Session W33: Nonequilibrium and Templated Assembly

Designing elastic sheets to self-assemble in a viscous environment

A recent work by Boncheva et al. (Proc. Nat. Acad. Sci. 2005 102: 3924-3929) has raised some basic issues about designable self-assembly within the context of planar elastic sheets which fold into 3D structures under magnetic forces. While being agitated in water, millimeter-scale structures were shown to fold with varying success depending on the locations of magnets on the sheets. Our work considers how to design such structures, an understanding of which will be necessary when moving this process to the micron scale. Among the important parameters are the geometry of the flat sheet, the configurations of the magnets, and the ratios of magnetic to elastic forces. We consider this problem using a numerical model of an elastic sheet, and restrict to the simpler case of electrostatic forces in a quasi-static limit. We identify a simple algorithm for choosing configurations of electrostatic charges, and select ratios of charge strength to elastic energy using physical arguments. We then demonstrate our algorithm on dynamical foldings of a sphere and more general geometries, in the overdamped viscous regime. We also give an asymptotic formula for the elastic energy in the thin-plate limit.   

Dynamic self-assembly of magnetic particles on the fluid interface: surface wave assisted effective magnetic exchange

Novel dynamic self-assembled multi-segment magnetic structures (``snakes'') induced by a vertical alternating magnetic field in an ensemble of magnetic particles suspended on a liquid/air interface are reported. We demonstrate that these structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. The segments of magnetic ``snake'' exhibit long-range antiferromagnetic ordering mediated by the surface waves, while each segment is composed of ferromagnetically aligned chains of microparticles. To describe observed magnetic behavior of the generated structures we propose a simple phenomenological model where the effect of surface waves is replaced by an effective exchange interaction. In the framework of the proposed model the effective exchange constants corresponding to different regimes of magnetic driving were extracted from the experimental data.   

Demonstration of shape selectivity in depletion-induced colloidal aggregation

We have developed a set of monodisperse, non-spherical colloids using photolithography in order to elucidate fundamental questions related to the role of shape in defining colloidal phase behaviour and, eventually, to build new microstructured materials. Our goal is to use depletion and DLVO forces to induce specific and directional interactions during the aggregation process of these non-spherical colloids. We will first describe the development and basic characterization of these particles, including index of refraction, zeta potential, polydispersity, and surface roughness. We will then present an initial state diagram of depletion-induced structure, and provide mechanistic insight into the role of specific characteristics of the particles in defining this behaviour. We will finally discuss theoretical calculations of the expected interactions and the possibility of generalizing the results to other colloidal systems.   

Pattern formation and liquid crystallinity in evaporating drops of gold nanorods.

The drying drops of colloidal rods on glass provide a coffee ring type stain accompanied by formation of highly birefringent deposit, suggesting lyotropic liquid crystalline phase forms prior to deposit formation. Further, Liesegang ring like patterns which have concentric deposits, appear on drying, only under specific conditions, and in optical microscope show similar birefringent bands. Similar experiments done on carbon coated copper TEM grids and observed under TEM, show smectic and nematic-like phases as well as create vortex-like assembly of nanorods reminiscent of defect structures in liquid crystals, and are likewise explained in terms of lowest energy configuration of twist configuration. In the present, work we compliment the rich experimental observations, by proposing mechanisms that explain formation of concentric rings, as well as other complex patterns using both the existing framework based on coffee ring stain models and on basis the observed liquid crystalline phase behavior.   

Molecular Detection with Self-Assembled Gold Nanoparticle Wires

Recently, we have reported the creation of gold nanowires by evaporation-driven vertical colloidal deposition (VCD) of gold nanoparticles. Subsequently, we have noted systematic changes in conductivity associated with post-deposition annealing. Here we describe the change in room temperature conductivity of gold nanoparticle wires after exposure to thiol-derivatized molecules. A self-assembled gold nanoparticle wire is immersed into a solution of octadecanethiol (ODT) dissolved in ethanol. An ODT molecule comprises a sulfur atom and a short hydrocarbon chain. The sulfur atoms form metallic bonds with the conduction electrons on the surface of the gold nanoparticles, and the high surface to volume ratio of the wire allows us to see a marked jump in resistance. We have seen roughly a 10 percent increase in the resistance of previously annealed wires when immersed in 2 millimolar ODT solution. Further experiments include measurement of resistance as a function of thiol-concentration and as a function of wire preparation prior to immersion.   

