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Phase transitions in complex systems

Growth processes in complex systems

Structures resulting from growth processes like crystallisation or gradient-driven assembly are formed at a finite rate, and thus under non-equilibrium conditions. Thus, they typically depend on kinetic parameters governing nucleation and growth, may result from rapid changes of temperature, fast solvent evaporation, or the kinetics of adsorption and phase separation. Consequently, these materials are normally not perfectly ordered and often relax in time which leads to morphological reorganisation, ageing or morphogenesis. An advantage of such growth processes is the possibility to generate a multitude of different structures and functional patterns from one single molecular system, simply by varying the conditions of the ordering processes.  In this context, macromolecules represent versatile systems for complex growth processes where a subtle balance between various physico-chemical processes and the sensitivity to even the slightest variations of the growth conditions determine the resulting morphologies and functional patterns. For predicting and controlling the resulting structure and function it is not sufficient to design, tailor and put together the right chemical units forming the macromolecules. A comprehensive understanding of growth and ordering processes is necessary in order to control and tune the assembly of these molecules over multiple length-scales up to functional macroscopic objects. 




Optical micrographs of the growth of a polymer crystal in a ca. 35nm thick film. The images were taken after A) t0, B) t0+30min, and C) t0 +60min. The average growth rate of the diagonals from center to tip is about 0.9 μm/min. The size of the images is 115 × 115 μm2.




AFM images showing the orientation of isotactic polystyrene crystal lamellae obtained after isothermal crystallization of a scratched thin film. a) Topographic image (size: 45×45 μm2; height range: 30 nm). The branched  features represent flat-on lamellar crystals. b, c) Topographic and phase mode image of the region indicated by the dotted box in a) (size: 5×5 μm2; height range: 60 nm) representing edge-on lamellae, continued by flat-on lamellae, oriented perpendicular to the scratching direction.

Isothermal crystallization of the rubbed thin film: phase image (size: 1 × 1 μm2)



 afm phase images

AFM phase images (1 x 1 µm2) representing the variation in the number and the distribution of crystalline cells in a thin PBh-PEO film after crystallization at -23°C for (a) 5 min, (b) 15 min, and (c) 120 min, respectively. Images (d)–(g) are enhanced 3D representations of (b) at different magnifications: (d) 1 x 1 µm2, (e) 500 x 500 nm2, (f) 250 x 250 nm2, and (g) 100 x 100 nm2




 Controlled melting of crystalline PEO cells with an AFM tip.




Schematic presentation of essential steps in polymer crystallization enabling cloning.




Transforming a large compact dendritic single crystal into a plethora of uniquely oriented small crystals. a, The starting crystal of P2VP-b-PEO, outlined by a dotted red square, after 22 min at 45°C. The inset shows the temperature protocol used for the samples shown in b,c. The dashed line indicates the nominal melting temperature. b, After an extra 20 s at 62°C plus 5 s at 63°C, and 4 min at 56°C followed by a quench to room temperature. The inset shows a magnification of the central area indicated by the dotted square. c, Another crystal analogous to a was annealed for 20 s at 62°C before it was recrystallized for 3 min at 56°C and then quenched to room temperature. d,e, AFM images of the selected regions of sample c. The red arrows in e indicate the orientation of the seeding crystal. f, Probability of orientation of the cloned crystals with respect to the seeding crystal 



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