## 3 Amphiphilic Miktoarm Star Polymers: Self-Assembly
### Micelle Characteristics: CMC and Stability  
There are several methodologies that have been employed for studying aqueous self-assembly of amphiphilic polymers, including co-solvent evaporation, thin-film, dialysis, and oil/water emulsion methods [127]. In the co-solvent evaporation and dialysis methods, the amphiphilic polymer is solubilized in a miscible organic solvent, added to water slowly, and then the organic phase is removed through evaporation or dialysis, triggering self-assembly. In the oil/water emulsion method, the polymer is dissolved in a water-immiscible organic phase, followed by the addition of water, and evaporation of the organic phase. Regardless of the method, the lowest concentration at which the hydrophobic segments of amphiphiles will begin to sequester is known as the critical aggregation concentration (CAC), or the critical micelle concentration (CMC) for micelles. Amphiphilic polymers in solution exist as unimers below their CMC and partition to the air/solution interface. Continuously increasing polymer concentrations past the CMC leads to the formation of a separate phase composed of the self-assembled polymers, which is accompanied by a decrease of free energy of the system [128]. Due to the large dilution that polymeric micelles undergo upon administration into the body, having a  
Figure 4: Aqueous self-assembly of AB\({}_{2}\) miktoarm polymers into micelles and polymersomes, depending on polymer hydrophilic fraction (red = hydrophobic, blue = hydrophilic). very low CMC not only represents the general stability of micelles, but it is integral in maintaining their morphology, and in preserving their function [4]. The methods for determining a polymer's CMC include tensiometry, conductometry, and fluorescence spectrometry, which measures the absorbance and emission spectra of encapsulated hydrophobic dyes. The onset of CMC is seen as a sudden shift in the rate of change of a measured variable as a function of polymer concentration [128]. The CMCs of miktoarm star polymer-based assemblies are often determined through fluorescence spectroscopy, using the hydrophobic fluorophore pyrene, or somewhat less commonly, Nile Red. With pyrene, for example, its partitioning from the aqueous phase (below the CMC) towards micelle interiors (above the CMC), is reflected by an increase in fluorescence intensity and a red-shift of its (0,0) vibronic band [129]. Consequently, the CMC can be found as a change in the intensity ratio of 1338-I339/I333-I336 in the excitation spectra [51, 130]. Importantly, the CMCs attained in miktoarm star assemblies (10\({}^{-7}\)-10\({}^{-9}\) M) have generally been found to be lower than those of diblock copolymers (10\({}^{-4}\)-10\({}^{-7}\) M), though it should be noted that most diblock systems have CMCs closer to 10\({}^{-7}\) M [4, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 75]. Incorporation of additional arms in miktoarm star polymers allows for further stabilization of micelles, leading to lower CMCs. This normally involves tailoring miktoarm stars to have a larger proportion of hydrophobic to hydrophilic segments, so that self-assembly is more energetically favorable. For example, in a study comparing AB and AB\({}_{2}\) (A = PEG, B = poly(glutamic acid (PGA)) polymers with conjugated DOX, the miktoarm star CMCs were lower at 5.4 mg/L compared to the diblock polymer's 9.0 mg/L [52]. Similarly, AB\({}_{3}\) miktoarm star polymers (A = PMMA, B = PNIPAM) were found to have considerably lower CMCs of 10 mg/L than their diblock equivalents (50 mg/L) [31, 125]. With miktoarm polymers, as in the case of more conventional block copolymers, CMCs tend to decrease with increasing hydrophobic chain length. This is generally attributed to the favorable de-solvation and aggregation of hydrophobic segments in aqueous media [131].