Orientational Order of Molecular Assemblies on Inorganic Crystals

Surfactant micelles form oriented arrays on crystalline substrates such as HOPG (Highly Ordered Pyrolytic Graphite) although registration is unexpected since the template unit cell is small compared to the size of a rod-like micelle. In addition, with atomic force microscopy, we show that orientational ordering is a dynamic, multi-molecule process. Interaction energy calculations based on molecular simulations reveal that orientational energy differences on a molecular scale are too small to explain matters. However, treating the cooperative processes as a balance between van der Waals torque on a large, rod-like micellar assembly and Brownian motion shows that orientation is favored. Our study provides a physical insight on regulation of self-assembly structures at small length scale.   

Vesicle-Templated Supramolecular Assembly of Alginate Nanogels

In this work, large uni- and multilamellar dipalmitoyl phosphatidylcholine (DPPC) liposomes (800-900 nm in diameter) were used as templates for the formation of alginate gels. DPPC liposomes encapsulating sodium alginate were prepared in a 15 mM NaCl buffer solution by the solvent injection method, followed by several freeze/thaw cycles to achieve higher encapsulation efficiency and larger vesicle size. Purified liposomes were placed in a 10 mM CaCl2 buffer solution and permeabilized by heating and cooling over the phase transition temperature (Tm) of DPPC. The increased membrane permeability at the Tm allowed calcium ions from the surrounding buffer solution to traverse the membrane to the interior region and subsequently crosslink the encapsulated alginate. Removal of the lipid by detergent resulted in nanogels that were similar in size (800-900 nm in diameter) to the template liposome, as characterized by multi-angle and dynamic light scattering techniques. In the future these nanogels may be useful for single-molecule encapsulation or controlled release applications.   

Self-Assembly of Two Dimensional Hard Rod Fluids in the Presence of Surface Barriers

Hard rods are interesting building blocks for assembly as they organize themselves into different phases depending on their aspect ratio and concentration. Much work has been done to develop an understanding of the various phases exhibited by bulk, hard-rod fluids in two and three dimensions. For applications in nanoelectronics, it is desirable to be able to assemble nanowires into various structures conducive to nanocircuitry. In this work, we use Monte Carlo simulations to examine the phase behavior of two different systems involving two-dimensional, colloidal nanowires. In the first study, we probe the influence of regularly spaced surface barriers on the ordering of two-dimensional hard rods. By varying the spacing between the barriers and their size relative to the rods, we demonstrate that a number of interesting phases can be achieved, indicating that surface barriers can effectively tune the alignment of the rods. In a second study, we probe the hard-sphere templated assembly of colloidal nanowires. We demonstrate that a number of interesting and potentially beneficial phases occur as the rod length relative to the sphere diameter, rod aspect ratio, and concentration is varied.   

Multipolar interaction model for microtubule self-assembly

Tubulin protein monomers (m = 50 kDa, d = 4-5 nm) are known to self-assemble into biologically significant structures called microtubules. Calculations for microtubule models using the full crystallographic structure of tubulin are prohibitive. As a substitute, we investigate a simpler multipolar interaction model of tubulin which can capture important features of microtubules. We present energy-minimization calculations showing that a four point-charge rectangular model reproduces the 0.93 nm staggering of observed microtubules. We then attempt to validate these static Coulomb calculations with molecular dynamics (MD) using NAMD (from the Theoretical and Computational Biophysics group at the University of Illinois). These simulations include electrostatic interactions, stiff bonded interactions, a Lennard-Jones potential and Langevin damping. The results of the MD simulations are strongly dependent on each of these influences. We find stable filaments of tubulin using the multipole model in MD simulations. When these filaments are combined into a realistic microtubule in MD, an energy minimum is found which supports a stable tube. The study encompasses fraying of tube ends, staggering angle, and ring stability for tubulin and microtubules based on our simple, four charge multipolar model.   

Thermoreversible Vesicle-to-Micelle Transitions in Surfactant-Salt Mixtures

Mixtures of the cationic surfactant, CTAB and the organic compound, 5-methyl salicylic acid (5mS) spontaneously self-assemble into unilamellar vesicles at room temperature. Upon heating, these vesicles undergo a thermoreversible transition to wormlike micelles. This phase transition results in a 1000-fold increase in the solution viscosity with increasing temperature. Small-angle neutron scattering (SANS) measurements show that the phase transition from vesicles to micelles is a continuous one, with the vesicles and micelles co-existing over a range of temperatures. A mechanism for the above phase transition is proposed, based on the desorption of bound aromatic counterions from the vesicle as a function of temperature.   

