A variational approach to necklaces formation in polyelectrolytes

By means of a variational approach we study the conditions under which a polyelectrolyte in a bad solvent will undergo a transition from a rod-like structure to a ``necklace'' structure in which the chain collapses into a series of globules joined by stretched chain segments.Comment: 6 pages, 4 figures (unfortunately big). Requires revtex, eps

Collapse of Flexible Polyelectrolytes in Multivalent Salt Solutions

The collapse of flexible polyelectrolytes in a solution of multivalent counterions is studied by means of a two state model. The states correspond to rod-like and spherically collapsed conformations respectively. We focus on the very dilute monomer concentration regime where the collapse transition is found to occur when the charge of the multivalent salt is comparable (but smaller) to that of the monomers. The main contribution to the free energy of the collapsed conformation is linear in the number of monomers $N$, since the internal state of the collapsed polymer approaches that of an amorphous ionic solid. The free energy of the rod-like state grows as $N\ln N$, due to the electrostatic energy associated with that shape. We show that practically all multivalent counterions added to the system are condensed into the polymer chain, even before the collapse.Comment: LaTeX-revtex, psfig file, 4 figure

Dismantling the Dichotomy: Latinx Identity and Assimilation in Early Childhood Education

An increasing number of children in early childhood education (ECE) are Latinx. Drawing on ethnic identity, culture, and language, this thesis describes the dichotomy between adherences to one’s ethnic identity and assimilation into the dominant societal culture. This paper describes how assimilation harms students and provokes negative implications such as identity loss, confusion, and loss of cultural ties. Dismantling the dichotomy is possible through the power of language, culture, and strengthening teacher-parent relationships

Surface-induced layer formation in polyelectrolytes

We analyze, by means of an RPA calculation, the conditions under which a mixture of oppositely charged polyelectrolytes can micro-segregate in the neighborhood of a charged surface creating a layered structure. A number of stable layers can be formed if the surface is sufficiently strongly charged even at temperatures at which the bulk of the mixture is homogeneous.Comment: 6 pages, 3 figures, revtex, epsf, psfi