The behavior of quantum dots (QDs) in solution and their interaction with other surfaces is of great importance to biological and industrial applications, such as optical displays, animal tagging, anti-counterfeiting dyes and paints, chemical sensing, and fluorescent tagging. However, unmodified quantum dots tend to be hydrophobic, which precludes their use in stable, water-based colloids. Furthermore, because the ratio of surface area to volume in a quantum dot is much higher than for larger particles, the thermodynamic free energy associated with dangling bonds on the surface is sufficient to impede the quantum confinement of excitons. Once solubilized by encapsulation in either a hydrophobic interior micelle or a hydrophilic exterior micelle, the QDs can be successfully introduced into an aqueous medium, in which they form an extended hydrogel network. In this form, quantum dots can be utilized in several applications that benefit from their unique properties, such as medical imaging and thermal destruction of malignant cancers.
Quantum dots Quantum dots (QDs) are nano-scale semiconductor particles on the order of 2–10 nm in diameter. They possess electrical properties between those of bulk semi-conductors and individual molecules, as well as optical characteristics that make them suitable for applications where fluorescence is desirable, such as medical imaging. Most QDs synthesized for medical imaging are in the form of CdSe(ZnS) core(shell) particles. CdSe QDs have been shown to possess optical properties superior to organic dyes. The ZnS shell has a two-fold effect:
to interact with dangling bonds that would otherwise result in particle aggregation, loss of visual resolution, and impedance of quantum confinement effects to further increase the fluorescence of the particles themselves.
Problems with CdSe(ZnS) quantum dots Despite their potential for use as contrast agents for medical imaging techniques, their use in vivo is hindered by the cytotoxicity of cadmium. To address this issue, methods have been developed to “wrap” or “encapsulate” potentially-toxic QDs in bio-inert polymers to facilitate use in living tissue. While Cd-free QDs are commercially available, they are unsuitable for use as a substitute for organic contrasts. Another issue with CdSe(ZnS) nanoparticles is significant hydrophobicity, which hinders their ability to enter solution with aqueous media, such as blood or spinal fluid. Certain hydrophilic polymers could be used to render the dots water-soluble.
Synthesizing the encapsulant polymer
Rf-PEG synthesis One notable quantum dot encapsulation technique involves utilizing a double fluoroalkyl-ended polyethylene glycol molecule (Rf-PEG) as a surfactant, which will spontaneously form micellular structures at its critical micelle concentration (CMC). The critical micelle concentration of the Rf-PEG depends on the length of the PEG portion of the polymer. This molecule consists of a hydrophilic PEG backbone with two hydrophilic terminal groups (CnF2n+1-CH2CH2O) attached via isophorone diurethane. It is synthesized by dehydrating a solution of 1,3-dimethyl-5-fluorouracil and PEG, mixing them in the presence of heavy water (D2O) via a sonicator to combine then.
Micellization
At the appropriate Krafft temperature and critical micelle concentration these molecules will form individual tear-drop loops, where the hydrophobic ends are attracted to one another, to other molecules, and also to the similarly hydrophobic QDs. This forms a loaded micelle with a hydrophilic outer shell and a hydrophobic core. When encapsulating hydrophobes in this way it is important to ensure the particle size is appropriate for the PEG backbone being utilized, as the number of PEG mer units (generally with a molecular weight of 6 kDa or 10 kDa) determines the maximum particle size that can be successfully contained at the core of the micelle. To determine the average diameter, D, of the QDs, the following empirical equation is used:
D = ( 1.6122 × 10 − 9 ) λ 4 − ( 2.66575 × 10 − 6 ) λ 3 + ( 1.6242 × 10 − 3 ) λ 2 − ( 0.4277 ) λ + 41.57 {\displaystyle {D=\ }{(1.6122\times 10^{-9})\lambda ^{4}}-{(2.66575\times 10^{-6})\lambda ^{3}}+{(1.6242\times 10^{-3})\lambda ^{2}}-{(0.4277)\lambda }+{41.57}}
Where
D {\displaystyle D} is the diameter of the CdSe QD in nm
λ {\displaystyle \lambda } is the wavelength of the first absorption peak in nm
Role of ZnS shell It is during encapsulation that the ZnS shell plays an especially important role, in that it helps prevent the agglomeration of CdSe particles that had no shell by occupying the previously mentioned bonds on the dot's surface; however, clumping can still occur through secondary forces that arise from common hydrophobicity. 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 form a network within the aqueous media called a hydrogel, creating a diffuse and relatively constant concentration of the encapsulated particle within the gel. The formation of hydrogels is a phenomenon observed in superabsorbent polymers, or "slush powders," in which the polymer, often in the form of a powder, absorbs water, becoming up to 99% liquid and 30-60 times larger in size.
Stokes-Einstein equation
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