Annealed Star-Branched Polyelectrolytes in Solution

Abstract

Equilibrium conformations of annealed star-branched polyelectrolytes (polyacids) are calculated with a numerical self-consistent-field (SCF) model. From the calculations we obtain also the size and charge of annealed polyelectrolyte stars as a function of the number of arms, pH, and the ionic strength. The results are compared with predictions from analytical theory. Upon varying the number of branches or the ionic strength of the solution, the star size changes nonmonotonically, which is in agreement with the analytical predictions. The salt concentration at this maximum is directly related to the charge density of the star. The internal structural properties of the star corona (the polymer density, the ionization profiles, and the distribution of the end points) are analyzed. The shape of the density profiles indicates increasing local stretching of the branches as a function of the distance from the star center. Furthermore, a bimodal end-point distribution is found and interpreted in analogy to that predicted earlier by analytical SCF theory for planar polyelectrolyte brushes. Results of recent experiments with annealed star-shaped micelles are discussed on the basis of our numerical model calculations.

Non-monotonic swelling of surface grafted hydrogels induced by pH and/or salt concentration

“…34 Interestingly, the magnitude of the observed thickness and non-monotonicity are similar to those calculated here for the thin film gel. Swellingdeswelling behavior has been theoretically predicted for starbranched weak polyelectrolytes 40 and weak polyelectrolyte microgels. 41 Reentrant behavior in terms of the solvent composition has been reported for a variety of other polymeric systems, including the condensation/precipitation and subsequent redissolution of globular proteins, 48,49 DNA, [50][51][52] and other strong polyelectrolytes [53][54][55] upon varying the concentration of multivalent ions in the solution.…”

“…35 Similarly, the radius of starbranched weak polyelectrolytes was calculated to have a maximum as a function of the ionic strength by a self-consistentfield model. 40 Recently, a reentrant swelling-to-collapse transition was theoretically predicted for micrometer-sized (or larger) weak polyelectrolyte gels in good solvent, assuming local electroneutrality. 41 The authors explain that initially, increasing c promotes dissociation until f d saturates once it reaches the value of the dilute solution.…”

Synthesis, Characterization and Behavior in Aqueous Solution of Star‐Shaped Poly(acrylic acid)

“…This is in qualitative agreement with theory. [24] It is due to the higher osmotic pressure inside the stars, caused by counterion confinement (see next section). This leads to a partial reversal of the acid-base reaction, that is to say, the formation of uncharged -COOH groups within the polyelectrolyte star.…”

“…[18][19][20][21] Intermediate effects on counterion condensation are expected for star-shaped polyelectrolytes, as predicted by previous work. [22] Scaling theory, together with self-consistent field calculations of polyelectrolyte stars, were given by Klein Wolterink et al [23,24] and Borisov and Zhulina. [25,26] Ordered, crystalline phases are expected at higher concentrations and arm numbers.…”

Micellar and fractal aggregates formed by two triblock terpolymers with different arrangements of one charged, one neutral hydrophilic and one hydrophobic block

“…In the mixed brush, this is anticipated to be an effective scaling exponent since it describes both charged and neutral blocks. Additionally a possible collapsing of monomers or parts of SCPI blocks on the PS-core could produce loops of SCPI segments that would decrease the exponent from the polyelectrolyte brush scaling; where 2 is the expected value [30]. The high values of the volume fraction of 0, (table 1) supports this explanation.…”