Athermal solvent condition

The simultaneous agreement of exponents in Eqs. (12) and (14) characterizes the crossover condition. Then it is derived that the validity of Eq. (14) corresponds to N(j>>f 3 . This means that for an athermal solvent, where 3=1, the intermediate region governed by Eq. (12) disappears, while for a theta solvent Eq. (14) is not applicable. 

However, the surface coverage is the same for both copolymers when weakly adsorbed to the surface. Surface density profiles were also compared. Finally, scaling relationships for triblock copolymer adsorption under weak adsorption conditions were derived (Haliloglu et al. 1997). In a related paper (Nguyen-Misra et al. 1996), adsorption and bridging of triblock copolymers in an athermal solvent and confined between two parallel flat surfaces were studied, and the dynamic response of the system to sinusoidal and step shear was examined. 

Table 9.1 shows that the number of Kuhn monomers in an entanglement strand in the melt state varies over a wide range (7 < A e(l) < 80) making 4 < 0e/0 < 30 for solutions in an athermal solvent. Since the entanglement concentration

overlap concentration (p, the expressions for a -solvent [Eqs (9.31), (9.33), and (9.34)] are valid for [A e(l)] - This condition is not very restrictive and it is satisfied for all experimental studies to date. 

According to the blob model, a flexible neutral star polymer can be envisioned as an array of concentric shells of closely packed blobs. For a visualization of the blobs, see Fig. la. The chain ends are assumed to be localized at the edge (i.e., within the outermost blobs), and each chain contributes one blob to each shell. The chain segment inside a blob remains unperturbed by the interactions with other branches and, therefore, exhibits Gaussian or excluded-volume statistics under theta- or good solvent conditions, respectively. For transparency, we consider first athermal, u = a, and theta-solvent, i = 0, conditions. The blob size at distance r from the star center is equal to the average interchain separation = which... 

In dilute solutions, the single polymer coil expands in the athermal solvent. In a good solvent, the coil will expand more significantly. In contrast, in a poor solvent, the chain units and the solvent undergo a phase separatiOTi under a proper thermodynamic condition. Consequently, the single chain will collapse drastically into a condensed sphere. Therefore, the internal concentration reaches... 

Simulations of chains grafted to interfaces in vacuum and in liquid solvents have been reviewed[73]. The repulsive force of interaction between surfaces coated with grafted athermal chains (good solvent conditions) has been calculated with lattice MC[74] and continuum molecular dynamics[75] methods. The first simulations of interfaces in supercritical fluids considered the adsorption of pure solvent (no chains) in a flat-wall pore[76]. Near the solvent critical temperature (7 ) a maximum in adsorbed amount was observed at densities slightly below the solvent critical density (pc) The maximum in adsorbed amount was attributed to local density enhancement of solvent in the pore. 

The basic theory of star polymer fluids developed by Grayce and Schweizer is general in its ability to treat polymer models of variable chemical detail. For simplicity, we discuss the theory in the context of the tangent, semiflexible chain model. As true for most of the results discussed in Section VIII, the bare bending energy is set equal to zero, and pure hard-core interactions (athermal or good solvent conditions) are employed in numerical studies carried out so far. 

The possibility of entropy-driven phase separation in purely hard-core fluids has been of considerable recent interest experimentally, theoretically, and via computer simulations. Systems studied include binary mixtures of spheres (or colloids) of different diameters, mixtures of large colloidal spheres and flexible polymers, mixtures of colloidal spheres and rods," and a polymer/small molecule solvent mixture under infinite dilution conditions (here an athermal conformational coil-to-globule transition can occur)." For the latter three problems, PRISM theory could be applied, but to the best of our knowledge has not. The first problem is an old one solved analytically using PY integral equation theory by Lebowitz and Rowlinson." No liquid-liquid phase separation... 

Sedimentation experiments on semi-dilute solutions are appropriate and many experiments have been performed on neutral polymers like polystyrene and poly(a-methylsty-rene) in good solvents It has been found that the effective exponent Xj increases from 0.59 up to 0.8 as the concentration rises from 0.1 to 10%. Good solvents used in these experiments (benzene, bromobenzene and toluene) are far from athermal conditions (x — 0.45). Two monomers, belonging to a subchain of size and separated by n monomers, experience excluded volume effects when n > n, where iic oc (1 - 2x). As the concentration decreases, the number of monomer per subchain g, increases and excluded volume effects become more and more important. The effective exponent Xs, which is a combination of effective dynamic and static exponents tends monoti-cally to the asymptotic value 0.5 (g > He). Inversely, if the concentration increases, g decreases when g < He, the subchain exhibits purely Gaussian behaviour, and v = 0.5 which leads to oc and Sd °o This cross-over between excluded volume and Gaussian behaviour qualitatively explains the increase of Xj, if p increases. Detaib on the dependence of x, on the concentration can be found in Ref. 110. Whatever the exact value of the exponent, these experiments show that the frictional properties of semi-dilute solutions depend only on the concentration they are independent of the molecular weight of the polymer used 1. 

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