Self Assembly – a viable manufacturing technique??

Self-assembly is scientifically interesting as it occurs inside the most basic form of life – the cell. The cell contains an astonishing range of complex structures such as lipid membranes, folded proteins, structured nucleic acids, protein aggregates, molecular machines, and many others that form by self-assembly. At the same time, self-assembly is technologically important as it provides routes to a range of materials with regular structures: molecular crystals, liquid crystals, and semicrystalline and phase-separated polymers are examples.Self-assembly is a process in which components, either separate or linked, spontaneously form ordered aggregates. Self-assembly can occur with building blocks from molecular to the macroscopic scales, provided that appropriate conditions are met. For customized materials on macroscopic length scales to be made, self-assembly is essential because the number of building blocks that would have to be precisely placed in the absence of a self-directed method are too large and the process is prohibitively time consuming. A Fermi approximation of the time required for building a 1cm cube using 10 nm building blocks with the help of optical tweezers would be in the order of a hundred million days.Self-Assembly is an alternative technique by which materials can be formed. The basic idea behind using self-assembly as a manufacturing technique is to develop building blocks that have sufficient information content inherent in them, such that a desired structure can form spontaneously from a collection of building blocks in a thermal bath.Amongst interesting building blocks that have been used to self-assemble custom materials are colloids. These mixtures of immiscible materials form fine suspensions that have potential photonic applications because the particles that make up the stabilized phase can be tuned to have diameters on the same scale as visible light (500nm) and can form periodic structures. Polystyrene colloidal crystals, consisting of charged monodisperse polystyrene microspheres suspended in water, organize into a face-centered-cubic (fcc) lattices with lattice spacings comparable to the wavelength of light (Clark, N.A. et al, Nature 1979, 281, 57-60). Such colloidal structures may also find applications in nanoscale electronics, miniature diagnostic systems and hierarchically structured catalysts amongst others. However, for the assembly of more complex structures, it has been recognized that anisotropic shape and specific interactions (or “patchiness”) are useful (Glotzer S.C., & Solomon M.J. Nature materials 2007, 6(8), 557-62).

A recent work by Chen et al., Nature (2011), 469 (7330), 381-384, has shown that triblock Janus particles can self-assemble into a Kagome lattice (see Figure 1). A triblock Janus particle has two hydrophobic poles of tunable area and an electrically charged middle band. There are two competing forces that drive self-assembly for suspensions of these particles: the hydrophobic poles agglomerate in aqueous solvents, while the charged middle bands repel. The balance between these forces can be tuned by screening the charged repulsion via the addition of an ionic compound like NaCl, and the particles can stabilize in a kagome lattice. Furthermore, sheets of kagome lattices are reported to stack in parallel layers. An interesting video of this self assembly process can be found at: http://www.nature.com/nature/journal/v469/n7330/extref/nature09713-s3.mov Thus self-assembly seems to offer a viable strategy for generating nanostructures. Recent advances in nanoparticle synthesis have led to the availability of various building blocks including spheres,cubes, rods, and tetrapods at both the nano and micro scales. Specific interactions between these building blocks can also be obtained by modifying chemical composition, changing shape, and by adding functional groups. With such a vast parameter space available to experimentalists, there is much opportunity for simulation to aid in the understanding of how such complicated building blocks assemble.

- N. Khalid Ahmed

PhD Pre-Candidate,

Glotzer Group,

Department of Chemical Engineering,

University of Michigan, Ann Arbor – 48109

nkahm@umich.edu

Solving First-order simultaneous ODEs

Solving a system of ordinary differential equations (ODEs) has always been a cakewalk. Given a pen and paper, it takes almost no time to solve a simple system such as this:

$ \frac{dx}{dt} + ax + by = 0$

$ \frac{dy}{dt} + cx + dy = 0$

One can introduce the differential operator $D$ and solve as if it were a set of algebraic equations. But when the system of equations gets bigger, things become messy. They can be solved only by an in-built solver routine in a high-level language like MATLAB. However, feeding such a huge system can still be troublesome. The purpose of this post is to expose a cute little trick in mathematics and exploit it to our advantage.

