Micelle block model

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

Fromherz P 1980 Micelle structure a surfactant block model Chem. Rhys. Lett. 77 460... 

Mean-Field Theory of Block Copolymer Micelles Boxlike Model. 81... 

Uhlik F, Limpouchova Z, Matejicek P, Prochazka K, Tuzar Z, Webber SE (2002) Nonradiative excitation energy transfer in hydrophobically modified amphiphilic block copolymer micelles theoretical model and Monte Carlo simulations. Macromolecules 35 (25) 9497-9505. doi 10.1021/ma012073o... 

The standard picture of ionic micelles forms a common starting point for three recent attempts at modelling the state of the chains in amphiphilic aggregates Dill and Flory s lattice model [15, 16], Fromherz surfactant-block model [18] and a model devised by the present author [19-21]. For each of these models, it is necessary to make further assumptions which are not part of the standard picture. These further assumptions are necessary in order to render the models soluble. 

The water solubiUty of PLA-PEG and PLGA-PEG copolymers depends on the molecular weight of the hydrophobic (PLGA-PEG) and hydrophilic (PEG) blocks. Water soluble PLA-PEG copolymers with relatively low molecular weight PLA blocks self-disperse in water to form block copolymer micelles. For example, water soluble PLA-PEG 2 5 (M of PLA 2000 Da and M of PEG is 5000 Dalton) form spherical micelles 25 run in diameter. These micelles solubilize model and anticancer drugs by micellar incorporation. However, in vivo, the systemic lifetimes produced were relatively short and the clearance rate was signihcantly faster when the micelles are administered at low concentration. This suggests micellar dissociation at concentrations below the cmc. 

The diffusion coefficients of this system were determined for disordered micelles and bcc spheres [47]. They were found to be retarded as compared to the disordered state. This retardation is consistent with a hindered diffusion process, D Do exp(- AxN ), with D0 being the diffusion coefficient in the absence of any interactions (i.e. for y -> 0), and A is a prefactor of order unity. Hence, the diffusion barrier increases with the enthalpic penalty xNa, where N represents the number of monomers in the foreign block. In the simplest description of hindered diffusion, the prefactor A remains constant. This model describes the experimental data poorly as A was found to increase with xNa [47]. 

As the final products—polystyrene-h-polyivinylperfluorooctanoic ester)— form micelles in tetrahydrofuran (THF) as well as in DMF, there are not direct GPC data to characterize molecular parameter. For this reason, we employed esterification of the hydroxylated block copolymers with benzoylchloride as a model reaction to obtain a comparable product with molecular solubility that can easily be characterized by DMF-GPC. The GPC data from PSB-II—our largest and therefore most sensitive block copolymer—are summarized in Table 10.2. Results for all the other polymers are similar. 

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]. 

Prochazka K, Limpouchova Z, Webber SE (1996) Block copolymer micelles 2. Flu-orimetric studies and computer modeling. In Salamone JC (ed) Polymer materials encyclopedia, vol 1. CRC Press, Boca Raton, FL... 

Zhao JQ, Pearce EM, Kwei TK, Jeon HS, Kesani PK, Balsam NP. Micelles formed by a model hydrogen-bonding block copolymer. Macromolecules 1995 28 1972-1978. 

In this chapter, the focus is largely on experimental and theoretical studies of micellization in a range of solutions of model block copolymers prepared by anionic polymerization. A discussion of both neutral and ionic block copolymers is included, and features specific to the latter type are detailed. The adsorption of block copolymers at the liquid interface is also considered in this chapter. Recent experiments on copolymer monolayers absorbed at liquid-air and liquid-liquid interfaces are summarized, and recent observations of surface micelles outlined. Thus this chapter is concerned both with bulk micellization and the surface properties of dilute copolymer solutions. 

This chapter is organized as follows. The thermodynamics of the critical micelle concentration are considered in Section 3.2. Section 3.3 is concerned with a summary of experiments characterizing micellization in block copolymers, and tables are used to provide a summary of some of the studies from the vast literature. Theories for dilute block copolymer solutions are described in Section 3.4, including both scaling models and mean field theories. Computer simulations of block copolymer micelles are discussed in Section 3.5. Micellization of ionic block copolymers is described in Section 3.6. Several methods for the study of dynamics in block copolymer solutions are sketched in Section 3.7. Finally, Section 3.8 is concerned with adsorption of block copolymers at the liquid interface. 

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

A self-consistent field theory (SCFT) for micelle formation of block copolymers in selective solvents was developed by Yuan el at. (1992). They emphasized the importance of treating the isolated chain at the same level of theoretical approximation at the micelle, in contrast to earlier approaches. This was achieved by modifying the Edwards diffusion equation for the excluded volume of polymers in solution to the case of block copolymers, with one block in a poor solvent. The results of the continuum model were compared to experimental results for PS-PI diblocks in hexadecane, which is a selective solvent for PI and satisfactory agreement was obtained. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

The adsorption of block copolymers from a selective solvent was considered by Ligoure (1991). He predicted the existence of surface micelles (see Fig. 3.22) in the case when the block interacting unfavourably with the solvent only partially wets the surface. The model predicts a critical surface micellar concentration (csmc) that differs from the bulk cmc. When the contact angle, which characterizes the interfacial interactions between the copolymer, adsorbing surface, and solvent is lower than some universal value, surface micelles were predicted to appear at a lower copolymer concentration than bulk ones. Experimental results on surfaces are discussed in Section 3.8.4. 

Xu et al. (1992) used light scattering to characterize micelles formed by a wide range of PS-PEO di- and tri-block copolymers in dilute solution in water. Although full analysis of the data was complicated by the tendency of the micelles to undergo secondary association, they did find that the micellar radius scaled as eqn 3.14, in agreement with the predictions of Halperin (1987). With values of p and RB from the star-like micelle model, Xu et al. (1992) were able to compute % parameters for the interactions of PEiO with water and with PS, in... 

Computer simulations of a range of properties of block copolymer micelles have been performed by Mattice and co-workers.These simulations have been based on bead models for copolymer chains on a cubic lattice. Types of allowed moves for bead chains are illustrated in Fig. 3.27. The formation of micelles by diblock copolymers under weak segregation conditions was simulated with pairwise interactions between A and B beads and between the A bead and vacant sites occupied by solvent, S (Wang et al. 19936). This leads to the formation of micelles with a B core. The cmc was found to depend strongly on fVB and % = x.w = %AS. In the range 3 < (xlz)N < 6, where z is the lattice constant, the cmc was found to be exponentially dependent onIt was found than in the micelles the insoluble block is slightly collapsed, and that the soluble block becomes stretched as Na increases, with [Pg.178]

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