Polyelectrolytes: Theory, Properties and Applications

Structural Properties and Phase Behavior ... 3

From the amphiphilic character of DCPs, the association of hydrophilic
and hydrophobic interactions, neutral and charged species result a variety of
smart materials with aimed functionalities opening new prospects for
applications in modern nanotechnologies [1, 2]. Forcing the two blocks to
belong to the same entity in spite of their incompatibility generates self
assemblies with a myriad of ordered nano structured morphologies [3, 4].
Progress in understanding the phase behavior of DCPs was boosted by
advances made in the chemical synthesis and the techniques of
characterization. DCPs with well defined molecular weight and narrow
polydispersity involving a variety of monomer species are now available with
routine processes and equipments. These advances facilitated systematic
investigations to determine precisely the effects of parameters influencing the
formation of self assemblies, the emergence of new functionalities and
improved performances under practical conditions of applications. Pure DCPs
have been studied in details by many authors combining theoretical models [5,
6], simulation methods [7, 8] and experimental techniques [9, 10]. The phase
diagram is completely known and validated by experiment and theory [11-14].
The case of pure DCPs is rather simple with essentially two parameters
determining the phase behavior and morphology. One is the product abN
where ab is the FloryHuggins [15] interaction parameter between A and B
monomers, N the total degree of polymerization, and the other parameter is x,
the fraction of A monomers per chain, i.e., x = Na/N. Here, we are referring to
a diblock A-B where Na is the number of A monomers per chain and Nb = N –
Na the number of B monomers per chain. In the weak segregation limit, below
the order/disorder transition, abN < 10 and DCPs are randomly dispersed.
Their behavior can be reasonably formulated within mean field theories such
as the random phase approximation (RPA) [16-18]. For very high values of
abN, (say, above 100), the system shows strong segregation properties
exhibiting ordered structures and other approaches are necessary [6, 19]. The
region of abN between these two limits presents intermediate situations where
mean field theories may still be able of predicting some reasonable trends. For
DCPs in solution, the understanding is not yet complete and studies are still
being performed to elucidate some phenomena that are not sufficiently
explored like in the case of neutral/charged DCPs with amphiphilic character
and a large number of impacting parameters. In addition to the nature and
architecture of the chain itself, one needs to account for polyelectrolyte effects
involving the degree of ionization and the ionic strength [18, 20, 21].
This chapter is a contribution along these lines and is organized as
follows. In section 2, the general RPA formalism for dispersed partially