**Pattern growth**

Among the observed morphologies which extend from polymeric to metallic materials and to biologic species, similar pattern growth is observed. Patterns extend, with a multilevel branching, from the nanometric **(Fig. 1.a-b)** to the micrometric **(Fig. 1.c-d-e)** scale structures.

Fig. 1. Two-dimensional (2D) observations of various polymer patterns. **(a)** nanometric scale pattern of poly(ethylene-oxide) cylinders (PEO in black dots) in amphiphilic diblock copolymer PEOm-*b*-PMA(Az)n (**a**, Iwamoto & Boyer, CREST-JSPS, Tokyo, Japan), **(b)**  nanometric scale lamellae of an isotactic polypropylene (iPP, crystallization at 0.1 °C.min-1, RuCl3 stained) with crystalline lamella thickness of 10 nm in order of magnitude, **(c)** micrometric scale of an iPP spherulite with lamellar crystals radiating from a nucleating point (iPP, crystallization at 140 °C), **(d)** micrometric scale structure of a polyether block amide after injection moulding (**b-c-d**, Boyer, CARNOT-MINES-CEMEF, Sophia Antipolis, France), **(e)** micrometric scale cellular structure of a polystyrene damaged under carbon dioxide sorption at 317 K (**e**, Hilic & Boyer, Brite Euram POLYFOAM Project BE-4154, Clermont-Ferrand, France).

The polycrystalline features, formed by freezing an undercooled melt, are governed by dynamical processes of growth that depend on the material nature and on the thermodynamic environment. Beautiful illustrations are available in the literature. To cite a few, the rod-like eutectic structure is observed in a dual-phase pattern, namely for metallic with ceramic, and for polymeric (De Rosa et al., 2000; Park et al., 2003) systems like nanometric length scale of hexagonal structure of poly(ethylene-oxide) PEO cylinders in amphiphilic diblock copolymer PEOm-*b*-PMA(Az)n with azobenzene part PMA(Az) (Tian et al., 2002). Dendritic patterns are embellished with images like snowflake ice dendrites from undercooled water (Kobayashi, 1993) and primary solidified phase in most metallic alloys (*e.g.*, steel, industrial alloys) (Trivedi & Laorchan, 1988a-b), and even dendrites in polymer blends (Ferreiro et al., 2002a) like PEO polymer dendrites formed under cooling PEO/polymethyl methacrylate PMMA blend (Gránásy et al., 2003; Okerberg et al., 2008). In the nanometric scale, immiscibility of polymer chains in block copolymers leads to microphase-separated structures with typical morphologies like hexagonally packed cylindrical structures, lamellae, spheres in centred cubic phases, double gyroid and double diamond networks (Park et al., 2003).

The development of polymer-type patterns is richly illustrated in the case of biological

Among the observed morphologies which extend from polymeric to metallic materials and to biologic species, similar pattern growth is observed. Patterns extend, with a multilevel branching, from the nanometric **(Fig. 1.a-b)** to the micrometric **(Fig. 1.c-d-e)** scale structures.

**(a) (b) (c) (d) (e)**

**50 µ<sup>m</sup> <sup>100</sup> nm <sup>100</sup> µm <sup>5</sup> µm <sup>40</sup> µm**

**Molecular nm µm cm**

Fig. 1. Two-dimensional (2D) observations of various polymer patterns. **(a)** nanometric scale

The polycrystalline features, formed by freezing an undercooled melt, are governed by dynamical processes of growth that depend on the material nature and on the thermodynamic environment. Beautiful illustrations are available in the literature. To cite a few, the rod-like eutectic structure is observed in a dual-phase pattern, namely for metallic with ceramic, and for polymeric (De Rosa et al., 2000; Park et al., 2003) systems like nanometric length scale of hexagonal structure of poly(ethylene-oxide) PEO cylinders in amphiphilic diblock copolymer PEOm-*b*-PMA(Az)n with azobenzene part PMA(Az) (Tian et al., 2002). Dendritic patterns are embellished with images like snowflake ice dendrites from undercooled water (Kobayashi, 1993) and primary solidified phase in most metallic alloys (*e.g.*, steel, industrial alloys) (Trivedi & Laorchan, 1988a-b), and even dendrites in polymer blends (Ferreiro et al., 2002a) like PEO polymer dendrites formed under cooling PEO/polymethyl methacrylate PMMA blend (Gránásy et al., 2003; Okerberg et al., 2008). In the nanometric scale, immiscibility of polymer chains in block copolymers leads to microphase-separated structures with typical morphologies like hexagonally packed cylindrical structures, lamellae, spheres in centred cubic phases, double gyroid and double

pattern of poly(ethylene-oxide) cylinders (PEO in black dots) in amphiphilic diblock copolymer PEOm-*b*-PMA(Az)n (**a**, Iwamoto & Boyer, CREST-JSPS, Tokyo, Japan), **(b)**  nanometric scale lamellae of an isotactic polypropylene (iPP, crystallization at 0.1 °C.min-1, RuCl3 stained) with crystalline lamella thickness of 10 nm in order of magnitude, **(c)** micrometric scale of an iPP spherulite with lamellar crystals radiating from a nucleating point (iPP, crystallization at 140 °C), **(d)** micrometric scale structure of a polyether block amide after injection moulding (**b-c-d**, Boyer, CARNOT-MINES-CEMEF, Sophia Antipolis, France), **(e)** micrometric scale cellular structure of a polystyrene damaged under carbon dioxide sorption at 317 K (**e**, Hilic & Boyer, Brite Euram POLYFOAM Project BE-4154,

**2. Multi-length scale pattern formation with** *in-situ* **advanced techniques** 

**2.1 Structure formation in various materials 2.1.1 Broad multi-length scale organization** 

**50 nm**

Clermont-Ferrand, France).

diamond networks (Park et al., 2003).

materials and metals.

**Pattern growth** 

In polymer physics, the spherulitic crystallization **(Fig. 1.c)** represents a classic example of pattern formation. It is one of the most illustrated in the literature. Besides their importance in technical polymers, spherulitic patterns are also interesting from a biological point of view like semicrystalline amyloid spherulites associated with the Alzheimer and Kreutzfeld-Jacob diseases (Jin et al., 2003; Krebs et al., 2005). The spherulitic pattern depends on polymer chemistry (Ferreiro et al., 2002b). Stereo irregular atactic or low molecular weight compounds are considered as impurities, which are rejected by growing crystals. The openness of structure, from spherulite-like to dendrite-like, together with the coarseness of texture (a measure of the 'diameters' of crystalline fibres between which impurities become concentrated during crystal growth) was illustrated in the work of Keith & Padden (1964). These processes induce thermal and solute transport. Thus pattern formation is defined by the dynamics of the crystal/melt interface involving the interfacial energy. In the nanometric scale domain, spherulite is a cluster of locally periodic arrays of crystalline layers distributed as radial stacks of parallel crystalline lamellae separated by amorphous layers **(Fig. 1.b)**. Molecular chains through the inter-lamellar amorphous layers act as tie molecules between crystalline layers, making a confined interphase crystalline lamellae/amorphous layer.
