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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Meeting the demand for a readily understandable introduction to nanomaterials and nanotechnology, this textbook specifically addresses the needs of students - and engineers - who need to get the gist of nanoscale phenomena in materials without having to delve too deeply into the physical and chemical details.
The book begins with an overview of the consequences of small particle size, such as the growing importance of surface effects, and covers successful, field-tested synthesis techniques of nanomaterials. The largest part of the book is devoted to the particular magnetic, optical, electrical and mechanical properties of materials at the nanoscale, leading on to emerging and already commercialized applications, such as nanofluids in magnetic resonance imaging, high-performance nanocomposites and carbon nanotube-based electronics.
Based on the author's experience in teaching nanomaterials courses and adapted, in style and level, for students with only limited background knowledge, the textbook includes further reading, as well as information boxes that can be skipped upon first reading.
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Seitenzahl: 460
Veröffentlichungsjahr: 2013
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Table of Contents
Related Titles
Title page
Copyright page
Preface
1: Introduction
2: Nanoparticles – Nanocomposites
2.1 Nanoparticles
2.2 Elementary Consequences of Small Particle Size
3: Surfaces in Nanomaterials
3.1 General Considerations
3.2 Surface Energy
3.3 Vapor Pressure of Small Particles
3.4 Hypothetical Nanomotors Driven by Surface Energy
4: Gas-Phase Synthesis of Nanoparticles
4.1 Fundamental Considerations
4.2 Inert-Gas Condensation Process
4.3 Physical and Chemical Vapor Synthesis Processes
4.4 Laser-Ablation Process
4.5 Plasma Processes
4.6 Flame Processes
4.7 Synthesis of Coated Particles
5: One- and Two-Dimensional Nanoparticles
5.1 Basic Considerations
5.2 Vibrations of Nanorods and Nanotubes – Scaling Law for Vibrations
5.3 Nanostructures Related to Compounds with Layered Structures
6: Nanofluids
6.1 Background
6.2 Nanofluids for Improved Heat Transfer
6.3 Ferrofluids
7: Thermodynamics of Nanoparticles and Phase Transformations
7.1 Basic Considerations
7.2 Influence of the Particle Size on Thermodynamic Properties and Phase Transformations
7.3 Thermal Instabilities Connected to Phase Transformations
7.4 Heat Capacity of Nanoparticles
8: Magnetic Nanomaterials, Superparamagnetism
8.1 Magnetic Materials
8.2 Fundamentals of Superparamagnetism
8.3 Susceptibility of Superparamagnetic Materials
8.4 Superparamagnetic Particles in the Mößbauer Spectrum
8.5 Applications of Superparamagnetic Materials
8.6 Exchange-Coupled Magnetic Nanoparticles
9: Optical Properties
9.1 General Remarks
9.2 Adjustment of the Index of Refraction and Visually Transparent UV Absorbers
9.3 Size-Dependent Optical Properties – Quantum Confinement
9.4 Semiconducting Particles in the Quantum-Confinement Range
9.5 Metallic Nanoparticles – Plasmon Resonance
9.6 Luminescent Nanocomposites
9.7 Selection of a Lumophore or Absorber
9.8 Electroluminescence
9.9 Photochromic and Electrochromic Materials
9.10 Magneto-Optic Applications
10: Electrical Properties
10.1 Fundamentals of Electric Conductivity; Diffusive versus Ballistic Conductivity
10.2 Carbon Nanotubes
10.3 Other One-Dimensional Electrical Conductors
10.4 Electrical Conductivity of Nanocomposites
11: Mechanical Properties
11.1 General Considerations
11.2 Mechanical Properties of Bulk Nanocrystalline Materials
11.3 Deformation Mechanisms of Nanocrystalline Materials
11.4 Superplasticity
11.5 Filled Polymer Composites
12: Characterization of Nanomaterials
12.1 Specific Surface Area
12.2 Analysis of the Crystalline Structure
12.3 Electron Microscopy
Index
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The Author
Prof. Dr. Dieter Vollath
NanoConsulting
Primelweg 3
76297 Stutensee
Germany
The coverpicture is based on a figure published in the article: Yun, Y.J., Park, G., Ah, C.S., Park, H.J., Yun, W.S., and Haa, D.H. (2005) Appl. Phys. Lett., 87, 233110–233113. With kind permission by The American Institute of Physics.
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Preface
This book is really two books. It gives an introduction to the topics connected to nanoparticles, nanocomposites, and nanomaterials on a descriptive level. Wherever it seems appropriate, some topics are explained in more detail in separate boxes. It is not necessary to read these boxes; however, it may be interesting and helpful to the reader.
This textbook is intended for persons wanting an introduction into the new and exciting field of nanomaterials without having a formal education in science. It discusses the whole range from nanoparticles to nanocomposites and finally nanomaterials, explaining the scientific background and some of the most important applications. I want to provoke the reader's curiosity; he/she should feel invited to learn more about this topic, to apply nanomaterials and, may be, to go deeper into this fascinating topic.
This book is an excerpt from the course on nanomaterials for engineers that I give at the University of Technology in Graz, Austria and on the courses that NanoConsulting organizes for participants from industry and academia. This book is not written for scientists, so may be some physicists will feel unhappy about the simplifications that I made to explain complicated quantum mechanical issues.
I want to apologize for the selection of examples from the literature, as my selection of examples is, to some extent, unfair against those who discovered these new phenomena. Unfortunately, when a new phenomenon was described for the first time, the effect is only shown in principle. Later papers instead showed these phenomena very clearly. Therefore, the examples from later publications seemed more adequate for a textbook like this.
As the size of this book is limited, I had to make a selection of phenomena for presentation. Unavoidably, this selection is influenced by personal experience and preferences. I really apologize if a reader does not find information of interest for themselves or their company.
It is an obligation for me to thank my family, in particular my wife Renate, for her steady support during the time when I wrote this book and her enduring understanding for my passion for science. Furthermore, I have to thank Dr. Waltraud Wüst from Wiley-VCH for her steady cooperation.
