1.3 The mechanism of Self-Assembly
Amphiphiles contain both hydrophilic and hydrophobic parts, and the two parts are linked by covalent bonds. Amphiphiles are able to self-assemble in water to form various well-defined molecular assemblies, such as micelles and vesicles. Due to this chemical incompatibility this molecules self-organize in aqueous solution and at the air-liquid interface. The surfactant molecule which is composed of a hydrophobic tail and a hydrophilic or polar head is the basic example of an amphiphile. Self-assembly of amphiphilic molecules can be also defined as a delicate equilibrium between the attractive (driving force) and repulsive (opposition force) intermolecular forces. It is also noteworthy that there is no strong chemical bond like for example covalent bond involved in self-organization. Generally, the hydrophobic attraction is considered as the driving force, and electrostatic repulsion and/or solvation force as the opposition force. Firstly, the surfactant molecules are brought in close proximity to each other by the long-range hydrophobic forces and with the progression of the process, opposition forces like hydration forces (short-range repulsive interaction ) or electric double-layer repulsion begin to call in. Origin of these forces comes from the charge bearing hydrated head groups which are comparatively short-range forces in comparison to the hydrophobic interaction . The variety of structures which can be generated by self-assembly is depending on slight modification of parameters such as concentration, polydispersity, molecular weight, hydrophilic weight fraction, charge, solvent, composition, water content and additives (ions, surfactants, and homopolymer) is enormous. Structures resulting from the organization of amphiphilic molecules are presented in Figure 1-5.
Figure 1-5. Self-organized structures of high molecular weight of diblock copolymer 
(Figure adapted with permission of John Wiley and Sons)
The idea of taking advantage of the self-assembly process for biomedical applications was extensively exploited in the area of targeted and controlled drug delivery . In dilute aqueous media, amphiphiles are soluble and embrace configurations of spherical or cylindrical core shell micelles as well as vesicles, being these architectures predominant for drug delivery [54, 55] to transport for example drugs or nucleic acids . The formation of bilayers and closure into vesicular structures is depicted in Figure 1-6. Moreover, to make delivery more efficient, it is possible to tailor the vesicular properties in order to improve targeting and transport (Figure 1-7) . Block copolymers are considered as promising alternative to lipids for drug delivery . Indeed, there are limitations arising from the lipid nature for this application because of their low molecular weight , poor mechanical stability and short shelf-life in comparison to more stable block copolymer structures owing to
their high molecular weight. However, block copolymers remain currently uncommon due to their lack of approval from the FDA (Federal Drug Administration)  in comparison to lipids which are extensively used. The immeasurable number of synthetic path to obtain self-organizing functional polymers is the key for their implementation in biomedical applications.
Figure 1-6. Schematic illustration of bilayer formation and its closure into vesicle(Edisk-line energy, γ-line tension, Ebend-bending energy, κ-bending modulus, RD-disc radius, RV-Vesicle radius) (Figure adapted with permission of John Wiley and Sons)
The need for forming such structures with tailored properties has drawn attention in various fields like enzymatic cascade reaction , drug delivery , amphiphilic copolymer nanocontainers  and nanoreactors .
Figure 1-7. Strategies for polymersomes/liposomes functionalization. (a) Grafting of a functional ligand to the surface of vesicles (b-c) pre-functionalized and non-functionalized amphiphilic block copolymers organization: (b) functional entity attached as the end-group (c) functional ligand along the hydrophilic block. L = Functionalization molecule:
fluorophore, biomolecules, polymer tentacle, etc.
188.8.131.52 Packing parameter and interfacial tension.
In order to be able to predict the morphology of self-assembled structures Israelachvili, Mitchell and Ninham introduced a model that takes into account the geometric parameters of the surfactant molecules . Following this approach in more detail it is possible to predict the expected morphology, micelle, vesicle, planar bilayer or other. This model is built on the idea of the so called packing parameter p, also named the surfactant parameter. In this classical representation the factor that controls the resulting self-assembled morphology is the size of the hydrophobic moiety in relation to the hydrophilic part. The curvature of the hydrophilic-hydrophobic interface is governed by its mean curvature H and its Gaussian curvature K, which are defined by the two radii of curvature R1(interfacial) and R2(mean)(Figure 1-8).
Figure 1-8. Depiction of amphiphile self-assembled morphology taking into account the packing parameter, interfacial curvature and Gaussian curvature. (Figure adapted with permission of John Wiley and Sons)
The correlation between the packing parameter and the curvature is described by the following equation;
𝑎𝑙= 1 + 𝐻𝑙 +𝐾𝑙3 3
Where v is the volume of the hydrophobic part of the amphiphilic molecule, l is the chain length and a is the interfacial area. This approach has been successfully applied to predict and justify formation of structures dependent on surfactant volume fractions such as spherical micelles (p ≈ 1/3 ), vesicles (p ≈ 1), and cylindrical micelles (p≈ 1/2) (Figure 1-9).
Figure 1-9. Examples of possible structures based on amphiphilic molecule geometry( V - volume of the hydrophobic part, lc - chain length, ao - the interfacial area. (Figure adapted with permission of Elsevier)
With the purpose of obtaining bilayers for a certain molecule characterized by volume v and length l, the interfacial area has to be tailored in a way to achieve the unity value of the packing parameter. Basically, the aggregates remain in a dynamic equilibrium with single
solvated macromolecules when the glass transition temperature (Tg) (temperature at which amorphous materials undergo reversible transition from a hard and relatively brittle state into a molten or rubber-like state) of most hydrophobic blocks is lower than the ambient temperature of self-organization . As a consequence, structure rearrange while molecules strive to reach their optimal thermodynamic equilibrium architecture . Shape transition along with the decrease of the hydrophilic weight fraction was demonstrated for the poly(butadiene)-block-poly(ethylene oxide) copolymer (Figure 1-10) . The model that is considered in this paragraph applies to molecules that can rearrange easily (such as surfactants, polymers or dendrons) and through these movements can fit the equilibrium shape and curvature.
Figure 1-10. Various shapes of PB-PEO copolymer self-assembled structures, from:
a)micelles, through b) cylindrical micelles to c) vesicles  (Figure adapted with permission of John Wiley and Sons)
The packing parameter does not describe sufficiently the laws governing the self-assembly process of high molecular weight polymer analogues of surfactants or lipids. With the purpose of elucidating the self-organization phenomenon the most important interaction are described in following subsection.