To explain the trick, we consider the above set of differential equations. We rewrite them in matrix form as:

$
\begin{bmatrix}
x'\\
y'
\end{bmatrix}
+
\begin{bmatrix}
a &b\\
c &d
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
=
\begin{bmatrix}
0\\
0
\end{bmatrix}
$

or simply,

$ X' + AX = 0$

where, $X$ is the unknown vector whose elements are $x$ and $y$.
Now, here is the trick:

Split the matrix $A$ into 3 matrices as $P^{-1} \Lambda P$, where $\Lambda$ is a diagonal matrix, with the eigenvalues of $A$ as the diagonal elements. $P$ is a matrix, which has the eigenvectors of $A$ as its columns.

This is called as Eigenvalue decomposition. This is actually an one-liner in MATLAB. Now, the matrix equation becomes:

$ X' + P^{-1}\Lambda P X = 0$

Pre-multiply by $P$ to get

$ PX' + \Lambda PX = 0$

Now, take $PX$ to be $U$, and owing to the fact that $\Lambda$ is diagonal, we get a system of the form:

$ \frac{du_1}{dt} + \lambda_1 u_1 = 0$

$\frac{du_2}{dt} + \lambda_2 u_2 = 0$

Now that we have separated the dependent variables, solving this should be a no-brainer. Finally, apply the reverse transformation $P^{-1}U$ to get the solution.

This works even when the right-hand side is non-zero. We just have to pre-multiply it by $P^{-1}$. Also, remember to transform the boundary conditions as well.

A variation to this problem may be something like this:

$ AX' + BX = c$

where $A$ and $B$ are square matrices. In such a case, first pre-multiply by $A^{-1}$ and convert it to the 'standard form' discussed above. The rest should be easy.

Always remember: The trick behind the trick is knowing when to use the trick. Else there is no point in knowing the trick.

3D printing

3D printing is a form of additive manufacturing technology where a three dimensional object is created by laying down successive layers of material^[1]. 3D printers are generally faster, more affordable and easier to use than other additive manufacturing technologies. 3D printers offer product developers the ability to print parts and assemblies made of several materials with different mechanical and physical properties in a single build process. Advanced 3D printing technologies yield models that closely emulate the look, feel and functionality of product prototypes.

In recent years 3D printers have become financially accessible to small- and medium-sized business, thereby taking prototyping out of the heavy industry and into the office environment. It is now also possible to simultaneously deposit different types of materials.

3D printers offer tremendous potential for production applications as well.^[2] The technology also finds use in the jewellery, footwear, industrial design, architecture, engineering and construction (AEC), automotive, aerospace, dental and medical industries. 

Additive Manufacturing : 

Additive manufacturing (AM) is defined by ASTM as the "process of joining materials to make objects from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies. Synonyms: additive fabrication, additive processes, additive techniques, additive layer manufacturing, layer manufacturing and freeform fabrication"^[1]

The term Additive manufacturing describes technologies which can be used anywhere throughout the product life cycle from pre-production (i.e. rapid prototyping) to full scale production (also known as rapid manufacturing) and even for tooling applications or post production customisation.

Technologies :

One variation of 3D printing consists of an inkjet printing system used by Z Corporation. A 3D CAD file is imported into the software. The software slices the file into thin cross-sectional slices, which are fed into the 3D printer. The printer creates the model one layer at a time by spreading a layer of powder (plaster, or resins) and inkjet printing a binder in the cross-section of the part. The process is repeated until every layer is printed. This technology is the only one that allows for the printing of full colour prototypes. It is also recognized as the fastest method.

Alternately, in DLP, or Digital Light Projection, a liquid polymer is exposed to light from a DLP projector under safelight conditions. The exposed liquid polymer hardens. The build plate then moves down in small increments and the liquid polymer is again exposed to light. The process repeats until the model is built. The liquid polymer is then drained from the vat, leaving the solid model. The ZBuilder Ultra is an example of a DLP rapid prototyping system.

Fused deposition modeling (FDM), a technology developed by Stratasys^[3] that is used in traditional rapid prototyping, uses a nozzle to deposit molten polymer onto a support structure, layer by layer.