Dieter Vollath
Stutensee, June 2013
1
Introduction
Everyone talks about nanomaterials. There are many publications, books and journals devoted to this topic. This is not surprising, as the economic importance is steadily increasing. Additionally, interested persons without specific education in one of these fields, have, at the moment, nearly no chance to understand this technology, its background and applications. This book fills this gap. It deals with the special phenomena found with nanomaterials and tries to give explanations, avoiding descriptions that are directed to specialists and need specialized education.
To get an idea about the actual size relations, think about a tennis ball, having a diameter of a little more than 6 cm = 6 × 10−2 m and compare it with a particle with diameter of 6 nm = 6 × 10−9 m. The ratio of the diameters of these two objects is 107. An object 107 times larger than a tennis ball has a diameter of 600 km. This simple comparison makes clear: nanoparticles are really small.
The difficulty with nanomaterials arises from the fact that – in contrast to conventional materials – knowledge of material science is not sufficient; rather some knowledge of physics, chemistry, and materials science is necessary. Additionally, as many applications are in the fields of biology and medicine, some knowledge in these fields is necessary to understand these important applications. Figure 1.1 demonstrates that science and technology of nanomaterials are influenced by materials science, physics, chemistry, and for many, economically most important applications, also of biology and medicine.
Figure 1.1 To understand and apply nanomaterials, besides knowledge on materials science, a basic understanding of physics and chemistry is necessary. As many applications are connected to biology and medicine; knowledge in these fields are also of advantage.
The number of additional facts introduced to materials science is not that large, therefore, this new situation is not that complicated, as it may look to the observer from the outside. However, the industrial user of nanomaterials, as a developer of new products, has to accept that the new properties of nanomaterials demand deeper insight to the physics and chemistry of the materials. Furthermore, in conventional materials, the interface to biotechnology and medicine depends on the application. This is different in nanotechnology, as biological molecules, such as proteins or DNAs are building blocks, quite often also for applications outside of biology and medicine.
The first question to be answered is: What are nanomaterials? There are two definitions. One, the broadest, says: nanomaterials are materials with sizes of the individual building blocks below 100 nm at least in one dimension. This definition is quite comfortable, as it does not require deeper thoughts about properties and applications. The second definition is more restrictive. It says that nanomaterials are ones with properties inherently depending on the small grain size. As nanomaterials usually are quite expensive, such a restrictive definition makes more sense.
The main difference between nanotechnology and conventional technologies is the “bottom-up” approach preferred in nanotechnology, whereas conventional technologies usually prefer the “top-down” approach. The difference between these two approaches is explained for example, using the example of powder production. In this context, chemical synthesis is typical of the “bottom-up” approach; whereas, crushing and milling are techniques that may be classified as “top-down” processes. Certainly, there are processes, which may be seen as “in between”. A typical example is the defoliation of silicates or graphite to obtain graphene.
The expression “top-down” describes processes starting from large pieces of material to produce the intended structure by mechanical or chemical methods. As long as the structures are in a range of sizes accessible by mechanical tools or photolithographic processes, top-down processes have an unmatched flexibility in application. Figure 1.2 summarizes the basic features of top-down processes.
Figure 1.2 Conventional goods are produced by top-down processes, which start from bulk material. Using mechanical or chemical processes, the intended product is obtained.
“Bottom-up” processes are, in general chemical processes starting from atoms or molecules as building blocks to produce nanoparticles, nanotubes or nanorods, thin films or layered structured. Using their dimensionality for classification, these features are also called zero-, one-, or two-dimensional nanostructures. This is graphically demonstrated in Figure 1.3. Bottom-up processes give tremendous freedom in the composition of the resulting products; however, the number of possible structures to be obtained is comparatively small. Ordered structures are obtained by processes that are supplemented by self-organization of individual particles. Often, top-down technologies are described as subtractive ones, in contrast to additive technologies describing bottom-up processes.
Figure 1.3 Chemical synthesis as bottom-up process. Bottom-up processes are characterized by the use of atoms or molecules as educts. Products are particles, nanotubes or nanorods, or layered structures.
Figure 1.4 shows the size ranges of the different processes applied in nanotechnology. Certainly, there is a broad range of overlapping, between the top-down and bottom-up technologies. Most interesting, there are improved top-down technologies, such as electron beam or X-ray lithography entering the size range typical for nanotechnologies. These improved top-down technologies obtain increasing importance, for example, in highly integrated electronic devices.
Figure 1.4 Estimated lateral limits of different structuring processes. The size range of bottom-up and conventional top-down processes is limited. New, advanced top-down processes expand the size range of conventional ones and enter the size range typical for bottom-up processes.
For industrial applications, the most important question is the price of the product in relation to the properties. As far as the properties are comparable, in most cases, nanomaterials and products applying nanomaterials are significantly more expensive than conventional products. This becomes problematic in cases where the increase in price is more pronounced than the improvement of the properties due to the application of nanomaterials. Therefore, economically interesting applications of nanomaterials are found primarily in areas where properties that are out of reach for conventional materials are demanded. Provided this condition is fulfilled, the price is no longer that important. However, in cases where nanomaterials are in direct competition to well-established conventional technologies, the price is decisive. This fierce price competition is extremely difficult for a young and expensive technology and may lead sometimes to severe, financial problems for newly founded companies. As a general rule one may say that in the case of nanomaterials one is rather selling “knowledge” than “tons”.
Nanoparticles are neither new nor unnatural. In nature, for example, some birds and mammals apply magnetic nanoparticles for navigation, a sense called magnetoception. In plants the phenomenon of self-cleaning of leafs caused by nanoparticles at the surface, called the Lotus effect is well known and meanwhile technically exploited for self cleaning windows or porcelain ware for sanitary use (see Box 1.1). Man-made nanomaterials, in this case nanocomposites, have been known for more than 2500 years. The Sumerians already produced a red pigment to decorate their pottery. This pigment consisted of gold nanoparticles embedded in a glass matrix stabilized with tin oxide. In science, especially chemistry, suspensions of nanoparticles have been well known since the nineteenth century; however, at that time, this science was called colloid chemistry.
