5.6: Nanomaterials

What do stained glass, sunscreen, magnetic hard drives, heterogeneous catalysts, consumer electronics, stain-resistant clothing, self-cleaning glass, and medical diagnostics all have in common? All of them derive some special property and utility from nanoscale materials: ordinary elements and inorganic compounds such as gold, silver, TiO₂, chromium, SiO₂, and silicon that acquire different properties when their characteristic dimensions are somewhere between 1 and 100 nm. In this section we will learn about the basic science of nanomaterials, i.e., what it is about their size that makes them different.

Surface Area

Nanoparticles have a substantial fraction of their atoms on the surface, as shown in Figure \(\PageIndex{1}\). This high surface area to volume ratio is an important factor in many of the physical properties of nanoparticles, such as their melting point and vapor pressure, and also in their reactivity. In some cases, such as TiO₂, it can change which polymorph is most stable. The most stable form of bulk TiO₂ is rutile, but in TiO₂ nanoparticles, the most stable polymorph is anatase. Heterogeneous catalysts, for example, are often based on nanoparticles because the catalytically reactive atoms are those that are on the surface of the particle, and this allows for the most reactive surface sites with the smallest amount of material.

Figure \(\PageIndex{1}\): Plot of how the ratio of surface to bulk atoms changes with particle size.

Surface Energy

The surface energy is always positive. A key quantity that is connected with the chemistry of all surfaces is the surface energy. This is the (thermodynamically unfavorable) energy of making "dangling bonds" at the surface. Atoms at the surface are under-coordinated, and because breaking bonds costs energy, surface atoms always have higher energy than atoms in the bulk. This happens regardless of whether the bonding is covalent (as in a metal), ionic (in a salt), or non-covalent (in a liquid such as water). We see this effect, for example, in water droplets that bead up on a waxy surface. The droplet contracts into a sphere (against the force of gravity that works to flatten it) in order to minimize the number of dangling hydrogen bonds at the surface.

In the case of metal or semiconductor particles, strong covalent bonds are broken at the surface. For example, a gold atom in bulk face-centered cubic Au has 12 nearest neighbors, but a gold atom on the surface of the crystal has six nearest neighbors in-plane and three underneath, for a total of 9. We might expect the surface energy of this crystal face to be a little less (because the remaining bonds will become slightly stronger) than 3/12 = 1/4 of the bonding energy of bulk Au, and this is in fact a fairly good rule of thumb for many materials. When translated into energy per unit area, the surface energy of metals and inorganic salts is usually in the range of 1-2 J/m².

Example \(\PageIndex{1}\)

The sublimation energy of bulk gold is 334 kJ/mol, and the surface energy is 1.5 J/m². What percentage of the bulk bonding energy is lost by atoms at the surface of a gold crystal?.

Solution

To solve this problem, we need to know the surface area per Au atom. Gold has the face-centered cubic structure, and the unit cell edge length is 4.08 Å. From this we can determine that the Au-Au distance is 4.08/1.414 = 2.88 Å. In a hexagonal array of gold atoms with this interatomic spacing, the surface area per atom is (2.88 Å)² x 0.866 = 7.2 Ų. Multiplying by Avogadro's number, we find that the area per mole of Au surface atoms on the crystal face is 4.3 x 10⁴ m².

Now we multiply this area by the surface energy:

\((4.3 \times 10^{4} \frac{m^{2}}{mol}) \times (1.5 \frac{J}{mol}) \times (\frac{1kJ}{1000J}) = \mathbf{+65 kJ}\) per mole of Au surface atoms.

\(\frac{65 kJ}{334kJ} \times 100 \% = \mathbf {19 \%}\) of the bulk bonding energy is lost by atoms at the surface.

It is clear from the above example that the surface energy of nanoparticles can have a major effect on their physical properties, since a large fraction of the atoms in a nanoparticle are on the surface. A good example of this is the dramatic depression of the melting point. Solid nanocrystals are in general faceted, whereas liquid droplets made by melting nanocrystals adopt a spherical shape to minimize the surface area.

Figure \(\PageIndex{2}\): A faceted solid nanocrystal melts into a spherical droplet in order to minimize its surface energy.