Another approach is selective fusing of print media in a granular bed. In this variation, the unfused media serves to support overhangs and thin walls in the part being produced, reducing the need for auxiliary temporary supports for the workpiece. Typically a laser is used to sinter the media and form the solid. Examples of this are SLS (Selective laser sintering) and DMLS (Direct Metal Laser Sintering), using metals.

Finally, ultra-small features may be made by the 3D microfabrication technique of 2-photon photopolymerization. In this approach, the desired 3D object is traced out in a block of gel by a focused laser. The gel is cured to a solid only in the places where the laser was focused, due to the nonlinear nature of photoexcitation, and then the remaining gel is washed away. Feature sizes of under 100 nm are easily produced, as well as complex structures such as moving and interlocked parts.^[4]

Each technology has its advantages and drawbacks, and consequently some companies offer a choice between powder and polymer as the material from which the object emerges.^[5]Generally, the main considerations are speed, cost of the printed prototype, cost of the 3D printer, choice of materials, colour capabilities, etc.^[6]

Unlike stereolithography, inkjet 3D printing is optimized for speed, low cost, and ease-of-use, making it suitable for visualizing during the conceptual stages of engineering design through to early-stage functional testing. No toxic chemicals like those used in stereolithography are required, and minimal post printing finish work is needed; one need only to use the printer itself to blow off surrounding powder after the printing process. Bonded powder prints can be further strengthened by wax or thermoset polymer impregnation. FDM parts can be strengthened by wicking another metal into the part.

The democratization of 3D printing is evolving in two streams, firstly with DIY 3D Printers such as BotMill, MakerBot and RepRap for home 'desktop manufacturing'. The second stream is through online services such as Shapeways or Sculpteo that allow users to upload their designs to have them 3D printed in a wide range of materials (currently 20 material options) and shipped worldwide. The creation of tools that enable 3D printing without the direct use of CAD are also currently being implemented.

Below is the video of MakerBot - A 3D printing robot .

http://www.youtube.com/watch?v=fScRYhq-5M0

The Future :

According to Neil G

ershenfeld , 

who runs MIT's Center for Bits and Atoms,

 foresees a time when computers will upgrade from PCs to PFs, or personal fabricators. His book on FAB at home reveals a lot on this topic.

Introduction to ALD and MLD

ALD and MLD refer to "Atomic Layer Deposition" and "molecular layer Deposition". They are used to produce both organic and inorganic polymers. Miniaturization to the nanometer scale has been one of the most important trends in science and technology over the last several years. The chemistry to fabricate nanolayers, the engineering for nanocomposite design and the physics of nanostructure properties have created many exciting opportunities for research. These new interdisciplinary areas in nanoscience and nanotechnology supersede the more traditional disciplines and demand new paradigms for collaboration.





Many of our surface chemistry and thin film growth investigations utilize atomic layer deposition (ALD) techniques. ALD is based on sequential, self-limiting surface reactions as illustrated in the accompanying figure. This unique growth technique can provide atomic layer control and allow conformal films to be deposited on very high aspect ratio structures. ALD methods and applications have developed rapidly over the last few years. In particular, ALD is on the semiconductor road map for high-k gate oxides and diffusion barriers for backend interconnects.


ALD is based on sequential, self-limiting surface chemical reactions. For example, for Al2O3 deposition, the binary reaction: 2Al(CH3)3 + 3H2O -> Al2O3 + 6CH4 can be split into the following two surface half-reactions


A) AlOH* + Al(CH3)3 -> AlOAl(CH3)2* + CH4
B) AlCH3* + H2O -> AlOH* + CH4


where the asterisks denote the surface species. In the (A) reaction, Al(CH3)3 reacts with the hydroxyl (OH*) species and deposits aluminum and methylates the surface. The (A) reactions stops after all the hydroxyl species have reacted with Al(CH3)3. In the (B) reaction, H2O reacts with the AlCH3* species and deposits oxygen and rehydroxlates the surface. The (B) reactions stops after all the methyl species have reacted with H2O. Because each reaction is self-limiting, the Al2O3 deposition occurs with atomic layer control. By applying these surface reactions repetitively in an ABAB... sequence, Al2O3 ALD is achieved with a growth rate of 1.1 Å per AB cycle. We have also extended the ALD method to deposit single-element metal films.





