U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat1 Chimica Fisica dei Materiali Avanzati Part 3 –Self-assembly Laurea specialistica in Scienza e

Corso CFMA. LS-SIMat 1

UUNIVERSITA’ DEGLI NIVERSITA’ DEGLI SSTUDI DI TUDI DI PPADOVAADOVAUUNIVERSITA’ DEGLI NIVERSITA’ DEGLI SSTUDI DI TUDI DI PPADOVAADOVA

Chimica Fisica dei Materiali AvanzatiChimica Fisica dei Materiali Avanzati

Part 3 –Self-assemblyPart 3 –Self-assembly

Laurea specialistica in Scienza e Ingegneria dei MaterialiCurriculum Scienza dei Materiali



Self-assemblySelf-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, Science 2002, 295, 2400



Self-assembly in biologySelf-assembly in biology



Self-organizationSelf-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.



Self-organization at the heart of lifeSelf-organization at the heart of life

Mem

bran

e

Cy

P

BC

BP

Q A

e-

e-

e-

h

A simplified view of the structure of the photosynthetic reaction center of Rhodopseudomonas viridis.



Self-assembly and self-organizationSelf-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.



Self-recognition: Instructed System Self-recognition: Instructed System ParadigmParadigm



Fundamental thermodynamics of self-assemblyFundamental thermodynamics of self-assembly

Individual molecules in a medium possess a cohesive energy or self energy i

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 i related with the pair potential w(r)? For an ideal gas of hard spheres of diameter with a pair potential

we already obtained (Part 1, slide 3)

In a condensed phase i must 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

nrCrw

3

4Energy Tot.

3

ni n

C

wwwi 6126c.p.

Cost of the cavity

Interactions of the reference molecule



Stacking of hexagonal close packed Stacking of hexagonal close packed layerslayers



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,

Fundamental thermodynamics … (cont’d)Fundamental thermodynamics … (cont’d)

smmmiliq ww 126

TkXX

B

ii21

21 exp

i1

i2

2211 lnln XTkXTk Bi

Bi Chemical potential



Self-assembly of amphiphilesSelf-assembly of amphiphiles

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.

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.



Some common amphiphilesSome common amphiphiles



Vesicles for drug deliveryVesicles for drug delivery

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.

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

Pharmaceutical Journal, Vol 263 No 7060 p309-318August 28, 1999 Special Feature



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)

Fundamental thermodynamic equations of self-Fundamental thermodynamic equations of self-assemblyassembly

N

XTk

N

XTk

XTkXTk

NBNN

BBB

ln1

or

3ln

3

1

2ln

2

1ln

0

303

2021

01

N0N

NX NX N

monomers dimers trimers



Law of mass action

Rate of association =

Rate of dissociation =

From the equilibrium constant

or, alternatively, from

Fundamental thermodynamic equations … Fundamental thermodynamic equations … (cont’d)(cont’d)

NXk 11

NXk NN

N

XNX Nk 1

1 Nk

Tk

N

k

k

X

NXK

B

N

NN

N01

01

1

exp

N

B

NN

NBNB

Tk

μμXNX

N

XTk

NXTk

001

1

01

01

exp

gets one

ln1

ln

1

321N

NXXXXC

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.



Conditions necessary for the formation of Conditions necessary for the formation of aggregatesaggregates

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.

. havemust we, 1 since and

then

11

1

003

02

01

XNXX

NXX

N

NN

N

0N

0N

01

0 N



Effect of aggregate dimensionalityEffect 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.

0N

TkB

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.

TkNN BN 10

N

TkTk

NB

BN

00 11

0N

0

001



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

Effect of aggregate dimensionality (cont’d)Effect of aggregate dimensionality (cont’d)

2R

R2 21

N

TkNNN BN

2

10

21

0

21

0 11

N

TkTk

N

BBN

3

34 R

24 R 32

N

32

00

N

TkBN



Summarizing, For the simplest shaped structures

– rods, sheets and spheres – the interaction free energy per molecule can be expressed as

: positive constant dependent on the strength of the intermolecular interaction

p: exponent dependent on the shape or dimensionality of the aggregates

Effect of aggregate dimensionality (cont’d)Effect of aggregate dimensionality (cont’d)

pB

N N

Tk 00

3-D

2-D

0

1-D

N

1

2

1

TkBN 0

0

0N



The critical micelle concentrationThe 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

pB

N N

Tk 00

N

B

NN Tk

μμXNX

001

1 exp

.

have we, when i.e., , smallfor

1

1exp

321

1 1

11

XXX

eXX

eXNN

XNXN

N

pN

CX 1

1X TkBN00

1exp e

NX

1X critX1



Critical Micelle ConcentrationCritical 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.

TkX BNcrit00

11 expCMC eX crit CMC1

Most single chain surfactants containing 1216 C atoms per chain have their CMC in the range 102105 M while the corresponding double-chained surfactants have much lower CMC values due to their greater hydrophobicity.



Phase separation vs. micellizationPhase 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)

3

2 spheresfor exp

2

1 discsfor exp

3

1

1

2

1

1

pNeXNX

pNeXNX

N

N

N

N

11 eX

2

1

exp NNX N

3

1

exp NNX N



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.

Phase separation vs. micellization (cont’d)Phase separation vs. micellization (cont’d)

. offunction decreasingrapidly an rather tha

constant a is termlexponentia second the

1For 1

N

eeXNXpN

N

11 eX

NNX N smallfor

NeX 1



Properties of polydispersityProperties 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.

CeMN max

MCe

Ce

CNXXNXN NNN

22

41

C

N

log

log2



More complex amphiphilic structuresMore 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.

pB

N N

Tk 00

M N

0N

In all such cases:

leading to monodisperse aggregates



Parameters determining packing typesParameters determining packing types

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.

Two opposing forces



Packing shapes of Packing shapes of amphiphilic moleculesamphiphilic molecules

For dimensionless packing parameter:

, spherical

micelles

, non

spherical micelles

, vescicles or

bilayers

, ‘inverted’

structures

clav 031

2131

121 1

Documents

U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat1 Chimica Fisica dei Materiali Avanzati Part 3 –Self-assembly Laurea specialistica in Scienza e