1 Why do some properties change at nanoscale?

Prof. Subhasis Ghosh

1.1  What is Nanoscale?

1.1.1 Size Matters

1.1.2 Surface to Volume Ratio

1.1.3 Importance of Random Motion

1.1.4 Biological Processes at Nanoscale

1.1.5 Macromolecular Devices

Properties of any material strongly depend on its size, as phenomena determining these properties are size dependent. The most dramatic effects are observed when the quantum nature of objects starts dominating these properties. These effects become observable at dimensions approaching the de-Broglie wavelength of electrons in the material, which is typically of the order of 1 nanometer.

1.1 What is Nanoscale?

The word ‘Nano’, originating from the Greek prefix nanos meaning dwarf, depicts a billionth of a unit (10-9). Nanoscale materials or objects therefore refer to materials with sub-nanometer dimensions. To get a better feel for the dimensions, a nanometer represents length scales tens of thousands of times smaller than the thickness of human hair. From the point of view of Physics, a copper wire with diameter more than 25 micron or a human hair and their interaction with the world are big, because they contains more than 1021 atoms. Therefore, to explain the mechanical and other properties of the copper wire, it is not required to solve either quantum or classical equations of motion for the constituent atoms. The particles on the nanoscale, however, exhibit unique properties. For example, bending of a 25 micron copper wire is accompanied with the movement of copper atoms at the scale of about 50 nm. This is one of the reasons that the copper nanoparticles smaller than 50 nm are considered to be extremely hard materials, however, that do not exhibit the same ductility as the normal “macroscopic” copper wire. In this case, it is justifiable to talk about average mass density and elastic modulus which relates the elongation of copper with tension, as predicted by Hooke’s law. Similar physics can be discussed in the context of the other properties of copper. These collective properties and their evolution in “macroscopic” systems are the foundation of condensed matter physics. But, the same foundation can’t be applied in case of deoxyribonucleic (DNA), which is topologically similar to copper wire. It turns out that this is the only similarity and continuum physics which is so successful in case of copper wire will fail miserably to explain mechanical, electronic and optical properties of DNA. But at the fundamental level, both copper wire or human hair and DNA are made up of stable atoms. Largely, the purpose of this course (Physics at Nanoscale) is to examine and describe the different properties of condensed systems at nanoscale. It is required to reach a transitional threshold where the different properties of nanosystems will no longer be described by classical physics. As shown in Figure 1.1, bulk materials have length scales larger than 0.01 meters. Atomic radii are typically smaller than 1 nanometer. The systems at the

Figure 1.1. A comparison of the scales of the sizes of various biological and technological objects. Image copyright: Image source: http://science.energy.gov/~/media/bes/images/scale-of-things-26may06.jpg.

nanoscale therefore consist of clusters of atoms or molecules or macromolecules. Even smaller length scales are associated with quarks present inside elementary particles such as electrons. Different branches of physics have emerged to probe the properties associated with these different length scales, starting from atomic physics to nuclear and particle physics and high energy physics.

1.1.1 Size Matters

Over the centuries, a great deal of information about the properties of different materials have been accumulated by scientists. Any material can be predominantly characterized by four properties (i) optical properties (such as absorptivity and reflectivity), (ii) electrical properties (such as conductivity),

(iii) physical properties (such as density and boiling point) and (iv) chemical properties (such as reactivity and reaction rates). This information can further be used to guide the choice of the material for a desired set of applications. A vast majority of our understanding of these properties is based on measurements made on bulk samples. However, this means measuring the average properties of a ‘pure’ sample of the material based on the collective behavior of billions of particles without looking at the behavior of individual atoms or molecules, which may be different. In fact it is seen that as the nanoscale is reached, the properties of the materials show significant deviations from these averages. One of the most dramatic examples can be that of gold and it is seen that a colloid of gold nanoparticles is not the usual ‘golden’ but in fact ruby red.

1.1.2 Surface Area to Volume Ratio

Several observed properties of a material are based on intermolecular forces. In a given bulk material, the majority of the particles are in the interior of the material and are thus subject to similar forces. Whereas the particles of the surface experience forces simultaneously from the substance and also from the surrounding environment. This lends the surface particles a higher energy and this effect is the reason for some interesting properties which are regularly observed at nanoscale.

