




What is soft matter?




Buckling thin disks and ribbons with nonEuclidean metrics
November 15, 2009
C.D. Santangelo, "Buckling thin disks and ribbons with nonEuclidean metrics," EPL 86 (2009) 34003.
Abstract:
I consider the problem of a thin membrane on which a metric has been prescribed, for example by lithographically controlling the local swelling properties of a polymer thin film. While any amount of swelling can be accommodated locally, geometry prohibits the existence of a global strainfree configuration. To study this geometrical frustration, I introduce a perturbative approach. I compute the optimal shape of an annular, thin ribbon as a function of its width. The topological constraint of closing the ribbon determines a relationship between the mean curvature and number of wrinkles that prevents a complete relaxation of the compression strain induced by swelling and buckles the ribbon out of the plane. These results are then applied to thin, buckled disks, where the expansion works surprisingly well. I identify a critical radius above which the disk inplane strain cannot be relaxed completely.




Coercing columns to curve
July 20, 2007
C.D. Santangelo, V. Vitelli, R.D. Kamien and D.R. Nelson, "Geometric Theory of Columnar Phases on Curved Substrates", Phys. Rev Lett. 99 (2007) 017801 (Editor's suggestion)
Abstract:
We study thin selfassembled columns constrained to lie on a curved, rigid substrate. The curvature presents no local obstruction to equally spaced columns in contrast with curved crystals for which the crystalline bonds are frustrated. Instead, the vanishing compressional strain of the columns implies that their normals lie on geodesics which converge (diverge) in regions of positive (negative) Gaussian curvature, in analogy to the focusing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field.




Packing soft particles to make complex mesophases
May 9, 2007
M.A. Glaser, G.M. Grason, R.D. Kamien, A. Kovsmrlj, C.D. Santangelo, and P. Ziherl, "Soft Spheres Make More Mesophases", Europhysics Lett. 78 (2007) 46004 [condmat/0609570].
Abstract:
We use both meanfield methods and numerical simulation to study the phase diagram of classical particles interacting with a hardcore and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hardcore and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant interaggregate separation.




Diblock copolymers: undulated cylinders driven by charge frustration
August 9, 2006
G.M. Grason and C.D. Santangelo, Eur. Phys. J. E 20 (2006) 335.
Abstract:
We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic
block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt
concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable.
By modeling the shape of the cylinder ends, we find that the free energy barrier for the transition from cylinders to
spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity.
This suggests that observed undulated cylinder phases are kinetically trapped structures.




Shnerk's first surface
August 9, 2006
C.D. Santangelo and R.D. Kamien, Phys. Rev. Lett. 96 (2006) 137801.
Abstract:
We develop an explicit and tractable representation of a twistgrainboundary phase of a smectic A liquid crystal.
This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the
bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and
discuss the relation of this structure to the Schwarz D surface.
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