Let's consider melting a silver nanocrystal that is 2 nm in diameter, meaning that about \(\frac{1}{2}\) of the atoms are on the surface. The spherical liquid droplet has lower surface area than the faceted crystal. For example, a cube has 1.24 times the surface area of a sphere of the same volume. If the decrease in surface area is about 20% upon melting, and the surface energy is about 1/4 of the bulk bonding energy of the atoms, then for a 2 nm diameter nanocrystal we would estimate that:

\[\Delta H^{o}_{fusion} \approx \Delta H^{o}_{fusion, \: bulk} - (\frac{1}{2})(0.25)(\frac{1}{4}) \Delta H^{o}_{vap} = \Delta H^{o}_{fusion, \: bulk} - 0.025 \Delta H^{o}_{vap, \: bulk}\]

where ΔH°_{vap, bulk}, the heat of vaporization, is the total bonding energy of atoms in a bulk crystal. For silver, ΔH°_{fusion, bulk} = 11.3 kJ/mol and ΔH°_{vap, bulk} = 250 kJ/mol. From this we can calculate the heat of fusion of a 2 nm Ag nanocrystal:

\[\Delta H^{o}_{fusion} \approx 11.3 - (0.025)(25) = 5.1 \frac{kJ}{mol}\]

The melting point of bulk silver is 962 °C = 1235 K. Assuming that the entropy of fusion is the same in the bulk and in the nanocrystal, the melting point of the nanocrystal should be \(1234K \times (\frac{5.1}{11.3}) = 557K = 284^{\circ} C\), a drop of almost 700 degrees from the bulk value. Experimentally, the melting point of a 2 nm diameter silver nanocrystal drops about 800 degrees below that of the bulk, to 127 °C. This is a whopping big change in the melting point, which is in reasonable agreement with our rough estimate. The same effect - energetic destabilization of the surface atoms relative to bulk atoms - results in the lower boiling point, higher vapor pressure, higher solubility, and higher reactivity of nanocrystals relative to larger crystals of the same material.

Quantum Dots

One of the most fascinating and well-studied mesoscopic effects occurs with semiconductor particles of various shapes when one or more of their dimensions is in the range of a few nanometers. These so-called "quantum dots" (0D), "quantum rods" (1D) and "nanosheets" (2D) acquire striking new electronic and optical properties.

Figure \(\PageIndex{3}\): Atomic resolution image of a CdSe nanoparticle.

The synthesis of semiconductor quantum dots, which is discussed in more detail below, is sufficiently well controlled to give essentially perfect crystals of a few thousand atoms, something that is statistically impossible in a macroscopic crystal. An image of such a crystal is shown in Figure \(\PageIndex{3}\). The band gap in many of these quantum dots is in a range where absorption of visible light can promote an electron from the valence band to the conduction band as shown in Figure \(\PageIndex{4}\). Relaxation of that electron back into the valence band results in emission. The quantum yield for band gap emission of semiconductor quantum dots is typically high, giving rise to the bright emission colors shown in (Figure \(\PageIndex{5}\)) for CdSe particles of different sizes. Because of their strong and narrow emission bands, quantum dots are of interest as luminescent tags for biological imaging applications, and also as light absorbers and emitters in solar cells and LEDs.

Figure \(\PageIndex{4}\): Diagram (left) showing the band gap absorption and emission of visible light in quantum dots. UV-visible spectrum (right) of a series of CdSe quantum dots. (CC BY-NC-SA, Catherine McCusker)

Figure \(\PageIndex{5}\): Emission colors of CdSe nanoparticles of different sizes. Smaller particles emit blue light because the exciton energy increases as the size decreases.

Size dependence

The size-dependence of the emission color comes primarily from a particle-in-a-box effect. The electron and hole that are created when the quantum dot absorbs light are bound together as an exciton by the confines of the "box". Louis Brus used first-order perturbation theory to determine that the band gap of a semiconductor quantum dot is given approximately by:

\[E_{gap} = E_{gap, bulk} + \frac{h^{2}}{8 \mu R^{2}} - \frac{1.8e^{2}}{4R \pi \varepsilon \varepsilon_{0}} + \dots\]

where R is the particle radius, µ is the electron-hole reduced mass (1/µ = 1/m_e* + 1/m_h*), m_e* and m_h* are the electron and hole effective masses, and ε is the dielectric constant of the semiconductor. In this equation, the first term after the bulk bandgap is the kinetic energy due to confinement of the exciton, and the second term represents the electrostatic attractive energy between the confined electron and hole. Because the energy is a function of R², it can be widely tuned across the visible spectrum by changing the size of the quantum dot.

