Bottom-up nanotechnology

When devices are built from the bottom up, macroscopic tools are not used to shape the devices. The important thing is to bring the right starting materials together in the right environment and let them construct themselves into nanodevices. Living cells are the best examples structures that grow from the bottom up. In this section first chemical binding will be reviewed the principles of self-assembly will be described. At the end of the section a few building blocks for bottom-up construction like carbon nanotubes, C60 and DNA will be discussed.

When two atoms form a bond, there will be a concentration of electron wavefunctions between the nuclei. A more electronegative atom will pull the average position of the electrons in the bond away from an atom with a lower electronegativity. Electronegativity is a measure of the tendency of an atom to attract electrons. The more electronegative an atom is, the more it pulls an electron towards itself. The electronegativity of atoms can be found in the periodic table of electronegativity.

Ionic bonds
If the electronegativity of one atom is much greater than another atom, then the more electronegative atom takes an electron almost completely away from the less electronegative atom and an almost purely ionic bond is formed. The atom that loses an electron becomes a positive ion and the atom that gains an electron becomes a negative ion. These ions are held together by the electrostatic force between the positive and negative charges. Ordinary table salt, NaCl, is held together by ionic bonds. The binding energy for NaCl is 7.97 eV per bond.

Since an ionic bond is mostly based on an electrostatic interaction, the order of magnitude of the bond strength can be estimated by calculating the energy that is needed to push a positive ion (charge e) away from a negative ion (charge -e). The Coulomb force between these two charges is,

F = e².
4πε0r²

The energy needed to push two charges apart from an interatomic distance of about 0.2 nm is,

E = ∞
∫
0.2 nm
-e²dr = 7 eV.
4πε0r²

Covalent bonds
In a covalent bond, atoms share electrons. This reduces the quantum confinement energy of the electrons because the electron wavefunctions spread out over the two atoms. A bond between two identical atoms is always a covalent bond. While electrostatic force also play a role in covalent bond, the most important energy is the quantum confinement energy.

To estimate the strength of a covalent bond, a three-dimensional square well can be used as a simple model for an atom. The lowest energy of an electron in a three-dimensional square well is,

E =  3h².
8mL²

When two such cubic atoms come together to form a molecule with dimensions L×L×2L, the electrons can spread out and their energies become lower. The lowest energy level of the molecule is,

E =  9h².
32mL²

Each of the electrons from the cubic atoms could occupy one of the two spin degenerate ground states of the rectangular molecule. The corresponding decrease in energy would be,

ΔE =  3h².
16mL²

For cubic atoms with a size L = 0.2 nm, this decrease in energy is ΔE = 14 eV.

To properly calculate the energy of a covalent bond, the electrostatic interactions of the electrons and ions would have to be taken into account. However, this calculation describes the essence of covalent bond; the energy is decreased because both electrons can spread out over a larger volume and that decreases the quantum confinement energy. Note that the energy of a covalent bond is approximately equal to the energy of an ionic bond. This is not a coincidence. The size of an atom is determined by a compromise between the electrostatic energy (that is lower when the electron comes closer to the ion) and the quantum confinement energy (that is higher as the electron is confined to a smaller region around the ion). At the length scale of an atomic radius, the electrostatic energy about balances the quantum confinement energy.

Polar bonds
Many bonds have a partly ionic character and partly covalent character. A bond between two atoms where one has a higher electronegativity than the other is called a polar bond because one end of the bond is more positively charge and the other end is more negatively charged. The reduction of confinement energy and electrostatic forces both play a role in a polar bond.

