Microphase separation transition of weakly charged copolymers in solution

Abstract

The microphase separation transition for neutral and weakly charged diblock copolymers in solution is investigated. The critical parameter for microphase transition is calculated as a function of the numbers of charges and the polymer and the salt concentrations. It is found that xm increases substantially either when one block is charged and the other neutral or when both blocks carry charges of opposite signs. Cases of symmetric and nonsymmetric diblocks are considered.

Microphase separation in polyelectrolytic diblock copolymer melt: Weak segregation limit

“…Science behind the complex behavior of amphiphilic systems continues to be of interest to scientific community. A great deal of theoretical 1,2,3,4,5,6,7,8 and experimental efforts 9,10,11,12,13,14 have been made to study this behavior. Especially, self-assembly of amphiphiles 11 is of significant importance in understanding many biological systems.…”

“…A number of researchers have tried to explore charged diblock systems. Some of these efforts are invested in studying dilute solutions (micelle regime) 20, 23 and others have been carried out in the concentrated regime 3,4,5,24,25 . The fundamental question is how Coulomb interactions affect the relative stabilities of ordered morphologies.…”

Self-Consistent Field Theory of Polyelectrolyte Systems

“…This could change and even generate new ordered morphologies. Theoretical study of microphase separation of block polyelectrolytes, however, has been limited to the random phase approximation (RPA) analysis on diblocks having the smeared charge distribution. − In these studies, the structure matrix of the homogeneous phase was constructed from the expansion of its free energy in terms of density fluctuations to the second order; the ODT temperature and the corresponding period of the microphase were then obtained by solving the generalized spinodal equations. − The ordered structures below the ODT, however, have not been studied theoretically. For such systems, the ground state dominance approximation is clearly not valid.…”

Microphase Separation and Phase Diagram of Concentrated Diblock Copolyelectrolyte Solutions Studied by Self-Consistent Field Theory Calculations in Two-Dimensional Space

“…It is worth noting that the spinodal line in this article is obtained by conducting a stability limit analysis on the partial structure factor, S AA (q) = AEδϕ A (q)δϕ A (Àq)ae in Fourier space, which characterizes the spatial correlation of the concentration fluctuations of A blocks. The partial structure factor S AA (q) has the form 21…”

“…It is worth noting that the spinodal line in this article is obtained by conducting a stability limit analysis on the partial structure factor, S AA ( q ) = ⟨δϕ A ( q )δϕ A (− q )⟩ in Fourier space, which characterizes the spatial correlation of the concentration fluctuations of A blocks. The partial structure factor S AA ( q ) has the form N S AA − 1 false( q false) = N S neutral − 1 false( q false) + false( normalα normalA N false) 2 normalε x + false( normalα normalA N false) f normalϕ̅ normalC where x = q 2 R g 2 . The first term in the right-hand side of the above equation contains the contributions of all interactions except the electrostatic interaction, which is identical to the corresponding partial structure factor of the neutral diblock copolymer solution.…”