View source for Phase Diagram and Effective Shape of Semiﬂexible Colloidal Rods and Biopolymers

''Entry by Max Darnell, AP 225, Fall 2011
''

Reference:

'''Title:''' Phase Diagram and Effective Shape of Semiﬂexible Colloidal Rods and Biopolymers

'''Authors:''' M. Dennison, M. Dijkstra, and R. van Roij

'''Journal:''' PRL 106, 208302 (2011)

'''Keywords:''' [[self-assembly]], [[liquid-crystal]], [[virus]], [[colloid]]

== Summary ==
Rodlike particles show great promise in bioengineering due to their ability to self-assemble into a wide variety of liquid-crystal phases. One of the most important systems is f n viruses, which can be engineered into needles by incorporating a polyethylene-glycol (PEG) coating. Unfortunately, however, these phase diagrams of such systems, and the mechanisms behind each phase, have been poorly understood. This paper identifies the key parameter in the state of the system as flexibility of the needles. Also, the stretching of micelles formed from these needles is examined.

== Methods/Results ==

The authors followed a segmented-chain model first introduced by Wessels and Mulder in which flexibility is incorporated into the model by introducing a bending potential parameter between segments in the chain. Also, the excluded volume is taken into account. The model is then generalized to two-component systems and the full phase behavior is mapped out. Also, the effective particle shape is calculated, which turns out to be strongly state-dependent and thus crucial in building phase diagrams. The authors calculated the phase diagrams for mixtures of bare fd particles (species 1, thin) and PEG-coated ones(species 2, thick), with equal contour and persistence lengths.

[[image:Darnell6_1.jpg|thumb|500px|center]]

Figure 2 shows the effective shape for a mixture of thick-thin fd virus particles throughout the phase diagram. It is immediately apparent that throughout the phase diagram, while the rods always behave as shorter,thicker rods, the effective shape varies considerably. Interestingly, the thick rods stretch out more than the thin rods, with the rods now effectively differing in both diameter and length. The authors conclude that  that a ﬁxed effective shape does not capture the essential physics of these suspensions; the state-point dependent stretching of the ﬂexible rods is a key feature.

[[image:Darnell6_2.jpg|thumb|500px|center]]

Finally, the authors studied worm-like micelles (Figure 3) in the I-N phase transition for different micelle models. In all, the incorporation of flexibility into the model improved the correlation of experimental results to the model as opposed to using rigid rods. Essentially, the effective shape of the particles is allowed to vary across the phase diagram. 

[[image:Darnell6_3.jpg|thumb|center|350px]]
== Connection to Soft Matter ==

Phase diagrams represent one of the most important tools in soft matter physics, since understanding of a phase diagram allows for the effective processing of different mixtures and materials. The system of interest, f n virus particles, is an increasingly interesting system as the field becomes more bio-oriented. In addition, this paper raises the question of applying similar ideas of introducing flexibility into models into inhomogeneous systems. The prospect of assessing the phase behavior of inhomogeneous systems, especially those which are biologically relevant, is extremely interesting since the mechanical interactions of biological systems are being increasingly appreciated.