Bondlength (nm) and bond energy (eV)

Bond

Length

Energy

Bond

Length

Energy

H--H

0.074

4.52

H--C

0.109

4.28

C--C

0.154

3.61

H--N

0.101

4.05

C=C

0.134

6.36

H--F

0.092

5.89

C≡C

0.120

8.70

H--O

0.096

3.79

C--O

0.143

3.73

H--Cl

0.127

4.48

C--S

0.182

2.82

H--Br

0.141

3.79

C--F

0.135

5.06

H--I

0.161

3.09

C--Cl

0.177

3.42

N--N

0.145

1.76

C--Br

0.194

2.98

I--I

0.267

1.57

C--I

0.214

2.24

O--O

0.148

1.50

C--N

0.147

3.19

O=O

0.121

5.16

N--N

0.145

1.76

N≡N

0.110

9.79

O--O

0.148

1.50

Cl-Cl

0.199

2.52

F--F

0.142

1.64

Br-Br

0.228

2.00

Quantum mechanics can be used to precisely calculate these bond lengths and energies. However, these calculations are mathematically complicated. A good approximation to potential of a molecular bond is the Morse potential.

U(r) = U0(e-2(r - r0)/a - 2e-(r - r0)/a)

Here U0 is the bond energy and r0 is the bond length that can be read from the above table. The parameter a describes the width of the Morse potential and is typically between r0/2 and r0/15.

The Morse potential with U0 = 3 eV, r0 = 0.15 nm, and a0 = 0.075 nm.

The minimum of the Morse potential occurs are r = r0. The potential rises sharply for small bondlengths due to the Coulomb repulsion of the positive nuclei when they get too close together.

Sigma bonds
In a sigma bond, the electrons wavefunctions that form the bond are concentrated along the line between the two nuclei. Examples of overlaping are shown below. Hybrid sp, sp², and sp³ orbitals can also form sigma bonds. Two parts of a molecule that are connected by a single sigma bond can rotate with respect to each other.

 →  A sigma bond formed by two s-orbitals.
 →  A sigma bond formed by an s-orbital and a p-orbital.
 →  A sigma bond formed by two p-orbitals.

Pi bonds
A pi bond forms when two side by side p-orbitals overlap. The electron wavefunction overlap in two places above and below the line connecting the two nuclei. Two parts of a molecule connected by a pi bond cannot rotate with respect to each other.

 →  A pi bond formed by two p-orbitals.

Single bond
In a single bond, one pair of electrons is shared between two atoms. Single bonds are always sigma bonds.

Double bonds
A double bond is a sigma bond and a pi bond. The pi part of a double bond does not allow for rotation.

Triple bonds
The triple bond is made up of one sigma bond and two pi bonds. It does not allow rotation.

Metallic bonds
In a metal, the electron wavefunctions of the valence electrons spread out over the whole crystal. This results in a large decrease in confinement energy and makes a strong bond. The electrons in a metal are delocalized. This makes metals good electrical and thermal conductors. The transition metals have high melting points because the d-electrons delocalize as well as the s-electrons and they all form metallic bonds.

Hydrogen bonds
Hydrogen tends to form polar bonds which leave the hydrogen atom with a net positive charge. The positively charged hydrogen can then be attracted to a negatively charged region of another molecule forming a hydrogen bond. Hydrogen bonds tend to be weaker than covalent or ionic bonds, typically 0.04 eV - 0.2 eV. The hydrogen bond formed between water molecules has a dissociation energy of 0.24 eV. A hydrogen bond has is approximately 90% ionic and 10% covalent.

Van der Waals bonds
Van der Waals bonds are weak bonds with a dissociation energy of about 0.01 eV. The binding force comes from charge fluctuations. All atoms exhibit charge fluctuations where the electrons are not symmetrically distributed around the nucleus. This results in a fluctuating electric dipole moment. Two nearby atoms can reduce their total energy if they fluctuate in unison so that the positive end of one of the atoms is located by the negative end of the other atom. This results in a dipole-dipole force that holds the atoms together.

Bottom-up production and assembly
One way to make structures with sizes of a few nanometers is to use biotechnology. Nanoscale components such as motors, bearings, sensors, acuators and pumps are available in biological systems. It is sometimes possible to find a bacteria that uses a component like a motor that is useful in another application. Many of these bacteria can then be cultured and the motors can be extracted from them. It is possible to use genetic engineering to modify the biological components making them more suitable for a certain application. Here's an excerpt from Scientific American about this approach.

Molecular motor

Fig. 4.1. ATPase bonded to a propeller made from protein. The propeller spins at the rate of 3 to 4 revolutions per second.

