Coronal blocks

The interest in these block copolymer micelles arises from the polyelectrolyte coronal block whose intrinsic properties are strongly influenced by many parameters including pH, salt concentration, and polar interactions. Moreover, they provide a unique model to mimic polyelectrolyte brushes at a high segment concentration, as noted by Forster [15]. 

In what follows, we will discriminate between two types of ABC triblock micelles (1) those in which two blocks are insoluble in the considered solvent and then contain a compartmentalized core and a homogenous corona (2) those in which only one block is insoluble and whose corona is heterogeneous due to the presence of two types of coronal blocks. 

Fig. 21 Formation of Janus micelles from PS-PB-PMMA copolymers. The copolymers are transformed into PS-PB-PMAA copolymers after hydrolysis of PMMA block. PS coronal blocks collapse in water and supermicelles are formed. A typical SEM picture of supermicelles is shown. Reprinted with permission from [55]. Copyright (2003) American Chemical Society... 

Fig. 22 Formation of vesicles with distinct inner (PB) and outer (PS) coronal blocks from a mixture of PS-P4VPQ and PB-PMACs copolymers. Vesicles are stained with Csl in the TEM pictures. TEM picture B is a magnification of the framed area in A. Reprinted with permission from [311]. Copyright (2003) American Chemical Society... 

Clearly, this model predicts a strong dependence of f B and p on the size of the coronal block 7VA, in contrast to the earlier theoretical work (de Gennes 1978 Leibler et al. 1983 Noolandi and Hong 1983). By combining numerical results for the systems PS-PB/heptane, PS-PI/heptane, PPO-PEO/water and two model systems, Nagarajan and Ganesh obtained universal scaling relations ... 

Here yBS is the core-solvent interfacial tension and AS is the coronal block-solvent interaction parameter. 

Fig. 3.22 Schematic illustration of a surface micelle with swollen A coronal blocks attached to a core formed by B blocks.

Due to the strong hydrophobicity of the blocks B, the interface between the collapsed hydrophobic domain and the surrounding aqueous environment is narrow compared to the size of the core. Therefore, the coronal blocks A can be envisioned as tethered to the interface to form a polymer brush [33, 39, 40]. The hydration of the corona and the repulsion between different coronae ensure the solubility (aggregative stability) of the micelles in water. 

For uncharged coronal blocks A, the short-ranged (van der Waals) interactions between monomer units are described in terms of a virial expansion. The latter accounts for the monomer-monomer binary (pair) interactions, with second virial coefficient VaO, or the ternary interactions with third virial coefficient waa . We assume that the monomer unit length, a, is the same for both blocks A and B. In the following, we use a as a unit length to make all lengths dimensionless and eliminate a in further equations. We also assume that the (dimensionless) second virial coefficient Va > 0 and that the third virial coefficient Wa 1. 

Here, the second virial coefficient (excluded-volume parameter), vb = [1 -2x T)]<0, is negative because water is a poor solvent for the hydrophobic block B. The third virial coefficient, Wb, is positive, and x= T- e /d is the relative deviation from the theta temperature. At small deviations from the theta point, r < 1, the surface tension y and the polymer volume fraction (p are related as y/k T = (p. However, at larger deviations from the theta point, (p becomes comparable to unity and the latter relationship breaks down. Because in a typical experimental situation (p = 1, we treat (p and y as two independent parameters. Note that in a general case, surface tension y and width A of the core-corona interface depend on both the polymer-solvent interaction parameter Xbs T) for the core-forming block and the incompatibility Xab between monomers of blocks A and B. That is, y could depend on the concentration of monomers of the coronal block A near the core surface. We, however, neglect this (weak) dependence and assume that the surface tension y is not affected by conformations of the coronal blocks in a micelle. 

Here, the term Fcorona includes contributions due to the conformational entropy of the coronal blocks and the (repulsive) interactions in the coronal domain. The term Finterfece is the excess free energy of the core-water interface. It is proportional to the interfacial area, x, per copolymer molecule ... 

An important feature of (27), (29) is the absence of a power law dependence of the aggregation number peq and / core on the length Na of the coronal block. Micelles are starlike, i.e., / corona > Rcore, provided that ... 

