The behavior of quantum dots (QDs) in solution and their interaction with surfaces is important for biological and industrial applications such as optical displays, animal tagging, anti-counterfeiting dyes and paints, chemical sensing, and fluorescent labeling. Unmodified QDs are typically hydrophobic, which prevents their use in stable water-based colloids. Because their surface-area-to-volume ratio is much higher than that of larger particles, surface dangling bonds raise the free energy and can disrupt quantum confinement of excitons. Encapsulation in micelles with hydrophobic interiors or hydrophilic exteriors allows QDs to be solubilized and introduced into aqueous media, where they can be incorporated into hydrogel networks for applications such as medical imaging and thermal destruction of malignant tumors.

Quantum dots are nanoscale semiconductor particles about 2-10 nm in diameter. They have electrical properties between those of bulk semiconductors and individual molecules, and optical properties that make them useful for fluorescence-based applications. Most QDs synthesized for medical imaging are CdSe/ZnS core-shell particles. CdSe quantum dots (QDs) have optical properties superior to those of organic dyes. Coating them with a ZnS shell has a twofold effect: it passivates dangling bonds that would otherwise cause particle aggregation and loss of optical resolution, and it preserves quantum confinement, thereby increasing particle fluorescence. Despite their potential as contrast agents for medical imaging, in vivo use is hindered by cadmium cytotoxicity. To address this, QDs can be encapsulated in biologically inert polymers to reduce toxicity and enable use in living tissue. Although cadmium-free QDs are commercially available, they are not yet suitable substitutes for organic contrast agents. Another challenge is the inherent hydrophobicity of CdSe(ZnS) nanoparticles, which limits their dispersibility in aqueous media such as blood or spinal fluid; hydrophilic polymers are often used to render the dots water-soluble. One notable encapsulation approach employs a fluoroalkyl-terminated polyethylene glycol (Rf-PEG) surfactant that spontaneously forms micellar structures above its critical micelle concentration (CMC); the CMC depends on the PEG chain length. This molecule consists of a hydrophilic PEG backbone with two hydrophobic terminal groups (CnF2n+1-CH2CH2O) attached via isophorone diurethane. 

Synthesis involves dehydrating a solution of 1,3-dimethyl-5-fluorouracil and PEG in the presence of heavy water (D2O) and combining them by sonication.

Micellization: at the appropriate Krafft temperature and above the critical micelle concentration, these molecules form individual tear-drop loops in which the hydrophobic ends associate with one another, with neighboring molecules, and with similarly hydrophobic quantum dots (QDs). This produces a loaded micelle with a hydrophilic outer shell and a hydrophobic core. When encapsulating hydrophobic particles, it is important to ensure the particle size is compatible with the PEG backbone: the number of PEG repeat units (typically corresponding to PEG molecular weights of ~6 kDa or ~10 kDa) determines the maximum particle diameter that can be stably contained in the micelle core.

To determine the average diameter, D, of the QDs, an empirical equation relating D to λ, the wavelength of the first absorption peak, is used.

Role of the ZnS shell: during encapsulation the ZnS shell helps prevent agglomeration of bare CdSe particles by passivating surface bonds; however, secondary aggregation can still occur due to hydrophobic interactions. This can result in multiple particles within each micelle, which may negatively impact overall resolution. For this reason, multiple combinations of PEG chain length and particle diameter are necessary to achieve optimal imaging properties.

Hydrogel network
After initial encapsulation, the remaining molecules form connections between the individual micelles to create a network within the aqueous medium called a hydrogel, producing a diffuse and relatively constant concentration of the encapsulated particles within the gel. Hydrogel formation is also observed in superabsorbent polymers, or "slush powders," in which the polymer, often in powder form, absorbs water, becoming up to 99% liquid and swelling 30–60 times in size.

Stokes–Einstein equation
The diffusivity of spherical particles in a suspension is approximated by the Stokes–Einstein equation:
D = k_B T / (6 π η r)
where D is the diffusivity, T is the temperature, r is the particle radius, k_B is the Boltzmann constant, and η is the hydrogel viscosity. Typical Rf-PEG hydrogel diffusivities for 2 nm quantum dots are on the order of 10^−16 m^2/s, so suspensions of quantum dots tend to be very stable. Hydrogel viscosity can be determined by rheological techniques.

Micelle rheology
When encapsulating hydrophobic or potentially toxic materials, it is important that the encapsulant remain intact while inside the body. Studying the rheological properties of micelles permits selection of the polymer most appropriate for long-term biological applications. Rf-PEG exhibits superior rheological properties in vivo.

Polymer length influences material behavior and encapsulant retention. The correct chain length prevents release of QDs and other toxic particles that could cause unintended cell necrosis. Polymer length is controlled by two factors: the weight of the PEG backbone (represented as #K, thousands of Daltons) and the length of the hydrophobic terminal groups (denoted C#, number of carbon atoms). Increasing PEG length increases solubility, but if the PEG chain is too long the micelle becomes unstable; stable hydrogels form only with PEG backbones of about 6–10 kDa. Increasing the length of the hydrophobic terminal groups decreases aqueous solubility.