As an example of a macroscopically observable phenomenon caused by nanostructures, the Lotus effect will be explained. It is well known that the leaves of the Lotus plant are always clean. This is caused by the fact that the lotus leaf can not be moistened, it is hydrophobic, each drop of water flows immediately off the leaf, picking up any dust, which is, in general, hydrophilic.
The Lotus effect is caused by an apparent increase of the contact angle between water and a solid surface. The undisturbed situation is depicted in Figure 1.5.
Figure 1.5 Equilibrium of surface stresses at a contact between a solid and a liquid.
The contact angle, in the case of a water/solid interface, at a maximum of 110° is a result of the equilibrium of the surface stresses.
(1.1)
The quantities in Eq. (1.1), σs−g describe the surface stresses at the interface between the solid and the gas phase, σs−1 the surface stress between the solid and the liquid phase, σ1−g the one between liquid and the gas pas phase, and α is the contact angle. (To be mathematically exact, the surface stress is described by a vector in the tangential plane of the particle. However, for these simplified considerations, it is correct to work with the absolute values of these vectors.)
Assuming a corrugated surface with nanoparticles, as depicted in Figure 1.6, the situation conveys the impression of a larger contact angle. However, this is not correct, as the contact angle to each one of the nanoparticles has the correct value.
Figure 1.6 Contact situation in the case of the Lotus effect. Due to the corrugated surface, one has the impression of a huge contact angle α. However, looking at the points of contact of the individual particles, it is obvious that there is nothing special there, one finds the standard values.
2
Nanoparticles – Nanocomposites
2.1 Nanoparticles
Nanoparticles may be classified as zero-dimensional, these are the nanoparticles per se, one-dimensional such as nanorods or nanotubes, and two-dimensional that are, in most cases, plates or stacks of plates. As a typical example of particles, Figure 2.1 displays an electron micrograph of zirconia (ZrO2) powder, zero-dimensional objects.
Figure 2.1 Electron micrograph of zirconia, ZrO2 powder. A very narrow distribution of grain sizes is characteristic of this material. In many cases, this is predicated as important, because the properties of nanomaterials depend on the grain size [1].
The particles depicted in Figure 2.1 show a size of ca. 7 nm. It is important to mention that the particles are in a very narrow range of sizes. This may be important, as many properties of nanomaterials are size dependent. On the other hand, many applications do not need such sophisticated material or they just need a broad variation of properties. Therefore, in many cases, cheaper materials with broader particle size distribution, as is depicted in Figure 2.2a, are necessary or, at least, sufficient. The material depicted in this figure shows particles in the size range from 5 to more than 50 nm. Such materials are perfectly suited for applications as pigments, UV-absorbers, etc.
Figure 2.2 Two extremely different types of nanoparticulate Fe2O3 powder. (a) Industrially produced nanomaterial with broad particle size distribution, typically of application as pigments or UV-protection. Courtesy Nanophase, Nanophase Technologies Corporation, 1319 Marquette Drive, Romeoville, IL 60446. (b) Nanoparticulate powder consisting of clusters of amorphous particles with sizes around 3 nm. Catalysis is the most important field of application of this material with extremely high surface. Courtesy MACH I, Inc. 340 East Church Road, King of Prussia, PA 19406 USA.
A further interesting class of particles may be described as clusters of extremely small particles. Typical examples of this type of materials are most of the amorphous silica particles, well known as “white soot”, and amorphous Fe2O3 particles. Typically, particles of this type, as shown in Figure 2.2b, are applied as catalysts.
In producing bulk nanocomposites, the central problem is to obtain a perfect distribution of the particulate phase in the matrix. Processes based on mechanical blending or synthesizing the two phases separately and mixing during the step of particle formation, never lead to homogeneous products on the nanometer scale. Provided there are no preferences and the process of blending is random, the probability that two or more particles are touching each other and form a cluster is very high. Usually, in such a mixture, one wants to obtain a relatively high concentration of “active” particles, carrying the physical property of interest. Assuming, in the simplest case, particles of equal size, the probability pn that a number of n particles with the volume concentration c are touching each other, is pn = cn. The consequences of this simple relation are severe: for example, assuming a concentration of 0.30, the probability of two touching particles is 0.09 and for three particles 0.027. Lastly, it is impossible to obtain the intended perfect distribution of two phases by blending. Further-reaching measures are necessary.
Except for properties related to grain boundaries, the special properties of nanomaterials are ones of single isolated particles that are altered or even lost in the case of interacting particles. Therefore, most of the basic considerations are related to isolated nanoparticles as the unavoidable interaction of two or more particles may change the properties significantly. Certainly, this is senseless in view of the technical applications.
The two problems described above and to exploit these very special properties of nanoparticles, composite particles of the core–shell type, with a second phase acting as distance holder were developed. The necessary distance depends on the phenomenon to be suppressed; it may be smaller, in the case of tunneling of electrons between particles, and is larger in the case of dipole–dipole interaction. Furthermore, such composite particles can be designed in a way to combine different “incompatible” properties, such as magnetism and luminescence. The typical design of these particles is depicted in Figure 2.3.
Figure 2.3 Typical design of a core–shell nanocomposite particle. The properties of the core and coating 1 are, in most cases, selected to the demand of the physics (e.g., magnetic and luminescence); the second coating is selected in view of the interaction with the surrounding medium (e.g., hydrophilic or hydrophobic) [2].
The core–shell composite design, as depicted in Figure 2.3 is typical for advanced applications, for example, in medicine or biotech. Such a core–shell nanocomposite consists of a core, carrying the property, which demand the largest volume, for example, magnetism. The property of Coating 1, is the case of a bifunctional particle, for example, luminescence. The outermost layer, Coating 2 in Figure 2.3 has to mediate with the surrounding medium. Therefore, in most cases, it is either hydrophilic or hydrophobic. In many medical applications, the outermost layer may consist of a protein or enzyme, which is characteristic for a specific type of cells.