In the case of crew-cut micelles, //corona < Rcok and the logarithm in (22) can be expanded up to the term linear in //corona// core, to give / corona/ B — Z/corona/i / = //corona/. The thickneSS Of the corona, //corona, scales as //corona = In the framework of the Alexander-de Gennes blob model [51, 52], the micellar corona (the planar brush) can be envisioned as an array of closely packed blobs with size = 5 /, equal to the average distance between the coronal blocks. We note that a constant size of the blobs implies //corona Na. The number of coronal blobs per chain //corona/ is proportional to the free energy of the interchain repulsion that equals fcorona/kBT = ... 

Interestingly, this area is independent of the length of core-forming block B. In contrast to the case of starlike micelles, the equilibrium aggregation number and the core radius in a crew-cut micelle strongly decrease upon an increase in the degree of polymerization of the coronal block, Na- The thickness of the corona is given by ... 

Similarly to the case of starlike micelles, the CMC is controlled by the gain in free energy upon association of blocks B and is only weakly affected by the properties of coronal block A ... 

The structure and the basic thermodynamics of micelles formed by amphiphilic block copolymers with a PE coronal block A can be analyzed using the blob model. However, the ionization of block A in a polymeric amphiphile introduces long-ranged repulsive interactions in the corona of a micelle. As a result, the blob picture for the micellar corona has to be modified, as explained in this section. 

Long-ranged repulsive Coulomb interactions between the coronal blocks A dominate over short-ranged excluded-volume monomer-monomer repulsions, provided that the fraction of charged monomer units is sufficiently large. The block copolymer solution also contains mobile counterions that spread fairly uniformly over the volume of the solution if the aggregation number p is small, p < Here,... 

The mean-field approach provides a convenient framework for the analysis of copolymer self-assembly leading to micellar structures. Combining the mean-field approach with the local electroneutrality approximation (LEA) enables us to generalize the theory for micelles with ionic coronal blocks that feature stimuli-responsive properties. 

In this equation, the first and the second terms describe the respective conformational entropies of stretched core and coronal blocks, whereas the third term, 7 ( core), accounts for excess interfacial free energy [here, s Rcore) is specified by (38)]. The last term in (69) accounts for repulsive interactions in the corona. 

For the crew-cut quasi-neutral micelles with //corona < Rears, that are formed by strongly asymmetric copolymers with short coronal blocks, Na < one finds ... 

Here, the average degree of ionization a of the coronal block A depends not only on the pH (via a ), but also on the ionic strength in the bulk solution (buffer), and the average polymer concentration in the corona, Cp, as ... 

Equation (97) can be used to obtain approximate expressions for the degree of ionization of the monomer units of the coronal block A in the limiting cases of low and high salt concentrations ... 

The coupling between the ionization of the coronal block A and the association equilibrium of the copolymers gives rise to unique features for the self-assembly of amphiphilic block copolymers with a weak (pH-sensitive) PE block. In other words, the levels of ionization for unimers in solution and for copolymers incorporated in micelles, can be noticeably different due to different values of the pH inside micellar corona and in the bulk solution. Furthermore, the strength of the electrostatic repulsion in the corona can be affected not only by variations in the ionic strength (as it is for micelles with quenched PE corona), but also by variations in the pH, which affect the ionization of the coronal chains. 

The block copolymer chains with a strongly asymmetric composition, Na > form starlike micelles at an arbitrary small degree of ionization of the coronal block. The free energy per chain in a starlike micelle with an annealing PE coronal block is given by ... 

An increase in the salt concentration leads to the progressive replacement of ions in the micellar corona by, e.g., ions of the added salt (i.e., increases the local pH in the corona). This promotes the increase in the degree of ionization a of the coronal blocks as ... 

Figure 6 shows the evolution of both the aggregation number and the radius of the corona for starlike miceiies upon variations in the salt concentration (6a, b) and in the pH (6c,d). All the structural properties of starlike micelles with pH-sensitive coronal blocks exhibit a non-monotonous and discontinuous variation as a function of Sion the aggregation number exhibits a minimum (with a jump down at Oion O ), whereas the coronal dimensions exhibit a weak maximum (with a jump up at Oion O ). 

Fig. 6 Dependency of (a) aggregation number p (b) radius of the corona /Jcorona for starlike micelles with annealing coronal block as a function of salt concentration. The pH is fixed according to the position of the dotted arrow in Fig. 5. Dependency of (c) p and (d) /Jcorona as a function of pH...

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