Living cells, too, have engines, such as those that wave bacterial cilia or transport energy across membranes. The scientists found their molecular stator and rotor in the form of an ubiquitous molecule, the enzyme ATPase. The ATPase molecular motors occur on the membranes of mitochondria, microscopic bodies in the cells of nearly all living organisms, as well as in chloroplasts of plant cells; within these organelles, the enzyme is responsible for converting food to usable energy.

The moving part of ATPase is a central protein shaft (or rotor, in electric-motor terms), less than 12 nanometers in diameter, that rotates in response to electrochemical reactions with each of the molecule's three proton channels (comparable to the electromagnets in the stator coil of an electric motor). ATP (adenosine triphosphate) is the fuel for the molecular motor's motion. Energy becomes available when atomic bonds between phosphate atoms are broken during hydrolysis, converting ATP into ADP (adenosine diphosphate). During hydrolysis, the shaft rotates in a counterclockwise direction, whereas it rotates clockwise during ATP synthesis from ADP.

To fashion ATPase into a motor capable of mechanical work, Montemagno, an assistant professor of agricultural and biological engineering, turned to genetic engineering. He produced the ATPase molecules using Escherichia coli bacteria that were altered to include a gene sequence for ATPase from the thermophilic bacterium Bacillus PS3.

He then separated the molecules from the cell membrane and attached them to a metallic substrate using a synthetic peptide composed of histidine and other amino acids. These histidine peptides, like little "legs," tied the molecular motors to the substrates, nanofabricated patterns of gold, copper or nickel--the three standard contact materials in integrated circuits that might one day provide control systems for the motors. Of the three metals, nickel showed the greatest adhesion.

Next, the researchers bonded propeller-like filaments made from polymerized proteins to the top of the motor shaft. With further genetic manipulation, the Cornell engineers expect E. coli to turn out ATPase molecules with tiny propellers built right in--making each a kind of nano-motorboat. The protein "props," ranging from 0.5 to 8 microns long, were made of a material that would fluoresce under certain wavelengths of laser light so their motion could be viewed.

From Molecular Model-T by Alan Hall, Scientific American September 21, 1999.

Another route to building nanostructures is to use supramolecular chemistry. Supramolecular chemists use weak noncovalent bonds such as hydrogen bonds or van der Waals bonds to assemble molecules into larger structures. Since weaker bonds are used, serveral binding sites are necessary. Two molecules that are assembled by supramolecular chemistry must have complementary shapes so that they fit like a lock and key. The two molecules can then bond by weak bond in several places where they come in contact with each other. This can be used for chemical recognition. If two molecules with complementary structures are added to a solution they will find each other and bind together. I well known example is the combination biotin - streptavidin. These two bio-molecules use about ten hydrogen bonds to stick together.

Fig. 4.2. Streptavidin bound to the (much smaller) molecule biotin.

DNA is another material that uses many weak bonds for recognition. Apart from its biological importance, DNA is also an interesting material for nanotechnology. Single strands of DNA with any base sequence desired up to lengths of about 100 bases can be ordered commercially. By cleverly choosing the base sequences of different strands and then letting them come together in solution, complicated nanostructures can be formed. Figure 3.2 shows an example of a structure constructed using DNA.

Fig. 4.3. A square knotted structure made by combining different strands of DNA. This picture was taken from Nadrian Seeman, DNA in a material world, Nature vol. 412 p. 427 (2003).

Paul W. K. Rothemund Folding DNA to create nanoscale shapes and patterns, Nature 440, 297-302 (16 March 2006)

Folding DNA to create nanoscale shapes and patterns

Top row, folding paths. a, square; b, rectangle; c, star; d, disk with three holes; e, triangle with rectangular domains; f, sharp triangle with trapezoidal domains and bridges between them (red lines in inset). Dangling curves and loops represent unfolded sequence. Second row from top, diagrams showing the bend of helices at crossovers (where helices touch) and away from crossovers (where helices bend apart). Colour indicates the base-pair index along the folding path; red is the 1st base, purple the 7,000th. Bottom two rows, AFM images. White lines and arrows indicate blunt-end stacking. White brackets in a mark the height of an unstretched square and that of a square stretched vertically (by a factor >1.5) into an hourglass. White features in f are hairpins; the triangle is labelled as in Fig. 3k but lies face down. All images and panels without scale bars are the same size, 165 nm × 165 nm. Scale bars for lower AFM images: b, 1 μ c - f, 100 nm.