Typical examples for coated particles are shown in Figures 2.4a–c. In Figure 2.4a, a ceramic core (ZrO2), which is coated with a ceramic layer (Al2O3), an amorphous one, is displayed. In Figure 2.4b, the ceramic core (Fe2O3) is coated with a polymer (PMMA). This type of composite is often used as a special magnetic material. As a third variety, a ceramic particle (TiO2) decorated with a metal (Pt) is displayed in Figure 2.4c. Coating of ceramic particles with thin metallic layers is, because of the relation in the surface energy, in most cases impossible. Instead of a coating, one obtains a decoration of the core with metallic clusters. This type of composite is often used as a catalyst.
Figure 2.4 Three typical examples of nanocomposite particles. In (a), a crystallized ceramic core (ZrO2) is coated with an amorphous ceramic layer (Al2O3). It is also possible (b) to coat a ceramic core (Fe2O3) with a polymer. Coating a ceramic core (TiO2) with a thin metal (Pt) layer (c) is impossible because of the difference in the surface energies. In such a case, tiny metal clusters decorate the ceramic particles [1, 3]. (a, b: Reproduced with permission by Elsevier; c: Vollath, Szabó unpublished results.)
Most interesting are the particles displayed in Figure 2.4a, as they show an important phenomenon, characteristic of nanomaterials. This figure shows three coated ceramic particles. The particle in the center of the figure originates from coagulation of two zirconia particles. As the process of coagulation was incomplete, there are concave regions of the zirconia core visible. During the coating process, these concave areas were filled with alumina; therefore, finally, the coated particle has only convex surfaces. This minimizes surface energy; an important principle acting in any type of nanomaterial.
As already mentioned above, multifunctional particles are widely used in biology and medicine. For this application, it is necessary to add proteins or other biological molecules, which are characteristic of cells, where the particle should attach at the surface of the particles. Biological molecules are attached at the particles only via specific types of molecules, accommodated in the outermost coupling layer [4]. The development of these coupling layers is one of the crucial points for this application. Figure 2.5 displays such a biologically functionalized particle. The ceramic core, usually, is either magnetic or luminescent, or multifunctional. In the design depicted in Figure 2.5, the coupling layer may consist of an appropriate polymer or a type of glucose; however, in many cases, hydroxylated silica is sufficient, too. At the surface of the coupling layer, the biological molecules, such as proteins or enzymes are attached.
Figure 2.5 Nanocomposite particle for application in biology or medicine. The ceramic core may be magnetic, luminescent, or even bifunctional. The cell or tumor-specific proteins or enzyme at the surface, necessary for coupling of the particle at the intended type of cells, need a coupling layer as; in general, these molecules cannot be attached directly at the ceramic surface.
Bulk nanocomposites – as described in this chapter – are composite materials with at least one phase exhibiting the special properties of a nanomaterial. In general, random arrangements of nanoparticles in the composite are assumed. Figure 2.6 displays the most important three different types of nanocomposites. The types differ in the dimensionality of the second phase. This phase may be zero-dimensional, isolated nanoparticles, one-dimensional, consisting of nanotubes or nanorods, or two-dimensional composites with platelets as second phase; one may also think of stacks of layers. In most cases, such composites are close to zero-dimensional ones. However, some of them with polymer matrix have existing mechanical and thermal properties; therefore, they are used primarily in the automotive industry. In particular, the latter ones will be discussed in detail in Chapter 11.
Figure 2.6 Three basic types of nanocomposites. (a) Composite consisting of zero-dimensional particles in a matrix. In the ideal case, the individual particles are not touching each other. (b) One-dimensional nanocomposite consisting of nanotubes or nanorods distributed in a second, in general, polymer matrix. (c) Two-dimensional nanocomposite consisting of platelets embedded in a second matrix.
A typical electron micrograph of a nearly ideal nanocomposite, a distribution of zirconia (ZrO2) nanoparticles in an alumina (Al2O3) matrix is displayed in Figure 2.7. This figure displays a micrograph of a sintered material. The starting material was alumina-coated zirconia powder. It is obvious that the particles remain separated. For products of this type, it is essential that there is no mutual solubility between the core and coating. After sintering of the powder, consisting of coated nanoparticles, the coating will form the matrix.
Figure 2.7 Transmission electron micrograph of a zero-dimensional nanocomposite. It depicts a composite zirconia particles embedded in an alumina matrix. The specimen was produced from zirconia particles coated with alumina. This micrograph was taken from an ion-beam-thinned sample. It is essential to realize that there is a high probability that particles are not touching each other, because they are lying in different planes [3]. (Reproduced with permission by Springer.)
Looking at applications, one will find zero-dimensional composites of the type depicted in Figure 2.4a quite often in connection to magnetic materials. One- and two-dimensional nanocomposites are often found in applications where high mechanical strength is demanded. Looking at carbon nanotubes (one-dimensional) or graphene (two-dimensional) as a filler, a very important application is found in the field of optically transparent electrical conductors. Because of the large aspect ratio of these particles, electrical conductivity is obtained already with extremely small concentrations of these particles.
Practically, the composites, as depicted in Figures 2.4a,b exist primarily using a polymer matrix. In all the other cases, there is the possibility that there is a mutual solubility between the nanoparticles and the matrix. To avoid dissolution of the particles, often it is necessary to coat the particles with a diffusion barrier. This situation is depicted in Figure 2.8.
Figure 2.8 Zero-dimensional nanocomposite. To avoid dissolution in the matrix, the particles are coated with a diffusion barrier.