Definition: Exciton

A conduction band electron and its valence band hole together form an exciton. Excitons are formed when an electron is promoted from the valence band to the conduction band of a material.

Synthesis

Early work on the quantum size effect in semiconductor nanoparticles used simple metathesis reactions in the synthesis. For example, CdSe and PbS can be precipitated at ambient temperature by the reactions:

\(\ce{CdCl2_{(aq)} + H2Se_{(g)} = CdSe_{(s)} + 2HCl_{(aq)}}\)

\(\ce{Pb(NO3)2 + H2S_{(g)} = PbS_{(s)} + 2HNO3_{(aq)}}\)

Figure \(\PageIndex{6}\): Complete atomistic model of a 5 nm diameter colloidal lead sulfide nanoparticle with surface passivation by oleic acid, oleyl and hydroxyl groups.

The growth of the particles was restricted by carrying out these reactions in different matrices, such as in polymer films or the silicate cages of zeolites, and capping ligands were also sometimes used to limit particle growth. While these reactions did produce nanoparticles, in general a broad distribution of particle sizes was obtained. The particles were also unstable to Ostwald ripening - in which large particles grow at the expense of smaller ones in order to minimize the total surface energy - because of the reversibility of the acid-forming synthetic reactions in aqueous media. The lack of good samples prevented detailed studies and the development of applications for semiconductor quantum dots.

A very important development in nanoparticle synthesis came in the early 1990's, when Murray, Norris, and Bawendi introduced the first non-aqueous, controlled growth process for II-VI semiconductor quantum dots. The keys to this synthesis were (1) to use non-aqueous solvents and capping ligands to stabilize the products against ripening, (2) to carry out the reaction at high temperature to ensure good crystallinity, and (3) to separate the steps of particle nucleation and growth, and thereby obtain particles of uniform size. This procedure is illustrated below in Figure \(\PageIndex{7}\).

Figure \(\PageIndex{7}\): Illustration of the steps of CdSe nanoparticle synthesis

The synthesis is carried out in a coordinating, high boiling solvent that is a mixture of trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO). IAt the start of the reaction, a selenium source is rapidly injected into the hot (350 °C) reaction mixture containing Cd. The reaction causes a rapid burst of nanoparticle nucleation, but the temperature also drops as the cold solvent is injected and so the nucleation event ends quickly. The cooled solution now contains nanocrystal seeds. It is supersaturated in TOPO-Cd and TOP-Se, but particle growth proceeds slowly until the solution is heated again to the growth temperature, ca. 250°C. Particle growth and size-focusing occurs because small particles require less added material to grow by an amount ΔR than larger particles. This is because the volume of an added shell around a spherical seed is 4πR²ΔR, so for larger R, ΔR is smaller. Very narrow particle size distributions can be obtained under conditions of high supersaturation, where the rate of nanoparticle growth is fast relative to particle dissolution and Ostwald ripening. Because the nanoparticles are capped with a ligand shell of TOP, they can be precipitated and re-suspended in organic solvents.

The high temperature synthesis of semiconductor quantum dots has been applied to a broad variety of materials. Monodisperse nanoparticles of controlled shapes can be made by variants of this method. For example, it is possible to adjust the conditions so that CdSe nucleates in the zincblende polymorph as tetrahedrally shaped seeds, and then grow polar wurtzite "arms" onto each triangular face, resulting in nanocrystal tetrapods. Numerous other nanocrystal shapes such as rods, arrowheads, rice (tapered rods), and polar structures such as Janus rods can be made by variants of this technique. These shape-control strategies often involve the use of ligands that adsorb specifically to certain crystal faces and inhibit their growth. For example, hexylphosphonic acid ligands adsorb selectively to Cd-rich crystal faces and thus lead to the growth of prismatic wurtzite-phase CdSe nanocrytals.

Figure \(\PageIndex{1}\): Scanning electron microscope (SEM) image of a ZnO tetrapod nanocrystal. (CC BY-NC-ND 3.0; ScienceDirect via https://doi.org/10.1016/S1369-7021(07)70079-2)

Metal nanoparticles

Nanoscale metal particles have been the subject of intense research over the past 20 years, especially because of their unusual optical, magnetic, and catalytic properties. The synthesis of metal nanocrystals in various shapes has become increasingly sophisticated and rational, like the synthesis of semiconductor nanocrystals described above. By controlling the separate phases of nucleation and growth, and by using ligands that cap specific crystal faces during growth, it is possible to make metal nanocrystals of uniform size in a variety of interesting and useful shapes including cubes, truncated cubes, octahedra, triangular prisms, and high aspect ratio rods. By exploiting displacement reactions that replace one metal with another, complex hollow shapes such as nanocages (as shown at the left) can be made starting with other shapes. In this case, solid silver nanocubes are transformed to gold nanocages.