Self-assembly models for lipid mixtures

Solutions of mixed long and short (detergent-like) phospholipids referred to as ``bicelle'' mixtures in the literature, are known to form a variety of different morphologies based on their total lipid composition and temperature in a complex phase diagram. Some of these morphologies have been found to orient in a magnetic field, and consequently bicelle mixtures are widely used to study the structure of soluble as well as membrane embedded proteins using NMR. In this work, we report on the low temperature phase of the DMPC and DHPC bicelle mixture, where there is agreement on the discoid structures but where molecular packing models are still being contested. The most widely accepted packing arrangement, first proposed by Vold and Prosser had the lipids completely segregated in the disk: DHPC in the rim and DMPC in the disk. Using data from small angle neutron scattering (SANS) experiments, we show how radius of the planar domain of the disks is governed by the effective molar ratio $q_{eff}$ of lipids in aggregate and not the molar ratio $q (q$ = [DMPC]/[DHPC] ) as has been understood previously. We propose a new quantitative (packing) model and show that in this self assembly scheme, $q_{eff }$is the real determinant of disk sizes. Based on $q_{eff }$, a master equation can then scale the radii of disks from mixtures with varying $q$ and total lipid concentration.   

End-to-End Adhesion of Short Duplex DNA Oligomers

The classic model for the formation of liquid crystal phases of rod shaped objects was presented by Onsager, who showed that hard rods of length L and diameter D form a nematic phase when volume fraction is f $>$ fc = 4D/L. This criterion is obeyed reasonably well for rod-shaped nucleosomal [150 base pair (bp)] B-DNA duplexes (L = 50nm, D = 2nm). Recently we found, however, that very short duplex B-DNA oligomers, 6bp -- 20bp (2 to 6nm) in length, form similar nematic and columnar LC phases, even though their L/D ratio is almost 1 and f $<<$ fc. We attribute these phases to intermolecular interaction which provides an end-to-end adhesion force between these short oligomers to form extended anisotropic ``living polymers.'' The theory of the formation of such anisotropic aggregates will be reviewed and applied to the DNA observations. Work supported by NSF MRSEC Grant DMR 0213918 and NSF Grant 0072989.   

Modeling of fractal intermediates in the self-assembly of silicatein filaments

Silicateins are proteins with catalytic, structure-directing activity that are responsible for silica biosynthesis in certain sponges, Self-assembly of the silicatein monomers and oligomers was previously shown experimentally (Murr and Morse 2005) to form fibrous structures through the formation of diffusion limited, fractally patterned aggregates on the path to filament formation. We present a diffusion-limited aggregation (DLA) based model that is capable of capturing the basic properties of this self-assembly process. The Silicatein oligomer is modeled with three sites of attachment. Rules of attachment are specified that allow for specific interaction between these sites when oligomers are in proximity. The process differs from a DLA process in the following: 1) The process of aggregation is continued dynamically, i.e. the growing structures are spatially distributed and keep diffusing as they are growing 2) The molecules are oriented. Thus rotational diffusion is important. 3) The attachment can happen at more than 1 site and the strength of the active sites can be varied. We show that the self-assembled structures have a good level of similarity with the in-vitro experimental results. We quantify this by comparing the fractal dimension of the experimental data and the model output.   

Structure of Porous Columns Self-assembled from Dendritic Dipeptides

Synthetic pores are an important step in the development of biomimetic materials incorporating features such as trans-membrane channels, gene delivery, protein folding, and selective encapsulation. We have used small-angle xray scattering to study helical pores self-assembled from dendritic dipeptides. The main features of the supramolecular assembly are computed by least-squares fitting the parameters of a simplified structural model to the x-ray diffraction data. This work reports the supramolecular assembly temperature stability and conformational changes of the 3-dimensional packing as a function of dipeptide structure and stereochemistry. The results provide a methodology to design the synthetic pores in order to control the pore size and separation at the \AA\, level, according to the desired function.   

X-ray Study of the Electrical Double Layer at the Oil - Water Interface

Our understanding of the structure of the insulator/electrolyte solution interface is of fundamental importance in describing electrochemical processes in systems involving membranes, absorbers, catalysts, surfactants, or surfaces of other dielectrics. Due to the specific interaction of the solvent with the insulator, a heterogeneous highly polarized region or an electrical double layer forms at the boundary between bulk phases. We studied the spatial structure of the transition region between n-hexane (insulator) and silica sol (electrolyte) solution by x-ray scattering. The structure factor of the interface and the angular dependence of the grazing incidence small-angle scattering can be explained by the interfacial model, which agrees with the theory of the electrical double layer, shows the separation of positive and negative charge, and consists of three layers, i.e., a thin layer of Na$^{+}$, a monolayer of nanocolloidal particles as the part of the diffuse layer, and a low-density layer sandwiched between them.