T. M. Birshtein

Temperature-concentration diagram for a solution of star-branched macromolecules

Abstract The temperature-concentration diagram of a star-branched macromolecule solution was constructed using scaling concepts. The quality of the solvent, solution concentration, the rigidity of star branches, their number and degree of polymerization were taken into account. The diagram obtained contains three regime types: I x -isolated stars in a dilute solution; II x -a semidilute solution of star branches (subscript characterizes the volume interactions); and III-the close packed system of impermeable (or almost impermeable) stars. Quasiglobular regime III is characterized by the universal dependence of star size on the concentration of the solution c and degree of polymerization N: R ∼ ( N c ) 1 3 independently of the quality of the solvent.

Collapse of a weak polyelectrolyte star in a poor solvent

We present a theory of intramolecular collapse transition in a weak (pH sensitive) polyelectrolyte (PE) star induced by a decrease in the solvent strength and/or variation in the ionic strength in the solution. Our system mimics conformational coil-to-globule transitions in individual star-shaped thermo- and pH-sensitive (e.g. poly(dimethylaminoethyl methacrylate)) macromolecules in dilute aqueous solutions. Systematic comparison with the behaviour of non-ionic and strong (quenched) polyelectrolyte stars in poor solvents enables us to unravel specific features of the collapse transition in weak polyelectrolyte stars. We demonstrate that, depending on temperature and the ionic strength of the solution, a vast diversity of different scenarios for the salt- or temperature-induced collapse transitions may take place. Both at high or low ionic strength a collapse transition induced by a decrease in the solvent strength occurs continuously resembling the collapse of a neutral polymer star. On the contrary, at intermediate salt concentrations the collapse of a weak polyelectrolyte star may feature a first order phase transition, which involves the co-existence of a collapsed, weakly ionized state with a swollen, strongly ionized state. At a fixed temperature the collapse transition can be triggered by an increase in salt concentration. In the latter case the transition may occur via a sequence of two co-existence regimes separated by continuous though non-monotonous variation in the star dimensions as a function of salt concentration.

Bending moduli of dendritic polymer brushes in a good solvent

The effect of branching on the Helfrich mean k C and Gaussian k G bending moduli of polymer brushes consisting of dendrons grafted to both sides of a thin impermeable surface (membrane) is studied theoretically. The case of an athermal solvent is considered. The moduli are calculated from a change in the free energy of a brush upon cylindrical and spherical bending of the grafting surface, respectively. The grafting density σ, the total number of monomer units N, and the number of generations g in tethered dendrons are varied. Two variants of the self-consistent field method are applied: the analytical approach and the numerical Scheutjens-Fleer method. The first method is applied at small values of σ, when the density profile of monomer units of grafted chains is parabolic in shape. The second method is free of these restrictions. The universal ratio between moduli is found: k G =−64/105k C . Both methods predict that the values of moduli decrease with increasing g at constant N and σ. The scaling dependence N 3 remains valid for the moduli of dendritic brushes with different generation numbers g at all of the considered values of σ. The analytical approach also gives the universal scaling dependence k C ∼ k G ∼ σ7/3; however, the numerical method predicts that the dependences of moduli on σ become stronger with increasing degree of branching of tethered dendrons.