Five-fold twinning in a gold nanoparticle

The interesting optical properties of nanocrystalline Au, Ag, Cu, and a number of other metals, derive from the collective oscillation of their valence electrons, a phenomenon known as plasmon resonance. Remember that in these metals, the electron mean free path is long (about 100 times larger than the size of the atoms), so the valence electrons feel only the average positive charge of the atomic cores as they zoom around the crystal. Light impinging on the metal acts as an oscillating electric field, pushing and pulling on the valence electrons at the characteristic frequency of the light wave. The situation is very much like a pendulum or a weight on a spring. The electrons, pushed away from their equilibrium positions, feel a restoring force that is proportional to their displacement. Their motion can be described by Hooke's Law:

\[F = kx\]

where the spring constant k determines the "stiffness" of the spring. In the case of the plasmon resonance, k is proportional to the number density of valence electrons n, and the square of the electronic charge e:

\[k = \frac{ne^{2}}{\varepsilon_{0}}\]

The resonant frequency of the plasma oscillation is given by:

\[\omega_{p} = (\frac{k}{m})^{\frac{1}{2}} = (\frac{ne^{2}}{m_{e}\varepsilon_{0}}^{\frac{1}{2}}\]

where m_e is the electron mass. For most metals, the plasmon resonance is in the ultraviolet part of the spectrum, but for a few metals like Au, Ag, and Cu it is in the visible.

The Lycurgus cup (4th century Roman glass) derives its unique coloration from noble metal nanoparticles. The cup is red in transmitted light and green in scattered (reflected) light.

For metal particles that are much smaller than the wavelength of light, this effect is called the localized surface plasmon resonance, or LSPR. There are three important consequences of the LSPR effect:

• The local electric field of the incoming light wave is greatly enhanced at the particle surface. This gives rise to huge enhancement factors in optical processes such as Raman scattering and fluorescence. Thus, certain analytical spectroscopic techniques are greatly enhanced by LSPR.
• Near the plasmon resonance frequency, metal nanocrystals absorb and scatter light very strongly. This makes them brightly reflective, and the strong light absorption can be exploited for light-induced local heating. These properties are being applied in medical diagnostics and therapy, e.g., for detection and photothermal destruction of cancer cells. By adjusting the size and shape of the gold nanoparticles, which are more stable than Ag and Cu in biological media, the plasmon frequency can be tuned to the tissue-transparent near-IR region of the spectrum between 700 and 900 nm. Small quantities of plasmonic Ag and Au particles also make brightly colored and strongly scattering pigments, e.g. in stained glass as shown above at the right.
• The plasmon frequency is sensitive to the refractive index of the particle's surroundings, i.e., its chemical environment. This makes metal nanoparticles of special interest for sensing and biosensing applications.

The colors of plasmonic gold nanoparticles depend on their size and shape.

Theory of light scattering and absorption by metal nanoparticles

The valence electrons in metal nanoparticles oscillate in the electric field of a light wave. While the nature of these oscillations is somewhat complex in metal particles that are non-spherical, the theory for spherical particles is relatively simple and in fact was worked out over 100 years ago by German physicist Gustav Mie.

Mie considered the interaction of a spherical particle with a uniform electric field, E, oscillating at angular frequency ω (= 2π f). This is a good approximation when the particle diameter is much smaller than the wavelength of light, as shown on the left. The particle is embedded in a uniform, insulating material (e.g. a solvent) that has a dielectric constant ε_diel. For insulators, ε_diel is a positive real number.

The dielectric constant ε of a metal is actually a complex number:

\[\varepsilon = \varepsilon^{'} + i \varepsilon^{"}\]

Here the real part, ε', is related to the refraction of light, and the imaginary part, ε", is related to light absorption. Both ε' and ε" are dependent on the frequency of the light. For metals near the plasmon resonance frequency, ε' is typically a negative number.

