for the absorbed single chain. Assuming each blob has the size d and contains g monomers, then... 

Blobs are chain segments exhibiting the behavior of a single unperturbed chain . The choice of the unperturbed reference state depends on the circumstances solvent quality, spatial dimensionality, role of surface interactions etc. For flexible chains the primary choice is between two models A random walk (RW), and a self avoiding random walk (SARW). The definition of a particular blob involves two ingredients Size, and the number of constituting monomers, g. The two are related via w g Cb where a is the monomer size and uj, is determined by the reference state. For a KW Ufj = 1/2 while for three and two dimensional SARW 3/5 and 1/5 3/4 respectively. 

VI - SINGLE CHAIN BLOBS AND CHAIN-CHAIN INTERACTIONS... 

Our preceding discussion focused on systems described in terms of close packed screening blobs. As was previously stressed, such a picture is inherently associated with multichain interactions. Single chain blobs may also occur in systems incorporating many chains. In such situations it is necessary to allow for the effect of chain-chain interactions. The precise method varies with the details of the system. In the following we present two illustrative examples concerned, respectively, with confinement and with Pincus blobs. 

Screening blobs can occur in a single chain upon confinement to a droplet. See F. Brochard and A. Halperin C. R. Acad. Sci. Paris 11302,1043 (1986)... 

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