Another way to use DNA for nanotechology is to attach a single strand to one component and the complementary DNA strand to a second component that should be attached to the first. In Delft, experiments are underway to attach DNA to carbon nanotubes. The complementary strands are attached to a substrate at a place where a nanotube should be included in an electronic circuit. The chemical recognition properties of DNA are used to construct a circuit.

Fig. 4.4. A short single strand of DNA is attached to a carbon nanotube. See http://www.mb.tn.tudelft.nl/projects/DNA_assembly_nanotubes/DNA_selfassembly.html.

Molecules like lipids that have both hydrophilic parts and hydrophobic parts can self-assemble in polar solvents like water or non-polar solvents like oil. Monolayers of these molecules tend to form at the interface between a polar solvent and a non-polar solvent or at the solvent air interface. Soap films are examples of this kind of monolayer. Molecules with polar and non-polar parts can also spontaneously form bilayers and micelles. Micelles are aggregates of tens to hundreds of molecules. They form if the concentration of molecules is above a critical concentration. Whether the polar parts or the non-polar parts arrange themselves on the surface of the micelles depends on whether the solvent is polar or non-polar.

Fig. 4.5. Micelles in a polar and a non-polar solvent.

A Liposome is a self-assembled container that can be used for drug delivery.

Some molecules that have very low monomer solubilities form bilayers instead of micelles. Bilayers are usually more rigid and ordered than micelles. An important example of a bilayer is a cell wall. Figure 3.5 shows cells incorporate many nanosale components in cell walls.

Fig. 4.6. A cell membrane. The membrane is made of a self organizing lipid bilayer. Various structures can be embedded into the lipid bilayer.

Self-assembly , U.S. National Academy of Sciences.

Self-assembly

Surfactant molecules (e.g., phospholipids, soaps, detergents, and block copolymers) self-assemble [15] in selective solvents (e.g., water) to form bilayer membranes and micelles of several structures (see figure). The membranes also organize in a variety of patterns. Such self-assembled structures may be swollen by adding an organic solvent to the system, which remains stable as a clear single phase. Such two-solvent composites are called microemulsions. Surfactant bilayers have been investigated for many years as model systems for biological membranes.

Repulsive forces between the surfactant head groups organize the bilayers on longer length scales. This process may form lamellar stacks, sponge phases, or microemulsions, depending on whether there are one or two solvents. Even more relevant to biomolecular systems is the formation of closed-film structures called vesicles, which are already being employed as simple containers to transport drugs within the blood system.

The self-organizing micelles may form in different shapes depending on the specific chemistry and on solvent conditions such as pH, ionic strength, and temperature. The most common form is spherical, but cylindrical micelles also occur. In fact, entropic optimization drives long cylindrical micelles into the form of flexible polymer-like chains. These polymeric micelles have many of the rheological properties of polymers with covalently bonded backbones, but their lengths are determined by equilibrium thermodynamics rather than being fixed.

An interesting example of a self-assembling structure is the tubule, a hollow phospholipid bilayer cylinder morphologically similar to a soda straw. The length of these ultrasmall cylinders is typically tens or hundreds of microns. [16] The diameter can vary from 0.1 mm or less to over 0.7 mm, with the wall thickness varying from less then 100 Å to well over 500 Å. A number of applications using both metal-clad and non-clad tubules are currently being evaluated for commercial application. A hollow tubule is essentially a ìmicrovialî in which a solid or liquid can be encapsulated. The use of such microvials has led to controlled-release applications for marine antifouling (release over many years) and drug delivery (release over several days to months). [17] These applications are now at the advanced development stage in several commercial firms both in the United States and abroad. The metal-clad structures also have interesting electromagnetic properties. Applications based on their dielectric properties (miniaturized microwave circuits) and as absorptive filters are currently under development in several universities and government laboratories. While several of the technical issues critical to successful commercialization of tubule applications have been solved, other issues (such as scale-up and a satisfactory cost/performance ratio) remain to be addressed prior to successful marketing.

