**Modulation of the decorative particles distribution**

652 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

changes are quantified *versus* the (high) pressure of either Hg, CO2, or N2 (Yamada et al., 2007a-b). The hydrostatic effect of "more or less chemically active" solvent CO2, or N2 is smaller than the hydrostatic effect of mercury. The adsorbed solvent induces smaller volume changes at the isotropic transition than the mercury pressure. This results from the low compressibility of solvent (gas) molecules compared to the free volume compressibility induced in BC. A particular behaviour is observed with "chemically active" CO2 where the quadrupole-dipole interactions favour the CO2 sorption into the PMA(Az) matrix during the isotropic liquid transition (Kamiya et al., 1998; Vogt et al., 2003). The hydrostatic effect by CO2 overcomes above 40 MPa with a CO2 desorption at higher pressures explained by the large change of molecular motions at the isotropic transition upon the disruption of π-

**Modulation of the surface topology and swelling of the CO2-modified nanometric-phase-**

Supercritical carbon dioxide (SCCO2) constitutes an excellent agent of microphase separation. From *ex-situ* Atomic Force Microscopy (AFM) and Transmission Electron Microscopy (TEM) analysis of the pattern organization, the fine control of the pressure together with the temperature at which the CO2 treatment is achieved demonstrates the possibility to modulate the surface topology inversion between the copolymer phases concomitantly with the swelling of the nano-phase-separated organization. The observed phase contrast results from the coupled effect of the different elastic moduli of the two

Remarkably, the preferential CO2 affinity is associated with the thermodynamic state of CO2, from liquid (9 MPa, room temperarture (r.t.)) to supercritical (9 MPa, 353 K) and then to gaseous (5 MPa, r.t.) state (Glasser, 2002). This is typically observed when annealing the copolymer for 2 hours to keep the dense periodic hexagonal honeycomb array **(Fig. 3.a-d)**. Under gaseous CO2, the surface morphology of PEO cylinders is not significantly expanded **(Fig. 3.a-b)**. However, liquid CO2 induces a first drastic shift at the surface with the emergence of a new surface state of PEO cylinders. This surface state inversion is attributed to domain-selective surface disorganization. PMA(Az) in the glassy smectic C (SmC) phase cannot expand. PEO cylinders dissolve favourably within liquid CO2, with polar interactions, get molecular movement, expand preferentially perpendicularly to the surface substrate **(Fig. 3.c)**. By increasing temperature, liquid CO2 changes to supercritical CO2. The PMA(Az) domain is in the SmC phase and get potential molecular mobility. At this stage, the copolymer chains should be easily swelled. The easiness of SCCO2 to dissolve within liquid PEO cylinders deals with a new drastic change of the surface topology where the

The preferential CO2 affinities produce porous membranes with a selective sorption in hydrophilic semicrystalline 'closed loop', *i.e.*, PEO channels (Boyer et al., 2006a). More especially, under supercritical SCCO2, the PEO cylinders kept in the ordered hexagonal display exhibit the highest expansion in diameter. In the case of PEO114-*b*-PMA(Az)46, the exposure to SCCO2 swells the PEO cylinders by 56 %, with arrays from 11.8 nm in diameter at r.t. to 18.4 nm in diameter at 353 K. The lattice of the PMA matrix, *i.e.*, periodic plane distance between PEO cylinders, slightly increases by 26 %, from 19.8 nm at r.t. to 24.9 nm at 353 K. This microphase separation is driven by disparity in free volumes between dissimilar segments of the polymer chain, as described from the entropic nature of the closed-loop

domains of the block-copolymer with chemo-diffuso phenomenology.

absorbed SCCO2 increases the diameter of the PEO nano-tubes **(Fig. 3.d)**.

miscibility gap (Lavery et al., 2006; Yamada et al., 2007a-b).

bounds with azobenzene moieties.

**separated organization** 

To create nano-scale hybrid of metal-polymer composites, the favourable SCCO2/PEO interactions are advantageously exploited, as illustrated in **Fig. 4.a-b**. They enable a tidy pattern of hydrophilic gold nano-particles (AuNPs). AuNPs are of about 3 nm in diameter and stabilized with thiol end-functional groups (Boal & Rotello, 2000). Preferentially, the metal NPs wet one of the two copolymer domains, the PEO channels, but de-wet the other, the PMA(Az) matrix. This requires a high mobility contrast between the two copolymer domains, heightened by CO2 plasticization that enhances the free volume disparity between copolymer parts. Each SCCO2-swollen PEO hydrophilic hexagonal honeycomb allows the metal NPs to cluster. A two-dimensional (2D) periodic arrangement of hydrophilic AuNPs is generated in the organic PEO in turn confined into smectic C phase of PMA(Az) matrix which has potential molecular mobility. Additionally to the plasticizing action, the force of the trap is driving chemically. It is due to the hydrophilic compatibility of AuNPs in PEO cylinders by grafted polar groups (Watanabe et al., 2007).