Figure 2.8 displays the oldest, man-made type of nanocomposite with more or less spherical nanoparticles. This composite is realized in the well-known gold-ruby glass. It consists of a glass matrix with gold nanoparticles as second phase. However, as gold can be dissolved in the glass matrix, a diffusion barrier is necessary. In the case of gold-ruby glass the diffusion barrier consists of tin oxide. In colloid chemistry, this principle of stabilization is well known as “colloid stabilization”. This material was produced for the first time by the Sumerians in the seventh century BC and re-invented by Kunkel in Leipzig in the seventeenth century. It is interesting to note that the composition used by the Sumerians was practically identical to the one reinvented by Kunkel and that is used nowadays.
Furthermore, the properties of a bulk solid made of coated nanoparticles may be adjusted gradually with the thickness of the coating. Depending on the requirements of the application, the coating material may be ceramic or polymer. Coating nanoparticles with a second and third layer leads to the following improvements:
The distribution of the two phases is homogenous on a nanometer scale.The kernels are arranged in a well-defined distance. Therefore, the interaction of the particles is controlled.The kernel and one or more different coatings may have different properties. This allows the combination of properties in one particle that are never found together in nature. Additionally, by selecting a proper polymer for the outermost coating, it is possible to adjust the interaction with the surrounding medium.During densification, i.e. sintering, the growth of the kernels is thwarted, provided core and coating show no mutual solubility. An example for this is depicted in Figure 2.7.These arguments demonstrate that the most advanced type of nanocomposites are coated nanoparticles. They allow not only the combination of different properties in one particle, but also in bulk materials.
In addition to the composites displayed in Figures 2.6 and 2.7, one observes nanocomposites with regular well-ordered structure, as displayed in Figure 2.9.
Figure 2.9 Typical examples of ordered nanocomposites. In the case of a zero-dimensional filler (a), it is necessary that the particles are more or less equal in size; whereas, in the case of one- or two-dimensional fillers, in general, the particles have different size; however, they are oriented in parallel.
In general, self-organization processes in the case of spherical filler particles or mechanical stretching are appropriate mechanisms to create this type of composite, if the filler particles are one- or two-dimensional. Successful realization of self-organization processes, leading to structures as depicted in Figure 2.9a, requires particles nearly identical in size.
2.2 Elementary Consequences of Small Particle Size
2.2.1 Surface of Nanoparticles
The first and most important consequence of the small particle size is the huge surface area. To get an impression of the importance of this geometric variable of nanoparticles, the surface over volume ratio is discussed. Simple calculations show that the ratio surface / volume is inversely proportional to the diameter of the particle. Similar to the surface over volume ratio for one particle, in molar quantities, this ratio is inversely proportional to the particle diameter, too.
Assuming spherical particles with the diameter d, the surface area a of one particle is given by
The volume v of this particle is
The surface/volume ratio R
(2.1)
This ratio is inversely proportional to the particle size. The surface A per mol, a quantity important in thermodynamics, is
(2.2)
with n the number of particles per mol, M the molecular weight, and ρ the density of the particles.
To get an idea about the magnitudes of surfaces that may be expected in case of nanoparticles, Figure 2.10 displays the theoretical surface of one gram of a powder consisting of spherical particles with a density of 3.5 × 103 kg m−3 (alumina).
Figure 2.10 Theoretical dependency of the specific surface area of the particle diameter. Due to the agglomeration of the particles, experimentally these values are not realized.
In Figure 2.10, the surface is given in the non-SI unit m2 g−1. This unit is applied because this is the only unit that is generally accepted for the specific surface area. In general, the specific areas visible in Figure 2.10 are never realized experimentally. The reason for this discrepancy is found in the agglomeration of the particles. The influence of this phenomenon increases with decreasing particle diameter, as the influence of the van der Waals forces increases too. (Van der Waals forces are weak interactions between molecules or small particles having their origin in quantum dynamics. These forces are neither covalent nor based on electrostatic or dipolar interaction.) Experimentally, the largest values are measured with activated charcoal in the range of 2000 m2 g−1 and finely dispersed amorphous silica with values up to 600 m2 g−1.
The surface is such an important topic for nanoparticles that there is a full chapter devoted to surface and surface-related problems (see Chapter 3).
2.2.2 Thermal Phenomena
Each isolated object, in this case a nanoparticle, has a thermal energy, which is directly proportional to the temperature. Furthermore, each object tries to be in a state where the energy is a minimum. Generally, this is a stable state. Certainly, energetically speaking, there are other states with higher energy possible. The energy difference between the state of lowest energy and the next one may depend for example, on the mass of the particle. As the mass of the particle decreases with particle diameter, there is the possibility that, starting at a sufficiently high temperature, the thermal energy gets larger than the difference between the two neighboring states. Now the system is no longer stable, and the system fluctuates.
Thermal energy uth of an isolated particle is given by
with k the Boltzmann constant and T the temperature.
Assuming an energy that depends on the volume of the particle u(v). The system is no longer stable, it fluctuates, if the condition
(2.3)
is fulfilled.
A simple example: The energy necessary to lift a particle with the density ρ the elevation x.
This particle moves around thermally and jumps up to a height x, if the condition
is fulfilled.
Schematically, this situation is depicted in Figure 2.11.
Figure 2.11 Schematic visualization of thermal fluctuation. In this case, the thermal energy is larger than the energy difference between level 1 and level 2.
Looking at thermal instabilities (fluctuations), one can design a simple example. One can ask for the size of a zirconia particle (ρ = 5.6 × 103 kg m−3) that could be lifted at room temperature to a height equal to its diameter. The answer is somewhat surprising, the diameter of 1100 nm. If one asks, how high could a particle of 5 nm diameter jump these simple calculations lead to a height of more than one meter. Certainly, these games with number do not have physical reality; however, they indicate that nanoparticles that are not fixed at a surface are moving around. Doing electron microscopy, this dynamic becomes reality. Provided the particles and the carbon film on the carrier mesh are clean, the particles of the specimen move around like ants on the carbon film. This makes electron microscopy difficult.
The thermal instability presented here, demonstrates a simple consequence of smallness; however, other physical properties may change significantly and this may lead to new properties. The most important phenomenon of this group, superparamagnetism, will be described in Chapter 8 on magnetic properties. Fluctuations are also observed in connection with phase transformation, for example, melting and crystallization of nanoparticles.