[15]. S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, New York, 1994).

[16]. J.M. Schnur, Science 262:1669 (1993).

[17]. Microstructure Controlled Release Group, Pharmaceutical News 2(1):10 (1995); J.M. Schnur, R. Price, and A.S. Rudolph, Journal of Controlled Release 28:3 (1994).

Fig. 4.7. Nanotube membranes can be prepared by depositing carbon into porous alumina templates. These nanotube membranes can be used in chemical analysis and in membrane-based chemical separations. They basically work as filters. Reference: Antibody-Based Bio/Nanotube Membranes for Enantiomeric Drug Separations, Lee, S.B.; Mitchell, D.T.; Trofin, L.; Nevanen, T.K.; Soderlund, H.; Martin, C.R., Science, 2002, 296, 2198-2200. .

Top-down meets bottom-up. A neuron connected to an integrated circuit. Source: Vision 2020: Nanoelectronics at the centre of change, European commission report of the high level group, June 2004.

Carbon nanotubes
Carbon nanotubes are cylindrical structures made only from carbon atoms that are about 1 nm in diameter and 1-100 microns in length. In a graphite sheet, carbon atoms arrange themselves in a two-dimensional hexagonal lattice. Carbon nanotubes can be though of as a strip of graphite sheet that is rolled up to form a cylinder. There are many different ways to cut up a piece of graphite and roll it up to form a tube. The tubes can have different diameters and different chiralities. The chirality is the twist of the rows of atoms along the length of the tube. Sometimes the atom rows are parallel to the axis of the tube and sometimes the rows form a helix that winds along the tube. When one or more tubes grow inside another carbon nanotube, it is called a multiwalled nanotube. Carbon naotubes are very strong; they are 10 times as strong as steel for the same wieght. The electrical properties of carbon nanotubes depend on their diameter and their chirality. Some tubes are metallic and some are semiconductors. Research on carbon nanotubes at TU Delft, Nanotech Now's nanotube and buckyball page.

Reference: Assembly of nanodevices with carbon nanotubes through nanorobotic manipulations, T. Fukuda, F. Arai, Lixin Dong, Proceedings of the IEEE, Vol 91, p. 1803 (2003).

Fig. 4.7. A model of a carbon nanotube.

Fig. 4.8. A single layer of grahpite is called a graphene sheet. Such a sheet can be rolled in a tube in many ways. A tube can be made by drawing a line between any two points in the lattice and rolling the tube perpendicular to this line. The tube is labeled by two indicies n and m which specify the number of cells this line spans in the x and y directions. If n - m = 3p (p = 0,1,2,...) the tube is metallic, otherwise it is a semiconducting tube. The diameter of a tube is 0.08(m² + mn + n²)1/2 nanometers.

Fig. 4.9. A carbon nanotube lying across four metal electrodes. Reference: A. Bachtold, J.-P. Salvetat, J.-M. Bonard, M. Henny, C. Terrier, C. Strunk, L. Forró, and C. Schönenberger, Contacting Carbon-Nanotubes selectively with Low-Ohmic Contacts for Four-Probe Electric Measurements, Appl. Phys. Lett. 73, 274 (1998). www.snf.ch/nfp/nfp36/progress/schoenenberger.html

1-D diamond crystal from The Fountains of Paradise by science fiction writer Arthur C. Clarke

It is a continuous pseudo-one dimensional diamond crystal - though it's not actually pure carbon. There are several trace elements in carefully controlled amounts. It can be mass-produced only in the orbiting factories, where there's no gravity to interfere with the growth process."

"Fascinating ... I can appreciate that this may have all sorts of technical applications. It would make a splendid cheese cutter."