Fig. 4. Pattern control in the nanometric scale of PEO-*b*-PMA(Az) under multifaceted *T, P,* CO2 constraints with AuNPs. TEM illustrations of BC on carbone coated copper grid **(a)** PEO114-*b*-PMA(Az)46, **(b)** PEO454-*b*-PMA(Az)155 doped with AuNPs under SCCO2 (9 MPa, 353 K). Black spots are AuNPs wetted hexagonal PEO honeycomb, selectively. PEO is **(a)** 8.6, **(b)** 24.3 nm in diameter with a periodicity of **(a)** 17.1, **(b)** 36.6 nm. (Step 1, BC film preparation before modification: 2 wt% toluene solution solvent-casting, annealing at 423 K for 24 hrs in vacuum. Step 2, AuNPs deposition before modification: droplet of an ethanol solution of hydrophilic AuNPs (solvent in toluene of 1 %) on dried BC film, drying at r.t. for 2 hrs.)

Thermodynamics and Thermokinetics to Model Phase Transitions of Polymers

suitable for a numerical simulation (Schneider et al., 1988).

by the general differential equation **eq. (8)**:

*dN t dt <sup>a</sup>*( )/ is the "extended" nucleation rate,

sphere appearing at time *t* , and ( ) *<sup>a</sup> dN*

**Assumptions on Nucleation** 

the following equations:

**Avrami's Equation** 

rate *G(t)*, is given by **eq. (9)**:

*τ* + *dτ.* 

over Extended Temperature and Pressure Ranges Under Various Hydrostatic Fluids 655

with an initial number per unit volume (or surface) *N0*. *N0* is implicitly considered as constant. The potential nuclei can only disappear during the transformation according to activation or absorption ("swallowing") processes. An activated nucleus becomes a growing entity, without time lag. Conversely, a nucleus which has been absorbed cannot be activated any longer. In the case of a complex temperature history *T(t)*, the assumption of a constant number of nuclei *N0* is no more valid, because *N0 = N0(T) = N0(T(t))* may be different at each temperature. Consequently, additional potential nuclei can be created in the nontransformed volume during a cooling stage. All these processes are governed by a set of differential equations (Haudin & Chenot, 2004), differential equations seeming to be most

Avrami's theory (Avrami, 1939, 1940, 1941) expresses the transformed volume fraction

0

 *t t*

( ) ( ) (1 ( )) *dt dt <sup>t</sup> dt dt*

 

( )*t* is the "extended" transformed fraction, which, for spheres growing at a radial growth

<sup>4</sup> ( ) () ( ) <sup>3</sup>

*<sup>a</sup> dN t G u du d*

The number of potential nuclei decreases by activation or absorption, and increases by creation in the non-transformed volume during cooling. All these processes are governed by

> ( ) ( ) () () *<sup>g</sup> a c dN t dN t dN t dN t dt dt dt dt*

> > ( ) () () *<sup>a</sup> dN t q tNt*

( ) () () 1 () *<sup>c</sup> dN t Nt d t dt t dt*

<sup>0</sup> ( ) ( ) (1 ( )) *<sup>g</sup> dN t dN T dT <sup>t</sup> dt dT dt* 

 

3

*d*

<sup>4</sup> ( ) <sup>3</sup> *t*

*G u du*

(9)

3

are spheres created per unit volume between *τ* and

(10a)

*dt* (10b)

(10c)

(10d)

(8)

is the volume at time *<sup>τ</sup>* of a

( )*t*

The local affinities of AuNPs with PEO/SCCO2 stabilize the thermodynamically unstable SCCO2-plasticized network and keep it stable with time, which cannot be observed without the insertion of gold nano-particles mainly because of diffusion effect of the solvent (Boyer et al., 2006a)**.** The mean height of AuNPs layer is about 3 nm, which is 20 times smaller than PEO cylinders with a 60 nm in length. Thus PEO channels could be considered as nano-dots receptors, schematically as a "compact core–shell model" consisting of a spherical or isotropic AuNP "core" embedded into a PEO channel "shell", consequently leading to isotropic two- and three-dimensional materials. Nicely, AuNPs clusters on PEO channel heads can be numerically expressed. The presence of, 4, 5 and 8 single Au nano-clusters for *m* = 114, 272 and 454 is identified, respectively. It represents a linear function between the number of AuNPs on swollen PEO *versus* SCCO2-swollen diameter with half of ligands of AuNPs linked with PEO polymer chain.

From this understanding, a fine thermodynamic-mechanical control over extended *T* and *P* ranges would provide a precious way to produce artificial and reliable nanostructured materials. SCCO2-based technology guides a differential diffusion of hydrophilic AuNPs to cluster selectively along the hydrophilic PEO scaffold. As a result, a highly organized hybrid metal-polymer composite is produced. Such understanding would be the origin of a 2D nanocrystal growth.