2.2.3 Diffusion Scaling Law
Diffusion is controlled by the two Fick's laws. Solutions of these equations, important for nanotechnology, say that the squared mean diffusion path of the atoms is proportional to the time. In other words: Assuming the particle diameter as the diffusion path, doubling of the diameter leads to a four-fold time needed for diffusion.
Mathematically, diffusion is described by the two laws of Fick, a set of two partial differential equations. The solution, important for the considerations connected to nanoparticles says:
(2.4)
The brackets 〈 〉 stand for the mean value of an ensemble; the quantity x stands for the diffusion path; therefore, 〈x〉2 is the mean square of the diffusion path, D is the diffusion coefficient and t the time. Generally, the diffusion coefficient depends exponentially on the temperature,
(2.5)
which means that the diffusion will get faster with increasing temperature. The quantity q is the activation energy.
This scaling law for diffusion has dramatic consequences when applied to nanomaterials. As an example, the homogenization time necessary in the case of conventional and nanomaterials are compared. Conventional materials usually have grain sizes of around 10 μm. It is well known that at elevated temperatures, these materials need homogenization times in the range of many hours. Looking at materials with grain sizes around 10 nm, which is 10−3 of the conventional grain size, according to the scaling law of diffusion Eq. (2.3) the time for homogenization is reduced by a factor of . This means that the homogenization time of hours, for conventional materials, is reduced to milliseconds; for nanomaterials. Lastly, this says that homogenization is virtually instantaneous. This phenomenon is often called “instantaneous alloying”. One may also say: Each thermally activated reaction will happen nearly instantaneously. Therefore, it is not possible to produce nonequilibrium systems of nanomaterials, well known for conventional materials, at elevated temperatures.
The possibility of nearly instantaneous diffusion through nanoparticles is exploited technically. The most important example is the gas sensor applying the variation in the electric conductivity due to changes in the stoichiometry of oxides. (The stoichiometry describes the ratio oxygen / metal.) Variations of stoichiometry are often observed in oxides of transition metals. Because of the small particle size, any change in the oxygen potential in the surrounding atmosphere changes the stoichiometry of the sensing particles immediately. In contrast to conventional gas sensors, the time response is now controlled by the gas diffusion through the narrow channels in between the nanoparticles. Figure 2.12 displays the general design of such a sensor.
Figure 2.12 General layout of a gas sensor based on nanoparticles. This gas sensor consists of a layer of sensing nanoparticles, in most cases SnO2, placed on a conductive substrate. The whole system is covered with a gas-permeable electrode. The diffusion within the nanosized grains is no longer time controlling, it is rather the diffusion in the open-pore network in-between the grains.
Such a gas sensor is set up on a conductive substrate on a carrier plate. The surface of this conductive layer is covered completely with the oxide sensor nanoparticles. Transition-metal oxides, well suited for this purpose are example, TiO2, SnO2, Fe2O3. On the top of the oxide particle layer, the counterelectrode, a gas-permeable conductive layer is applied. Variations in the oxygen potential in the surrounding atmosphere changes the stoichiometry of the oxide, and, therefore, the electrical conductivity. This process is reversible.
Figure 2.13 displays schematically a comparison of the response of a sensor made of conventional material with grains in the micrometer size range and a sensor using nanomaterials.
Figure 2.13 Comparison of the sensor response between a sensor using conventional particles and one applying nanoparticles.
Analyzing Figure 2.13, one realizes that the response of the sensor using nanoparticles is faster and the signal is better. Having the diffusion scaling law in mind, Eq. (2.4), one expects an even faster response. In a sensor using nanoparticles, as depicted in Figure 2.13, the time constant depends primarily on the diffusion of the gas molecules in the open-pore network and through the conducting cover layer.
Figure 2.14 displays a further design for gas sensors using particulate oxides as the detector; Figure 2.15 displays the topview of such a sensor. This design avoids the response-delaying conductive surface layer, however, the electric path through the sensing particles is significantly longer. With respect to fabrication, this type of sensor is more economical, as the carrier plate with electrical leads can be produced in large quantities independently of the sensor material. The layer with the sensing properties is producible either by sputtering or by wet chemical methods.
Figure 2.14 Alternative design of a gas sensor using nanoparticles. In this design, the electrodes are fixed on a carrier plate (in the figure, the electrodes are marked by “+” or “−”, symbolizing electrical connectors for DC). Compared with the design depicted in Figure 2.12, this design has the advantage that it is possible to assemble many of these sensors on one chip.
Figure 2.15 Top view of a gas sensor of the design depicted in Figure 2.13. The crucial advantage of this design is the fact that the carrier plate with the electrical leads can be produced independently in large quantities.
The design depicted in Figures 2.13 and 2.14 is thus more progressed as it can be miniaturized, a fact that allows the integration of many of these sensor elements on a chip. This has two major advantages: (i) By averaging of many signals, the noise can be reduced significantly; therefore, the measured signal is more reliable, and (ii) the whole sensor chip can be coated with a diffusion layer, for example, made of silica or alumina, of varying thickness and heated in a way that each sensing element is at a different temperature. Depending on the molecular size the time response of the different elements depends on the thickness of the surface coating and the temperature of the individual element. After empirical calibration, such a design is able to give, besides the oxygen potential (this is the thermodynamic quantity, which is, in technical applications, mathematically converted to concentrations), information on the gas species, too.
References
1 Vollath, D., and Szabó, D.V. (2002) Innovative Processing of Films and Nanocrystalline Powders (ed. K.-L. Choi), Imperial College Press, pp. 219–225.
