Semidilute region

In the semidilute region, the repulsion between adsorbed chains is dominated by the osmotic term. Hence, the chemical potential fx is represented by... 

Note that this is completely consistent with our RG result (8.57). The crossover from the dilute to the semidilute region takes place at a concentration c = c (n, t), where the chains just fill the volume ... 

Furthermore Eq. (13.27 iii) shows that either w is very small (semidilute region) or q2 —> g2. Keeping s,z fixed we find from Eq. (13.27 i) that w cannot vanish. Thus the limit q2 — oc implies q2 — g2. 

From the surface pressure - area isotherms of these polymers, the surface parameters could be calculated. The areas per monomer unit projected to zero surface -pressure, obtained from the linear variation of -it with the surface concentration (A0) in semidilute region [39] for the polymers, are summarized in Table 3.3. 

Leiva et al. [65] have reported for poly(itaconates) monolayers the surface behavior at the air - water interface at different surface concentrations. They have found that for these type of polymers, the air - water interface at 298 K, is a bad solvent, very close to the theta solvent. At the semidilute region concentration, the surface pressure variation was expressed in terms of the scaling laws as a power function of the surface concentration. According to equation (3.3), the log it vs log T plot shows a linear variation with slope 2 v/(2 u-1). 

When rigid rods become concentrated, and enter the semidilute region discussed... 

The most interesting result of Refs. [58, 59] concerns the crossover regime between dilute and semidilute regions of polymer 0-solution. The author shows that in this crossover regime there exists the critical concentration c corresponding to the appearance of an infinite cluster of entangled with each other macromolecules. It is also shown that near this critical concentration the relative viscosity t r of the 0-solution has a scaling form ... 

This chapter will focus on infinitely-extended suspensions in which potential complications introduced by the presence of walls are avoided. The only wall-effect case that can be treated with relative ease is the interaction of a sphere with a plane wall (Goldman et ai, 1967a,b). The presence of walls can lead to relevant suspension rheological effects (Tozeren and Skalak, 1977 Brunn, 1981), which result from the existence of particle depeletion boundary layers (Cox and Brenner, 1971) in the proximity of the walls arising from the finite size of the suspended spheres. Going beyond the dilute and semidilute regions considered by the authors just mentioned is the ad hoc percolation approach, in which an infinite cluster—assumed to occur above some threshold particle concentration—necessarily interacts with the walls (cf. Section VI). 

Noda, I. Higo, Y. Ueno, N. Fujimoto, T., "Semidilute Region for Linear Polymers in Good Solvents," Macromolecules, 17, 1055 (1984). 

Interpretation of rheological results The trends in the variation of Xg with are similar to those obtained recently (3) using a model polystyrene latex dispersion. The 1 values obtained in the present system are also close to tSose obtained with the model dispersion(0.017, 0.008 and 0.005 for PEO 20,000, 35,000 and 90,000 respectively). As mentioned before the sharp increase in x above + indicates that at the onset of flocculation the dispersions show marked viscoelasticity. The flocculation obtained at corresponds to the onset of the "semidilute" region, p, i.e., where the polymer coils in solution begin to arremge themselves in some... 

In the semidilute region, the coils contract (Figure 4-4), but the shrinking does not continue indefinitely and the polymer chain reaches a minimum (0) dimensions at a concentration that is independent of molecular weight. 

At the highest polymer concentration studies (0.6%), however, this mechanism cannot apply because stable emulsion can be reproducibly prepared at higher pH values with 0.4% polymer. A possible explanation for the instability at the highest concentrations may be that these concentrations lie in the semidilute region, where the polymer coils just touch (23). Vincent (24) has shown that in this concentration range, dimensional collapse of the polymer chains occurs, and stabilization is lost. 

In the semidilute region, with the polymer chains interpenetrated, the segment concentration has the form... 

The essence of this theory can be grasped from Fig. 15.4. In the semidilute region, the free polymer molecules can be assumed to overlap the polymer in the steric layers. However, these unattached interpenetrated chains are displaced into the bulk phase on the close approach of two sterically stabilized particles. The free energy change that accompanies this displacement is simply... 

In semidilute regions, 57 °r is given by the following scaling law by assuming that in entangled systems [2-5]. 

Thus, JcR is expressed as a universal function of CM. Moreover, it was reported that the cross-over concentration from dilute to entangled regions for J is about 5 times higher than that from dilute to semidilute regions for 7 at the constant molecular weight[5]. 

As reported previously[13], the form anisotropy in flow birefringence is negligible in semidilute regions for thermodynamic properties so that we evaluated J in 0. OIM NaCl aqueous solutions at two polymer concentrations from the data of flow birefringence by using the following relationships[14],... 

Figure 1. Polymer concentration dependences of 7 sp in the absence and presence of added-salt. The triangles, squares and circles denote the data for MVPK-11, MVPK-12 and MVPK-13, respectively. The upward, rightward and downward pips indicate the data in 0.01, 0.1 and 0.5M NaCl solutions, respectively. The symbols without pip denote the data in the absence of added-salt. The dotted and solid lines were drawn to connect smoothly the data in dilute and semidilute regions, respectively. (Reproduced from ref. 10).

Introducing eqs 6 and 9 into eq 10, we have the empirical formulas for Tw in the semidilute region for 7° entangled region for Jc. ... 

According to the reptation model, t and G in semidilute regions can be given by[1,18]... 

---