Chimica Fisica dei Materiali Avanzati Part 3 –Self-assembly

1. Chimica Fisica dei Materiali AvanzatiPart 3 –Self-assembly Laurea specialistica in Scienza e Ingegneria dei Materiali Curriculum Scienza dei Materiali Corso CFMA. LS-SIMat

2. Self-assembly • Supramolecular self-assembly concerns the spontaneous association of either a few or many molecular components resulting in the generation of either discrete oligomolecular supermolecules or extended polymolecular assemblies (layers, films, membranes…). • The final product is obtained entirely spontaneously when the components are mixed together in the correct ratios under a given set of conditions (solvent, temperature, pH, …) • The formation of supermolecules results from the recognition-directed spontaneous association of a well-defined and limited number of molecular components under the intermolecular control of the noncovalent interactions that hold them together. J.-M. Lehn, Science2002, 295, 2400 Corso CFMA. LS-SIMat

3. Self-assembly in biology Corso CFMA. LS-SIMat

4. Self-organization • Self-organization can be considered as ordered self-assembly. It concerns systems presenting a spontaneous emergence of order in either space or time or both. Structure of the LH2 light-harvesting antenna system of Rhodopseudomonas acidophila which contains rings of 18 (a) and 9 (b) bacteriochlorophyll molecules. Corso CFMA. LS-SIMat

5. e- hn e- e- Self-organization at the heart of life A simplified view of the structure of the photosynthetic reaction center of Rhodopseudomonasviridis. Corso CFMA. LS-SIMat

6. Self-assembly and self-organization • Self-assembly and self-organization of a supramolecular architecture are both multistep processes implying information and instructed components. • They may follow a sequence and a hierarchy of assembly steps, and require reversibility of the connecting events, i.e., kinetic lability and rather weak bonding (compared with covalent bonds), in order to allow the full exploration of the energy hypersurface of the system. • In other words, the product formation must be completely reversible and represent the thermodynamic minimum for the system. In essence, all the information necessary for the assembly to occur is coded into the constituent parts. Corso CFMA. LS-SIMat

7. Self-recognition: Instructed System Paradigm Corso CFMA. LS-SIMat

8. Fundamental thermodynamics of self-assembly • Individual molecules in a medium possess a cohesive energy or self energymi • It is the sum of its interactions with all the surrounding molecules (including any change of the energy of the solvent caused by the solute molecules) • How is mirelated with the pair potentialw(r)? • For an ideal gas of hard spheres of diameter s with a pair potential we already obtained (Part 1, slide 3) • In a condensed phase mimust also include the cavity energy, i.e.the cost of creating the cavity in which the reference molecule sits. • In a closed-packed structure with 12 nearest neighbors Interactions of the reference molecule Cost of the cavity Corso CFMA. LS-SIMat

9. Stacking of hexagonal close packed layers Corso CFMA. LS-SIMat

10. Fundamental thermodynamics … (cont’d) • For a solute molecule (s) in a solvent medium (m) of similar size, one might roughly estimate • Six solvent pairs must first be separated before the solute molecule can enter the medium and interact with 12 solvent molecules. • Note: the effective pair potential between two dissolved molecules is just the change in the sum of their free energies as they approach each other • Boltzmann distribution with X1 and X2 the equilibrium concentrations of molecule X in region (environment, phase) 1 and 2, respectively, where the self-energy is and . Hence, Chemical potential Corso CFMA. LS-SIMat

11. Self-assembly of amphiphiles • In amphiphilic molecules, such as surfactants, lipids and certain copolymers, one end contains a hydrophilic group while the rest of the molecule is hydrophobic, usually a long hydrocarbon chain. • The hydrophilic and hydrophobic interactions rely on the structure of the water H-bonds adopted around the dissolved end groups. Amphiphiles such as surfactants and lipids can associate into a variety of structures in aqueous solutions. These can transform from one to another by changing the solution conditions such as the electrolyte or lipid concentration, pH or temperature. Most single chained surfactants form micelles, while most double chained surfactants form bilayers. Corso CFMA. LS-SIMat

12. Some common amphiphiles Corso CFMA. LS-SIMat

13. Vesicles for drug delivery Figure 1: Liposomes - (left) A = aqueous soluble drug encapsulated in aqueous compartment; (centre) B = a hydrophobic drug in the liposome bilayer; (right) C = hydrophilic polyoxyethylene lipids incorporated into liposome Liposomes were discovered in the mid 1960s2 and originally studied as cell membrane models. They have since gained recognition in the field of drug delivery. Liposomes are formed by the self-assembly of phospholipid molecules in an aqueous environment. Shown schematically in Figure 1a, the amphiphilic phospholipid molecules form a closed bilayer sphere in an attempt to shield their hydrophobic groups from the aqueous environment while still maintaining contact with the aqueous phase via the hydrophilic head group. The resulting closed sphere may encapsulate aqueous soluble drugs within the central aqueous compartment (Figure 1, left) or lipid soluble drugs within the bilayer membrane (Figure 1, centre). Alternatively, lipid soluble drugs may be complexed with cyclodextrins and subsequently encapsulated within the liposome aqueous compartment.3 The encapsulation within/association of drugs with liposomes alters drug pharmacokinetics, and this may be exploited to achieve targeted therapies. Alteration of the liposome surface is necessary in order to optimise liposomal drug targeting. Pharmaceutical Journal, Vol 263 No 7060 p309-318August 28, 1999 Special Feature Corso CFMA. LS-SIMat