The cross-section for absorption of the light wave by the particle is:

\[\sigma_{absorption} = \frac{9 \omega}{c} \epsilon^{\frac{3}{2}}_{diel} V \frac{\epsilon^{"}_{metal}}{(\epsilon^{'}_{metal} + 2 \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}\]

and the cross-section for scattering is:

\[ \sigma_{scattering} = \frac{3}{2\pi} (\frac{\omega^{4}}{c}) \epsilon^{2}_{diel} V^{2} \frac{(\epsilon^{'}_{metal} - \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}{(\epsilon^{'}_{metal} + 2 \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}\]

The sum of these two is the cross-section for extinction:

\[\sigma_{extinction} = \sigma_{absorption} + \sigma_{scattering}\]

These cross-sections become large when the (ε'_metal + 2ε_diel) term in the denominator becomes small. This occurs when

\[\epsilon^{'}_{metal} \simeq -2\epsilon_{diel}\]

For 15 nm diameter gold nanoparticles in water, this happens at about 580 nm, resulting in the characteristic wine-red color of colloidal gold solutions. Changing the solution environment (e.g., by adsorbing a molecule onto the gold surface) changes ε_diel and thus alters the color slightly.

It is important to note that the cross-section for scattering is proportional to the square of the volume of the particle, V², whereas the absorption is proportional to V. This means that very small gold particles (< 5 nm) are strongly absorbing but not strongly scattering. Larger particles (>30 nm) scatter light very strongly. Depending on the application, therefore, we choose larger or smaller particles.

One of the key complementary properties of noble metal nanoparticles that is important to their use in biomedicine is the ease with which they can be covalently conjugated with polymers or small molecules, typically via thiol or amine bonds at their surface. This imparts biological recognition properties to the particles that enables them to bind to specific biomolecular targets. The figure at the left illustrates some of the functionality that can be imparted to nanoparticles through surface functionalization.

Functionalization of gold nanoparticles with thiol-terminated single-stranded DNA was the basis of one of the first nanoparticle sensors, developed by the Mirkin group at Northwestern University. DNA-coated nanoparticles have the characterstic wine-red plasmonic color of spherical nano-gold. However, when these particles are linked together by a complementary DNA strand, the resonance frequency shifs, resulting in a blue color. This color change, illustrated in the figure at the right, provides a "litmus test" for the presence of the target DNA sequence.^[10] "Melting" of the DNA - heating it to the temperature at which double stranded DNA dissociates to make single strands - reverses the color change. The DNA hybridization/melting transition is highly cooperative because of the aggregation of many gold particles, so the transition temperature is very sharp. With proper temperature control, the color change can be sensitive to a single base mismatch in the target DNA that is detected by this method.

Aggregation of Au nanoparticles (in this case by adding salt to a colloidal solution) causes a color change from wine red (left) to blue (right). Photo credit: George Lisensky, Beloit College

Subsequent research has developed sophisticated diagnostic and therapeutic ("theranostic") applications for these spherical nucleic acid^[11] particles. These particles easily penetrate cell membranes and can report on the chemistry happening inside living cells.

General schematic of nanoflare-based detection.

An important property of gold nanoparticles in these applications is their ability to quench the fluorescence of reporter molecules that are near their surface. Nucleic acid strands that contain a hairpin loop can position fluorescent molecules near the gold surface, where their fluorescence is turned off by nanoparticle quenching. Hybridization of these sequences to target RNA or DNA causes the fluorescence to turn on by moving the fluorescent molecule away from the nanoparticle surface. These so called "nanoflares" can thus signal the up- or down-regulation of specific genes inside cells. Nanoflares are the basis of the Verigene System, developed and commercialized by Nanosphere, Inc. to detect markers for infectious diseases and cancers.

References

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2. Brus, Louis E. (1984). "Electron–electron and electron‐hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state". J. Chem. Phys. 80, 4403. DOI: 10.1063/1.447218.
3. C. B. Murray, D. J. Norris, and M. G. Bawendi, "Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites," J. Am. Chem. Soc. 1993, 115, 8706–8715. DOI: 10.1021/ja00072a025.
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6. Mirkin, C. A., et al., A DNA-based method for rationally assembling nanoparticles into macroscopic materials. Nature 1996, 382 (6592), 607-609.
7. Cutler, J. I., et al., Spherical Nucleic Acids. J Am Chem Soc 2012, 134 (3), 1376-1391.