2 Vollath, D. (2010) Adv. Mater., 22, 4410–4415.
3 Vollath, D., and Szabó, D.V. (1999) J. Nanoparticle Res., 1, 235–242.
4 Niemeyer, C.M. (2001) Angew. Chem. Int. Ed., 40, 4128–4158.
3
Surfaces in Nanomaterials
3.1 General Considerations
The surface forms a sharp interface between a particle and the surrounding atmosphere or between a precipitated phase and the parent phase. In mathematics, the surface of a body, for example, a sphere or a polyhedron, is clearly defined. As already mentioned in Chapter 2, in a sphere, the ratio surface over volume is indirectly proportional to the diameter. This is different in the case of a real, physically existing material. In this case, one has to distinguish between free surfaces in the case of particulate materials and grain boundaries in bulk material. As nanoparticles are small, they have large surfaces. However, what is a surface of a real solid? The answer must not be restricted to the geometrical surface. Looking at a solid and its behavior, one has to take note of the surface-influenced volume. A simplified model assumes a layer with a thickness δ at the surface. Depending on the property in question, this thickness is found experimentally in the range between 0.5 and 1 nm.
Assuming a sphere with the diameter d and a layer with the thickness δ, which is influenced by the surface. In this case the volume of this shell is
(3.1)
Now a dimensionless volume ratio R* is defined as:
(3.2)
This ratio approaches one if d ≈ 2δ.
Figure 3.1 depicts the ratio of the surface-influenced volume over the total volume of the particle. For reasons of simplicity, the shape of the particles was assumed to be spherical.
Figure 3.1 Ratio of the surface shell volume over the total volume of the particle. The thickness of the surface layer was selected to be 0.5 or 1.0 nm.
Scrutinizing this graph, one realizes that in case of a 5-nm particle, 49% or 78%, respectively, of the volume belongs to the surface-influenced volume. In the case of smaller particles, the relative amount of material influenced by surface phenomena is significantly larger. There are applications where this has severe consequences. For example, in a first approximation the magnetic moment at saturation and the susceptibility depend primarily on the part of the particles, which is not influenced by the surface; hence, magnetic nanoparticles exhibit only low values for these parameters (see Chapter 8). Lastly, the considerations, valid for free nanoparticles, may be adapted for nanocrystalline bulk materials; one has just to replace the term “free surface” by grain boundaries. Schematically, this situation is depicted in Figure 3.2. It is interesting to note that the atoms located in the grain boundaries are highly mobile; sometimes this behavior is called “liquid-like”.
Figure 3.2 Nanocrystalline material. The full circles represent atoms in the crystallized phase, whereas the open circles represent atoms at the grain boundary.
Surfaces and grain boundaries are connected to surface energy. The surface energy is proportional to the surface. In this context, as the surface of the particle, the geometrical value is used.
One particle with a geometrical surface a = πd2 and a specific surface energy γ has a surface energy of
(3.3)
With respect to thermodynamic considerations, the surface energy per mol is needed.
The number of particles per mol and the volume of one particle is .
(M is the molar weight, d is the particle diameter, ρ is the density of the material). One obtains for the surface energy per mol
(3.4)
Equation (3.4) shows that the surface energy per mol is indirectly proportional to the particle diameter.
Please note: Quantities related to one particle are printed in lower case letters and quantities valid for one mol in capital letters.
It is important to realize that the surface energy per mol is inversely proportional to the particle diameter; this means that the surface energy increases drastically when the particle size gets very small. In cases related to very small particles, this has dramatic consequences.
3.2 Surface Energy
A model to explain the origin of surface energy starts with an infinitely extended solid. As a next step, the production of a particle by dividing this large chunk of material into small particles is assumed. To do this, the bonds between neighboring atoms are separated. (Within this introductory text, the word atom is used equally for atoms, ions and molecules.) Now, between each two atoms in the lattice, the energy of bonding, u is needed to break the bonds. This is demonstrated in Figure 3.3.
Figure 3.3 Creating new surfaces, for example, by breaking a larger part into smaller pieces requires the energy u for each bond to be broken.
Therefore, to break a larger part of material into smaller pieces, each bond between two neighboring atoms must be broken. After breaking, two new surfaces emerge. Hence, on both sides, for each atom at the new surface, half of the binding energy is stored at the surface. In the interior of a particle, the atoms are in a mechanical equilibrium of binding forces, fixing them at their lattice positions. Arrows mark these forces in Figure 3.4. It is obvious that atoms at the surface have lost bonds at the outside. Because of the reduced number of neighbors, at each atom at the surface, a force acts perpendicular to the surface. At a plane surface (to be mathematically exact: the surface of a plane infinite half-space), against any intuition, this does not lead to a hydrostatic pressure in the material, rather to a stress in the surface plane. Consequently, the surface stress deforming the surface results in the surface stretching. In a spherical particle of limited size, the situation is different. Caused by the curvature, in connection with the surface stress, a hydrostatic pressure, comparable with one stemming from a gas or a liquid at the outside, in the particle comes into action. This allows modeling of the surfaces of particles as a skin made of elastic material. Consequently, the rubber skin model of the surface was developed.
Figure 3.4 Forces acting between atoms at lattice positions. Because of the reduced number of neighbors, the atoms at the surface are pulled in the direction to the interior of the particle. However, this does not lead to a pressure comparable with a hydrostatic pressure, rather, it leads to a stress in the surface, the surface stress. For the estimation of thermal effects, for example, during coagulation of two particles, the sum value of the surface energy of both particles, Eq. (3.6), is the ruling one.
Breaking a chunk of material into two parts forms two surfaces, with n broken bonds. The binding energy u per atom is split to both sides. Hence, for breaking, the energy
The specific energy to break the bonds is
(3.5)
where N* is the number of broken bonds per square meter. Due to the uncompensated bonds at the surface, a force f perpendicular to the surface emerges. If a is the area occupied by one atom, the resulting surface stress is
The stress σ leads to a surface stretch εs, assumed constant in any direction of the tangent plane of the particle, of the surface, (To be mathematically exact, σ and εs are vectors in the tangential plane of the surface. For reasons of simplicity, they are replaced by their absolute values. In the context of these considerations, this does not make any difference.) leading to the contribution γS to the surface energy.
(3.6)
The contribution γ0 exists only in the case of solids; for liquids γ0 = 0 is valid.
