Polymer chains in a good solvent

The large-scale structure of polymer chains in a good solvent is that of a self-avoiding random walk (SAW), but in melts it is that of a random walk (RW).11 The large-scale structure of these mathematical models, however, is... 

If neutral and charged polymer brushes are exposed to solvents, a very interesting and rich phase behavior can be observed. As a consequence, such surface-attached brushes have become the focus of considerable theoretical efforts in studies on the structure and phase behavior of such polymer chains in contact with a solvent. The thickness of a neutral brush scales linearly with the degree of polymerization, N, which is in stark contrast to the well-known characteristics of free polymer chains in a good solvent, where the radius of the coils scales as R oc AT0 58. For neutral brushes the simple scaling... 

In order to determine the swelling of a polymer chain in a good solvent, we have to measure its size and to compare it with the size of the equivalent Brownian chain, i.e. the size that the chain would have in the Brownian state. This Brownian state is, in fact, only a concept however, by setting the sample in an adequate environment, one can get a situation close to this concept. 

The box-like cell model of a PE star can be considered as a generalization of a classical mean-field Flory approach, which was first suggested to describe the swelling of a polymer chain in a good solvent [90], The Flory approach estimates the equilibrium dimensions of a macromolecule, as a function of its parameters, by balancing the free energy of intramolecular (repulsive) interactions with the conformational entropy loss of a swollen chain. Within the box-like approximation, the star is characterized by the radius of its corona, R (end-to-end distanee of the arms), or by the average intramolecular concentration of its monomers ... 

Dilute polymer chains in a good solvent are swollea... 

In thermal concentrated solutions, polymer chains in a good solvent behave similarly to those in an athermal solvent, while in a poor solvent, polymer chains experience a phase separation with the coexistence of polymer-rich and polymer-poor phases. We will give more descriptions about the phase separation behaviors in Chap. 9. 

This quantity of sizes reflects the effective volume-exclusion range of the moving particle interacting with its surrounding particles. For a single polymer chain in a good solvent, the theoretical hydrodynamic radius Rh ° can be defined as... 

When a polymer chain adsorbs on a colloidal surface, it loses its entropy in two ways. First, there is a loss of conformational entropy that the polymer chain experiences when one of its ends is fixed. The total number of configurations for a free polymer chain in a good solvent scales as, where N is the... 

Fig. 5.2. Schematic view of the polymer coil expansion due to the solvation of the polymer chain in a good solvent...

Fig. 6.10 Phase diagrams calculated using generalized free volume theory for spherocylinders with L/D = 20 plus interacting polymer chains in a good solvent dashed curves) for size ratios q = 1 left) and q = 2.5 right) in the reservoir representation. Full curves are FVT results for (noninteracting) penetrable hard spheres as depletants as identical to those in Fig. 6.7. As in Fig. 6.7 the Gaussian form for the ODF was used...

Figure 3 End-grafted polymer chains in a good solvent. If d > 2Rg, the chains assume a conformation similar to that of free chains in solution, for which Rg is the radius of gyration. This is known as the mushroom conformation. If d < 2Rg, the chains stretch out into the solvent to...

Adsorption Isotherms. Because of the strong tendency of polymer chains to adsorb at attractive surfaces, the surface gets saturated at very small bulk concentrations. Adsorption isotherms of this nature are known as high affinity isotherms. The adsorption isotherm of polymer chains adsorbing on solid substrates depends on the polymer molecular weight, solvent quality, and polymer-surface interactions. Figure 3 a illustrates the adsorption isotherms for polymer chains in a good solvent as a function of concentration. The surface excess... 

Dilute polymer chains in a good solvent aie swollen the size Rp increases as iV rather than N. When we squeeze the chains together and reach a concentrated solution or a melt, we might expect the situation to become even more complicated because the interactions between monomers ate much stronger. Actually the correct conclusion is different. In a dense system of chains each chain is gaussian and ideal. This was first understood by Floty, but the notion is so unexpected that it took a long time to reach the community of polymer scientists. Here we give two presentations of this Hory theorem and discuss fine correlation effects between chains in the melt. 

Up to this point, we have treated in parallel the hydrodynamic properties of good and 0 solvents, the only difference being the fractal dimension of the polymer in each type of solvent. However, while the scaling dynamic theory is well supported for polymer chains in a good solvent, this is not the case for a 0 solvent, where, quite surprisingly, dynamical problems look more difficult to understand. 

Polymers are often used to stabilize dispersion and prevent particles from aggregation. This is due to steric repulsion. In this section, we discuss the force between surfaces coated with grafted polymer chains in a good solvent. 

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