Similar self-limiting surface reactions can be employed for the growth of organic polymer films. This film growth is described as molecular layer deposition (MLD) because a molecular fragment is deposited during each reaction cycle.The precursors for MLD have typically been homobifunctional reactants. A cartoon illustrating the MLD process is shown in the nearby figure. MLD methods have been developed for the growth of organic polymers such as polyamides.The polyamides have been deposited using dicarboxylic acid and diamines as the reactants. New approaches to MLD involve heterobifunctional and ringopening precursors. In addition to organic polymers, the precursors for ALD and MLD can be combined to grow hybrid organic-inorganic polymers.


Source:
One of the research groups that pioneers in this study can be visited from here.

Fluidics

Fluidics (also known as Fluidic logic) is the use of a fluid or compressible medium to perform analog or digital operations similar to those performed with electronics. 

The physical basis of fluidics is pneumatics and hydraulics, based on the theoretical foundation of fluid dynamics. The term Fluidics is normally used when the devices have no moving parts, so ordinary hydraulic components such as hydraulic cylinders and spool valves are not referred to as fluidic devices. The 1960s saw the application of fluidics to sophisticated control systems, with the introduction of the fluidic amplifier. 

A jet of fluid can be deflected by a weaker jet striking it at the side. This provides non-linear amplification, similar to the transistor used in electronic digital logic. It is used mostly in environments where electronic digital logic would be unreliable (e.g., systems exposed to high levels of electromagnetic interference or ionizing radiation).

Nanotechnology considers fluidics as one of its instruments. In this domain, effects such as fluid-solid and fluid-fluid interface forces are often highly significant. Fluidics have also been used for military applications.

Amplifiers :

The basic concept of the fluidic amplifier is shown here. A fluid supply, which may be air, water, or hydraulic fluid, enters at the bottom. Pressure applied to the control ports C₁ or C₂ deflects the stream, so that it exits via either port O₁ or O₂. The stream entering the control ports may be much weaker than the stream being deflected, so the device has gain.

Given this basic device, flip flops and other fluidic logic elements can be constructed. Simple systems of digital logic can thus be built.

Fluidic amplifiers typically have bandwidths in the low kilohertz range, so systems built from them are quite slow compared to electronic devices.

Systems :

Fluidic components appear in some hydraulic and pneumatic systems, including some automotive automatic transmissions. As digital logic has become more accepted in industrial control, the role of fluidics in industrial control has declined.Fluidic injection is being researched for thrust vectoring in aircraft jet engine nozzles, and for ships. Such systems divert thrust via fluid effects . Tests show that air forced into a jet engine exhaust stream can deflect thrust up to 15 degrees. Such nozzles are desirable for their lower: mass, cost (up to 50% less), inertia (for faster, stronger control response), complexity (mechanically simpler, no moving parts or surfaces), and radar cross section for Stealth. This will likely be used in many unmanned aircraft and 6th generation fighter aircraft.

Professor Nikolai Priezjev of the Department of Mechanical Engineering writes about fluidics and micro - fluidics  here .The transport and manipulation of small amounts of fluids are crucial for emerging technologies. A brisk demand for micro-devices, which are  used for the transportation of nanovolume  liquid samples, gave rise to a new exciting field called microfluidics. This field combines various  disciplines including engineering, chemistry, physics, and biology. The long range goal in modern technology is a reduction in size and the further development of microfluidic devices, which could be used for diagnoses of diseases, for the autonomous or remote detecting of biological and chemical  agents, and for gene and drug delivery.  

A very good introduction to microfluidics can be found at the wiki page. Microfluidics news is another kind of a aggregator for papers published on this subject . 

Food for thought :

  Is it possible to use constructal theory as a basis to design applications using microfluidics  ?? What would be the implications of doing so ?

Sources of information :

Wikipedia and Google .