The pressure p caused by surface stress σ is given by
(3.7)
For more details see [1].
Even when the situation at the surface can be described by quite plausible physical and exact mathematical models, the experimental situation is very poor. Usually, it is impossible to discriminate between the total surface energy and the surface stress. Therefore, it is necessary to use the values published for the surface energy for all applications. From the considerations above it is clear that the determination of the surface energy by measuring the interface stress is not sufficient. These methods deliver only the surface stress, whereas calorimetric measurements, e.g. connected to grain growth, result in a value for the surface energy. Lastly, only these values are useful for thermodynamic considerations.
In the case of anisotropic lattices, the relations are more complex since there are directional bonds. The surface energy of these materials depends on the direction; hence, to minimize surface energy, these materials crystallize in rods or platelets. Furthermore, surface-active substances can influence the surface energy. Technically, this fact is used for the production of one- or two-dimensional particles such as needles or plates.
In the case of small particles, the surface energy dominates the behavior. Whenever possible, particles that are touching each other will coagulate with a temperature flash. Figure 3.5 displays a graph showing the temperature flash occurring as a consequence of the coagulation of two spherical particles of equal size. For reasons of simplicity, it is assumed the resulting particle is spherical too. Furthermore, as material, zirconia particles with a density ρ = 5.6 × 103 kg m−3, a surface energy γ = 1 J mol−1, and a heat capacity Cp = 56.2 J mol−1 K−1 781 J kg−1 was selected. (For reasons of simplicity, the materials data are those of conventional materials; the value for the surface energy is a rough approximation. According to more recent results, this value may be too low.) From Figure 3.5 one learns that, in the case of small particles, the temperature flash may be in the range of a few hundred Kelvin. Considering more recent values of the surface energy, which are a few times higher, the temperature flash may further increase by a few hundred Kelvin.
Figure 3.5 Temperature flash occurring as a consequence of the adiabatic coagulation of two spherical zirconia particles of equal size.
During coagulation of two particles with the diameter d, the surface aresulting of the new particle with the diameter dresulting is smaller than the sum of the surfaces astarting of two starting particles.
This leads to an excess of surface energy
The system contains particles per mol and the increase of the temperature ΔT in an adiabatic system is: (ρ is the density, Cp is the heat capacity, M is the molecular weight)
(3.8)
Lastly, one has to realize that the temperature flash makes coagulation possible at all, as the increased temperature increases the mobility of the atoms. The significant decrease of the temperature flash with increasing particle size explains the occurrence of odd-shaped particles in the size range above 3 or 4 nm. This is not pure theory. The process of coagulation can be observed in the electron microscope, too. Figure 3.6 displays a series of excellent electron micrographs displaying the process of coagulation of two gold particles. The series starts with two particles; one is in an orientation where lattice fringes are visible. These particles are moving around on the surface of the carbon specimen carrier. This movement changes the relative orientation of the particle lattice to the electron beam and; therefore, the lattice fringes. When, by chance, the particles touch each other, the particles rotate until their orientation is equal. Now coagulation starts; the larger particle swallows the smaller one. This process needs a significant thermal mobility of the atoms, to some extent, the necessary thermal energy is provided from the reduction of the surface.
Figure 3.6 A series of electron micrographs depicting the coagulation of two gold particles. The orientation of the lattice fringes changes from frame to frame, indicating the movement of the particles. During coagulation, a grain boundary is not formed; rather, the orientation of the two particles is aligned. With progression of the time, the resulting particle becomes more and more rounded (Ascencio, J., Univ. Nacional Autonoma de Mexico, private communication, 2008).
The temperature flash occurring due to coagulation has a severe influence on the particle formation during synthesis. Lastly, the consequence is that, using a random process; it is nearly impossible to obtain very small particles, provided one does not take special measures to thwart coagulation. This will be discussed in Chapter 4 in great detail.
To demonstrate the relative amount and importance of surface energy, Figure 3.7 displays for zirconia as an example, the free enthalpy of formation, the free enthalpy for the transformation monoclinic–tetragonal ΔGmonoc.−tetr. in comparison to the surface energy, and the difference of the surface energy caused by the transformation from the monoclinic to the tetragonal phase. Again, for the surface energy a value of 1 J m−2 was used.
Figure 3.7 Surface energy of zirconia particles as a function of grain size. For comparison, the free enthalpy of formation and the free enthalpy of the monoclinic – tetragonal phase transformation ΔGmonoc.-tetr.; and, additionally, the difference of the surface energy between the monoclinic and the tetragonal phase (as volume difference a value of 4% was used) is plotted.
In Figure 3.7 one sees that for particles smaller than 2 nm the surface energy is comparable to the energy of formation. The free enthalpy of the monoclinic–tetragonal transformation is significantly smaller than the surface energy. However, in the latter case one has to look only at the surface change during this phase transformation. The small difference of the surface caused by the volume change of roughly 4% during phase transformation leads to a change of the surface energy, which is comparable to the free enthalpy of transformation. It is obvious that the particle size influences the phase transformation significantly (see also Chapter 7).
Looking at isolated particles, one has to take note of the hydrostatic pressure caused by surface stress in the particles (see Box 3.3). (The surface-induced hydrostatic pressure is also why free water drops are spherical.) This hydrostatic pressure p is a function of the curvature and the surface stress; and most importantly, in the case of a spherical particle, it is inversely proportional to the particle diameter. Figure 3.8 depicts the hydrostatic pressure caused by surface energy within a nanoparticle. For the surface stress, a value of 1 N m 1 J m−2 was selected. As values for the surface energy and surface stress are poorly known for ceramic materials, this value is often selected.
Figure 3.8 Hydrostatic pressure in nanoparticles as a function of the particle diameter. The surface stress σ was assumed as 1 N m−1.
The hydrostatic pressure in a spherical particle with a diameter of 5 nm and a surface energy of 1 N m−1 is, according to Figure 3.8, 4 × 108 Pa 4 × 103