Let us consider a simple rectangular solid of height, h, length, l, and thickness, t, such that each of these dimensions can be represented by a generalized dimension, D (which represents the dimension on the same scale, i. e. unit). Consider, f denotes the fraction or percentage of atoms at a surface, relative to the total number of atoms in a given sample. The surface area, S, and volume, V, of the solid are given by,

= 2{ℎ   + —+   ℎ} =   .     +   .      +   .              ~  2

= ℎ     =   .   .   . =    3

=   ~  −1

The above scaling law extrapolates to infinity as D goes to zero, which is unphysical, but highlights the role of this scaling as we go to nanoscale dimensions. The greater surface area to volume ratio for small aggregations of substances as compared to larger aggregations leads to differences in the properties of the two. Surface properties are pivotal in determining the physical and chemical properties of the material. The larger proportion of atoms on the surface has a profound effect on processes that occur at the surface including catalysis and adsorption and changes physical properties such as the melting point. Nanomaterials will show a lower melting point than bulk materials with the same composition because lesser energy is needed to remove the atoms at the surface than those in the bulk.

The importance of surfaces can be understood by looking at a drop of water on a waxy surface (see Figure 1.2). For instance, the force of attraction, known as cohesive forces, of the water molecules to each other is much greater than the force of attraction, known as adhesive forces, of the water molecules to the surface of the wax paper. This is responsible for the spherical shape of drops of the collection of water molecules and serves as the evidence for a high surface tension. However, when the surface upon which the molecules rest is changed to one to which the molecules of water are more attracted such as plastic, then the drop shape of water collapses. This is due the fact that the adhesive forces between the water and the plastic are strong enough to overcome the cohesive forces between the water molecules.

Figure 1.2. Surface tension and surface attractive forces for a drop of water on a non-wettable surface like wax paper (left), or a more attractive surface (right).

1.1.3 Importance of Random Motion

Random motion is exhibited by the constituent molecules/atoms of a substance by virtue of their thermal energy. This motion can be translational, rotational or vibrational. At macro level, this random thermal motion is small as compared to the size of the substance, that’s why we can barely detect motion of dust particles on the surface of water. While at nanoscale, random motion becomes significant when compared to the size of the particles exhibiting it. Thus, the molecules that make up the dust particles are moving wildly compared to the size of the object. The momentum of an object determines how easy it moves or it can be moved or how easy it changes its direction of movement if it is already in motion. This easiness depends on how smaller the object i and this easiness facilititate the random motion, known as Brownian motion, of particles suspended in a fluid due to their collision with the fast-moving atoms or molecules in the fluid (gas or liquid). Even pollen grains which are typically between 6 and 100µm in diameter are too large to exhibit Brownian Motion or random motion, which is seen in particles of a few microns or less. This can be better understood by an analogy.

1.1.4 Biological Processes at Nanoscale

Nature has almost perfected the art of biology over billion of years by the millions of processes that occur at nanoscale. Most of the inner workings and functions of cells occur at nanoscale. All the information and the processes of life are encoded in a strand of DNA (deoxyribonucleic acid) which controls growth, development, functioning and reproduction of all known living organisms including bacteria and viruses. DNA is located in the cell nucleus and the information encoded in DNA is stored as a code made up of four chemical bases: adenine, guanine, cytosine, and thymine. All the control processes occur in a 2 nm diameter strand. The two helixes in the DNA strand are held together by a large number of hydrogen bonds. At a bulk level, hydrogen bonds are weak but due to the large surface area at the nanoscale, these small bonds become increasingly relevant. Another example, hemoglobin, the protein that carries oxygen in the human body, is a little over 5 nm in diameter. Recent research activities and subsequent understanding of biological processes at nanoscale are leading to target specific smart medicine and impacting other fields such as use of nanoscale biological principles for molecular self-assembly, self-organization and photosynthesis as a model for “green energy” nanosystems for inexpensive production and storage of solar energy.

1.1.5 Macromolecular Devices

Nearly all electronic processes occur at the molecular level by means of charge transfer. The use of molecules to make electronic devices such as wires, rectifiers, transistors etc, is yet another field of research that we can associate with the nanoscale with sizes of molecule falling in the range of 1 to 100 nm. Molecules themselves are used as devices, with their bonds as electronic components. At these scales, the transfer of a single electron from the source electrode to the molecule can charge it, and increases the amount of energy required for the subsequent transfer. Carbon nanotubes are a class of materials that show promising possibilities for use as molecular electronic devices.

Suggested Reading:

1. Nanostructure and Nanotechnology by Douglas Natelson, Cambridge University Press, 2015
2. Nanophysics and Nanotechnology by Edward L. Wolf, Wiley-VCH, 2015
3. Solid State Physics by N. W. Ashcroft and N. D. Mermin, Cengage Publishing, 1976
4. Condensed Matter Physics by M. P. Marder, Wiley, 2011.