14. Fundamental thermodynamic equations of self-assembly • At equilibrium, the chemical potential of all identical molecules in different aggregates must be the same • In an aggregate of aggregation number N : chemical potential of a molecule : standard chemical potential (mean interaction energy per free molecule) : concentration of molecules ( is the concentration of aggregates) monomers dimers trimers Corso CFMA. LS-SIMat

15. Fundamental thermodynamic equations … (cont’d) • Law of mass action • Rate of association = • Rate of dissociation = • From the equilibrium constant or, alternatively, from The system is completely defined by this equation and by the conservation of solute molecules Note that C and XN are expressed in mole fraction units, therefore, they are always < 1. Corso CFMA. LS-SIMat

16. Conditions necessary for the formation of aggregates • Aggregates form only when there is a difference in the cohesive energies between the molecules in the aggregate and in monomeric form • Suppose that • Most of the molecules will be in the monomer state, the more so the more increases with increasing N. • The necessary condition for the formation of large stable aggregates is that for some values of N. • The dependence of upon N determines many of the physical properties of aggregates, such as their mean size and the polydispersity. Corso CFMA. LS-SIMat

17. Effect of aggregate dimensionality • The dependence of on N is usually determined by the shape of the aggregate. One-dimensional case • Consider a suspension of rod-like (linear chain) aggregates of identical molecules • Let be the (positive) monomer-monomer ‘bond’ energy in the aggregate relative to monomers in solution. • The total interaction free-energy is (assuming ) • The factor (N – 1) accounts for the fact that the terminal molecules are bound on one side only • Hence • As N increases, decreases asymptotically towards , the ‘bulk’ energy of a molecule in an infinite aggregate. Corso CFMA. LS-SIMat

18. Effect of aggregate dimensionality (cont’d) Two-dimensional aggregates (disks, sheets) • The number N of molecules is proportional to the area • The number of unbound molecules is proportional to the circumference , hence to . • The mean free energy per molecule, considering that is Three-dimensional aggregates (spheres) • N is proportional to , while the number of unbounded surface molecules is proportional to the area and hence to . • By arguments similar to the previous ones, the mean free energy per molecule is Corso CFMA. LS-SIMat

19. 3-D 2-D 1-D 0 Effect of aggregate dimensionality (cont’d) • Summarizing, • For the simplest shaped structures – rods, sheets and spheres – the interaction free energy per molecule can be expressed as • a : positive constant dependent on the strength of the intermolecular interaction • p: exponent dependent on the shape or dimensionality of the aggregates Corso CFMA. LS-SIMat

20. The critical micelle concentration • At what concentration will aggregates form? • Using into one gets Most of the molecules will be isolated monomers, or • When approaches or , it can increase no further (otherwise, could even exceed unity, which is not possible by definition). • The saturation of occurs at the critical micelle concentration (CMC) denoted Corso CFMA. LS-SIMat

21. Critical Micelle Concentration • At or for all p, further addition of solute molecules results in the formation of more aggregates with the monomer concentration unchanged at CMC. Most single chain surfactants containing 12-16 C atoms per chain have their CMC in the range 10-2-10-5 M while the corresponding double-chained surfactants have much lower CMC values due to their greater hydrophobicity. Corso CFMA. LS-SIMat

22. Phase separation vs. micellization • For simple disc-like and spherical aggregates • Above the CMC where the above two eqns. become and , respectively. • For positive values of , usually > 1, there will be very few aggregates of any appreciable size. • There is a phase separation, strictly to an aggregate of infinite size at the CMC (e.g., formation of droplets) Corso CFMA. LS-SIMat

23. Phase separation vs. micellization (cont’d) • Polydispersity comes about for rod-like (p = 1)aggregates, such as cylindrical micelles , fibrous structures, microtubules, etc. • Since above the CMC , The concentration of molecules grows in proportion to the aggregate size and there is no phase separation. • For very large N the term begins to dominate, eventually bringing XN to zero as N approaches infinity. • The distribution is highly polydisperse. Corso CFMA. LS-SIMat

24. Properties of polydispersity • The density distribution of molecules in aggregates of N molecules peaks at i.e., the mean aggregation number is concentration dependent • With an expectation value of N i.e., the distribution is skewed towards large N. Corso CFMA. LS-SIMat

25. N M More complex amphiphilic structures • The value of the exponent p in is constant only for aggregates consisting of very simple geometrical shapes (spheres, disks, rods). • Complex amphiphilic molecules can assemble into more complex shapes (bilayers, vesicles, liposomes; cf. slide 10). • This is determined by the type of anisotropic binding forces acting between different parts of the amphiphilic molecules. • Different degrees of molecular flexibility also affect the ability of the molecules to adopt different type of aggregation. • In all such cases: leading to monodisperse aggregates Corso CFMA. LS-SIMat

26. Parameters determining packing types Two opposing forces • The packing shape depends on the balance between hydrophobic attraction at the hydrocarbon/water interface and the hydrophilic, ionic or steric repulsion of the head-groups • This balance determines an optimal surface area a0. • The chain volume v and chain length lc set limits on how the fluid chains can pack together. • Different structures may be consistent with these constraints. Eventually, entropy favors the structure with the smallest aggregation number. Corso CFMA. LS-SIMat

27. Packing shapes of amphiphilic molecules • For dimensionless packing parameter: • , spherical micelles • , non spherical micelles • , vescicles or bilayers • , ‘inverted’ structures Corso CFMA. LS-SIMat