Nature’s fundamental principle of self-assembly drives components of a system to form ordered structures or patterns out of a pre-existing chaotic arrangement.49 This autonomous organization represents a basic process not just in our immediate environment but also on a galaxy scale.101 Saturn’s rings,102 for instance, or the human body that again are built-up by even smaller macromolecules.103-106 Both of these examples employ the principle of bottom-up assembly on very different length scales to form ordered superstructures with an energetic minimum.106,107 Concerning the process of droplet breakup of a liquid jet in chapter 2.1.2, the reduction of surface tension is the driving force for reaching a more favorable energy level.89 A similar principle based on a fast adaptable and effective energy balance can be observed on macro scale for penguins: their body size is decreasing approaching the equator where the climate is warmer.108 Due to their greater surface to volume ratio, they can easily use the heat of the sun to keep up their body temperature, but at the same time also cool down much more effective.109 In very cold regions, like Antarctica, however, they need to keep their energy in form of heat, which is working better with a bigger body because the volume increases cubic, whereas the surface rises just quadratic.110
This thesis focuses on self-assembled anisotropic colloids, as wormlike micelles shown in the cryo-transmission electron microscopy (cryo-TEM) images of later Figure 13. The process of static self-assembly is thermodynamically reversible and needs little to no activation energy from an external source. Self-assembly is the result and can be controlled by the design of the components, which makes an attractive method for the formation of nanomaterials, drug delivery systems or other superstructures with new properties.101
Figure 13 | Cryo-transmission electron microscopy (cryo-TEM) images of wormlike micelles that have self-assembled out of the diblock copolymer polyisoprene-block-polyethylene oxide (PI-b-PEO).
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In chemistry, well-known types of substances that carry out autonomous organization are amphiphilic molecules, which consist of both a lipophilic as well as hydrophilic part. Here, the most famous examples are molecular surfactants used in soap to form soap bubbles out of micelles via self-assembly as soon as the critical micelle concentration (CMC) is reached.49 The self-assembly process aims to minimize the surface area between the solvent and an insoluble block, as well as the immiscible blocks.111 Self-assembly phenomena create new systems with higher order, therefore, a theoretical description using an order parameter ξ was found to be useful.49 This parameter defines the degree of order of a system, where a completely chaotic system would have the order parameter of ξ = 0 and a perfectly ordered one would reach a value of ξ = 1.107 A prerequisite for the formation of organized domains are specific forces between molecules. A balance of short-range attractive as well as long-range repulsive forces is required to form specific structure patterns. Such short-range forces can be covalent or ionic bonds, while coulomb repulsion, hydrophobic interactions or chemical incompatibility of polymers appear as long-rangeforces.107
Micelles created out of copolymers, like the used wormlike micelles in Figure 13, are also a well-known product of self-assembly. Such copolymers that can be synthesized adjustable and tailor-made via living polymerization exhibit micellar superstructures. Thus, this field of chemistry is predestined for constructing a great variety of components as building blocks for assembly processes.112 Hence, block copolymers, consisting of two or more immiscible or functionalized blocks of chemically different polymeric moieties covalently bound together, extend the possibilities to create new materials for medical, catalytical, or photoelectric and ceramic applications.107,113 Most common are diblock copolymers with an insoluble block that forms the micellar core and a soluble block wrapped around it. Copolymers with a soluble block larger than the insoluble one always self-assemble to spherical micelles.114 Apparently, not all copolymers self-assemble to spherical shapes. There are certain requirements with respect to composition and structure of self-assembling copolymers.115 The size and shape of the micelle depends on length and ratio of the polymer blocks.49 And based on the size and shape of the building block, it is possible to manipulate the interface to create an interfacial curvature. This relation is described by the micelle’s mean curvature H and its Gaussian curvature K, both of
35 The resulting interfacial curvature in turn is related to the dimensionless packing parameter P that dictates the molecular shape of copolymer molecules in solution. Thus, P determines the morphology of the corresponding self-assembled copolymer aggregate upon phase separation of the hydrophobic and hydrophilic block.118 P is defined as the size of the hydrophobic block relative to the hydrophilic block and connected to the interface curvature as follows:116
𝑃 = 𝑣
𝑎∙𝑙= 1 − 𝐻 ∙ 𝑙 +𝐾∙𝑙2
3 = 1 −𝑙
2(1
𝑅1+ 1
𝑅2) + 𝑙²
3𝑅1∙𝑅2 (21) where v is the volume of the hydrophobic block, a the hydrophilic-hydrophobic interfacial area, and l the hydrophobic block length normal to the interface, as shown in Figure 14. For instance, employing symmetric copolymers with a lager core compared to the corona, leads to the generation of cylindrical micelles.119 This is the case for the wormlike micelles studied in this thesis which have a packing parameter of P = 0.5 and therefore assume a cylindrical shape. The respective diblock copolymer polyisoprene110-block-polyethylene oxide198 (PI110-PEO198) was synthesized via living anionic polymerization, where K = 0, and H = 1/2r turns into 1/2l and yield to P = 0.5 which represents a cylindrical shape.42
Figure 14 | Chemical formula of the used diblock copolymer PI110-PEO198 and illustration of the packing parameter P with the related geometric parameters known from equations (20) and (21) as well as the various structures attainable by self-assembly of the block copolymers. PI110-PEO198 forms wormlike micelles represented by a cylindrical shape for P.
Increasing values of P turn the morphology of the assembly from spherical over cylindrical and vesicular to planar bilayer aggregates. This transition is illustrated in Figure 14 and supported by the theoretical values in following Table 1:
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Table 1 | Packing parameter P of different aggregated structures as well as their corresponding mean curvature H and Gaussian curvature K.118
Shape 𝑷 = 𝒗
𝒂 ∙ 𝒍 R1 R2 H K
Sphere P < 1
3
R R 1/R 1/R²
Cylinder 1
3 ≤ P < 1
2
R ∞ 1/2R 0
Vesicle 1
2 ≤ P < 1 R ∞ 1/2R 0
Bilayer P = 1 ∞ ∞ 0 0
In comparison to low molecular weight amphiphiles, micelles formed by polymeric amphiphiles are kinetically and thermodynamically much more stable. Therefore, they provide a variety of applications, such as colloid stabilization or emulsion polymerization.120
In diluted solutions, mainly individual particles like micelles or vesicles are formed. In contrast, in higher concentration cubic phases of spherical micelles develop and can arrange into even higher ordered body-centered cubic (BCC) or face-centered cubic (FCC) phases.121 Moreover, there are known hexagonal packed (HEX) patterns and lamellar (LAM) phases from the used wormlike or cylindrical micelles in bulk with domains sizes over several micrometers.107 An overview of some of the modulated or porous phases that can be generated in bulk is shown in Figure 15.
Figure 15 | Illustration of different structures attainable by self-assembly of block copolymers in dilute solutions (top) as well as favored orders with higher concentration in bulk (bottom).
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